Daily Papers

Model-based reinforcement learning is a powerful tool, but collecting data to fit an accurate model of the system can be costly. Exploring an unknown environment in a sample-efficient manner is hence of great importance. However, the complexity of dynamics and the computational limitations of real systems make this task challenging. In this work, we introduce FLEX, an exploration algorithm for nonlinear dynamics based on optimal experimental design. Our policy maximizes the information of the next step and results in an adaptive exploration algorithm, compatible with generic parametric learning models and requiring minimal resources. We test our method on a number of nonlinear environments covering different settings, including time-varying dynamics. Keeping in mind that exploration is intended to serve an exploitation objective, we also test our algorithm on downstream model-based classical control tasks and compare it to other state-of-the-art model-based and model-free approaches. The performance achieved by FLEX is competitive and its computational cost is low.

The Mechanistic Interpretability (MI) program has mapped the Transformer as a precise computational graph. We extend this graph with a conservation law and time-varying AC dynamics, viewing it as a physical circuit. We introduce Momentum Attention, a symplectic augmentation embedding physical priors via the kinematic difference operator p_t = q_t - q_{t-1}, implementing the symplectic shear q_t = q_t + γp_t on queries and keys. We identify a fundamental Symplectic-Filter Duality: the physical shear is mathematically equivalent to a High-Pass Filter. This duality is our cornerstone contribution -- by injecting kinematic momentum, we sidestep the topological depth constraint (L geq 2) for induction head formation. While standard architectures require two layers for induction from static positions, our extension grants direct access to velocity, enabling Single-Layer Induction and Spectral Forensics via Bode Plots. We formalize an Orthogonality Theorem proving that DC (semantic) and AC (mechanistic) signals segregate into orthogonal frequency bands when Low-Pass RoPE interacts with High-Pass Momentum. Validated through 5,100+ controlled experiments (documented in Supplementary Appendices A--R and 27 Jupyter notebooks), our 125M Momentum model exceeds expectations on induction-heavy tasks while tracking a 350M baseline within sim2.9% validation loss. Dedicated associative recall experiments reveal a scaling law γ^* = 4.17 times N^{-0.74} establishing momentum-depth fungibility. We offer this framework as a complementary analytical toolkit connecting Generative AI, Hamiltonian Physics, and Signal Processing.

Text-to-music generation models are now capable of generating high-quality music audio in broad styles. However, text control is primarily suitable for the manipulation of global musical attributes like genre, mood, and tempo, and is less suitable for precise control over time-varying attributes such as the positions of beats in time or the changing dynamics of the music. We propose Music ControlNet, a diffusion-based music generation model that offers multiple precise, time-varying controls over generated audio. To imbue text-to-music models with time-varying control, we propose an approach analogous to pixel-wise control of the image-domain ControlNet method. Specifically, we extract controls from training audio yielding paired data, and fine-tune a diffusion-based conditional generative model over audio spectrograms given melody, dynamics, and rhythm controls. While the image-domain Uni-ControlNet method already allows generation with any subset of controls, we devise a new strategy to allow creators to input controls that are only partially specified in time. We evaluate both on controls extracted from audio and controls we expect creators to provide, demonstrating that we can generate realistic music that corresponds to control inputs in both settings. While few comparable music generation models exist, we benchmark against MusicGen, a recent model that accepts text and melody input, and show that our model generates music that is 49% more faithful to input melodies despite having 35x fewer parameters, training on 11x less data, and enabling two additional forms of time-varying control. Sound examples can be found at https://MusicControlNet.github.io/web/.

Optimal execution is an important problem faced by any trader. Most solutions are based on the assumption of constant market impact, while liquidity is known to be dynamic. Moreover, models with time-varying liquidity typically assume that it is observable, despite the fact that, in reality, it is latent and hard to measure in real time. In this paper we show that the use of Double Deep Q-learning, a form of Reinforcement Learning based on neural networks, is able to learn optimal trading policies when liquidity is time-varying. Specifically, we consider an Almgren-Chriss framework with temporary and permanent impact parameters following several deterministic and stochastic dynamics. Using extensive numerical experiments, we show that the trained algorithm learns the optimal policy when the analytical solution is available, and overcomes benchmarks and approximated solutions when the solution is not available.

Four-dimensional computed tomography (4D CT) reconstruction is crucial for capturing dynamic anatomical changes but faces inherent limitations from conventional phase-binning workflows. Current methods discretize temporal resolution into fixed phases with respiratory gating devices, introducing motion misalignment and restricting clinical practicality. In this paper, We propose X^2-Gaussian, a novel framework that enables continuous-time 4D-CT reconstruction by integrating dynamic radiative Gaussian splatting with self-supervised respiratory motion learning. Our approach models anatomical dynamics through a spatiotemporal encoder-decoder architecture that predicts time-varying Gaussian deformations, eliminating phase discretization. To remove dependency on external gating devices, we introduce a physiology-driven periodic consistency loss that learns patient-specific breathing cycles directly from projections via differentiable optimization. Extensive experiments demonstrate state-of-the-art performance, achieving a 9.93 dB PSNR gain over traditional methods and 2.25 dB improvement against prior Gaussian splatting techniques. By unifying continuous motion modeling with hardware-free period learning, X^2-Gaussian advances high-fidelity 4D CT reconstruction for dynamic clinical imaging. Code is publicly available at: https://x2-gaussian.github.io/.

Generative posterior sampling using diffusion models has emerged as a dominant paradigm for solving inverse problems in imaging, which usually consists of three main components: data consistency (DC) guidance, classifier-free guidance (CFG) and stochasticity. While prior arts have focused on how to develop each or all components, less attention has given to how to schedule them, leading to heuristically fixed or partially adjusted suboptimal schedules. In this work, we argue that the interactions among all three components in terms of scheduling are crucial for significantly improved performance in solving inverse problems in imaging. Our analysis shows that aggressive CFG early in sampling conflict with DC guidance, while stochasticity brings the trajectory back to higher-probability regions. Based on these findings, we propose Triadic Dynamics Aware Posterior Sampling (TriPS), which reformulates posterior sampling as a time-varying control problem and optimizes schedules following a triadic trend of decreasing DC and stochasticity scales alongside increasing CFG scale. TriPS achieves this through two strategies: template-based search over functional priors for reliable baseline schedules, and Group Relative Policy Optimization (GRPO)-based reinforcement learning for more flexible temporal curves. Experiments demonstrate TriPS outperforms state-of-the-art baselines in data fidelity and perceptual realism.

Sequence models must decide what to write into memory and what to retain. In quantum and quantum-inspired sequence learning, nonlinear recurrent updates often require repeated circuit evaluations and sequential backpropagation through time, making long contexts costly. Gated fast-weight programmers (FWPs) based on quantum-inspired Kolmogorov-Arnold networks (QKANs) alleviate this bottleneck by storing context in time-varying fast parameters. However, their scalar gate applies one retention-write balance to every fast-state coordinate, forcing all parameters to share a memory timescale. We introduce Self-Modulating QKAN-based FWPs, which replace this broadcast gate with low-rank-generated element-wise modulation of the new-proposal branch, a bounded old-state branch, or both. We further propose Complementary Matrix Gating (CMG), which uses one sigmoid matrix gate to retain the old state and its complement to write the new proposal. CMG provides coordinate-wise memory control while preserving the bounded convex update and affine prefix-scan structure of scalar gating, at the modulation-head cost of a single-branch rule. We compare four self-modulating rules with scalar gating across four FWP architectures combining classical and QKAN-based slow and fast programmers. Across seven single-step forecasting benchmarks and five sequence lengths, CMG gives the most consistent improvements for architectures whose fast programmer incorporates a QKAN-based module. In direct multi-step forecasting of Jaynes-Cummings and transmon-resonator dynamics simulated with CUDA-Q Dynamics, CMG models maintain mean-squared errors on the order of 0.001 or lower across forecasting horizons of 4, 8, and 16 steps, while improving on their scalar-gated counterparts by at least 91.2%. These results establish coordinate-wise complementary modulation as a stable and effective update for QKAN-based FWPs.

Prior-data fitted networks (PFNs) have emerged as powerful foundation models for tabular causal inference, yet their extension to time series remains limited by the absence of synthetic data generators that provide interventional targets. Existing time series benchmarks generate observational data with ground-truth causal graphs but lack the interventional data required for training causal foundation models. To address this, we propose CausalTimePrior, a principled framework for generating synthetic temporal structural causal models (TSCMs) with paired observational and interventional time series. Our prior supports configurable causal graph structures, nonlinear autoregressive mechanisms, regime-switching dynamics, and multiple intervention types (hard, soft, time-varying). We demonstrate that PFNs trained on CausalTimePrior can perform in-context causal effect estimation on held-out TSCMs, establishing a pathway toward foundation models for time series causal inference.

Covariates provide valuable information on external factors that influence time series and are critical in many real-world time series forecasting tasks. For example, in retail, covariates may indicate promotions or peak dates such as holiday seasons that heavily influence demand forecasts. Recent advances in pretraining large language model architectures for time series forecasting have led to highly accurate forecasters. However, the majority of these models do not readily use covariates as they are often specific to a certain task or domain. This paper introduces a new method to incorporate covariates into pretrained time series forecasting models. Our proposed approach incorporates covariate information into pretrained forecasting models through modular blocks that inject past and future covariate information, without necessarily modifying the pretrained model in consideration. In order to evaluate our approach, we introduce a benchmark composed of 32 different synthetic datasets with varying dynamics to evaluate the effectivity of forecasting models with covariates. Extensive evaluations on both synthetic and real datasets show that our approach effectively incorporates covariate information into pretrained models, outperforming existing baselines.

Large Language Models (LLMs) have been integrated into recommendation systems to enhance user behavior comprehension. The Retrieval Augmented Generation (RAG) technique is further incorporated into these systems to retrieve more relevant items and improve system performance. However, existing RAG methods rely primarily on textual semantics and often fail to incorporate the most relevant items, limiting the effectiveness of the systems. In this paper, we propose Representation learning for retrieval-Augmented Large Language model Recommendation (RALLRec). Specifically, we enhance textual semantics by prompting LLMs to generate more detailed item descriptions, followed by joint representation learning of textual and collaborative semantics, which are extracted by the LLM and recommendation models, respectively. Considering the potential time-varying characteristics of user interest, a simple yet effective reranking method is further introduced to capture the dynamics of user preference. We conducted extensive experiments on three real-world datasets, and the evaluation results validated the effectiveness of our method. Code is made public at https://github.com/JianXu95/RALLRec.

Conventional federated learning (FL) frameworks follow a server-driven model where the server determines session initiation and client participation, which faces challenges in accommodating clients' asynchronous needs for model updates. We introduce Client-Driven Federated Learning (CDFL), a novel FL framework that puts clients at the driving role. In CDFL, each client independently and asynchronously updates its model by uploading the locally trained model to the server and receiving a customized model tailored to its local task. The server maintains a repository of cluster models, iteratively refining them using received client models. Our framework accommodates complex dynamics in clients' data distributions, characterized by time-varying mixtures of cluster distributions, enabling rapid adaptation to new tasks with superior performance. In contrast to traditional clustered FL protocols that send multiple cluster models to a client to perform distribution estimation, we propose a paradigm that offloads the estimation task to the server and only sends a single model to a client, and novel strategies to improve estimation accuracy. We provide a theoretical analysis of CDFL's convergence. Extensive experiments across various datasets and system settings highlight CDFL's substantial advantages in model performance and computation efficiency over baselines.

Longitudinal treatment decisions require predicting potential outcomes under future treatment sequences in the presence of time-varying confounding, heterogeneous patient dynamics, and limited domain-specific data. Existing longitudinal causal estimators typically train a new model for each cohort or simulator. We introduce Causal Longitudinal Prior-Fitted Networks (CausalLongPFN), a prior-fitted in-context predictor for longitudinal causal prediction. The model is pretrained entirely on synthetic episodes sampled from a broad prior over temporal structural causal models, exposing it to treatment-confounder feedback, latent heterogeneity, nonlinear state evolution, delayed effects, and cumulative treatment responses. At test time, CausalLongPFN is frozen: it conditions on support trajectories, a query history, and a proposed future treatment sequence, and returns a predictive distribution over future outcomes without gradient updates or propensity-model fitting. Multi-step predictions are obtained by recursively applying the one-step predictor under the specified treatment sequence. We evaluate on branchable cancer, HIV, and warfarin benchmarks with ground-truth counterfactual labels, and on factual-only rolling-origin prediction in MIMIC-III ICU trajectories. CausalLongPFN is competitive with domain-trained longitudinal baselines on counterfactual benchmarks and performs strongly on factual MIMIC-III prediction, suggesting that broad synthetic causal pretraining can provide a useful frozen alternative when repeated domain-specific training is costly or impractical.

