Daily Papers

Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited. We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response, thereby reducing factual fidelity. To address this issue, we propose MR-ALIGN, a Meta-Reasoning informed alignment framework that enhances factuality without relying on external verifiers. MR-ALIGN quantifies state transition probabilities along the model's thinking process and constructs a transition-aware implicit reward that reinforces beneficial reasoning patterns while suppressing defective ones at the atomic thinking segments. This re-weighting reshapes token-level signals into probability-aware segment scores, encouraging coherent reasoning trajectories that are more conducive to factual correctness. Empirical evaluations across four factual QA datasets and one long-form factuality benchmark show that MR-ALIGN consistently improves accuracy and truthfulness while reducing misleading reasoning. These results highlight that aligning the reasoning process itself, rather than merely the outputs, is pivotal for advancing factuality in LRMs.

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Diffusion and flow matching models have significantly advanced media generation, yet their design space is well-explored, somewhat limiting further improvements. Concurrently, autoregressive (AR) models, particularly those generating continuous tokens, have emerged as a promising direction for unifying text and media generation. This paper introduces Transition Matching (TM), a novel discrete-time, continuous-state generative paradigm that unifies and advances both diffusion/flow models and continuous AR generation. TM decomposes complex generation tasks into simpler Markov transitions, allowing for expressive non-deterministic probability transition kernels and arbitrary non-continuous supervision processes, thereby unlocking new flexible design avenues. We explore these choices through three TM variants: (i) Difference Transition Matching (DTM), which generalizes flow matching to discrete-time by directly learning transition probabilities, yielding state-of-the-art image quality and text adherence as well as improved sampling efficiency. (ii) Autoregressive Transition Matching (ARTM) and (iii) Full History Transition Matching (FHTM) are partially and fully causal models, respectively, that generalize continuous AR methods. They achieve continuous causal AR generation quality comparable to non-causal approaches and potentially enable seamless integration with existing AR text generation techniques. Notably, FHTM is the first fully causal model to match or surpass the performance of flow-based methods on text-to-image task in continuous domains. We demonstrate these contributions through a rigorous large-scale comparison of TM variants and relevant baselines, maintaining a fixed architecture, training data, and hyperparameters.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the N users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with N user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When N is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics remains lacking. This Letter proposes a method based on the least action principle to estimate the underlying generative directionality of LLMs embedded within agents. By experimentally measuring the transition probabilities between LLM-generated states, we statistically discover a detailed balance in LLM-generated transitions, indicating that LLM generation may not be achieved by generally learning rule sets and strategies, but rather by implicitly learning a class of underlying potential functions that may transcend different LLM architectures and prompt templates. To our knowledge, this is the first discovery of a macroscopic physical law in LLM generative dynamics that does not depend on specific model details. This work is an attempt to establish a macroscopic dynamics theory of complex AI systems, aiming to elevate the study of AI agents from a collection of engineering practices to a science built on effective measurements that are predictable and quantifiable.

In many real-world multi-agent cooperative tasks, due to high cost and risk, agents cannot continuously interact with the environment and collect experiences during learning, but have to learn from offline datasets. However, the transition dynamics in the dataset of each agent can be much different from the ones induced by the learned policies of other agents in execution, creating large errors in value estimates. Consequently, agents learn uncoordinated low-performing policies. In this paper, we propose a framework for offline decentralized multi-agent reinforcement learning, which exploits value deviation and transition normalization to deliberately modify the transition probabilities. Value deviation optimistically increases the transition probabilities of high-value next states, and transition normalization normalizes the transition probabilities of next states. They together enable agents to learn high-performing and coordinated policies. Theoretically, we prove the convergence of Q-learning under the altered non-stationary transition dynamics. Empirically, we show that the framework can be easily built on many existing offline reinforcement learning algorithms and achieve substantial improvement in a variety of multi-agent tasks.

Multi-turn agents solve complex tasks through extended sequences of tool interactions before producing a final answer, making credit assignment a fundamental challenge during post-training. Outcome rewards provide reliable supervision for short-horizon reasoning, but become sparse and high-variance as trajectories grow to tens or hundreds of tool calls. They can also be misleading: a failed rollout may contain many useful actions that move the agent closer to the goal, yet outcome-only training assigns them the same negative advantage as the eventual mistake. We propose TRACE (Turn-level Reward Assignment via Credit Estimation), a dense credit-assignment method for agentic reinforcement learning. TRACE represents rollouts as state transitions at tool-call boundaries, obtains gold-answer log-probabilities from a frozen reference model, transforms them into log-ratio state values, and derives per-action rewards as Temporal-Difference changes in those values. This requires no additional critic or process-label training, and its one-step log-ratio TD component telescopes across redundant tool calls. On long-horizon complex search, TRACE substantially improves base-model tool-use ability using pure RL, without a cold-start supervised fine-tuning stage, an agentic mid-training stage, or training on live-web data. On the closed-web BrowseComp-Plus benchmark, it raises Qwen3-4B from 7.2 to 35.6 and Qwen3-30B-A3B from 8.4 to 42.6. The learned search behavior also transfers to open-web benchmarks, and the learning curves show earlier improvement and faster convergence during RL training.

