Daily Papers

The trouble in detecting low mass dark matter due to its low kinetic energy can be ameliorated in the boosted dark matter framework, where a sub-population of galactic dark matter attains very high energy after being up-scattered by energetic standard model particles. However, in such a scenario the upper limits on the cross-section obtained hitherto are typically large. Hence in the minimal extension of standard model where new mediators act as a portal between the dark and visible sectors, the direct detection limits for sub-GeV dark matter might lie within the exclusion region of other ground based searches of the mediator. To evade this deadlock, we allude to blazar boosted dark matter electron scattering in multi-ton neutrino detector Super kamiokande. We consider minimal models such as axion like particle (ALP) and vector portal dark matter being upscattered by high energy blazar jet and analyse the interesting parameter reaches from Super kamiokande in the parameter space of the mediator, surpassing the existing constraints. Besides, this scenario exhibits stronger limits for previously unexplored ALP mediated sub-MeV dark matter search which is difficult due to associated momentum suppression.

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.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

We present a continuous geometric framework that models the discrete algebraic operations of the Transformer architecture as an integro-differential equation (IDE) on a semantic fiber bundle calE = calM times R^d. Beginning from a single geometric axiom -- that the token sequence forms a discrete 1-manifold equipped with a canonical measure lattice -- we translate every core component of the modern Transformer (RMSNorm, RoPE, Softmax Attention, FFN, Residual Stream, SGD, Weight Decay) into a cohesive vocabulary of differential geometry, measure theory, and stochastic calculus. The resulting framework yields quantitative predictions spanning entropic optimal transport (Attention as a Schrödinger bridge) and non-equilibrium thermodynamics (SGD as Itô diffusion violating detailed balance). We conduct a six-part experimental campaign across five architectures (Qwen3, LLaMA\nobreakdash-3.1, Gemma\nobreakdash-3, GPT-2, Mistral) spanning 124M to 8B parameters. The empirical observables are quantitatively consistent with the geometric predictions: the ε^{-1/2} Lipschitz scaling calibration at machine precision (R^2 = 1.000), the Lie--Trotter operator-splitting torsion, the symmetric ablation instability confirming the Dual-Law of Topological Stability, the calO(1/k) thermodynamic suppression of Poincaré recurrence on the RoPE torus, the thermodynamic context-limit phase transition, and the Non-Equilibrium Steady State parameter vortex -- verified across two optimizers (AdamW and Pure SGD) to exclude momentum artifacts. The results demonstrate that analyzing Transformers through the lens of continuous stochastic differential geometry provides a predictive descriptive vocabulary for the stability limits, context bounds, and optimization dynamics of Large Language Models.

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM pretraining, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

We demonstrate the possibility of what we call sparse learning: accelerated training of deep neural networks that maintain sparse weights throughout training while achieving dense performance levels. We accomplish this by developing sparse momentum, an algorithm which uses exponentially smoothed gradients (momentum) to identify layers and weights which reduce the error efficiently. Sparse momentum redistributes pruned weights across layers according to the mean momentum magnitude of each layer. Within a layer, sparse momentum grows weights according to the momentum magnitude of zero-valued weights. We demonstrate state-of-the-art sparse performance on MNIST, CIFAR-10, and ImageNet, decreasing the mean error by a relative 8%, 15%, and 6% compared to other sparse algorithms. Furthermore, we show that sparse momentum reliably reproduces dense performance levels while providing up to 5.61x faster training. In our analysis, ablations show that the benefits of momentum redistribution and growth increase with the depth and size of the network. Additionally, we find that sparse momentum is insensitive to the choice of its hyperparameters suggesting that sparse momentum is robust and easy to use.

Momentum is known to accelerate the convergence of gradient descent in strongly convex settings without stochastic gradient noise. In stochastic optimization, such as training neural networks, folklore suggests that momentum may help deep learning optimization by reducing the variance of the stochastic gradient update, but previous theoretical analyses do not find momentum to offer any provable acceleration. Theoretical results in this paper clarify the role of momentum in stochastic settings where the learning rate is small and gradient noise is the dominant source of instability, suggesting that SGD with and without momentum behave similarly in the short and long time horizons. Experiments show that momentum indeed has limited benefits for both optimization and generalization in practical training regimes where the optimal learning rate is not very large, including small- to medium-batch training from scratch on ImageNet and fine-tuning language models on downstream tasks.

Stochastic optimizers are central to deep learning, yet widely used methods such as Adam and Adan can degrade in non-stationary or noisy environments, partly due to their reliance on momentum-based magnitude estimates. We introduce Ano, a novel optimizer that decouples direction and magnitude: momentum is used for directional smoothing, while instantaneous gradient magnitudes determine step size. This design improves robustness to gradient noise while retaining the simplicity and efficiency of first-order methods. We further propose Anolog, which removes sensitivity to the momentum coefficient by expanding its window over time via a logarithmic schedule. We establish non-convex convergence guarantees with a convergence rate similar to other sign-based methods, and empirically show that Ano provides substantial gains in noisy and non-stationary regimes such as reinforcement learning, while remaining competitive on low-noise tasks such as standard computer vision benchmarks.

Efficiently exploring complex loss landscapes is key to the performance of deep neural networks. While momentum-based optimizers are widely used in state-of-the-art setups, classical momentum can still struggle with large, misaligned gradients, leading to oscillations. To address this, we propose Torque-Aware Momentum (TAM), which introduces a damping factor based on the angle between the new gradients and previous momentum, stabilizing the update direction during training. Empirical results show that TAM, which can be combined with both SGD and Adam, enhances exploration, handles distribution shifts more effectively, and improves generalization performance across various tasks, including image classification and large language model fine-tuning, when compared to classical momentum-based optimizers.

We study the momentum-based minimization of a diffuse perimeter functional on Euclidean spaces and on graphs with applications to semi-supervised classification tasks in machine learning. While the gradient flow in the task at hand is a parabolic partial differential equation, the momentum-method corresponds to a damped hyperbolic PDE, leading to qualitatively and quantitatively different trajectories. Using a convex-concave splitting-based FISTA-type time discretization, we demonstrate empirically that momentum can lead to faster convergence if the time step size is large but not too large. With large time steps, the PDE analysis offers only limited insight into the geometric behavior of solutions and typical hyperbolic phenomena like loss of regularity are not be observed in sample simulations.