Accurate air quality forecasting is crucial for protecting public health and guiding environmental policy, yet it remains challenging due to nonlinear spatiotemporal dynamics, wind-driven transport, and distribution shifts across regions. Physics-based models are interpretable but computationally expensive and often rely on restrictive assumptions, whereas purely data-driven models can be accurate but may lack robustness and calibrated uncertainty. To address these limitations, we propose Neural Dynamic Diffusion-Advection Fields (NeuroDDAF), a physics-informed forecasting framework that unifies neural representation learning with open-system transport modeling. NeuroDDAF integrates (i) a GRU-Graph Attention encoder to capture temporal dynamics and wind-aware spatial interactions, (ii) a Fourier-domain diffusion-advection module with learnable residuals, (iii) a wind-modulated latent Neural ODE to model continuous-time evolution under time-varying connectivity, and (iv) an evidential fusion mechanism that adaptively combines physics-guided and neural forecasts while quantifying uncertainty. Experiments on four urban datasets (Beijing, Shenzhen, Tianjin, and Ancona) across 1-3 day horizons show that NeuroDDAF consistently outperforms strong baselines, including AirPhyNet, achieving up to 9.7% reduction in RMSE and 9.4% reduction in MAE on long-term forecasts. On the Beijing dataset, NeuroDDAF attains an RMSE of 41.63 μg/m^3 for 1-day prediction and 48.88 μg/m^3 for 3-day prediction, representing the best performance among all compared methods. In addition, NeuroDDAF improves cross-city generalization and yields well-calibrated uncertainty estimates, as confirmed by ensemble variance analysis and case studies under varying wind conditions.

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the-art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer's favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https://github.com/tung-nd/stormer.

Transformers for time series forecasting mainly model time series from limited or fixed scales, making it challenging to capture different characteristics spanning various scales. We propose Pathformer, a multi-scale Transformer with adaptive pathways. It integrates both temporal resolution and temporal distance for multi-scale modeling. Multi-scale division divides the time series into different temporal resolutions using patches of various sizes. Based on the division of each scale, dual attention is performed over these patches to capture global correlations and local details as temporal dependencies. We further enrich the multi-scale Transformer with adaptive pathways, which adaptively adjust the multi-scale modeling process based on the varying temporal dynamics of the input, improving the accuracy and generalization of Pathformer. Extensive experiments on eleven real-world datasets demonstrate that Pathformer not only achieves state-of-the-art performance by surpassing all current models but also exhibits stronger generalization abilities under various transfer scenarios. The code is made available at https://github.com/decisionintelligence/pathformer.

We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters, allowing for finding solutions faster and of better quality. The diffusion models used in our approach are trained on randomly cut solution trajectories. These trajectories are created by solving randomly generated problem instances with a kinodynamic motion planner. Experimental results show significant improvements up to 30 percent in both computation time and solution quality across varying robot dynamics such as second-order unicycle or car with trailer.

Reinforcement learning (RL) has emerged as a dominant paradigm for eliciting long-horizon reasoning in Large Language Models (LLMs). However, scaling Tool-Integrated Reasoning (TIR) via RL remains challenging due to interaction collapse: a pathological state where models fail to sustain multi-turn tool usage, instead degenerating into heavy internal reasoning with only trivial, post-hoc code verification. We systematically study three questions: (i) how cold-start SFT induces an agentic, tool-using behavioral prior, (ii) how the interaction density of cold-start trajectories shapes exploration and downstream RL outcomes, and (iii) how the RL interaction budget affects learning dynamics and generalization under varying inference-time budgets. We then introduce ASTER (Agentic Scaling with Tool-integrated Extended Reasoning), a framework that circumvents this collapse through a targeted cold-start strategy prioritizing interaction-dense trajectories. We find that a small expert cold-start set of just 4K interaction-dense trajectories yields the strongest downstream performance, establishing a robust prior that enables superior exploration during extended RL training. Extensive evaluations demonstrate that ASTER-4B achieves state-of-the-art results on competitive mathematical benchmarks, reaching 90.0% on AIME 2025, surpassing leading frontier open-source models, including DeepSeek-V3.2-Exp.

This letter presents an analytical linear parameter-varying (LPV) representation of quadrotor dynamics utilizing Koopman theory, facilitating computationally efficient linear model predictive control (LMPC) for real-time trajectory tracking. By leveraging carefully designed Koopman observables, the proposed approach enables a compact lifted-space evolution that mitigates the curse of dimensionality while preserving the nonlinear characteristics of the system. Although model predictive control (MPC) is a powerful strategy for quadrotor control, it faces a trade-off between the high computational cost of nonlinear MPC (NMPC) and the reduced accuracy of LMPC. To address this gap, we introduce KQ-LMPC (Koopman Quasilinear LPV MPC), which leverages the Koopman-lifted LPV formulation to enforce constraints, ensure lower computational burden and real-time feasibility, and deliver tracking performance comparable to NMPC. Experimental validation confirms the effectiveness of the framework in reasonably agile flight. To the best of our knowledge, this is the first experimentally validated LMPC for quadrotors that employs analytically derived Koopman observables without requiring training data.

Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators producing multiple solution candidates, with LLM verifiers assessing the correctness of these candidates without reference answers. In this paper, we study generative verifiers, which perform verification by generating chain-of-thought (CoT) reasoning followed by a binary verdict. We systematically analyze verification dynamics across three dimensions - problem difficulty, generator capability, and verifier generation capability - with empirical studies on 12 benchmarks across mathematical reasoning, knowledge, and natural language reasoning tasks using 14 open-source models (2B to 72B parameter range) and GPT-4o. Our experiments reveal three key findings about verification effectiveness: (1) Easy problems allow verifiers to more reliably certify correct responses; (2) Weak generators produce errors that are easier to detect than strong generators; (3) Verification ability is generally correlated with the verifier's own problem-solving capability, but this relationship varies with problem difficulty. These findings reveal opportunities to optimize basic verification strategies in TTS applications. First, given the same verifier, some weak generators can nearly match stronger ones in post-verification TTS performance (e.g., the Gemma2-9B to Gemma2-27B performance gap shrinks by 75.5%). Second, we identify cases where strong verifiers offer limited advantage over weak ones, as both fail to provide meaningful verification gains, suggesting that verifier scaling alone cannot overcome fundamental verification challenges.

Collaborative perception is dedicated to tackling the constraints of single-agent perception, such as occlusions, based on the multiple agents' multi-view sensor inputs. However, most existing works assume an ideal condition that all agents' multi-view cameras are continuously available. In reality, cameras may be highly noisy, obscured or even failed during the collaboration. In this work, we introduce a new robust camera-insensitivity problem: how to overcome the issues caused by the failed camera perspectives, while stabilizing high collaborative performance with low calibration cost? To address above problems, we propose RCDN, a Robust Camera-insensitivity collaborative perception with a novel Dynamic feature-based 3D Neural modeling mechanism. The key intuition of RCDN is to construct collaborative neural rendering field representations to recover failed perceptual messages sent by multiple agents. To better model collaborative neural rendering field, RCDN first establishes a geometry BEV feature based time-invariant static field with other agents via fast hash grid modeling. Based on the static background field, the proposed time-varying dynamic field can model corresponding motion vectors for foregrounds with appropriate positions. To validate RCDN, we create OPV2V-N, a new large-scale dataset with manual labelling under different camera failed scenarios. Extensive experiments conducted on OPV2V-N show that RCDN can be ported to other baselines and improve their robustness in extreme camera-insensitivity settings.

Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers and lack online error feedback, resulting in suboptimal, open-loop control. To address this, we show empirically that, despite the nonlinear structure of transformer blocks, layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models. Exploiting this property, we model LLM inference as a linear time-varying dynamical system and adapt the classical linear quadratic regulator to compute feedback controllers using layer-wise Jacobians, steering activations toward desired semantic setpoints in closed-loop with minimal computational overhead and no offline training. We also derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance. Using a novel adaptive semantic feature setpoint signal, our method yields robust, fine-grained behavior control across models, scales, and tasks, including state-of-the-art modulation of toxicity, truthfulness, refusal, and arbitrary concepts, surpassing baseline steering methods. Our code is available at: https://github.com/trustworthyrobotics/lqr-activation-steering

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Model-free and reinforcement learning-based adaptive filtering methods are gaining traction for denoising in dynamic, non-stationary environments such as wireless signal channels, biomedical monitoring, and sensor networks. Traditional filters such as LMS, RLS, Wiener, and Kalman are often limited by assumptions of stationarity, the need for exact noise statistics, or fragile parameter tuning. This paper proposes an adaptive filtering framework using Proximal Policy Optimization (PPO), guided by a composite reward that balances SNR improvement, MSE reduction, and residual smoothness. We frame adaptive filtering as a Markov decision process and train a PPO agent to adjust filter coefficients directly in response to changing noise. Experiments on synthetic nonstationary signals with diverse noise types show that the PPO agent generalizes beyond its training distribution. Moreover, real-world analysis is made and evaluated on ECG recordings from the MIT-BIH Noise Stress Test Database corrupted by baseline wander, electrode motion, and muscle artifacts. The learned PPO policy achieves real-time inference and slightly outperforms strong classical baselines on ECG denoising. These results demonstrate the viability of policy-gradient reinforcement learning as a computationally efficient and flexible tool for adaptive filtering in nonlinear, time-varying dynamical systems.

Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing the evolutionary mechanisms of complex real-world dynamic systems. Matrix factorization-based methods are promising approaches for this task; however, these methods often struggle with scalability and can be time-consuming when applied to large-scale dynamic graphs. Moreover, they tend to lack robustness and are vulnerable to real-world noisy data. To address these issues, we make three key contributions. First, to improve scalability, we propose temporal separated matrix factorization, where a single matrix is divided into multiple smaller matrices for independent factorization, resulting in faster computation. Second, to improve robustness, we introduce bi-clustering regularization, which jointly optimizes graph embedding and clustering, thereby filtering out noisy features from the graph embeddings. Third, to further enhance effectiveness and efficiency, we propose selective embedding updating, where we update only the embeddings of dynamic nodes while the embeddings of static nodes are fixed among different timestamps. Experimental results on six synthetic and five real-world benchmarks demonstrate the scalability, robustness and effectiveness of our proposed method. Source code is available at https://github.com/Clearloveyuan/DyG-MF.

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient updates through the lens of signal processing and reveal that fixed momentum coefficients inherently distort the balance between bias and variance, leading to skewed or suboptimal parameter updates. To address this, we propose SGDF (SGD with Filter), an optimizer inspired by the principles of Optimal Linear Filtering. SGDF computes an online, time-varying gain to dynamically refine gradient estimation by minimizing the mean-squared error, thereby achieving an optimal trade-off between noise suppression and signal preservation. Furthermore, our approach could extend to other optimizers, showcasing its broad applicability to optimization frameworks. Extensive experiments across diverse architectures and benchmarks demonstrate SGDF surpasses conventional momentum methods and achieves performance on par with or surpassing state-of-the-art optimizers.

Complex systems are characterized by intricate interactions between entities that evolve dynamically over time. Accurate inference of these dynamic relationships is crucial for understanding and predicting system behavior. In this paper, we propose Regulatory Temporal Interaction Network Inference (RiTINI) for inferring time-varying interaction graphs in complex systems using a novel combination of space-and-time graph attentions and graph neural ordinary differential equations (ODEs). RiTINI leverages time-lapse signals on a graph prior, as well as perturbations of signals at various nodes in order to effectively capture the dynamics of the underlying system. This approach is distinct from traditional causal inference networks, which are limited to inferring acyclic and static graphs. In contrast, RiTINI can infer cyclic, directed, and time-varying graphs, providing a more comprehensive and accurate representation of complex systems. The graph attention mechanism in RiTINI allows the model to adaptively focus on the most relevant interactions in time and space, while the graph neural ODEs enable continuous-time modeling of the system's dynamics. We evaluate RiTINI's performance on various simulated and real-world datasets, demonstrating its state-of-the-art capability in inferring interaction graphs compared to previous methods.