Generative world models provide robots with predictive models of how the world evolves under interaction, with growing potential for simulation, planning, policy evaluation, and robot learning. Beyond clip-level future prediction, a unified generative formulation should relate actions to consequences, support flexible horizons and continuous interaction, and enable reward-driven optimization. We introduce WALL-SS, a world model that generates visual futures through Scale-wise autoregressive Scaling, enabling action-controllable and long-horizon robotic simulation. WALL-SS represents embodied trajectories as causal sequences of temporally interleaved observations and actions, making action-dependent state transitions explicit while naturally supporting variable-length generation, streaming extension through reusable causal states, and direct optimization through sequence probabilities. To make this formulation effective over long horizons, we generate each future observation in a coarse-to-fine manner and develop three complementary components within the same hierarchy. Action-conditioned next-scale prediction injects scale-aligned action representations to improve action-future coupling and model both successful and failed behaviors. Scale-compressed long-horizon memory retains recent interactions at fine resolution while compressing distant observations and actions, with scale-wise dream forcing enhancing robustness to self-generated context. Finally, on-policy alignment optimizes autoregressive visual dynamics with action-following and long-term consistency rewards while preserving the pretrained visual distribution. Experiments show that WALL-SS improves action following and trajectory accuracy, supports coherent minute-long streaming rollout under bounded memory, and consistently benefits from on-policy alignment in reducing action drift and long-horizon inconsistency.

The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence measures. Surprisingly, an equally important problem, estimating an unknown Markov chain from its samples, is still far from understood. We consider two problems related to the min-max risk (expected loss) of estimating an unknown k-state Markov chain from its n sequential samples: predicting the conditional distribution of the next sample with respect to the KL-divergence, and estimating the transition matrix with respect to a natural loss induced by KL or a more general f-divergence measure. For the first measure, we determine the min-max prediction risk to within a linear factor in the alphabet size, showing it is Omega(kloglog n / n) and O(k^2loglog n / n). For the second, if the transition probabilities can be arbitrarily small, then only trivial uniform risk upper bounds can be derived. We therefore consider transition probabilities that are bounded away from zero, and resolve the problem for essentially all sufficiently smooth f-divergences, including KL-, L_2-, Chi-squared, Hellinger, and Alpha-divergences.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Early warning signals have been proposed to forecast the possibility of a critical transition, such as the eutrophication of a lake, the collapse of a coral reef, or the end of a glacial period. Because such transitions often unfold on temporal and spatial scales that can be difficult to approach by experimental manipulation, research has often relied on historical observations as a source of natural experiments. Here we examine a critical difference between selecting systems for study based on the fact that we have observed a critical transition and those systems for which we wish to forecast the approach of a transition. This difference arises by conditionally selecting systems known to experience a transition of some sort and failing to account for the bias this introduces -- a statistical error often known as the Prosecutor's Fallacy. By analysing simulated systems that have experienced transitions purely by chance, we reveal an elevated rate of false positives in common warning signal statistics. We further demonstrate a model-based approach that is less subject to this bias than these more commonly used summary statistics. We note that experimental studies with replicates avoid this pitfall entirely.

Symbolic world modeling requires inferring and representing an environment's transitional dynamics as an executable program. Prior work has focused on largely deterministic environments with abundant interaction data, simple mechanics, and human guidance. We address a more realistic and challenging setting, learning in a complex, stochastic environment where the agent has only "one life" to explore a hostile environment without human guidance. We introduce OneLife, a framework that models world dynamics through conditionally-activated programmatic laws within a probabilistic programming framework. Each law operates through a precondition-effect structure, activating in relevant world states. This creates a dynamic computation graph that routes inference and optimization only through relevant laws, avoiding scaling challenges when all laws contribute to predictions about a complex, hierarchical state, and enabling the learning of stochastic dynamics even with sparse rule activation. To evaluate our approach under these demanding constraints, we introduce a new evaluation protocol that measures (a) state ranking, the ability to distinguish plausible future states from implausible ones, and (b) state fidelity, the ability to generate future states that closely resemble reality. We develop and evaluate our framework on Crafter-OO, our reimplementation of the Crafter environment that exposes a structured, object-oriented symbolic state and a pure transition function that operates on that state alone. OneLife can successfully learn key environment dynamics from minimal, unguided interaction, outperforming a strong baseline on 16 out of 23 scenarios tested. We also test OneLife's planning ability, with simulated rollouts successfully identifying superior strategies. Our work establishes a foundation for autonomously constructing programmatic world models of unknown, complex environments.