Training large neural networks typically requires sharing gradients between accelerators through specialized high-speed interconnects. Drawing from the signal processing principles of frequency decomposition and energy compaction, we demonstrate that synchronizing full optimizer states and model parameters during training is unnecessary. By decoupling momentum updates and allowing controlled divergence in optimizer states across accelerators, we achieve improved convergence compared to state-of-the-art optimizers. We introduce {De}coupled {Mo}mentum (DeMo), a fused optimizer and data parallel algorithm that reduces inter-accelerator communication requirements by several orders of magnitude. This enables training of large neural networks even with limited network bandwidth and heterogeneous hardware. Our method is topology-agnostic and architecture-independent and supports scalable clock-synchronous distributed training with negligible compute and memory overhead. Empirical results show that models trained with DeMo match or exceed the performance of equivalent models trained with AdamW, while eliminating the need for high-speed interconnects when pre-training large scale foundation models. An open source reference PyTorch implementation is published on GitHub at https://github.com/bloc97/DeMo

The residual update of a pre-norm Transformer layer admits an interpretation as one step of a first-order optimizer acting on a surrogate token energy, wherein the attention and MLP sublayers function as gradient oracles. Based on this observation, we build a family of optimizer-inspired Transformers (triple-momentum, Adam/AdamW, Muon, SOAP) and compare them under matched compute. In our main pretraining experiment, the triple-momentum TMMFormer achieves the lowest validation loss, outperforming the vanilla Transformer and prior architectural variants. A controlled ablation and supporting theory show that momentum, not preconditioning, is the main source of the gain. We further show that TMMFormer and other momentum-based designs reach flatter minima than the vanilla Transformer, which leads to less forgetting and better generalization.

Diffusion models can generate realistic videos, but existing methods rely on implicitly learning physical reasoning from large-scale text-video datasets, which is costly, difficult to scale, and still prone to producing implausible motions that violate fundamental physical laws. We introduce a training-free framework that improves physical plausibility at inference time by explicitly reasoning about implausibility and guiding the generation away from it. Specifically, we employ a lightweight physics-aware reasoning pipeline to construct counterfactual prompts that deliberately encode physics-violating behaviors. Then, we propose a novel Synchronized Decoupled Guidance (SDG) strategy, which leverages these prompts through synchronized directional normalization to counteract lagged suppression and trajectory-decoupled denoising to mitigate cumulative trajectory bias, ensuring that implausible content is suppressed immediately and consistently throughout denoising. Experiments across different physical domains show that our approach substantially enhances physical fidelity while maintaining photorealism, despite requiring no additional training. Ablation studies confirm the complementary effectiveness of both the physics-aware reasoning component and SDG. In particular, the aforementioned two designs of SDG are also individually validated to contribute critically to the suppression of implausible content and the overall gains in physical plausibility. This establishes a new and plug-and-play physics-aware paradigm for video generation.

In the training of large language models, momentum is widely used and often demonstrated to achieve significant acceleration. However, storing momentum typically presents memory challenges. In this paper, we propose AdaPM, an adaptive training strategy that leverages partial momentum to implement a memory-efficient optimizer. To this end, AdaPM utilizes a non-uniform momentum design: for most blocks, full momentum is not necessary to preserve the performance of the optimization. In the momentum design of AdaPM, to mitigate the bias and performance loss caused by partial momentum, we enhance the partial momentum by a bias correction technique. Empirically, we verify that our approach reduces memory by over 90% in momentum while maintaining both efficiency and performance for pretraining various language models ranging from 60M to 1.5B, as well as for supervised fine-tuning and RLHF. AdaPM can further reduce memory by up to 95% in optimizer states by combining the memory-efficient technique on the second-order statistic, saving over 30% GPU hours for pretraining GPT-2 1.5B.

Neural network training is commonly accelerated by using multiple synchronized workers to compute gradient updates in parallel. Asynchronous methods remove synchronization overheads and improve hardware utilization at the cost of introducing gradient delay, which impedes optimization and can lead to lower final model performance. We introduce Adaptive Braking (AB), a modification for momentum-based optimizers that mitigates the effects of gradient delay. AB dynamically scales the gradient based on the alignment of the gradient and the velocity. This can dampen oscillations along high curvature directions of the loss surface, stabilizing and accelerating asynchronous training. We show that applying AB on top of SGD with momentum enables training ResNets on CIFAR-10 and ImageNet-1k with delays D geq 32 update steps with minimal drop in final test accuracy.

Flow-based generative models have become a strong framework for high-quality generative modeling, yet pretrained models are rarely used in their vanilla conditional form: conditional samples without guidance often appear diffuse and lack fine-grained detail due to the smoothing effects of neural networks. Existing guidance techniques such as classifier-free guidance (CFG) improve fidelity but double the inference cost and typically reduce sample diversity. We introduce Momentum Guidance (MG), a new dimension of guidance that leverages the ODE trajectory itself. MG extrapolates the current velocity using an exponential moving average of past velocities and preserves the standard one-evaluation-per-step cost. It matches the effect of standard guidance without extra computation and can further improve quality when combined with CFG. Experiments demonstrate MG's effectiveness across benchmarks. Specifically, on ImageNet-256, MG achieves average improvements in FID of 36.68% without CFG and 25.52% with CFG across various sampling settings, attaining an FID of 1.597 at 64 sampling steps. Evaluations on large flow-based models like Stable Diffusion 3 and FLUX.1-dev further confirm consistent quality enhancements across standard metrics.

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence direction. Fundamental momentum methods, such as Nesterov Accelerated Gradient and the Heavy Ball method, as well as more recent optimizers such as AdamW and Lion, all rely on the momentum coefficient that is customarily set to β= 0.9 and kept constant during model training, a strategy widely used by practitioners, yet suboptimal. In this paper, we introduce an adaptive memory mechanism that replaces constant momentum with a dynamic momentum coefficient that is adjusted online during optimization. We derive our method by approximating the objective function using two planes: one derived from the gradient at the current iterate and the other obtained from the accumulated memory of the past gradients. To the best of our knowledge, such a proximal framework was never used for momentum-based optimization. Our proposed approach is novel, extremely simple to use, and does not rely on extra assumptions or hyperparameter tuning. We implement adaptive memory variants of both SGD and AdamW across a wide range of learning tasks, from simple convex problems to large-scale deep learning scenarios, demonstrating that our approach can outperform standard SGD and Adam with hand-tuned momentum coefficients. Finally, our work opens doors for new ways of inducing adaptivity in optimization.

We propose a novel framework, Stable Diffusion-based Momentum Integrated Adversarial Examples (SD-MIAE), for generating adversarial examples that can effectively mislead neural network classifiers while maintaining visual imperceptibility and preserving the semantic similarity to the original class label. Our method leverages the text-to-image generation capabilities of the Stable Diffusion model by manipulating token embeddings corresponding to the specified class in its latent space. These token embeddings guide the generation of adversarial images that maintain high visual fidelity. The SD-MIAE framework consists of two phases: (1) an initial adversarial optimization phase that modifies token embeddings to produce misclassified yet natural-looking images and (2) a momentum-based optimization phase that refines the adversarial perturbations. By introducing momentum, our approach stabilizes the optimization of perturbations across iterations, enhancing both the misclassification rate and visual fidelity of the generated adversarial examples. Experimental results demonstrate that SD-MIAE achieves a high misclassification rate of 79%, improving by 35% over the state-of-the-art method while preserving the imperceptibility of adversarial perturbations and the semantic similarity to the original class label, making it a practical method for robust adversarial evaluation.