Autonomous systems often must predict the motions of nearby agents from partial and noisy data. This paper asks and answers the question: "can we learn, in real-time, a nonlinear predictive model of another agent's motions?" Our online framework denoises and forecasts such dynamics using a modified sliding-window Hankel Dynamic Mode Decomposition (Hankel-DMD). Partial noisy measurements are embedded into a Hankel matrix, while an associated Page matrix enables singular-value hard thresholding (SVHT) to estimate the effective rank. A Cadzow projection enforces structured low-rank consistency, yielding a denoised trajectory and local noise variance estimates. From this representation, a time-varying Hankel-DMD lifted linear predictor is constructed for multi-step forecasts. The residual analysis provides variance-tracking signals that can support downstream estimators and risk-aware planning. We validate the approach in simulation under Gaussian and heavy-tailed noise, and experimentally on a dynamic crane testbed. Results show that the method achieves stable variance-aware denoising and short-horizon prediction suitable for integration into real-time control frameworks.

Deep learning approaches for black-box modelling of audio effects have shown promise, however, the majority of existing work focuses on nonlinear effects with behaviour on relatively short time-scales, such as guitar amplifiers and distortion. While recurrent and convolutional architectures can theoretically be extended to capture behaviour at longer time scales, we show that simply scaling the width, depth, or dilation factor of existing architectures does not result in satisfactory performance when modelling audio effects such as fuzz and dynamic range compression. To address this, we propose the integration of time-varying feature-wise linear modulation into existing temporal convolutional backbones, an approach that enables learnable adaptation of the intermediate activations. We demonstrate that our approach more accurately captures long-range dependencies for a range of fuzz and compressor implementations across both time and frequency domain metrics. We provide sound examples, source code, and pretrained models to faciliate reproducibility.

Reinforcement learning provides a framework for learning control policies that can reproduce diverse motions for simulated characters. However, such policies often exploit unnatural high-frequency signals that are unachievable by humans or physical robots, making them poor representations of real-world behaviors. Existing work addresses this issue by adding a reward term that penalizes a large change in actions over time. This term often requires substantial tuning efforts. We propose to use the action Jacobian penalty, which penalizes changes in action with respect to the changes in simulated state directly through auto differentiation. This effectively eliminates unrealistic high-frequency control signals without task specific tuning. While effective, the action Jacobian penalty introduces significant computational overhead when used with traditional fully connected neural network architectures. To mitigate this, we introduce a new architecture called a Linear Policy Net (LPN) that significantly reduces the computational burden for calculating the action Jacobian penalty during training. In addition, a LPN requires no parameter tuning, exhibits faster learning convergence compared to baseline methods, and can be more efficiently queried during inference time compared to a fully connected neural network. We demonstrate that a Linear Policy Net, combined with the action Jacobian penalty, is able to learn policies that generate smooth signals while solving a number of motion imitation tasks with different characteristics, including dynamic motions such as a backflip and various challenging parkour skills. Finally, we apply this approach to create policies for dynamic motions on a physical quadrupedal robot equipped with an arm.

Detection of rolling-element bearing faults is crucial for implementing proactive maintenance strategies and for minimizing the economic and operational consequences of unexpected failures. However, many existing techniques are developed and tested under strictly controlled conditions, limiting their adaptability to the diverse and dynamic settings encountered in practical applications. This paper presents an efficient real-time convolutional neural network (CNN) for diagnosing multiple bearing faults under various noise levels and time-varying rotational speeds. Additionally, we propose a novel Fisher-based spectral separability analysis (SSA) method to elucidate the effectiveness of the designed CNN model. We conducted experiments on both healthy bearings and bearings afflicted with inner race, outer race, and roller ball faults. The experimental results show the superiority of our model over the current state-of-the-art approach in three folds: it achieves substantial accuracy gains of up to 15.8%, it is robust to noise with high performance across various signal-to-noise ratios, and it runs in real-time with processing durations five times less than acquisition. Additionally, by using the proposed SSA technique, we offer insights into the model's performance and underscore its effectiveness in tackling real-world challenges.

Unsupervised representation learning for dynamic graphs has attracted a lot of research attention in recent years. Compared with static graph, the dynamic graph is a comprehensive embodiment of both the intrinsic stable characteristics of nodes and the time-related dynamic preference. However, existing methods generally mix these two types of information into a single representation space, which may lead to poor explanation, less robustness, and a limited ability when applied to different downstream tasks. To solve the above problems, in this paper, we propose a novel disenTangled representation learning framework for discrete-time Dynamic graphs, namely DyTed. We specially design a temporal-clips contrastive learning task together with a structure contrastive learning to effectively identify the time-invariant and time-varying representations respectively. To further enhance the disentanglement of these two types of representation, we propose a disentanglement-aware discriminator under an adversarial learning framework from the perspective of information theory. Extensive experiments on Tencent and five commonly used public datasets demonstrate that DyTed, as a general framework that can be applied to existing methods, achieves state-of-the-art performance on various downstream tasks, as well as be more robust against noise.

Deep learning approaches have demonstrated success in modeling analog audio effects. Nevertheless, challenges remain in modeling more complex effects that involve time-varying nonlinear elements, such as dynamic range compressors. Existing neural network approaches for modeling compression either ignore the device parameters, do not attain sufficient accuracy, or otherwise require large noncausal models prohibiting real-time operation. In this work, we propose a modification to temporal convolutional networks (TCNs) enabling greater efficiency without sacrificing performance. By utilizing very sparse convolutional kernels through rapidly growing dilations, our model attains a significant receptive field using fewer layers, reducing computation. Through a detailed evaluation we demonstrate our efficient and causal approach achieves state-of-the-art performance in modeling the analog LA-2A, is capable of real-time operation on CPU, and only requires 10 minutes of training data.

Accurate grasp force control is one of the key skills for ensuring successful and damage-free robotic grasping of objects. Although existing methods have conducted in-depth research on slip detection and grasping force planning, they often overlook the issue of adaptive tracking of the actual force to the target force when handling objects with different material properties. The optimal parameters of a force tracking controller are significantly influenced by the object's stiffness, and many adaptive force tracking algorithms rely on stiffness estimation. However, real-world objects often exhibit viscous, plastic, or other more complex nonlinear time-varying behaviors, and existing studies provide insufficient support for these materials in terms of stiffness definition and estimation. To address this, this paper introduces the concept of generalized stiffness, extending the definition of stiffness to nonlinear time-varying grasp system models, and proposes an online generalized stiffness estimator based on Long Short-Term Memory (LSTM) networks. Based on generalized stiffness, this paper proposes an adaptive parameter adjustment strategy using a PI controller as an example, enabling dynamic force tracking for objects with varying characteristics. Experimental results demonstrate that the proposed method achieves high precision and short probing time, while showing better adaptability to non-ideal objects compared to existing methods. The method effectively solves the problem of grasp force tracking in unknown, nonlinear, and time-varying grasp systems, demonstrating the generalization capability of our neural network and enhancing the robotic grasping ability in unstructured environments.

Demystifying the interactions among multiple agents from their past trajectories is fundamental to precise and interpretable trajectory prediction. However, previous works mainly consider static, pair-wise interactions with limited relational reasoning. To promote more comprehensive interaction modeling and relational reasoning, we propose DynGroupNet, a dynamic-group-aware network, which can i) model time-varying interactions in highly dynamic scenes; ii) capture both pair-wise and group-wise interactions; and iii) reason both interaction strength and category without direct supervision. Based on DynGroupNet, we further design a prediction system to forecast socially plausible trajectories with dynamic relational reasoning. The proposed prediction system leverages the Gaussian mixture model, multiple sampling and prediction refinement to promote prediction diversity, training stability and trajectory smoothness, respectively. Extensive experiments show that: 1)DynGroupNet can capture time-varying group behaviors, infer time-varying interaction category and interaction strength during trajectory prediction without any relation supervision on physical simulation datasets; 2)DynGroupNet outperforms the state-of-the-art trajectory prediction methods by a significant improvement of 22.6%/28.0%, 26.9%/34.9%, 5.1%/13.0% in ADE/FDE on the NBA, NFL Football and SDD datasets and achieve the state-of-the-art performance on the ETH-UCY dataset.

Video generative models are receiving particular attention given their ability to generate realistic and imaginative frames. Besides, these models are also observed to exhibit strong 3D consistency, significantly enhancing their potential to act as world simulators. In this work, we present Vidu4D, a novel reconstruction model that excels in accurately reconstructing 4D (i.e., sequential 3D) representations from single generated videos, addressing challenges associated with non-rigidity and frame distortion. This capability is pivotal for creating high-fidelity virtual contents that maintain both spatial and temporal coherence. At the core of Vidu4D is our proposed Dynamic Gaussian Surfels (DGS) technique. DGS optimizes time-varying warping functions to transform Gaussian surfels (surface elements) from a static state to a dynamically warped state. This transformation enables a precise depiction of motion and deformation over time. To preserve the structural integrity of surface-aligned Gaussian surfels, we design the warped-state geometric regularization based on continuous warping fields for estimating normals. Additionally, we learn refinements on rotation and scaling parameters of Gaussian surfels, which greatly alleviates texture flickering during the warping process and enhances the capture of fine-grained appearance details. Vidu4D also contains a novel initialization state that provides a proper start for the warping fields in DGS. Equipping Vidu4D with an existing video generative model, the overall framework demonstrates high-fidelity text-to-4D generation in both appearance and geometry.

Visualization of large-scale time-dependent simulation data is crucial for domain scientists to analyze complex phenomena, but it demands significant I/O bandwidth, storage, and computational resources. To enable effective visualization on local, low-end machines, recent advances in view synthesis techniques, such as neural radiance fields, utilize neural networks to generate novel visualizations for volumetric scenes. However, these methods focus on reconstruction quality rather than facilitating interactive visualization exploration, such as feature extraction and tracking. We introduce VolSegGS, a novel Gaussian splatting framework that supports interactive segmentation and tracking in dynamic volumetric scenes for exploratory visualization and analysis. Our approach utilizes deformable 3D Gaussians to represent a dynamic volumetric scene, allowing for real-time novel view synthesis. For accurate segmentation, we leverage the view-independent colors of Gaussians for coarse-level segmentation and refine the results with an affinity field network for fine-level segmentation. Additionally, by embedding segmentation results within the Gaussians, we ensure that their deformation enables continuous tracking of segmented regions over time. We demonstrate the effectiveness of VolSegGS with several time-varying datasets and compare our solutions against state-of-the-art methods. With the ability to interact with a dynamic scene in real time and provide flexible segmentation and tracking capabilities, VolSegGS offers a powerful solution under low computational demands. This framework unlocks exciting new possibilities for time-varying volumetric data analysis and visualization.

Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be available at a time, making the problem severely ill-posed. In this work, we propose an approach, RED-PSM, which combines for the first time two powerful techniques to address this challenging imaging problem. The first, are partially separable models, which have been used to efficiently introduce a low-rank prior for the spatio-temporal object. The second is the recent Regularization by Denoising (RED), which provides a flexible framework to exploit the impressive performance of state-of-the-art image denoising algorithms, for various inverse problems. We propose a partially separable objective with RED and a computationally efficient and scalable optimization scheme with variable splitting and ADMM. Theoretical analysis proves the convergence of our objective to a value corresponding to a stationary point satisfying the first-order optimality conditions. Convergence is accelerated by a particular projection-domain-based initialization. We demonstrate the performance and computational improvements of our proposed RED-PSM with a learned image denoiser by comparing it to a recent deep-prior-based method known as TD-DIP. Although the main focus is on dynamic tomography, we also show the performance advantages of RED-PSM in a cardiac dynamic MRI setting.

Novel view synthesis for dynamic scenes is still a challenging problem in computer vision and graphics. Recently, Gaussian splatting has emerged as a robust technique to represent static scenes and enable high-quality and real-time novel view synthesis. Building upon this technique, we propose a new representation that explicitly decomposes the motion and appearance of dynamic scenes into sparse control points and dense Gaussians, respectively. Our key idea is to use sparse control points, significantly fewer in number than the Gaussians, to learn compact 6 DoF transformation bases, which can be locally interpolated through learned interpolation weights to yield the motion field of 3D Gaussians. We employ a deformation MLP to predict time-varying 6 DoF transformations for each control point, which reduces learning complexities, enhances learning abilities, and facilitates obtaining temporal and spatial coherent motion patterns. Then, we jointly learn the 3D Gaussians, the canonical space locations of control points, and the deformation MLP to reconstruct the appearance, geometry, and dynamics of 3D scenes. During learning, the location and number of control points are adaptively adjusted to accommodate varying motion complexities in different regions, and an ARAP loss following the principle of as rigid as possible is developed to enforce spatial continuity and local rigidity of learned motions. Finally, thanks to the explicit sparse motion representation and its decomposition from appearance, our method can enable user-controlled motion editing while retaining high-fidelity appearances. Extensive experiments demonstrate that our approach outperforms existing approaches on novel view synthesis with a high rendering speed and enables novel appearance-preserved motion editing applications. Project page: https://yihua7.github.io/SC-GS-web/

Dynamic radiance field reconstruction methods aim to model the time-varying structure and appearance of a dynamic scene. Existing methods, however, assume that accurate camera poses can be reliably estimated by Structure from Motion (SfM) algorithms. These methods, thus, are unreliable as SfM algorithms often fail or produce erroneous poses on challenging videos with highly dynamic objects, poorly textured surfaces, and rotating camera motion. We address this robustness issue by jointly estimating the static and dynamic radiance fields along with the camera parameters (poses and focal length). We demonstrate the robustness of our approach via extensive quantitative and qualitative experiments. Our results show favorable performance over the state-of-the-art dynamic view synthesis methods.