We consider the problem of learning in a non-stationary reinforcement learning (RL) environment, where the setting can be fully described by a piecewise stationary discrete-time Markov decision process (MDP). We introduce a variant of the Restarted Bayesian Online Change-Point Detection algorithm (R-BOCPD) that operates on input streams originating from the more general multinomial distribution and provides near-optimal theoretical guarantees in terms of false-alarm rate and detection delay. Based on this, we propose an improved version of the UCRL2 algorithm for MDPs with state transition kernel sampled from a multinomial distribution, which we call R-BOCPD-UCRL2. We perform a finite-time performance analysis and show that R-BOCPD-UCRL2 enjoys a favorable regret bound of Oleft(D O A T K_T logleft (frac{T{delta} right) + K_T log frac{K_T{delta}}{minlimits_ell : KLleft( {theta^{(ell+1)}}midmathbf{theta^{(ell)}}right)}}right), where D is the largest MDP diameter from the set of MDPs defining the piecewise stationary MDP setting, O is the finite number of states (constant over all changes), A is the finite number of actions (constant over all changes), K_T is the number of change points up to horizon T, and theta^{(ell)} is the transition kernel during the interval [c_ell, c_{ell+1}), which we assume to be multinomially distributed over the set of states O. Interestingly, the performance bound does not directly scale with the variation in MDP state transition distributions and rewards, ie. can also model abrupt changes. In practice, R-BOCPD-UCRL2 outperforms the state-of-the-art in a variety of scenarios in synthetic environments. We provide a detailed experimental setup along with a code repository (upon publication) that can be used to easily reproduce our experiments.

Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers all times. The quantum formalism arises once one focuses on the evolution of the time-local probabilistic information. Wave functions or the density matrix allow the formulation of a general linear evolution law for classical statistics. The quantum formalism for classical statistics is a powerful tool which allows us to implement for generalized Ising models the momentum observable with the associated Fourier representation. The association of operators to observables permits the computation of expectation values in terms of the density matrix by the usual quantum rule. We show that probabilistic cellular automata are quantum systems in a formulation with discrete time steps and real wave functions. With a complex structure the evolution operator for automata can be expressed in terms of a Hamiltonian involving fermionic creation and annihilation operators. The time-local probabilistic information amounts to a subsystem of the overall probabilistic system which is correlated with its environment consisting of the past and future. Such subsystems typically involve probabilistic observables for which only a probability distribution for their possible measurement values is available. Incomplete statistics does not permit to compute classical correlation functions for arbitrary subsystem-observables. Bell's inequalities are not generally applicable.

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.

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is computationally and statistically challenging due to the large number of latent variables in the model and the strong temporal dependencies between them. In this paper, we propose a new method for inference in Bayesian GPSSMs, which overcomes the drawbacks of previous approaches, namely over-simplified assumptions, and high computational requirements. Our method is based on free-form variational inference via stochastic gradient Hamiltonian Monte Carlo within the inducing-variable formalism. Furthermore, by exploiting our proposed variational distribution, we provide a collapsed extension of our method where the inducing variables are marginalized analytically. We also showcase results when combining our framework with particle MCMC methods. We show that, on six real-world datasets, our approach can learn transition dynamics and latent states more accurately than competing methods.

The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These notions exist in the literature, in concrete situations, but are presented here in abstract graphical formulations. The resulting abstract descriptions are used for proving basic results in conditional probability theory. The existence of disintegration and Bayesian inversion is discussed for discrete probability, and also for measure-theoretic probability --- via standard Borel spaces and via likelihoods. Finally, the usefulness of disintegration and Bayesian inversion is illustrated in several examples.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

Probabilistic model checking is a technique for formal automated reasoning about software or hardware systems that operate in the context of uncertainty or stochasticity. It builds upon ideas and techniques from a diverse range of fields, from logic, automata and graph theory, to optimisation, numerical methods and control. In recent years, probabilistic model checking has also been extended to integrate ideas from game theory, notably using models such as stochastic games and solution concepts such as equilibria, to formally verify the interaction of multiple rational agents with distinct objectives. This provides a means to reason flexibly about agents acting in either an adversarial or a collaborative fashion, and opens up opportunities to tackle new problems within, for example, artificial intelligence, robotics and autonomous systems. In this paper, we summarise some of the advances in this area, and highlight applications for which they have already been used. We discuss how the strengths of probabilistic model checking apply, or have the potential to apply, to the multi-agent setting and outline some of the key challenges required to make further progress in this field.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational "phase transitions". Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems.