We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from O(d) to O(d) through step-size sharing, where d is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

Unified humanoid policies handle agile whole-body motion, yet stumble on a simple demand: staying balanced on one leg. On our single-leg-balance benchmark, eight released state-of-the-art general policies hold a clean single-leg stance on 0 of 90 test motions; they stay up only by stepping or hopping, recovering from imbalance rather than preventing it. Prevention needs the capture point (xCoM), the center of mass (CoM) extrapolated by its velocity, which has never driven a hardware policy because it requires a base linear velocity no on-board sensor provides; expressed relative to the support foot, that velocity cancels exactly, leaving an observation reconstructible from encoders and IMU alone. We put this first deployable dynamic-CoM observation directly into the actor that runs on hardware, and pair it with a reward library translated term by term from human postural control, under one principle: prevention over repair. Trained by asymmetric FastSAC with a privileged critic and no distillation, the resulting policy, FDDC (First Deployable Dynamic-CoM), holds clean single-leg balance on 86 of 90 held-out motions across nine stratified pose classes and transfers to a real Unitree G1; in ablation, the dynamic-CoM observation is the single largest driver: removing it alone costs 40 points of clean single-leg balance. We release the full stack with the first method-agnostic, reproducible sim2sim benchmark for humanoid single-leg balance, scoring each policy in a simulator distinct from its training one, a step toward turning balance from a per-task trick into a capability the field can measure.

Denoising diffusion models hold great promise for generating diverse and realistic human motions. However, existing motion diffusion models largely disregard the laws of physics in the diffusion process and often generate physically-implausible motions with pronounced artifacts such as floating, foot sliding, and ground penetration. This seriously impacts the quality of generated motions and limits their real-world application. To address this issue, we present a novel physics-guided motion diffusion model (PhysDiff), which incorporates physical constraints into the diffusion process. Specifically, we propose a physics-based motion projection module that uses motion imitation in a physics simulator to project the denoised motion of a diffusion step to a physically-plausible motion. The projected motion is further used in the next diffusion step to guide the denoising diffusion process. Intuitively, the use of physics in our model iteratively pulls the motion toward a physically-plausible space, which cannot be achieved by simple post-processing. Experiments on large-scale human motion datasets show that our approach achieves state-of-the-art motion quality and improves physical plausibility drastically (>78% for all datasets).

Operating robots precisely and at high speeds has been a long-standing goal of robotics research. Balancing these competing demands is key to enabling the seamless collaboration of robots and humans and increasing task performance. However, traditional motor-driven systems often fall short in this balancing act. Due to their rigid and often heavy design exacerbated by positioning the motors into the joints, faster motions of such robots transfer high forces at impact. To enable precise and safe dynamic motions, we introduce a four degree-of-freedom~(DoF) tendon-driven robot arm. Tendons allow placing the actuation at the base to reduce the robot's inertia, which we show significantly reduces peak collision forces compared to conventional robots with motors placed near the joints. Pairing our robot with pneumatic muscles allows generating high forces and highly accelerated motions, while benefiting from impact resilience through passive compliance. Since tendons are subject to additional friction and hence prone to wear and tear, we validate the reliability of our robotic arm on various experiments, including long-term dynamic motions. We also demonstrate its ease of control by quantifying the nonlinearities of the system and the performance on a challenging dynamic table tennis task learned from scratch using reinforcement learning. We open-source the entire hardware design, which can be largely 3D printed, the control software, and a proprioceptive dataset of 25 days of diverse robot motions at webdav.tuebingen.mpg.de/pamy2.

Variance reduction (VR) techniques have contributed significantly to accelerating learning with massive datasets in the smooth and strongly convex setting (Schmidt et al., 2017; Johnson & Zhang, 2013; Roux et al., 2012). However, such techniques have not yet met the same success in the realm of large-scale deep learning due to various factors such as the use of data augmentation or regularization methods like dropout (Defazio & Bottou, 2019). This challenge has recently motivated the design of novel variance reduction techniques tailored explicitly for deep learning (Arnold et al., 2019; Ma & Yarats, 2018). This work is an additional step in this direction. In particular, we exploit the ubiquitous clustering structure of rich datasets used in deep learning to design a family of scalable variance reduced optimization procedures by combining existing optimizers (e.g., SGD+Momentum, Quasi Hyperbolic Momentum, Implicit Gradient Transport) with a multi-momentum strategy (Yuan et al., 2019). Our proposal leads to faster convergence than vanilla methods on standard benchmark datasets (e.g., CIFAR and ImageNet). It is robust to label noise and amenable to distributed optimization. We provide a parallel implementation in JAX.

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

Training large language models (LLMs) relies almost exclusively on dense adaptive optimizers with increasingly sophisticated preconditioners. We challenge this by showing that randomly masking parameter updates can be highly effective, with a masked variant of RMSProp consistently outperforming recent state-of-the-art optimizers. Our analysis reveals that the random masking induces a curvature-dependent geometric regularization that smooths the optimization trajectory. Motivated by this finding, we introduce Momentum-aligned gradient masking (Magma), which modulates the masked updates using momentum-gradient alignment. Extensive LLM pre-training experiments show that Magma is a simple drop-in replacement for adaptive optimizers with consistent gains and negligible computational overhead. Notably, for the 1B model size, Magma reduces perplexity by over 19\% and 9\% compared to Adam and Muon, respectively.

Prior motion generation largely follows two paradigms: continuous diffusion models that excel at kinematic control, and discrete token-based generators that are effective for semantic conditioning. To combine their strengths, we propose a three-stage framework comprising condition feature extraction (Perception), discrete token generation (Planning), and diffusion-based motion synthesis (Control). Central to this framework is MoTok, a diffusion-based discrete motion tokenizer that decouples semantic abstraction from fine-grained reconstruction by delegating motion recovery to a diffusion decoder, enabling compact single-layer tokens while preserving motion fidelity. For kinematic conditions, coarse constraints guide token generation during planning, while fine-grained constraints are enforced during control through diffusion-based optimization. This design prevents kinematic details from disrupting semantic token planning. On HumanML3D, our method significantly improves controllability and fidelity over MaskControl while using only one-sixth of the tokens, reducing trajectory error from 0.72 cm to 0.08 cm and FID from 0.083 to 0.029. Unlike prior methods that degrade under stronger kinematic constraints, ours improves fidelity, reducing FID from 0.033 to 0.014.

Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that effect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semi-analytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any arbitrary astrophysical system of interest. Here, we adopt that the assigned magnetic turbulence is constrained on a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump -- that has for some special cases long been established -- is a universal feature of stochastic acceleration that emerges around the momentum chi_{rm eq} where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at chi_{rm eq}. In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.

Reinforcement learning (RL) post-training improves the reward alignment of flow-based generators, but often degrades perceptual quality in ways that are not captured by the reward proxy. We identify a simple structural signature of this drift: across three post-training methods (NFT, AWM, DPO), RL fine-tuning inflates the per-step velocity norm |v_θ| by 5% to 15% relative to the reference. A form of norm inflation has been studied in classifier-free guidance (CFG), where rescaling the velocity back to a reference norm at inference time can mitigate the resulting artifacts. However, this inference-time correction does not transfer cleanly to RL: rescaling v_θ to match |v_{ref}| at inference time neither improves reward nor fixes the quality degradation, because the inflation is co-adapted into the model weights. Furthermore, an adjoint sensitivity analysis shows that velocity magnitude rescaling carries no coherent first-order reward signal at the batch level, indicating that suppressing norm inflation is unlikely to remove a consistently reward-carrying component. Since inference-time renormalization fails while norm suppression carries no reward cost, training-time intervention is the appropriate strategy. Together, these findings motivate \methodname, a hinge penalty that activates only when |v_θ| exceeds |v_{ref}| and composes additively with any velocity-local base loss. Across two base models, three post-training methods, and two reward proxies, \methodname consistently improves MLLM-judged image quality and forensic realism while preserving reward, with gains that amplify under few-step inference and are not explained by early stopping.

We present H-Node Adversarial Noise Cancellation (H-Node ANC), a mechanistic framework that identifies, exploits, and defends hallucination representations in transformer-based large language models (LLMs) at the level of individual hidden-state dimensions. A logistic regression probe trained on last-token hidden states localizes hallucination signal to a small set of high-variance dimensions -- termed Hallucination Nodes (H-Nodes) -- with probe AUC reaching 0.90 across four architectures. A white-box adversarial attack amplifies these dimensions at inference time via a real-time forward hook, achieving a selectivity of 3.02x with less than 10% visibility to the defender. Adaptive ANC defense suppresses H-Node excess in-pass using confidence-weighted cancellation, reducing grounded activation drift by 33-42% over static cancellation. A dynamic iterative extension that re-ranks cancellation targets across successive passes recovers up to 0.69 robustness from a single-pass baseline of 8%. All contributions are validated on OPT-125M, Phi-3-mini-4k-instruct, LLaMA-3-8B-Instruct, and Mistral-7B-Instruct-v0.3 (125M-8B parameters). Perplexity impact is surgical (<5%) and MMLU degradation is at most 3%, confirming that the defense does not impair general reasoning capability.

In this work, we significantly enhance masked particle modeling (MPM), a self-supervised learning scheme for constructing highly expressive representations of unordered sets relevant to developing foundation models for high-energy physics. In MPM, a model is trained to recover the missing elements of a set, a learning objective that requires no labels and can be applied directly to experimental data. We achieve significant performance improvements over previous work on MPM by addressing inefficiencies in the implementation and incorporating a more powerful decoder. We compare several pre-training tasks and introduce new reconstruction methods that utilize conditional generative models without data tokenization or discretization. We show that these new methods outperform the tokenized learning objective from the original MPM on a new test bed for foundation models for jets, which includes using a wide variety of downstream tasks relevant to jet physics, such as classification, secondary vertex finding, and track identification.

Motivated in part by their relevance for low-precision training and quantization, massive activations in large language models (LLMs) have recently emerged as a topic of interest. However, existing analyses are limited in scope, and generalizability across architectures is unclear. This paper helps address some of these gaps by conducting an analysis of massive activations across a broad range of LLMs, including both GLU-based and non-GLU-based architectures. Our findings challenge several prior assumptions, most importantly: (1) not all massive activations are detrimental, i.e. suppressing them does not lead to an explosion of perplexity or a collapse in downstream task performance; (2) proposed mitigation strategies such as Attention KV bias are model-specific and ineffective in certain cases. We consequently investigate novel hybrid mitigation strategies; in particular pairing Target Variance Rescaling (TVR) with Attention KV bias or Dynamic Tanh (DyT) successfully balances the mitigation of massive activations with preserved downstream model performance in the scenarios we investigated. Our code is available at: https://github.com/bluorion-com/refine_massive_activations.

Active Motor Noise Cancellation (AMNC) ships in commercial fused deposition modeling (FDM) 3D printers as a hardware countermeasure against acoustic side-channel attacks that target intellectual property (IP). We present the first empirical evaluation of a deployed AMNC countermeasure, using a public dataset of synchronized acoustic and vibration recordings from two AMNC-equipped Bambu Lab printers across 12 object classes. AMNC fully neutralizes the acoustic channel: classification accuracy is indistinguishable from the 8.33% random baseline. The vibration channel, which AMNC does not target, still leaks. With summary statistics the leak is coarse and amplitude-driven (vibration accuracy approximately 31% pooled, 36-47% within-printer), while the waveform shape carries essentially nothing (frequency-only features at chance). A full-sequence temporal model that ingests the ordered evolution of the print raises accuracy to approximately 61%, and an order-shuffling control (approximately 33%) shows that a substantial component is genuinely sequential and tied to print progression. The leak is device-specific: a classifier trained on one printer transfers near chance to the other. We conclude that AMNC is an acoustic-only defense: vibration remains a partial, geometry-correlated side channel it does not address, but one that does not, on this dataset, support full geometric reconstruction; reconstruction-grade attacks would require the magnetic or power channels AMNC also leaves untouched. We release all code.

We present a comprehensive study of the Muonic Portal to Vector Dark Matter (MPVDM), a minimal yet phenomenologically rich extension of the Standard Model featuring a new SU(2)_D gauge symmetry and vector-like muons. In this framework the dark sector interacts with the Standard Model only through these heavy leptons, linking dark matter and the muon sector. The MPVDM can simultaneously explain the observed relic abundance and the muon anomalous magnetic moment a_mu under both the "tension" and "compatibility" scenarios motivated by recent (g-2)_mu results. A key finding is a generic off-resonance velocity suppression mechanism that allows light (<1 GeV) vector dark matter to evade CMB limits near 2*m_DM ~ m_H_D. Unlike scenarios based on ultra narrow Breit-Wigner resonances and early kinetic decoupling, the suppression follows from the temperature evolution of the annihilation cross section in a moderately detuned near resonant regime, where being 10-20 percent below resonance gives the required CMB era suppression without fine tuning. A five dimensional parameter scan shows that the tension scenario requires sub GeV dark matter with g_D ~ 1e-3 and TeV scale vector like muons, while the compatibility scenario admits a broad mass range up to multi TeV. Recasting ATLAS and CMS searches for mu+ mu- + E_T^miss sets a lower bound of about 850 GeV on vector like muons. The MPVDM thus offers a unified, predictive, and experimentally accessible framework linking dark matter and muon physics across cosmological and collider frontiers.