We investigate the temporal concatenation of sub-policies in Markov Decision Processes (MDP) with time-varying reward functions. We introduce General Dijkstra Search (GDS), and prove that globally optimal goal-reaching policies can be recovered through temporal composition of intermediate optimal sub-policies. Motivated by the "search, select, update" principle underlying GDS, we propose Dynamic Latent Routing (DLR), a language-model post-training method that jointly learns discrete latent codes, routing policies, and model parameters through dynamic search in a single training stage. In low-data fine-tuning settings, DLR matches or outperforms supervised fine-tuning across four datasets and six models, achieving a mean gain of +6.6 percentage points, while prior discrete-latent baselines consistently underperform SFT. Mechanistic analyses and targeted code ablations show that DLR learns structured routing behaviors with distinct causal roles.

Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using moment-based semidefinite programs (SDPs). In particular, they showed that moment-based SDPs can be used to calculate rigorous bounds on various descriptions of the stochastic chemical kinetic system's stationary distribution(s) -- for example, mean molecular counts, variances in these counts, and so on. In this paper, we show that these ideas can be extended to the corresponding dynamic problem, calculating time-varying bounds on the same descriptions.

The quantity that defines the behavior of a dynamic range compressor is the time-varying gain applied to the signal as a function of the input level. However, models of these devices are typically evaluated using proxy metrics because isolating the gain reduction signal from the audio input-output data included in existing datasets creates an ill-conditioned inverse problem. It is unclear how accurately these metrics describe the behavior the model is tasked with emulating, particularly as waveform-based metrics can be influenced by secondary effects introduced by analog processing and capture, even when those effects are inaudible. We investigate a method of evaluation in which the gain-reduction signal produced by a model is measured directly against a gain-reduction control voltage signal produced by the hardware. To evaluate the efficacy of this metric as a learning objective, a gray-box model is trained using loss computed directly over the gain control signals alongside two models trained using common proxy losses. The models trained using proxy losses did not achieve parity with models trained directly on the gain control signal when evaluated with respect to the underlying control trajectory, and the waveform-domain metrics assigned similar errors to models that were clearly separated by the direct metric. To facilitate further exploration of this method of evaluation, we present a Solid State Logic bus compressor dataset that includes the gain control voltage signal captured alongside the audio output.

We present MoVieS, a novel feed-forward model that synthesizes 4D dynamic novel views from monocular videos in one second. MoVieS represents dynamic 3D scenes using pixel-aligned grids of Gaussian primitives, explicitly supervising their time-varying motion. This allows, for the first time, the unified modeling of appearance, geometry and motion, and enables view synthesis, reconstruction and 3D point tracking within a single learning-based framework. By bridging novel view synthesis with dynamic geometry reconstruction, MoVieS enables large-scale training on diverse datasets with minimal dependence on task-specific supervision. As a result, it also naturally supports a wide range of zero-shot applications, such as scene flow estimation and moving object segmentation. Extensive experiments validate the effectiveness and efficiency of MoVieS across multiple tasks, achieving competitive performance while offering several orders of magnitude speedups.

We investigate the challenging problem of adversarial multi-armed bandits operating under time-varying constraints, a scenario motivated by numerous real-world applications. To address this complex setting, we propose a novel primal-dual algorithm that extends online mirror descent through the incorporation of suitable gradient estimators and effective constraint handling. We provide theoretical guarantees establishing sublinear dynamic regret and sublinear constraint violation for our proposed policy. Our algorithm achieves state-of-the-art performance in terms of both regret and constraint violation. Empirical evaluations demonstrate the superiority of our approach.

Spoken language models (SLMs) extend LLMs to speech input and output. Existing SLMs represent speech at fixed frame rates (e.g., 25 or 12.5 Hz), ignoring the time-varying information density of speech and offering no flexibility to trade off quality for speed at inference time. Recent audio tokenizer research has proposed dynamic frame rate speech coding, which exploits this non-uniformity and enables two new capabilities: very low average frame rates and frame rate controllability. However, this technique has not yet been applied to SLMs. We introduce Flexible Spoken Language Model (FlexiSLM), the first SLM that supports dynamic and controllable frame rates on both speech input and output. Using dynamic frame rate representations, FlexiSLM outperforms fixed-frame-rate 7B models including Qwen2.5-Omni and Kimi-Audio at its high-quality operating points. We further verify that FlexiSLM can be accurately steered down to 4.0 Hz; at 6.25 Hz, it roughly halves inference time relative to 12.5 Hz while retaining strong speech-to-speech quality. Audio samples are available at https://flexislm.github.io .

In novel view synthesis of scenes from multiple input views, 3D Gaussian splatting emerges as a viable alternative to existing radiance field approaches, delivering great visual quality and real-time rendering. While successful in static scenes, the present advancement of 3D Gaussian representation, however, faces challenges in dynamic scenes in terms of memory consumption and the need for numerous observations per time step, due to the onus of storing 3D Gaussian parameters per time step. In this study, we present an efficient 3D Gaussian representation tailored for dynamic scenes in which we define positions and rotations as functions of time while leaving other time-invariant properties of the static 3D Gaussian unchanged. Notably, our representation reduces memory usage, which is consistent regardless of the input sequence length. Additionally, it mitigates the risk of overfitting observed frames by accounting for temporal changes. The optimization of our Gaussian representation based on image and flow reconstruction results in a powerful framework for dynamic scene view synthesis in both monocular and multi-view cases. We obtain the highest rendering speed of 118 frames per second (FPS) at a resolution of 1352 times 1014 with a single GPU, showing the practical usability and effectiveness of our proposed method in dynamic scene rendering scenarios.

Dynamic 3D scene representation and novel view synthesis are crucial for enabling immersive experiences required by AR/VR and metaverse applications. It is a challenging task due to the complexity of unconstrained real-world scenes and their temporal dynamics. In this paper, we reformulate the reconstruction of a time-varying 3D scene as approximating its underlying spatiotemporal 4D volume by optimizing a collection of native 4D primitives, i.e., 4D Gaussians, with explicit geometry and appearance modeling. Equipped with a tailored rendering pipeline, our representation can be end-to-end optimized using only photometric supervision while free viewpoint viewing at interactive frame rate, making it suitable for representing real world scene with complex dynamic. This approach has been the first solution to achieve real-time rendering of high-resolution, photorealistic novel views for complex dynamic scenes. To facilitate real-world applications, we derive several compact variants that effectively reduce the memory footprint to address its storage bottleneck. Extensive experiments validate the superiority of 4DGS in terms of visual quality and efficiency across a range of dynamic scene-related tasks (e.g., novel view synthesis, 4D generation, scene understanding) and scenarios (e.g., single object, indoor scenes, driving environments, synthetic and real data).

We present SpectroMotion, a novel approach that combines 3D Gaussian Splatting (3DGS) with physically-based rendering (PBR) and deformation fields to reconstruct dynamic specular scenes. Previous methods extending 3DGS to model dynamic scenes have struggled to accurately represent specular surfaces. Our method addresses this limitation by introducing a residual correction technique for accurate surface normal computation during deformation, complemented by a deformable environment map that adapts to time-varying lighting conditions. We implement a coarse-to-fine training strategy that significantly enhances both scene geometry and specular color prediction. We demonstrate that our model outperforms prior methods for view synthesis of scenes containing dynamic specular objects and that it is the only existing 3DGS method capable of synthesizing photorealistic real-world dynamic specular scenes, outperforming state-of-the-art methods in rendering complex, dynamic, and specular scenes.

A recent frontier in computer vision has been the task of 3D video generation, which consists of generating a time-varying 3D representation of a scene. To generate dynamic 3D scenes, current methods explicitly model 3D temporal dynamics by jointly optimizing for consistency across both time and views of the scene. In this paper, we instead investigate whether it is necessary to explicitly enforce multiview consistency over time, as current approaches do, or if it is sufficient for a model to generate 3D representations of each timestep independently. We hence propose a model, Vid3D, that leverages 2D video diffusion to generate 3D videos by first generating a 2D "seed" of the video's temporal dynamics and then independently generating a 3D representation for each timestep in the seed video. We evaluate Vid3D against two state-of-the-art 3D video generation methods and find that Vid3D is achieves comparable results despite not explicitly modeling 3D temporal dynamics. We further ablate how the quality of Vid3D depends on the number of views generated per frame. While we observe some degradation with fewer views, performance degradation remains minor. Our results thus suggest that 3D temporal knowledge may not be necessary to generate high-quality dynamic 3D scenes, potentially enabling simpler generative algorithms for this task.

Multi-round LLM-based multi-agent systems rely on effective communication structures to support collaboration across rounds. However, most existing methods employ a fixed communication topology during inference, which falls short in many realistic applications where the agents' roles may change across rounds due to dynamic adversary, task progression, or time-varying constraints such as communication bandwidth. In this paper, we propose addressing this issue through TodyComm, a task-oriented dynamic communication algorithm. It produces behavior-driven collaboration topologies that adapt to the dynamics at each round, optimizing the utility for the task through policy gradient. Experiments on five benchmarks demonstrate that under both dynamic adversary and communications budgets, TodyComm delivers superior task effectiveness while retaining token efficiency and scalability.

The bio-inspired event camera has garnered extensive research attention in recent years, owing to its significant potential derived from its high dynamic range and low latency characteristics. Similar to the standard camera, the event camera requires precise intrinsic calibration to facilitate further high-level visual applications, such as pose estimation and mapping. While several calibration methods for event cameras have been proposed, most of them are either (i) engineering-driven, heavily relying on conventional image-based calibration pipelines, or (ii) inconvenient, requiring complex instrumentation. To this end, we propose an accurate and convenient intrinsic calibration method for event cameras, named eKalibr, which builds upon a carefully designed event-based circle grid pattern recognition algorithm. To extract target patterns from events, we perform event-based normal flow estimation to identify potential events generated by circle edges, and cluster them spatially. Subsequently, event clusters associated with the same grid circles are matched and grouped using normal flows, for subsequent time-varying ellipse estimation. Fitted ellipse centers are time-synchronized, for final grid pattern recognition. We conducted extensive experiments to evaluate the performance of eKalibr in terms of pattern extraction and intrinsic calibration. The implementation of eKalibr is open-sourced at (https://github.com/Unsigned-Long/eKalibr) to benefit the research community.

We consider the problem of novel view synthesis (NVS) for dynamic scenes. Recent neural approaches have accomplished exceptional NVS results for static 3D scenes, but extensions to 4D time-varying scenes remain non-trivial. Prior efforts often encode dynamics by learning a canonical space plus implicit or explicit deformation fields, which struggle in challenging scenarios like sudden movements or capturing high-fidelity renderings. In this paper, we introduce 4D Gaussian Splatting (4DGS), a novel method that represents dynamic scenes with anisotropic 4D XYZT Gaussians, inspired by the success of 3D Gaussian Splatting in static scenes. We model dynamics at each timestamp by temporally slicing the 4D Gaussians, which naturally compose dynamic 3D Gaussians and can be seamlessly projected into images. As an explicit spatial-temporal representation, 4DGS demonstrates powerful capabilities for modeling complicated dynamics and fine details, especially for scenes with abrupt motions. We further implement our temporal slicing and splatting techniques in a highly optimized CUDA acceleration framework, achieving real-time inference rendering speeds of up to 277 FPS on an RTX 3090 GPU and 583 FPS on an RTX 4090 GPU. Rigorous evaluations on scenes with diverse motions showcase the superior efficiency and effectiveness of 4DGS, which consistently outperforms existing methods both quantitatively and qualitatively.