In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from measurement data, where exact inference of latent variables is typically intractable. A recently surfaced option pertains to leveraging variational inference to perform approximate inference. In such a scheme, transition and emission functions of the system are parameterized via feed-forward neural networks (deep generative models). However, due to the generalized and highly versatile formulation of neural network functions, the learned latent space often lacks physical interpretation and structured representation. To address this, we bridge physics-based state space models with Deep Markov Models, thus delivering a hybrid modeling framework for unsupervised learning and identification of nonlinear dynamical systems. The proposed framework takes advantage of the expressive power of deep learning, while retaining the driving physics of the dynamical system by imposing physics-driven restrictions on the side of the latent space. We demonstrate the benefits of such a fusion in terms of achieving improved performance on illustrative simulation examples and experimental case studies of nonlinear systems. Our results indicate that the physics-based models involved in the employed transition and emission functions essentially enforce a more structured and physically interpretable latent space, which is essential for enhancing and generalizing the predictive capabilities of deep learning-based models.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Understanding the temporal dynamics of Earth's surface is a mission of multi-temporal remote sensing image analysis, significantly promoted by deep vision models with its fuel -- labeled multi-temporal images. However, collecting, preprocessing, and annotating multi-temporal remote sensing images at scale is non-trivial since it is expensive and knowledge-intensive. In this paper, we present a scalable multi-temporal remote sensing change data generator via generative modeling, which is cheap and automatic, alleviating these problems. Our main idea is to simulate a stochastic change process over time. We consider the stochastic change process as a probabilistic semantic state transition, namely generative probabilistic change model (GPCM), which decouples the complex simulation problem into two more trackable sub-problems, \ie, change event simulation and semantic change synthesis. To solve these two problems, we present the change generator (Changen), a GAN-based GPCM, enabling controllable object change data generation, including customizable object property, and change event. The extensive experiments suggest that our Changen has superior generation capability, and the change detectors with Changen pre-training exhibit excellent transferability to real-world change datasets.

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.

Large language models can answer scientific questions, yet a correct output does not reveal whether the model represents or uses the governing physics. Here we show that materials science mechanism information in the open-weight google/gemma-4-E4B-it model has three experimentally separable forms: concepts are readable in individual hidden states, constitutive orientation is carried by controlled transformations between states, and selected internal representations causally control engineering answers. We combine matched direct and Jacobian vocabulary readouts, option-free state geometry, a 60-law counterfactual benchmark and causal interventions. In 50 held-out materials descriptions, three independently fitted Jacobian lenses reproduced concept ranks, and target-free word sets from both readouts enabled blinded identification of 9 of 10 mechanism families. A separate 72-prompt benchmark produced mechanism-specific hidden-state neighborhoods, but an exact graph audit showed that this apparent physical organization was equally explained by numerical comparison. We therefore compared otherwise identical prompts in which only the direction of the physical input was reversed, asking whether the resulting hidden-state movement followed the supplied constitutive law. These state transformations ordered direct, physically neutral and inverse laws across 60 frozen relations and correctly oriented 39 of 40 directional laws, whereas lexical controls were near chance. Bidirectional interventions shifted answer probabilities toward or away from the physically appropriate outcome across all 12 matched cases, while counterfactual state patches transferred opposing decision signals across mechanisms and answer formats. Physical relationships were therefore more visible in controlled state changes than in absolute states alone.

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic foundation. This paper begins by providing a theoretical justification for the role of perturbations in UQ for LLMs. We then introduce a dual random walk perspective, modeling input-output pairs as two Markov chains with transition probabilities defined by semantic similarity. Building on this, we propose a fully probabilistic framework based on an inverse model, which quantifies uncertainty by evaluating the diversity of the input space conditioned on a given output through systematic perturbations. Within this framework, we define a new uncertainty measure, Inv-Entropy. A key strength of our framework is its flexibility: it supports various definitions of uncertainty measures, embeddings, perturbation strategies, and similarity metrics. We also propose GAAP, a perturbation algorithm based on genetic algorithms, which enhances the diversity of sampled inputs. In addition, we introduce a new evaluation metric, Temperature Sensitivity of Uncertainty (TSU), which directly assesses uncertainty without relying on correctness as a proxy. Extensive experiments demonstrate that Inv-Entropy outperforms existing semantic UQ methods. The code to reproduce the results can be found at https://github.com/UMDataScienceLab/Uncertainty-Quantification-for-LLMs.