Generative world models (WMs) are increasingly used to synthesize controllable, sensor-conditioned driving videos, yet their reliance on physical priors exposes novel attack surfaces. In this paper, we present Physical-Conditioned World Model Attack (PhysCond-WMA), the first white-box world model attack that perturbs physical-condition channels, such as HDMap embeddings and 3D-box features, to induce semantic, logic, or decision-level distortion while preserving perceptual fidelity. PhysCond-WMA is optimized in two stages: (1) a quality-preserving guidance stage that constrains reverse-diffusion loss below a calibrated threshold, and (2) a momentum-guided denoising stage that accumulates target-aligned gradients along the denoising trajectory for stable, temporally coherent semantic shifts. Extensive experimental results demonstrate that our approach remains effective while increasing FID by about 9% on average and FVD by about 3.9% on average. Under the targeted attack setting, the attack success rate (ASR) reaches 0.55. Downstream studies further show tangible risk, which using attacked videos for training decreases 3D detection performance by about 4%, and worsens open-loop planning performance by about 20%. These findings has for the first time revealed and quantified security vulnerabilities in generative world models, driving more comprehensive security checkers.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

Adaptive moment methods such as Adam use a diagonal, coordinate-wise preconditioner based on exponential moving averages of squared gradients. This diagonal scaling is coordinate-system dependent and can struggle with dense or rotated parameter couplings, including those in matrix factorization, tensor decomposition, and graph neural networks, because it treats each parameter independently. We introduce FlowAdam, a hybrid optimizer that augments Adam with continuous gradient-flow integration via an ordinary differential equation (ODE). When EMA-based statistics detect landscape difficulty, FlowAdam switches to clipped ODE integration. Our central contribution is Soft Momentum Injection, which blends ODE velocity with Adam's momentum during mode transitions. This prevents the training collapse observed with naive hybrid approaches. Across coupled optimization benchmarks, the ODE integration provides implicit regularization, reducing held-out error by 10-22% on low-rank matrix/tensor recovery and 6% on Jester (real-world collaborative filtering), also surpassing tuned Lion and AdaBelief, while matching Adam on well-conditioned workloads (CIFAR-10). MovieLens-100K confirms benefits arise specifically from coupled parameter interactions rather than bias estimation. Ablation studies show that soft injection is essential, as hard replacement reduces accuracy from 100% to 82.5%.

Heavy-ball momentum with decaying learning rates is widely used with SGD for optimizing deep learning models. In contrast to its empirical popularity, the understanding of its theoretical property is still quite limited, especially under the standard anisotropic gradient noise condition for quadratic regression problems. Although it is widely conjectured that heavy-ball momentum method can provide accelerated convergence and should work well in large batch settings, there is no rigorous theoretical analysis. In this paper, we fill this theoretical gap by establishing a non-asymptotic convergence bound for stochastic heavy-ball methods with step decay scheduler on quadratic objectives, under the anisotropic gradient noise condition. As a direct implication, we show that heavy-ball momentum can provide mathcal{O}(kappa) accelerated convergence of the bias term of SGD while still achieving near-optimal convergence rate with respect to the stochastic variance term. The combined effect implies an overall convergence rate within log factors from the statistical minimax rate. This means SGD with heavy-ball momentum is useful in the large-batch settings such as distributed machine learning or federated learning, where a smaller number of iterations can significantly reduce the number of communication rounds, leading to acceleration in practice.

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

Large Language Models (LLMs) have demonstrated exceptional performance across diverse tasks, yet their training remains highly resource-intensive and susceptible to critical challenges such as training instability. A predominant source of this instability stems from gradient and loss spikes, which disrupt the learning process, often leading to costly interventions like checkpoint recovery and experiment restarts, further amplifying inefficiencies. This paper presents a comprehensive investigation into gradient spikes observed during LLM training, revealing their prevalence across multiple architectures and datasets. Our analysis shows that these spikes can be up to 1000times larger than typical gradients, substantially deteriorating model performance. To address this issue, we propose Spike-Aware Adam with Momentum Reset SPAM, a novel optimizer designed to counteract gradient spikes through momentum reset and spike-aware gradient clipping. Extensive experiments, including both pre-training and fine-tuning, demonstrate that SPAM consistently surpasses Adam and its variants across various tasks, including (1) LLM pre-training from 60M to 1B, (2) 4-bit LLM pre-training,(3) reinforcement learning, and (4) Time Series Forecasting. Additionally, SPAM facilitates memory-efficient training by enabling sparse momentum, where only a subset of momentum terms are maintained and updated. When operating under memory constraints, SPAM outperforms state-of-the-art memory-efficient optimizers such as GaLore and Adam-Mini. Our work underscores the importance of mitigating gradient spikes in LLM training and introduces an effective optimization strategy that enhances both training stability and resource efficiency at scale. Code is available at https://github.com/TianjinYellow/SPAM-Optimizer.git

Training large neural network models requires extensive computational resources, often distributed across several nodes and accelerators. Recent findings suggest that it may be sufficient to only exchange the fast moving components of the gradients, while accumulating momentum locally (Decoupled Momentum, or DeMo). However, DeMo assumes that models fit on a single accelerator. We relax this assumption and introduce FlexDeMo, whereby nodes fully shard model parameters locally between different accelerators, while inter-node communication is reduced by synchronizing only fast-moving components instead of the full gradients -- resulting in a hybrid sharded data parallel training strategy. We further introduce a framework, denoted as DeToNATION, that generalizes DeMo, FlexDeMo, and other popular distributed training schemes such as DiLoCo -- introducing new variations of replication schemes and challenging choices made in DeMo. Our results across language and vision domains show that FlexDeMo attains similar validation loss as hybrid sharded data parallel training employing AdamW and full gradient synchronization, while being substantially faster. FlexDeMo is thus a promising distributed training scheme for the largest machine learning models.