This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both observational and past interventional data collected from the system. We give theoretical results detailing how one can transfer interventional information across time steps and define a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. We demonstrate how DCBO identifies optimal interventions faster than competing approaches in multiple settings and applications.

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes (e.g., information diffusion, virus propagation) occurring over the unobserved network. While there have been efforts to infer networks based on such data, providing a generative probabilistic model that is able to identify the underlying time-varying network remains an open question. Here we consider the problem of inferring generative dynamic network models based on network cascade diffusion data. We propose a novel framework for providing a non-parametric dynamic network model--based on a mixture of coupled hierarchical Dirichlet processes-- based on data capturing cascade node infection times. Our approach allows us to infer the evolving community structure in networks and to obtain an explicit predictive distribution over the edges of the underlying network--including those that were not involved in transmission of any cascade, or are likely to appear in the future. We show the effectiveness of our approach using extensive experiments on synthetic as well as real-world networks.

We introduce Diff4Splat, a feed-forward method that synthesizes controllable and explicit 4D scenes from a single image. Our approach unifies the generative priors of video diffusion models with geometry and motion constraints learned from large-scale 4D datasets. Given a single input image, a camera trajectory, and an optional text prompt, Diff4Splat directly predicts a deformable 3D Gaussian field that encodes appearance, geometry, and motion, all in a single forward pass, without test-time optimization or post-hoc refinement. At the core of our framework lies a video latent transformer, which augments video diffusion models to jointly capture spatio-temporal dependencies and predict time-varying 3D Gaussian primitives. Training is guided by objectives on appearance fidelity, geometric accuracy, and motion consistency, enabling Diff4Splat to synthesize high-quality 4D scenes in 30 seconds. We demonstrate the effectiveness of Diff4Splatacross video generation, novel view synthesis, and geometry extraction, where it matches or surpasses optimization-based methods for dynamic scene synthesis while being significantly more efficient.

Complex tasks are increasingly delegated to ensembles of specialized LLM-based agents that reason, communicate, and coordinate actions-both among themselves and through interactions with external tools, APIs, and databases. While persistent memory has been shown to enhance single-agent performance, most approaches assume a monolithic, single-user context-overlooking the benefits and challenges of knowledge transfer across users under dynamic, asymmetric permissions. We introduce Collaborative Memory, a framework for multi-user, multi-agent environments with asymmetric, time-evolving access controls encoded as bipartite graphs linking users, agents, and resources. Our system maintains two memory tiers: (1) private memory-private fragments visible only to their originating user; and (2) shared memory-selectively shared fragments. Each fragment carries immutable provenance attributes (contributing agents, accessed resources, and timestamps) to support retrospective permission checks. Granular read policies enforce current user-agent-resource constraints and project existing memory fragments into filtered transformed views. Write policies determine fragment retention and sharing, applying context-aware transformations to update the memory. Both policies may be designed conditioned on system, agent, and user-level information. Our framework enables safe, efficient, and interpretable cross-user knowledge sharing, with provable adherence to asymmetric, time-varying policies and full auditability of memory operations.

This paper explores Large Batch Training techniques using layer-wise adaptive scaling ratio (LARS) across diverse settings, uncovering insights. LARS algorithms with warm-up tend to be trapped in sharp minimizers early on due to redundant ratio scaling. Additionally, a fixed steep decline in the latter phase restricts deep neural networks from effectively navigating early-phase sharp minimizers. Building on these findings, we propose Time Varying LARS (TVLARS), a novel algorithm that replaces warm-up with a configurable sigmoid-like function for robust training in the initial phase. TVLARS promotes gradient exploration early on, surpassing sharp optimizers and gradually transitioning to LARS for robustness in later phases. Extensive experiments demonstrate that TVLARS consistently outperforms LARS and LAMB in most cases, with up to 2\% improvement in classification scenarios. Notably, in all self-supervised learning cases, TVLARS dominates LARS and LAMB with performance improvements of up to 10\%.

Modeling the time-varying 3D appearance of plants during growth poses unique challenges: unlike most dynamic scenes, plants continuously generate new geometry as they expand, branch, and differentiate. Existing dynamic scene representations are ill-suited to this setting: deformation fields provide insufficient constraints to yield physically plausible scene dynamics, and 4D Gaussian splatting represents the same physical structures with different Gaussian primitives at different times, breaking temporal consistency. We introduce GrowFlow, a dynamic representation that couples 3D Gaussian primitives with a neural ordinary differential equation to model plant growth as a continuous flow field over geometric parameters (position, scale, and orientation). Our representation enables consistent appearance rendering and models nonlinear, continuous-time growth dynamics with full temporal correspondences for every primitive. To initialize a sufficient set of Gaussian primitives, we first reconstruct the mature plant and then learn a reverse-growth process, effectively simulating the plant's developmental history in reverse. GrowFlow achieves superior image quality and geometric coherence compared to prior methods on a new, multi-view timelapse dataset of plant growth, and provides the first temporally coherent representation for appearance modeling of growing 3D structures.

Temporal graphs are widely used to model dynamic systems with time-varying interactions. In real-world scenarios, the underlying mechanisms of generating future interactions in dynamic systems are typically governed by a set of recurring substructures within the graph, known as temporal motifs. Despite the success and prevalence of current temporal graph neural networks (TGNN), it remains uncertain which temporal motifs are recognized as the significant indications that trigger a certain prediction from the model, which is a critical challenge for advancing the explainability and trustworthiness of current TGNNs. To address this challenge, we propose a novel approach, called Temporal Motifs Explainer (TempME), which uncovers the most pivotal temporal motifs guiding the prediction of TGNNs. Derived from the information bottleneck principle, TempME extracts the most interaction-related motifs while minimizing the amount of contained information to preserve the sparsity and succinctness of the explanation. Events in the explanations generated by TempME are verified to be more spatiotemporally correlated than those of existing approaches, providing more understandable insights. Extensive experiments validate the superiority of TempME, with up to 8.21% increase in terms of explanation accuracy across six real-world datasets and up to 22.96% increase in boosting the prediction Average Precision of current TGNNs.

Dynamic scene reconstruction poses a persistent challenge in 3D vision. Deformable 3D Gaussian Splatting has emerged as an effective method for this task, offering real-time rendering and high visual fidelity. This approach decomposes a dynamic scene into a static representation in a canonical space and time-varying scene motion. Scene motion is defined as the collective movement of all Gaussian points, and for compactness, existing approaches commonly adopt implicit neural fields or sparse control points. However, these methods predominantly rely on gradient-based optimization for all motion information. Due to the high degree of freedom, they struggle to converge on real-world datasets exhibiting complex motion. To preserve the compactness of motion representation and address convergence challenges, this paper proposes heterogeneous 3D control points, termed H3D control points, whose attributes are obtained using a hybrid strategy combining optical flow back-projection and gradient-based methods. This design decouples directly observable motion components from those that are geometrically occluded. Specifically, components of 3D motion that project onto the image plane are directly acquired via optical flow back projection, while unobservable portions are refined through gradient-based optimization. Experiments on the Neu3DV and CMU-Panoptic datasets demonstrate that our method achieves superior performance over state-of-the-art deformable 3D Gaussian splatting techniques. Remarkably, our method converges within just 100 iterations and achieves a per-frame processing speed of 2 seconds on a single NVIDIA RTX 4070 GPU.

Self-supervised novel view synthesis (NVS) remains challenging to scale, despite the abundance of video data, largely due to the brittleness of training on realistic videos and the hard-to-predict scaling behavior of multi-network system designs. We introduce RayDer, a unified, feed-forward transformer that consolidates camera estimation, scene reconstruction, and rendering into a single backbone, turning self-supervised NVS into a well-posed single-model scaling problem. A minimal dynamic state, treated as a nuisance factor, absorbs time-varying content and enables stable training on unconstrained real-world video. Importantly, RayDer keeps static-scene NVS as its target task: dynamic content is leveraged purely as scalable supervision, not reconstructed as in dynamic-scene (4D) NVS. Across multiple model sizes and orders of magnitude in data, RayDer exhibits clean power-law scaling with data and compute, and outperforms static-scene data mixtures. On a large number of benchmarks, RayDer achieves strong zero-shot open-set performance competitive with state-of-the-art supervised approaches. Project Page: https://compvis.github.io/rayder

Deep learning-based speech enhancement methods have significantly improved speech quality and intelligibility. Convolutional neural networks (CNNs) have been proven to be essential components of many high-performance models. In this paper, we introduce adaptive convolution, an efficient and versatile convolutional module that enhances the model's capability to adaptively represent speech signals. Adaptive convolution performs frame-wise causal dynamic convolution, generating time-varying kernels for each frame by assembling multiple parallel candidate kernels. A lightweight attention mechanism is proposed for adaptive convolution, leveraging both current and historical information to assign adaptive weights to each candidate kernel. This enables the convolution operation to adapt to frame-level speech spectral features, leading to more efficient extraction and reconstruction. We integrate adaptive convolution into various CNN-based models, highlighting its generalizability. Experimental results demonstrate that adaptive convolution significantly improves the performance with negligible increases in computational complexity, especially for lightweight models. Moreover, we present an intuitive analysis revealing a strong correlation between kernel selection and signal characteristics. Furthermore, we propose the adaptive convolutional recurrent network (AdaptCRN), an ultra-lightweight model that incorporates adaptive convolution and an efficient encoder-decoder design, achieving superior performance compared to models with similar or even higher computational costs.

Deploying large language models (LLMs) in mobile and edge computing environments is constrained by limited on-device resources, scarce wireless bandwidth, and frequent model evolution. Although edge-cloud collaborative inference with speculative decoding (SD) can reduce end-to-end latency by executing a lightweight draft model at the edge and verifying it with a cloud-side target model, existing frameworks fundamentally rely on tight coupling between the two models. Consequently, repeated model synchronization introduces excessive communication overhead, increasing end-to-end latency, and ultimately limiting the scalability of SD in edge environments. To address these limitations, we propose FlexSpec, a communication-efficient collaborative inference framework tailored for evolving edge-cloud systems. The core design of FlexSpec is a shared-backbone architecture that allows a single and static edge-side draft model to remain compatible with a large family of evolving cloud-side target models. By decoupling edge deployment from cloud-side model updates, FlexSpec eliminates the need for edge-side retraining or repeated model downloads, substantially reducing communication and maintenance costs. Furthermore, to accommodate time-varying wireless conditions and heterogeneous device constraints, we develop a channel-aware adaptive speculation mechanism that dynamically adjusts the speculative draft length based on real-time channel state information and device energy budgets. Extensive experiments demonstrate that FlexSpec achieves superior performance compared to conventional SD approaches in terms of inference efficiency.

The ability to dynamically adjust the computational load of neural models during inference in a resource aware manner is crucial for on-device processing scenarios, characterised by limited and time-varying computational resources. Early-exit architectures represent an elegant and effective solution, since they can process the input with a subset of their layers, exiting at intermediate branches (the upmost layers are hence removed from the model). From a different perspective, for automatic speech recognition applications there are memory-efficient neural architectures that apply variable frame rate analysis, through downsampling/upsampling operations in the middle layers, reducing the overall number of operations and improving significantly the performance on well established benchmarks. One example is the Zipformer. However, these architectures lack the modularity necessary to inject early-exit branches. With the aim of improving the performance in early-exit models, we propose introducing parallel layers in the architecture that process downsampled versions of their inputs. % in conjunction with standard processing layers. We show that in this way the speech recognition performance on standard benchmarks significantly improve, at the cost of a small increase in the overall number of model parameters but without affecting the inference time.

We propose 4DGT, a 4D Gaussian-based Transformer model for dynamic scene reconstruction, trained entirely on real-world monocular posed videos. Using 4D Gaussian as an inductive bias, 4DGT unifies static and dynamic components, enabling the modeling of complex, time-varying environments with varying object lifespans. We proposed a novel density control strategy in training, which enables our 4DGT to handle longer space-time input and remain efficient rendering at runtime. Our model processes 64 consecutive posed frames in a rolling-window fashion, predicting consistent 4D Gaussians in the scene. Unlike optimization-based methods, 4DGT performs purely feed-forward inference, reducing reconstruction time from hours to seconds and scaling effectively to long video sequences. Trained only on large-scale monocular posed video datasets, 4DGT can outperform prior Gaussian-based networks significantly in real-world videos and achieve on-par accuracy with optimization-based methods on cross-domain videos. Project page: https://4dgt.github.io

Finding multiple temporal relationships among locations can benefit a bunch of urban applications, such as dynamic offline advertising and smart public transport planning. While some efforts have been made on finding static relationships among locations, little attention is focused on studying time-aware location relationships. Indeed, abundant location-based human activities are time-varying and the availability of these data enables a new paradigm for understanding the dynamic relationships in a period among connective locations. To this end, we propose to study a new problem, namely multi-Temporal relationship inference among locations (Trial for short), where the major challenge is how to integrate dynamic and geographical influence under the relationship sparsity constraint. Specifically, we propose a solution to Trial with a graph learning scheme, which includes a spatially evolving graph neural network (SEENet) with two collaborative components: spatially evolving graph convolution module (SEConv) and spatially evolving self-supervised learning strategy (SE-SSL). SEConv performs the intra-time aggregation and inter-time propagation to capture the multifaceted spatially evolving contexts from the view of location message passing. In addition, SE-SSL designs time-aware self-supervised learning tasks in a global-local manner with additional evolving constraint to enhance the location representation learning and further handle the relationship sparsity. Finally, experiments on four real-world datasets demonstrate the superiority of our method over several state-of-the-art approaches.

Controllable music generation remains a significant challenge, with existing methods often requiring model retraining or introducing audible artifacts. We introduce MusicRFM, a framework that adapts Recursive Feature Machines (RFMs) to enable fine-grained, interpretable control over frozen, pre-trained music models by directly steering their internal activations. RFMs analyze a model's internal gradients to produce interpretable "concept directions", or specific axes in the activation space that correspond to musical attributes like notes or chords. We first train lightweight RFM probes to discover these directions within MusicGen's hidden states; then, during inference, we inject them back into the model to guide the generation process in real-time without per-step optimization. We present advanced mechanisms for this control, including dynamic, time-varying schedules and methods for the simultaneous enforcement of multiple musical properties. Our method successfully navigates the trade-off between control and generation quality: we can increase the accuracy of generating a target musical note from 0.23 to 0.82, while text prompt adherence remains within approximately 0.02 of the unsteered baseline, demonstrating effective control with minimal impact on prompt fidelity. We release code to encourage further exploration on RFMs in the music domain.

With the rapid development of Model Context Protocol (MCP), the number of MCP servers has surpassed 10,000. However, existing MCP benchmarks are limited to single-server settings with only a few tools, hindering effective evaluation of agent capabilities in large-scale, real-world scenarios. To address this limitation, we present LiveMCPBench, the first comprehensive benchmark comprising 95 real-world tasks grounded in the MCP ecosystem, designed to evaluate LLM agents at scale across diverse servers. To support a scalable and reproducible evaluation pipeline in large-scale MCP environments, we curate LiveMCPTool, a diverse and readily deployable collection of 70 MCP servers and 527 tools. Furthermore, we introduce LiveMCPEval, an LLM-as-a-Judge framework that enables automated and adaptive evaluation in dynamic, time-varying task environments, achieving 81% agreement with human reviewers. Finally, we propose the MCP Copilot Agent, a multi-step agent that routes tools for dynamic planning and executes tools for API interaction across the entire LiveMCPTool suite. Our evaluation covers 10 leading models, with the best-performing model (Claude-Sonnet-4) reaching a 78.95% success rate. However, we observe large performance variance across models, and several widely-used models perform poorly in LiveMCPBench's complex, tool-rich environments. Overall, LiveMCPBench offers the first unified framework for benchmarking LLM agents in realistic, tool-rich, and dynamic MCP environments, laying a solid foundation for scalable and reproducible research on agent capabilities. Our code and data will be publicly available at https://icip-cas.github.io/LiveMCPBench.

Motion forecasting for autonomous driving is a challenging task because complex driving scenarios result in a heterogeneous mix of static and dynamic inputs. It is an open problem how best to represent and fuse information about road geometry, lane connectivity, time-varying traffic light state, and history of a dynamic set of agents and their interactions into an effective encoding. To model this diverse set of input features, many approaches proposed to design an equally complex system with a diverse set of modality specific modules. This results in systems that are difficult to scale, extend, or tune in rigorous ways to trade off quality and efficiency. In this paper, we present Wayformer, a family of attention based architectures for motion forecasting that are simple and homogeneous. Wayformer offers a compact model description consisting of an attention based scene encoder and a decoder. In the scene encoder we study the choice of early, late and hierarchical fusion of the input modalities. For each fusion type we explore strategies to tradeoff efficiency and quality via factorized attention or latent query attention. We show that early fusion, despite its simplicity of construction, is not only modality agnostic but also achieves state-of-the-art results on both Waymo Open MotionDataset (WOMD) and Argoverse leaderboards, demonstrating the effectiveness of our design philosophy

Climbing grades are used to classify a climbing route based on its perceived difficulty, and have come to play a central role in the sport of rock climbing. Recently, the first statistically rigorous method for estimating climbing grades from whole-history ascent data was described, based on the dynamic Bradley-Terry model for games between players of time-varying ability. In this paper, we implement inference under the whole-history rating model using Markov chain Monte Carlo and apply the method to a curated data set made up of climbers who climb regularly. We use these data to get an estimate of the model's fundamental scale parameter m, which defines the proportional increase in difficulty associated with an increment of grade. We show that the data conform to assumptions that the climbing grade scale is a logarithmic scale of difficulty, like decibels or stellar magnitude. We estimate that an increment in Ewbank, French and UIAA climbing grade systems corresponds to 2.1, 2.09 and 2.13 times increase in difficulty respectively, assuming a logistic model of probability of success as a function of grade. Whereas we find that the Vermin scale for bouldering (V-grade scale) corresponds to a 3.17 increase in difficulty per grade increment. In addition, we highlight potential connections between the logarithmic properties of climbing grade scales and the psychophysical laws of Weber and Fechner.

We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks

Knowledge-intensive language understanding tasks require Language Models (LMs) to integrate relevant context, mitigating their inherent weaknesses, such as incomplete or outdated knowledge. Nevertheless, studies indicate that LMs often ignore the provided context as it can conflict with the pre-existing LM's memory learned during pre-training. Moreover, conflicting knowledge can already be present in the LM's parameters, termed intra-memory conflict. Existing works have studied the two types of knowledge conflicts only in isolation. We conjecture that the (degree of) intra-memory conflicts can in turn affect LM's handling of context-memory conflicts. To study this, we introduce the DYNAMICQA dataset, which includes facts with a temporal dynamic nature where a fact can change with a varying time frequency and disputable dynamic facts, which can change depending on the viewpoint. DYNAMICQA is the first to include real-world knowledge conflicts and provide context to study the link between the different types of knowledge conflicts. With the proposed dataset, we assess the use of uncertainty for measuring the intra-memory conflict and introduce a novel Coherent Persuasion (CP) score to evaluate the context's ability to sway LM's semantic output. Our extensive experiments reveal that static facts, which are unlikely to change, are more easily updated with additional context, relative to temporal and disputable facts.

Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the observations. This paper provides a selective review of recent advancements in deep neural network-based approaches for SSMs, and presents a unified perspective for discrete time deep state space models and continuous time ones such as latent neural Ordinary Differential and Stochastic Differential Equations. It starts with an overview of the classical maximum likelihood based approach for learning SSMs, reviews variational autoencoder as a general learning pipeline for neural network-based approaches in the presence of latent variables, and discusses in detail representative deep learning models that fall under the SSM framework. Very recent developments, where SSMs are used as standalone architectural modules for improving efficiency in sequence modeling, are also examined. Finally, examples involving mixed frequency and irregularly-spaced time series data are presented to demonstrate the advantage of SSMs in these settings.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Misinformation verification increasingly occurs in public, fast-moving, and multilingual online settings, where static benchmarks provide an incomplete measure of model reliability. We introduce CommunityFact, a refreshable benchmark for misinformation detection in the wild, with three major goals: coverage, granularity, and redistributability. This release contains 15,992 standalone claims across five languages and two domains. We evaluate ten LLMs under varying inference-time capabilities, including thinking and web-search. Our results show that closed-input verification remains challenging, web access yields the largest gains, and web-enabled LLMs' source-selection policies are systematically misaligned with the sources human Community Notes raters converge on -- a gap that closes through model-specific mechanisms of retrieval expansion or pruning. We further find substantial variation across language-domain slices and across the evidence ecosystems used by web-enabled systems. Beyond evaluation, CommunityFact positions Community Notes as a training signal for claim-conditioned source suggesters that could improve factual verification on novel claims.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching behaviour from one mode to another. Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depends on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. We introduce two new datasets for this setting, a synthesized ODE-driven particles dataset and a real-world Salsa Couple Dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that are irregularly sampled and/or contain missing observations. In this work, we propose the Neural Continuous-Discrete State Space Model (NCDSSM) for continuous-time modeling of time series through discrete-time observations. NCDSSM employs auxiliary variables to disentangle recognition from dynamics, thus requiring amortized inference only for the auxiliary variables. Leveraging techniques from continuous-discrete filtering theory, we demonstrate how to perform accurate Bayesian inference for the dynamic states. We propose three flexible parameterizations of the latent dynamics and an efficient training objective that marginalizes the dynamic states during inference. Empirical results on multiple benchmark datasets across various domains show improved imputation and forecasting performance of NCDSSM over existing models.

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-your-own coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Deep neural networks have become increasingly of interest in dynamical system prediction, but out-of-distribution generalization and long-term stability still remains challenging. In this work, we treat the domain parameters of dynamical systems as factors of variation of the data generating process. By leveraging ideas from supervised disentanglement and causal factorization, we aim to separate the domain parameters from the dynamics in the latent space of generative models. In our experiments we model dynamics both in phase space and in video sequences and conduct rigorous OOD evaluations. Results indicate that disentangled VAEs adapt better to domain parameters spaces that were not present in the training data. At the same time, disentanglement can improve the long-term and out-of-distribution predictions of state-of-the-art models in video sequences.

Temporal causal representation learning methods assume that causal mechanisms switch instantaneously between discrete domains, yet real-world systems often exhibit continuous mechanism transitions. For example, a vehicle's dynamics evolve gradually through a turning maneuver, and human gait shifts smoothly from walking to running. We formalize this setting by modeling transitional mechanisms as convex combinations of finitely many atomic mechanisms, governed by time-varying mixing coefficients. Our theoretical contributions establish that both the latent causal variables and the continuous mixing trajectory are jointly identifiable. We further propose TRACE, a Mixture-of-Experts framework where each expert learns one atomic mechanism during training, enabling recovery of mechanism trajectories at test time. This formulation generalizes to intermediate mechanism states never observed during training. Experiments on synthetic and real-world data demonstrate that TRACE recovers mixing trajectories with up to 0.99 correlation, substantially outperforming discrete-switching baselines.

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common approach to facilitate mathematical tractability and interpretability of DS models involves decomposing nonlinear DS into multiple linear DS separated by switching manifolds, i.e. piecewise linear (PWL) systems. PWL models are popular in engineering and a frequent choice in mathematics for analyzing the topological properties of DS. However, hand-crafting such models is tedious and only possible for very low-dimensional scenarios, while inferring them from data usually gives rise to unnecessarily complex representations with very many linear subregions. Here we introduce Almost-Linear Recurrent Neural Networks (AL-RNNs) which automatically and robustly produce most parsimonious PWL representations of DS from time series data, using as few PWL nonlinearities as possible. AL-RNNs can be efficiently trained with any SOTA algorithm for dynamical systems reconstruction (DSR), and naturally give rise to a symbolic encoding of the underlying DS that provably preserves important topological properties. We show that for the Lorenz and R\"ossler systems, AL-RNNs discover, in a purely data-driven way, the known topologically minimal PWL representations of the corresponding chaotic attractors. We further illustrate on two challenging empirical datasets that interpretable symbolic encodings of the dynamics can be achieved, tremendously facilitating mathematical and computational analysis of the underlying systems.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Continual Test-Time Adaptation (CTTA) seeks to adapt source pre-trained models to continually changing, unseen target domains. While existing CTTA methods assume structured domain changes with uniform durations, real-world environments often exhibit dynamic patterns where domains recur with varying frequencies and durations. Current approaches, which adapt the same parameters across different domains, struggle in such dynamic conditions-they face convergence issues with brief domain exposures, risk forgetting previously learned knowledge, or misapplying it to irrelevant domains. To remedy this, we propose DPCore, a method designed for robust performance across diverse domain change patterns while ensuring computational efficiency. DPCore integrates three key components: Visual Prompt Adaptation for efficient domain alignment, a Prompt Coreset for knowledge preservation, and a Dynamic Update mechanism that intelligently adjusts existing prompts for similar domains while creating new ones for substantially different domains. Extensive experiments on four benchmarks demonstrate that DPCore consistently outperforms various CTTA methods, achieving state-of-the-art performance in both structured and dynamic settings while reducing trainable parameters by 99% and computation time by 64% compared to previous approaches.