In this paper, we propose Scene Splatter, a momentum-based paradigm for video diffusion to generate generic scenes from single image. Existing methods, which employ video generation models to synthesize novel views, suffer from limited video length and scene inconsistency, leading to artifacts and distortions during further reconstruction. To address this issue, we construct noisy samples from original features as momentum to enhance video details and maintain scene consistency. However, for latent features with the perception field that spans both known and unknown regions, such latent-level momentum restricts the generative ability of video diffusion in unknown regions. Therefore, we further introduce the aforementioned consistent video as a pixel-level momentum to a directly generated video without momentum for better recovery of unseen regions. Our cascaded momentum enables video diffusion models to generate both high-fidelity and consistent novel views. We further finetune the global Gaussian representations with enhanced frames and render new frames for momentum update in the next step. In this manner, we can iteratively recover a 3D scene, avoiding the limitation of video length. Extensive experiments demonstrate the generalization capability and superior performance of our method in high-fidelity and consistent scene generation.

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights provides an advantageous ground for gradient descent (GD) optimizers: the effective step sizes are automatically reduced over time, stabilizing the overall training procedure. It is often overlooked, however, that the additional introduction of momentum in GD optimizers results in a far more rapid reduction in effective step sizes for scale-invariant weights, a phenomenon that has not yet been studied and may have caused unwanted side effects in the current practice. This is a crucial issue because arguably the vast majority of modern deep neural networks consist of (1) momentum-based GD (e.g. SGD or Adam) and (2) scale-invariant parameters. In this paper, we verify that the widely-adopted combination of the two ingredients lead to the premature decay of effective step sizes and sub-optimal model performances. We propose a simple and effective remedy, SGDP and AdamP: get rid of the radial component, or the norm-increasing direction, at each optimizer step. Because of the scale invariance, this modification only alters the effective step sizes without changing the effective update directions, thus enjoying the original convergence properties of GD optimizers. Given the ubiquity of momentum GD and scale invariance in machine learning, we have evaluated our methods against the baselines on 13 benchmarks. They range from vision tasks like classification (e.g. ImageNet), retrieval (e.g. CUB and SOP), and detection (e.g. COCO) to language modelling (e.g. WikiText) and audio classification (e.g. DCASE) tasks. We verify that our solution brings about uniform gains in those benchmarks. Source code is available at https://github.com/clovaai/AdamP.

We investigate the coupling effects of the two-phase interface, viscosity ratio, and density ratio of the dispersed phase to the continuous phase on the flow statistics in two-phase Taylor-Couette turbulence at a system Reynolds number of 6000 and a system Weber number of 10 using interface-resolved three-dimensional direct numerical simulations with the volume-of-fluid method. Our study focuses on four different scenarios: neutral droplets, low-viscosity droplets, light droplets, and low-viscosity light droplets. We find that neutral droplets and low-viscosity droplets primarily contribute to drag enhancement through the two-phase interface, while light droplets reduce the system's drag by explicitly reducing Reynolds stress due to the density dependence of Reynolds stress. Additionally, low-viscosity light droplets contribute to greater drag reduction by further reducing momentum transport near the inner cylinder and implicitly reducing Reynolds stress. While interfacial tension enhances turbulent kinetic energy (TKE) transport, drag enhancement is not strongly correlated with TKE transport for both neutral droplets and low-viscosity droplets. Light droplets primarily reduce the production term by diminishing Reynolds stress, whereas the density contrast between the phases boosts TKE transport near the inner wall. Therefore, the reduction in the dissipation rate is predominantly attributed to decreased turbulence production, causing drag reduction. For low-viscosity light droplets, the production term diminishes further, primarily due to their greater reduction in Reynolds stress, while reduced viscosity weakens the density difference's contribution to TKE transport near the inner cylinder, resulting in a more pronounced reduction in the dissipation rate and consequently stronger drag reduction. Our findings provide new insights into the turbulence modulation in two-phase flow.

Open-ended text generation with autoregressive language models (LMs) is one of the core tasks in natural language processing. However, maximization-based decoding methods (e.g., greedy/beam search) often lead to the degeneration problem, i.e., the generated text is unnatural and contains undesirable repetitions. Existing solutions to this problem either introduce randomness prone to incoherence or require a look-ahead mechanism that demands extra computational overhead. In this study, we formulate open-ended text generation from a new perspective, i.e., we view it as an exploration process within a directed graph. Thereby, we understand the phenomenon of degeneration as circular loops within the directed graph. Based on our formulation, we propose a novel decoding method -- momentum decoding -- which encourages the LM to greedily explore new nodes outside the current graph. Meanwhile, it also allows the LM to return to the existing nodes with a momentum downgraded by a pre-defined resistance function. We extensively test our approach on three benchmarks from different domains through automatic and human evaluations. The results show that momentum decoding performs comparably with the current state of the art while enjoying notably improved inference speed and computation FLOPs. Furthermore, we conduct a detailed analysis to reveal the merits and inner workings of our approach. Our codes and other related resources are publicly available at https://github.com/gmftbyGMFTBY/MomentumDecoding.

Recent video diffusion models can synthesize visually compelling clips, yet often violate basic physical laws-objects float, accelerations drift, and collisions behave inconsistently-revealing a persistent gap between visual realism and physical realism. We propose NewtonRewards, the first physics-grounded post-training framework for video generation based on verifiable rewards. Instead of relying on human or VLM feedback, NewtonRewards extracts measurable proxies from generated videos using frozen utility models: optical flow serves as a proxy for velocity, while high-level appearance features serve as a proxy for mass. These proxies enable explicit enforcement of Newtonian structure through two complementary rewards: a Newtonian kinematic constraint enforcing constant-acceleration dynamics, and a mass conservation reward preventing trivial, degenerate solutions. We evaluate NewtonRewards on five Newtonian Motion Primitives (free fall, horizontal/parabolic throw, and ramp sliding down/up) using our newly constructed large-scale benchmark, NewtonBench-60K. Across all primitives in visual and physics metrics, NewtonRewards consistently improves physical plausibility, motion smoothness, and temporal coherence over prior post-training methods. It further maintains strong performance under out-of-distribution shifts in height, speed, and friction. Our results show that physics-grounded verifiable rewards offer a scalable path toward physics-aware video generation.

Designing urban spaces that provide pedestrian wind comfort and safety requires time-resolved Computational Fluid Dynamics (CFD) simulations, but their current computational cost makes extensive design exploration impractical. We introduce WinDiNet (Wind Diffusion Network), a pretrained video diffusion model that is repurposed as a fast, differentiable surrogate for this task. Starting from LTX-Video, a 2B-parameter latent video transformer, we fine-tune on 10,000 2D incompressible CFD simulations over procedurally generated building layouts. A systematic study of training regimes, conditioning mechanisms, and VAE adaptation strategies, including a physics-informed decoder loss, identifies a configuration that outperforms purpose-built neural PDE solvers. The resulting model generates full 112-frame rollouts in under a second. As the surrogate is end-to-end differentiable, it doubles as a physics simulator for gradient-based inverse optimization: given an urban footprint layout, we optimize building positions directly through backpropagation to improve wind safety as well as pedestrian wind comfort. Experiments on single- and multi-inlet layouts show that the optimizer discovers effective layouts even under challenging multi-objective configurations, with all improvements confirmed by ground-truth CFD simulations.