Test-Time Scaling (TTS) enhances the reasoning ability of large language models (LLMs) by allocating additional computation during inference. However, existing approaches primarily rely on output-level sampling while overlooking the role of model architecture. In mainstream Mixture-of-Experts (MoE) LLMs, we observe that varying the number of activated experts yields complementary solution sets with stable accuracy, revealing a new and underexplored source of diversity. Motivated by this observation, we propose Dynamic Experts Search (DES), a TTS strategy that elevates expert activation into a controllable dimension of the search space. DES integrates two key components: (1) Dynamic MoE, which enables direct control of expert counts during inference to generate diverse reasoning trajectories without additional cost; and (2) Expert Configuration Inheritance, which preserves consistent expert counts within a reasoning path while varying them across runs, thereby balancing stability and diversity throughout the search. Extensive experiments across MoE architectures, verifiers and reasoning benchmarks (i.e., math, code and knowledge) demonstrate that DES reliably outperforms TTS baselines, enhancing accuracy and stability without additional cost. These results highlight DES as a practical and scalable form of architecture-aware TTS, illustrating how structural flexibility in modern LLMs can advance reasoning.

Synthesizing novel views from in-the-wild monocular videos is challenging due to scene dynamics and the lack of multi-view cues. To address this, we propose SplineGS, a COLMAP-free dynamic 3D Gaussian Splatting (3DGS) framework for high-quality reconstruction and fast rendering from monocular videos. At its core is a novel Motion-Adaptive Spline (MAS) method, which represents continuous dynamic 3D Gaussian trajectories using cubic Hermite splines with a small number of control points. For MAS, we introduce a Motion-Adaptive Control points Pruning (MACP) method to model the deformation of each dynamic 3D Gaussian across varying motions, progressively pruning control points while maintaining dynamic modeling integrity. Additionally, we present a joint optimization strategy for camera parameter estimation and 3D Gaussian attributes, leveraging photometric and geometric consistency. This eliminates the need for Structure-from-Motion preprocessing and enhances SplineGS's robustness in real-world conditions. Experiments show that SplineGS significantly outperforms state-of-the-art methods in novel view synthesis quality for dynamic scenes from monocular videos, achieving thousands times faster rendering speed.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Varying dynamics parameters in simulation is a popular Domain Randomization (DR) approach for overcoming the reality gap in Reinforcement Learning (RL). Nevertheless, DR heavily hinges on the choice of the sampling distribution of the dynamics parameters, since high variability is crucial to regularize the agent's behavior but notoriously leads to overly conservative policies when randomizing excessively. In this paper, we propose a novel approach to address sim-to-real transfer, which automatically shapes dynamics distributions during training in simulation without requiring real-world data. We introduce DOmain RAndomization via Entropy MaximizatiON (DORAEMON), a constrained optimization problem that directly maximizes the entropy of the training distribution while retaining generalization capabilities. In achieving this, DORAEMON gradually increases the diversity of sampled dynamics parameters as long as the probability of success of the current policy is sufficiently high. We empirically validate the consistent benefits of DORAEMON in obtaining highly adaptive and generalizable policies, i.e. solving the task at hand across the widest range of dynamics parameters, as opposed to representative baselines from the DR literature. Notably, we also demonstrate the Sim2Real applicability of DORAEMON through its successful zero-shot transfer in a robotic manipulation setup under unknown real-world parameters.

Generating realistic time series data is important for many engineering and scientific applications. Existing work tackles this problem using generative adversarial networks (GANs). However, GANs are often unstable during training, and they can suffer from mode collapse. While variational autoencoders (VAEs) are known to be more robust to these issues, they are (surprisingly) less often considered for time series generation. In this work, we introduce Koopman VAE (KVAE), a new generative framework that is based on a novel design for the model prior, and that can be optimized for either regular and irregular training data. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. Our approach enhances generative modeling with two desired features: (i) incorporating domain knowledge can be achieved by leverageing spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stablity of the system can be performed using tools from dynamical systems theory. Our results show that KVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks. Whether trained on regular or irregular data, KVAE generates time series that improve both discriminative and predictive metrics. We also present visual evidence suggesting that KVAE learns probability density functions that better approximate empirical ground truth distributions.

Real-world time series are characterized by intrinsic non-stationarity that poses a principal challenge for deep forecasting models. While previous models suffer from complicated series variations induced by changing temporal distribution, we tackle non-stationary time series with modern Koopman theory that fundamentally considers the underlying time-variant dynamics. Inspired by Koopman theory of portraying complex dynamical systems, we disentangle time-variant and time-invariant components from intricate non-stationary series by Fourier Filter and design Koopman Predictor to advance respective dynamics forward. Technically, we propose Koopa as a novel Koopman forecaster composed of stackable blocks that learn hierarchical dynamics. Koopa seeks measurement functions for Koopman embedding and utilizes Koopman operators as linear portraits of implicit transition. To cope with time-variant dynamics that exhibits strong locality, Koopa calculates context-aware operators in the temporal neighborhood and is able to utilize incoming ground truth to scale up forecast horizon. Besides, by integrating Koopman Predictors into deep residual structure, we ravel out the binding reconstruction loss in previous Koopman forecasters and achieve end-to-end forecasting objective optimization. Compared with the state-of-the-art model, Koopa achieves competitive performance while saving 77.3% training time and 76.0% memory.

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to understand how covariance structure in data, latent state size, and initialization affect the evolution of parameters throughout learning with gradient descent. We show that focusing on the learning dynamics in the frequency domain affords analytical solutions under mild assumptions, and we establish a link between one-dimensional SSMs and the dynamics of deep linear feed-forward networks. Finally, we analyze how latent state over-parameterization affects convergence time and describe future work in extending our results to the study of deep SSMs with nonlinear connections. This work is a step toward a theory of learning dynamics in deep state space models.

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to learning the transfer operator or the generator of the system, which in turn can be used for numerous tasks, such as forecasting and interpreting the system dynamics. We show that the search for a good representation can be cast as an optimization problem over neural networks. Our approach is supported by recent results in statistical learning theory, highlighting the role of approximation error and metric distortion in the learning problem. The objective function we propose is associated with projection operators from the representation space to the data space, overcomes metric distortion, and can be empirically estimated from data. In the discrete-time setting, we further derive a relaxed objective function that is differentiable and numerically well-conditioned. We compare our method against state-of-the-art approaches on different datasets, showing better performance across the board.

Large language models (LLMs) are powerful tools but are often expensive to deploy at scale. LLM query routing mitigates this by dynamically assigning queries to models of varying cost and quality to obtain a desired trade-off. Prior query routing approaches generate only one response from the selected model and a single response from a small (inexpensive) model was often not good enough to beat a response from a large (expensive) model due to which they end up overusing the large model and missing out on potential cost savings. However, it is well known that for small models, generating multiple responses and selecting the best can enhance quality while remaining cheaper than a single large-model response. We leverage this idea to propose BEST-Route, a novel routing framework that chooses a model and the number of responses to sample from it based on query difficulty and the quality thresholds. Experiments on real-world datasets demonstrate that our method reduces costs by up to 60% with less than 1% performance drop.

Test-time scaling (TTS) has proven effective in enhancing the reasoning capabilities of large language models (LLMs). Verification plays a key role in TTS, simultaneously influencing (1) reasoning performance and (2) compute efficiency, due to the quality and computational cost of verification. In this work, we challenge the conventional paradigms of verification, and make the first attempt toward systematically investigating the impact of verification granularity-that is, how frequently the verifier is invoked during generation, beyond verifying only the final output or individual generation steps. To this end, we introduce Variable Granularity Search (VG-Search), a unified algorithm that generalizes beam search and Best-of-N sampling via a tunable granularity parameter g. Extensive experiments with VG-Search under varying compute budgets, generator-verifier configurations, and task attributes reveal that dynamically selecting g can improve the compute efficiency and scaling behavior. Building on these findings, we propose adaptive VG-Search strategies that achieve accuracy gains of up to 3.1\% over Beam Search and 3.6\% over Best-of-N, while reducing FLOPs by over 52\%. We will open-source the code to support future research.

The current paradigm for safety alignment of large language models (LLMs) follows a one-size-fits-all approach: the model refuses to interact with any content deemed unsafe by the model provider. This approach lacks flexibility in the face of varying social norms across cultures and regions. In addition, users may have diverse safety needs, making a model with static safety standards too restrictive to be useful, as well as too costly to be re-aligned. We propose Controllable Safety Alignment (CoSA), a framework designed to adapt models to diverse safety requirements without re-training. Instead of aligning a fixed model, we align models to follow safety configs -- free-form natural language descriptions of the desired safety behaviors -- that are provided as part of the system prompt. To adjust model safety behavior, authorized users only need to modify such safety configs at inference time. To enable that, we propose CoSAlign, a data-centric method for aligning LLMs to easily adapt to diverse safety configs. Furthermore, we devise a novel controllability evaluation protocol that considers both helpfulness and configured safety, summarizing them into CoSA-Score, and construct CoSApien, a human-authored benchmark that consists of real-world LLM use cases with diverse safety requirements and corresponding evaluation prompts. We show that CoSAlign leads to substantial gains of controllability over strong baselines including in-context alignment. Our framework encourages better representation and adaptation to pluralistic human values in LLMs, and thereby increasing their practicality.

Vision-language models exhibit remarkable zero-shot capabilities but suffer significant performance degradation under distribution shifts. While test-time adaptation (TTA) via Low-Rank Adaptation offers a parameter-efficient solution, we identify a fundamental bottleneck in current methods: the reliance on static rank configurations. Because visual inputs inherently possess varying information densities, a fixed rank forces an inevitable optimization compromise, leading to underfitting on complex scenes and overfitting on simple ones. To bridge this gap, we propose Multi-Rank Adaptation (MuRA), a novel framework that dynamically selects and fuses adaptation modules of varying capacities based on token-level visual complexity. MuRA synergizes Multi-Rank Orthogonal Decomposition to provide a superior, knowledge-preserving initialization, and Unified Component Fusion with Continuous Router Updating to sustainably learn semantic-to-rank mappings. Furthermore, we provide rigorous theoretical justifications mathematically proving the necessity and gradient stability of this adaptive mechanism. Crucially, MuRA's dynamic design uniquely thrives at the deepest visual layer, capitalizing on the shortest gradient backpropagation path. Extensive experiments demonstrate that MuRA achieves state-of-the-art accuracy across extensive domain generalization and cross-dataset benchmarks while significantly reducing both computational and memory overhead.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

Neural ordinary differential equations (neural ODEs) have rapidly gained prominence as a powerful and unifying framework for conceptualizing artificial neural networks, elegantly connecting the continuous-time modeling of dynamical systems with the discrete, data-driven paradigm of modern deep learning. Beyond their practical advantages they offer fresh theoretical insights into the training and generalization properties of neural networks. The distinctive feature of this framework is its dual dynamical nature: inference dynamics, which govern the ODE evolution during forward computation, and training dynamics, which control the optimization of model parameters. This makes neural ODEs a particularly well-suited theoretical framework for studying a large variety of settings such as multi-layer neural networks (ResNets for example), autoregressive models (with next-token generation dynamics), generative models, and recurrent neural networks in theoretical neuroscience. In this work, we introduce a theoretically grounded class of models for studying neural ODEs trained via online stochastic gradient descent. We solve the training dynamics of these models via dynamical mean field theory and derive learning curves in the high-dimensional limit.

Learning domain adaptive policies that can generalize to unseen transition dynamics, remains a fundamental challenge in learning-based control. Substantial progress has been made through domain representation learning to capture domain-specific information, thus enabling domain-aware decision making. We analyze the process of learning domain representations through dynamical prediction and find that selecting contexts adjacent to the current step causes the learned representations to entangle static domain information with varying dynamical properties. Such mixture can confuse the conditioned policy, thereby constraining zero-shot adaptation. To tackle the challenge, we propose DADP (Domain Adaptive Diffusion Policy), which achieves robust adaptation through unsupervised disentanglement and domain-aware diffusion injection. First, we introduce Lagged Context Dynamical Prediction, a strategy that conditions future state estimation on a historical offset context; by increasing this temporal gap, we unsupervisedly disentangle static domain representations by filtering out transient properties. Second, we integrate the learned domain representations directly into the generative process by biasing the prior distribution and reformulating the diffusion target. Extensive experiments on challenging benchmarks across locomotion and manipulation demonstrate the superior performance, and the generalizability of DADP over prior methods. More visualization results are available on the https://outsider86.github.io/DomainAdaptiveDiffusionPolicy/.

Graph Neural Networks (GNNs) are emerging as powerful tools for nonlinear Model Order Reduction (MOR) of time-dependent parameterized Partial Differential Equations (PDEs). However, existing methodologies struggle to combine geometric inductive biases with interpretable latent behavior, overlooking dynamics-driven features or disregarding spatial information. In this work, we address this gap by introducing Latent Dynamics Graph Convolutional Network (LD-GCN), a purely data-driven, encoder-free architecture that learns a global, low-dimensional representation of dynamical systems conditioned on external inputs and parameters. The temporal evolution is modeled in the latent space and advanced through time-stepping, allowing for time-extrapolation, and the trajectories are consistently decoded onto geometrically parameterized domains using a GNN. Our framework enhances interpretability by enabling the analysis of the reduced dynamics and supporting zero-shot prediction through latent interpolation. The methodology is mathematically validated via a universal approximation theorem for encoder-free architectures, and numerically tested on complex computational mechanics problems involving physical and geometric parameters, including the detection of bifurcating phenomena for Navier-Stokes equations. Code availability: https://github.com/lorenzotomada/ld-gcn-rom

Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated once per observation gap, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing. We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a construction realising the top tier on a random DAG with OU or small-MLP nonlinear drifts, irregular observation schedules, and hard / soft / time-varying interventions. A 2 times 2 encoder times integrator ablation, run independently on a linear and a nonlinear prior, finds fine-grid integration beats naive on 8/8 cells (sign-consistency p < 1/256) with the gap growing as the eval grid refines; the encoder axis is null with fine integration but time-aware-leading with naive. We release the prior and a preliminary zero-shot protocol on pharmacokinetic and physical-system data.

Even for known nonlinear dynamical systems, feedback controller synthesis is a difficult problem that often requires leveraging the particular structure of the dynamics to induce a stable closed-loop system. For general nonlinear models, including those fit to data, there may not be enough known structure to reliably synthesize a stabilizing feedback controller. In this paper, we discuss a state-dependent nonlinear tracking controller formulation based on a state-dependent Riccati equation for general nonlinear control-affine systems. This formulation depends on a nonlinear factorization of the system of vector fields defining the control-affine dynamics, which always exists under mild smoothness assumptions. We propose a method for learning this factorization from a finite set of data. On a variety of simulated nonlinear dynamical systems, we empirically demonstrate the efficacy of learned versions of this controller in stable trajectory tracking. Alongside our learning method, we evaluate recent ideas in jointly learning a controller and stabilizability certificate for known dynamical systems; we show experimentally that such methods can be frail in comparison.

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many existing approaches do not explicitly model the dynamics. To bridge this gap, we introduce DeepEDM, a framework that integrates nonlinear dynamical systems modeling with deep neural networks. Inspired by empirical dynamic modeling (EDM) and rooted in Takens' theorem, DeepEDM presents a novel deep model that learns a latent space from time-delayed embeddings, and employs kernel regression to approximate the underlying dynamics, while leveraging efficient implementation of softmax attention and allowing for accurate prediction of future time steps. To evaluate our method, we conduct comprehensive experiments on synthetic data of nonlinear dynamical systems as well as real-world time series across domains. Our results show that DeepEDM is robust to input noise, and outperforms state-of-the-art methods in forecasting accuracy. Our code is available at: https://abrarmajeedi.github.io/deep_edm.

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based simulation models described by ODEs/PDEs remain interpretable, but may have missing or unknown terms, unable to fully describe real-world observations. We bridge this gap with a novel grey-box method that integrates incomplete physics models directly into generative models. Our approach learns dynamics from observational trajectories alone, without ground-truth physics parameters, in a simulation-free manner that avoids scalability and stability issues of Neural ODEs. The core of our method lies in modelling a structured variational distribution within the flow matching framework, by using two latent encodings: one to model the missing stochasticity and multi-modal velocity, and a second to encode physics parameters as a latent variable with a physics-informed prior. Furthermore, we present an adaptation of the framework to handle second-order dynamics. Our experiments on representative ODE/PDE problems show that our method performs on par with or superior to fully data-driven approaches and previous grey-box baselines, while preserving the interpretability of the physics model. Our code is available at https://github.com/DMML-Geneva/VGB-DM.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality. To address these limitations, we presents a novel paradigm: modeling dynamics directly in the weight space of a neural network by projecting the evolving probability distribution. We first theoretically establish the connection between dynamic optimal transport in measure space and an equivalent energy functional in weight space. Subsequently, we design WeightFlow, which constructs the neural network weights into a graph and learns its evolution via a graph controlled differential equation. Experiments on interdisciplinary datasets demonstrate that WeightFlow improves performance by an average of 43.02\% over state-of-the-art methods, providing an effective and scalable solution for modeling high-dimensional stochastic dynamics.

Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in W_infty. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle.

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose \textbf{Multi-Marginal temporal Schr\"odinger Bridge Matching} (MMtSBM) for video generation from unpaired data, extending the theoretical guarantees and empirical efficiency of Diffusion Schr\"odinger Bridge Matching (arXiv:archive/2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real world datasets such as transcriptomic trajectory inference in 100 dimensions, and for the first time recovers couplings and dynamics in very high dimensional image settings. Our work establishes multi-marginal Schr\"odinger bridges as a practical and principled approach for recovering hidden dynamics from static data.

We introduce Qwen2.5-VL, the latest flagship model of Qwen vision-language series, which demonstrates significant advancements in both foundational capabilities and innovative functionalities. Qwen2.5-VL achieves a major leap forward in understanding and interacting with the world through enhanced visual recognition, precise object localization, robust document parsing, and long-video comprehension. A standout feature of Qwen2.5-VL is its ability to localize objects using bounding boxes or points accurately. It provides robust structured data extraction from invoices, forms, and tables, as well as detailed analysis of charts, diagrams, and layouts. To handle complex inputs, Qwen2.5-VL introduces dynamic resolution processing and absolute time encoding, enabling it to process images of varying sizes and videos of extended durations (up to hours) with second-level event localization. This allows the model to natively perceive spatial scales and temporal dynamics without relying on traditional normalization techniques. By training a native dynamic-resolution Vision Transformer (ViT) from scratch and incorporating Window Attention, we reduce computational overhead while maintaining native resolution. As a result, Qwen2.5-VL excels not only in static image and document understanding but also as an interactive visual agent capable of reasoning, tool usage, and task execution in real-world scenarios such as operating computers and mobile devices. Qwen2.5-VL is available in three sizes, addressing diverse use cases from edge AI to high-performance computing. The flagship Qwen2.5-VL-72B model matches state-of-the-art models like GPT-4o and Claude 3.5 Sonnet, particularly excelling in document and diagram understanding. Additionally, Qwen2.5-VL maintains robust linguistic performance, preserving the core language competencies of the Qwen2.5 LLM.

In this paper, we propose a novel framework, Tracking-free Relightable Avatar (TRAvatar), for capturing and reconstructing high-fidelity 3D avatars. Compared to previous methods, TRAvatar works in a more practical and efficient setting. Specifically, TRAvatar is trained with dynamic image sequences captured in a Light Stage under varying lighting conditions, enabling realistic relighting and real-time animation for avatars in diverse scenes. Additionally, TRAvatar allows for tracking-free avatar capture and obviates the need for accurate surface tracking under varying illumination conditions. Our contributions are two-fold: First, we propose a novel network architecture that explicitly builds on and ensures the satisfaction of the linear nature of lighting. Trained on simple group light captures, TRAvatar can predict the appearance in real-time with a single forward pass, achieving high-quality relighting effects under illuminations of arbitrary environment maps. Second, we jointly optimize the facial geometry and relightable appearance from scratch based on image sequences, where the tracking is implicitly learned. This tracking-free approach brings robustness for establishing temporal correspondences between frames under different lighting conditions. Extensive qualitative and quantitative experiments demonstrate that our framework achieves superior performance for photorealistic avatar animation and relighting.

In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world. We introduce Physical-Time Flow (PT-Flow), a novel approach that learns a continuous latent velocity field operating in physical time. Crucially, the underlying dynamics of sequential data are parameterized by an ordinary differential equation (ODE) embedded in a well-structured representation space. Under this paradigm, the prediction of future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct ODEWorld, a continuous-time latent world model that is both efficient and versatile. By extracting time-variant features and enforcing ODE properties on both the dynamical representation space and the latent velocity field, ODEWorld effectively addresses the long-standing representation collapse issue in latent world model literature. This also enables high-quality image reconstruction even after long-horizon prediction. Moreover, its continuous nature allows for arbitrary temporal resolution and even backward prediction, which is impossible for most discrete-time models. Lastly, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. https://dstate.github.io/odeworld_website/{Project Website}.

Despite the increasing interest in enhancing perception systems for autonomous vehicles, the online calibration between event cameras and LiDAR - two sensors pivotal in capturing comprehensive environmental information - remains unexplored. We introduce MULi-Ev, the first online, deep learning-based framework tailored for the extrinsic calibration of event cameras with LiDAR. This advancement is instrumental for the seamless integration of LiDAR and event cameras, enabling dynamic, real-time calibration adjustments that are essential for maintaining optimal sensor alignment amidst varying operational conditions. Rigorously evaluated against the real-world scenarios presented in the DSEC dataset, MULi-Ev not only achieves substantial improvements in calibration accuracy but also sets a new standard for integrating LiDAR with event cameras in mobile platforms. Our findings reveal the potential of MULi-Ev to bolster the safety, reliability, and overall performance of event-based perception systems in autonomous driving, marking a significant step forward in their real-world deployment and effectiveness.

Many real-world systems exhibit temporal, dynamic behaviors, which are captured as time series of complex agent interactions. To perform temporal reasoning, current methods primarily encode temporal dynamics through simple sequence-based models. However, in general these models fail to efficiently capture the full spectrum of rich dynamics in the input, since the dynamics is not uniformly distributed. In particular, relevant information might be harder to extract and computing power is wasted for processing all individual timesteps, even if they contain no significant changes or no new information. Here we propose TimeGraphs, a novel approach that characterizes dynamic interactions as a hierarchical temporal graph, diverging from traditional sequential representations. Our approach models the interactions using a compact graph-based representation, enabling adaptive reasoning across diverse time scales. Adopting a self-supervised method, TimeGraphs constructs a multi-level event hierarchy from a temporal input, which is then used to efficiently reason about the unevenly distributed dynamics. This construction process is scalable and incremental to accommodate streaming data. We evaluate TimeGraphs on multiple datasets with complex, dynamic agent interactions, including a football simulator, the Resistance game, and the MOMA human activity dataset. The results demonstrate both robustness and efficiency of TimeGraphs on a range of temporal reasoning tasks. Our approach obtains state-of-the-art performance and leads to a performance increase of up to 12.2% on event prediction and recognition tasks over current approaches. Our experiments further demonstrate a wide array of capabilities including zero-shot generalization, robustness in case of data sparsity, and adaptability to streaming data flow.

Seeking high-quality representations with latent variable models (LVMs) to reveal the intrinsic correlation between neural activity and behavior or sensory stimuli has attracted much interest. In the study of the biological visual system, naturalistic visual stimuli are inherently high-dimensional and time-dependent, leading to intricate dynamics within visual neural activity. However, most work on LVMs has not explicitly considered neural temporal relationships. To cope with such conditions, we propose Time-Evolving Visual Dynamical System (TE-ViDS), a sequential LVM that decomposes neural activity into low-dimensional latent representations that evolve over time. To better align the model with the characteristics of visual neural activity, we split latent representations into two parts and apply contrastive learning to shape them. Extensive experiments on synthetic datasets and real neural datasets from the mouse visual cortex demonstrate that TE-ViDS achieves the best decoding performance on naturalistic scenes/movies, extracts interpretable latent trajectories that uncover clear underlying neural dynamics, and provides new insights into differences in visual information processing between subjects and between cortical regions. In summary, TE-ViDS is markedly competent in extracting stimulus-relevant embeddings from visual neural activity and contributes to the understanding of visual processing mechanisms. Our codes are available at https://github.com/Grasshlw/Time-Evolving-Visual-Dynamical-System.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.