A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition.

Recent models for video generation have achieved remarkable progress and are now deployed in film, social media production, and advertising. Beyond their creative potential, such models also hold promise as world simulators for robotics and embodied decision making. Despite strong advances, however, current approaches still struggle to generate physically plausible object interactions and lack physics-grounded control mechanisms. To address this limitation, we introduce KineMask, an approach for physics-guided video generation that enables realistic rigid body control, interactions, and effects. Given a single image and a specified object velocity, our method generates videos with inferred motions and future object interactions. We propose a two-stage training strategy that gradually removes future motion supervision via object masks. Using this strategy we train video diffusion models (VDMs) on synthetic scenes of simple interactions and demonstrate significant improvements of object interactions in real scenes. Furthermore, KineMask integrates low-level motion control with high-level textual conditioning via predictive scene descriptions, leading to effective support for synthesis of complex dynamical phenomena. Extensive experiments show that KineMask achieves strong improvements over recent models of comparable size. Ablation studies further highlight the complementary roles of low- and high-level conditioning in VDMs. Our code, model, and data will be made publicly available.

Sparse Mixture of Experts (SMoE) has become the key to unlocking unparalleled scalability in deep learning. SMoE has the potential to exponentially increase parameter count while maintaining the efficiency of the model by only activating a small subset of these parameters for a given sample. However, it has been observed that SMoE suffers from unstable training and has difficulty adapting to new distributions, leading to the model's lack of robustness to data contamination. To overcome these limitations, we first establish a connection between the dynamics of the expert representations in SMoEs and gradient descent on a multi-objective optimization problem. Leveraging our framework, we then integrate momentum into SMoE and propose a new family of SMoEs named MomentumSMoE. We theoretically prove and numerically demonstrate that MomentumSMoE is more stable and robust than SMoE. In particular, we verify the advantages of MomentumSMoE over SMoE on a variety of practical tasks including ImageNet-1K object recognition and WikiText-103 language modeling. We demonstrate the applicability of MomentumSMoE to many types of SMoE models, including those in the Sparse MoE model for vision (V-MoE) and the Generalist Language Model (GLaM). We also show that other advanced momentum-based optimization methods, such as Adam, can be easily incorporated into the MomentumSMoE framework for designing new SMoE models with even better performance, almost negligible additional computation cost, and simple implementations.

Communication costs within Federated learning hinder the system scalability for reaching more data from more clients. The proposed FL adopts a hub-and-spoke network topology. All clients communicate through the central server. Hence, reducing communication overheads via techniques such as data compression has been proposed to mitigate this issue. Another challenge of federated learning is unbalanced data distribution, data on each client are not independent and identically distributed (non-IID) in a typical federated learning setting. In this paper, we proposed a new compression compensation scheme called Global Momentum Fusion (GMF) which reduces communication overheads between FL clients and the server and maintains comparable model accuracy in the presence of non-IID data. GitHub repository: https://github.com/tony92151/global-momentum-fusion-fl

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.

A number of recent self-supervised learning methods have shown impressive performance on image classification and other tasks. A somewhat bewildering variety of techniques have been used, not always with a clear understanding of the reasons for their benefits, especially when used in combination. Here we treat the embeddings of images as point particles and consider model optimization as a dynamic process on this system of particles. Our dynamic model combines an attractive force for similar images, a locally dispersive force to avoid local collapse, and a global dispersive force to achieve a globally-homogeneous distribution of particles. The dynamic perspective highlights the advantage of using a delayed-parameter image embedding (a la BYOL) together with multiple views of the same image. It also uses a purely-dynamic local dispersive force (Brownian motion) that shows improved performance over other methods and does not require knowledge of other particle coordinates. The method is called MSBReg which stands for (i) a Multiview centroid loss, which applies an attractive force to pull different image view embeddings toward their centroid, (ii) a Singular value loss, which pushes the particle system toward spatially homogeneous density, (iii) a Brownian diffusive loss. We evaluate downstream classification performance of MSBReg on ImageNet as well as transfer learning tasks including fine-grained classification, multi-class object classification, object detection, and instance segmentation. In addition, we also show that applying our regularization term to other methods further improves their performance and stabilize the training by preventing a mode collapse.

We propose masked particle modeling (MPM) as a self-supervised method for learning generic, transferable, and reusable representations on unordered sets of inputs for use in high energy physics (HEP) scientific data. This work provides a novel scheme to perform masked modeling based pre-training to learn permutation invariant functions on sets. More generally, this work provides a step towards building large foundation models for HEP that can be generically pre-trained with self-supervised learning and later fine-tuned for a variety of down-stream tasks. In MPM, particles in a set are masked and the training objective is to recover their identity, as defined by a discretized token representation of a pre-trained vector quantized variational autoencoder. We study the efficacy of the method in samples of high energy jets at collider physics experiments, including studies on the impact of discretization, permutation invariance, and ordering. We also study the fine-tuning capability of the model, showing that it can be adapted to tasks such as supervised and weakly supervised jet classification, and that the model can transfer efficiently with small fine-tuning data sets to new classes and new data domains.

Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability p_0 is small. Using the Tsallis q-logarithm, we define a loss family J_Q that interpolates between RLVR (at q{=}0, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at q{=}1, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification P_{θ^{-q}} that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires Ω(1{p_0}) time to escape cold start, while the density-estimation pole escapes in Θbig(log(1{p_0})big); intermediate q trades escape speed against noise memorization. Because P_θ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias Obig(q{M P_θ^{q+1}}big); GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at q{=}0.75 substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low q dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at q{=}0.75 provides stable gradients (best overall on HotPotQA at 47.9 maj@16, +14.4 over GRPO).

LLMs utilizing chain-of-thought reasoning often waste substantial compute by producing long, incorrect responses. Abstention can mitigate this by withholding outputs unlikely to be correct. While most abstention methods decide to withhold outputs before or after generation, dynamic mid-generation abstention considers early termination of unpromising reasoning traces at each token position. Prior work has explored empirical variants of this idea, but principled guidance for the abstention rule remains lacking. We present a formal analysis of dynamic abstention for LLMs, modeling abstention as an explicit action within a regularized reinforcement learning framework. An abstention reward parameter controls the trade-off between compute and information. We show that abstaining when the value function falls below this reward strictly outperforms natural baselines under general conditions. We further derive a principled and efficient method to approximate the value function. Empirical results on mathematical reasoning and toxicity avoidance tasks support our theory and demonstrate improved selective accuracy over existing methods.

We present a single attention head in GPT-2 Small that has one main role across the entire training distribution. If components in earlier layers predict a certain token, and this token appears earlier in the context, the head suppresses it: we call this copy suppression. Attention Head 10.7 (L10H7) suppresses naive copying behavior which improves overall model calibration. This explains why multiple prior works studying certain narrow tasks found negative heads that systematically favored the wrong answer. We uncover the mechanism that the Negative Heads use for copy suppression with weights-based evidence and are able to explain 76.9% of the impact of L10H7 in GPT-2 Small. To the best of our knowledge, this is the most comprehensive description of the complete role of a component in a language model to date. One major effect of copy suppression is its role in self-repair. Self-repair refers to how ablating crucial model components results in downstream neural network parts compensating for this ablation. Copy suppression leads to self-repair: if an initial overconfident copier is ablated, then there is nothing to suppress. We show that self-repair is implemented by several mechanisms, one of which is copy suppression, which explains 39% of the behavior in a narrow task. Interactive visualisations of the copy suppression phenomena may be seen at our web app https://copy-suppression.streamlit.app/

We analyze Muon as originally proposed and used in practice -- using the momentum orthogonalization with a few Newton-Schulz steps. The prior theoretical results replace this key step in Muon with an exact SVD-based polar factor. We prove that Muon with Newton-Schulz converges to a stationary point at the same rate as the SVD-polar idealization, up to a constant factor for a given number q of Newton-Schulz steps. We further analyze this constant factor and prove that it converges to 1 doubly exponentially in q and improves with the degree of the polynomial used in Newton-Schulz for approximating the orthogonalization direction. We also prove that Muon removes the typical square-root-of-rank loss compared to its vector-based counterpart, SGD with momentum. Our results explain why Muon with a few low-degree Newton-Schulz steps matches exact-polar (SVD) behavior at a much faster wall-clock time and explain how much momentum matrix orthogonalization via Newton-Schulz benefits over the vector-based optimizer. Overall, our theory justifies the practical Newton-Schulz design of Muon, narrowing its practice-theory gap.

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting methods are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

We present Momentum Contrast (MoCo) for unsupervised visual representation learning. From a perspective on contrastive learning as dictionary look-up, we build a dynamic dictionary with a queue and a moving-averaged encoder. This enables building a large and consistent dictionary on-the-fly that facilitates contrastive unsupervised learning. MoCo provides competitive results under the common linear protocol on ImageNet classification. More importantly, the representations learned by MoCo transfer well to downstream tasks. MoCo can outperform its supervised pre-training counterpart in 7 detection/segmentation tasks on PASCAL VOC, COCO, and other datasets, sometimes surpassing it by large margins. This suggests that the gap between unsupervised and supervised representation learning has been largely closed in many vision tasks.

We study the implicit bias of momentum-based optimizers on smooth homogeneous models. We show that momentum steepest descent algorithms like Muon (spectral norm), MomentumGD (ell_2 norm), and Signum (ell_infty norm) are approximate steepest descent trajectories under a decaying learning rate schedule, proving that these algorithms have a bias towards KKT points of the corresponding margin maximization problem. We extend the analysis to Adam (without the stability constant), which maximizes the ell_infty margin, and to Muon-Signum and Muon-Adam, which maximize a hybrid norm. Our experiments corroborate the theory and show that the identity of the margin maximized depends on the choice of optimizer. Overall, our results extend earlier lines of work on steepest descent in homogeneous models and momentum-based optimizers in linear models.

Although deep learning has produced dazzling successes for applications of image, speech, and video processing in the past few years, most trainings are with suboptimal hyper-parameters, requiring unnecessarily long training times. Setting the hyper-parameters remains a black art that requires years of experience to acquire. This report proposes several efficient ways to set the hyper-parameters that significantly reduce training time and improves performance. Specifically, this report shows how to examine the training validation/test loss function for subtle clues of underfitting and overfitting and suggests guidelines for moving toward the optimal balance point. Then it discusses how to increase/decrease the learning rate/momentum to speed up training. Our experiments show that it is crucial to balance every manner of regularization for each dataset and architecture. Weight decay is used as a sample regularizer to show how its optimal value is tightly coupled with the learning rates and momentums. Files to help replicate the results reported here are available.

We present a self-supervised framework for learning implicit 3D physical dynamics directly from video-derived supervisory signals. While current generative video models achieve high visual fidelity, they lack a 3D geometric foundation, often resulting in physical inconsistencies and a failure to maintain object permanence. We address this by shifting the predictive bottleneck from 2D image space to a `lifted' 3D Volumetric Latent Space. Our method unprojects semantic features from a Video Joint-Embedding Predictive Architecture (V-JEPA) into a voxelized grid, grounded by monocular depth priors. This lifting enables a Volumetric Feature Advection to learn an action-conditioned transition operator that treats physics as a spatio-temporal state advection problem, i.e., learn implicit 3D physics. Unlike state-of-the-art hybrid models that rely on explicit classical simulators for training and/or inference, our architecture tracks material states implicitly within high-dimensional V-JEPA features. This allows for the emergent simulation of heterogeneous phenomena (e.g., rigid body motion in fluid flow) within a single, unified pipeline. Supervised solely via end-to-end video-derived signal plus action conditions, without access to physics engine internal states, labels, or surrogate models, our model demonstrates good long-term structural stability and physical plausibility on multiple benchmarks (CLEVERER, PhysInOne, PhysGaia). We believe that this work opens a scalable pathway toward general-purpose dynamic world models that internalize the 3D invariants of the physical world solely through passive observation of monocular videos.

Image-to-Video diffusion models leverage input images to generate visually stunning content, yet frequently produce motion that violates physical laws. We reveal a surprising finding: a 2-step generation often exhibits better physical consistency than a 50-step output from the same model. Through spectral analysis, we trace this to phase erosion during denoising; the phase degrades significantly (dropping by approx 18% from step 2 to step 50), whereas the magnitude remains relatively stable. Building on this insight, we propose PhaseLock, a training-free framework that preserves the valid motion priors from few-step inference throughout the denoising trajectory. Rather than relying on full-step inference for physical consistency, PhaseLock extracts a motion prior from just 2 steps and enforces it onto high-fidelity generation via Latent Delta Guidance. Our approach effectively mitigates phase degradation, improving physical consistency by an average of 6.2 points across diverse models while largely maintaining visual fidelity, with negligible overhead (1.06times time, 1.02times memory) and reduced reliance on expensive external guidance methods (sim5times time).