Water looks unchanged as it warms, then at a critical point it boils. We ask whether long-horizon language agents show an analogous transition in their implicit world models. In some parameter settings, changing state load by a small amount, or adding a single step of horizon, leaves behavior nearly unchanged; near a critical boundary, the same small change causes a sudden world collapse. We study this effect in a deterministic task family with exact per-step gold state. A large grid search over state cardinality, dependency density, horizon, branching, observation mode, and mutation rate reveals a phase diagram: a solved plateau, a narrow transition band, and a collapse floor. Per-step traces show the mechanism: world-state fidelity fails before action validity, so the agent is not merely choosing a bad action; it is acting from a corrupted world. Stronger models translate the critical boundary but do not remove the qualitative transition. These results make world-model collapse a measurable bottleneck for long-horizon agents.

We study one-sided and α-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set P of stochastic matrices, and the alternative corresponds to a disjoint set Q. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the alternative, which is asymptotically tight. Our novel analysis improves the existing lower bounds, which are either asymptotic or provably sub-optimal in this setting. Our lower bound incorporates both the stationary distribution and the transition structure induced by the unknown Markov chain. We further propose an optimal test whose expected stopping time matches this lower bound asymptotically as αto 0. We illustrate the usefulness of our framework through applications to sequential detection of model misspecification in Markov Chain Monte Carlo and to testing structural properties, such as the linearity of transition dynamics, in Markov decision processes. Our findings yield a sharp and general characterization of optimal sequential testing procedures under Markovian dependence.

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of early warning indicators such as rising variance or increased return times. Despite widespread appreciation of the difficulties and uncertainty involved in such forecasts, proposed methods hardly ever characterize their expected error rates. Without the benefits of replicates, controls, or hindsight, applications of these approaches must quantify how reliable different indicators are in avoiding false alarms, and how sensitive they are to missing subtle warning signs. We propose a model based approach in order to quantify this trade-off between reliability and sensitivity and allow comparisons between different indicators. We show these error rates can be quite severe for common indicators even under favorable assumptions, and also illustrate how a model-based indicator can improve this performance. We demonstrate how the performance of an early warning indicator varies in different data sets, and suggest that uncertainty quantification become a more central part of early warning predictions.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Under the conditions of superfluid-Mott-insulator criticality in two dimensions, the trapping centers--i.e., local potential wells and bumps--are generically characterized by an integer charge corresponding to the number of trapped particles (if positive) or holes (if negative). Varying the strength of the center leads to a transition between two competing ground states with charges differing by pm 1. The hallmark of the transition scenario is a splitting of the number density distortion, δn(r), into a half-integer core and a large halo carrying the complementary charge of pm 1/2. The sign of the halo changes across the transition and the radius of the halo, r_0, diverges on the approach to the critical strength of the center, V = V_c, by the law r_0 propto |V-V_c|^{-tildeν}, with tildeν approx 2.33(5).

This paper presents Post-Decision Proximal Policy Optimization (PDPPO), a novel variation of the leading deep reinforcement learning method, Proximal Policy Optimization (PPO). The PDPPO state transition process is divided into two steps: a deterministic step resulting in the post-decision state and a stochastic step leading to the next state. Our approach incorporates post-decision states and dual critics to reduce the problem's dimensionality and enhance the accuracy of value function estimation. Lot-sizing is a mixed integer programming problem for which we exemplify such dynamics. The objective of lot-sizing is to optimize production, delivery fulfillment, and inventory levels in uncertain demand and cost parameters. This paper evaluates the performance of PDPPO across various environments and configurations. Notably, PDPPO with a dual critic architecture achieves nearly double the maximum reward of vanilla PPO in specific scenarios, requiring fewer episode iterations and demonstrating faster and more consistent learning across different initializations. On average, PDPPO outperforms PPO in environments with a stochastic component in the state transition. These results support the benefits of using a post-decision state. Integrating this post-decision state in the value function approximation leads to more informed and efficient learning in high-dimensional and stochastic environments.

This is an extended version of our publication Learning state machines from data streams: A generic strategy and an improved heuristic, International Conference on Grammatical Inference (ICGI) 2023, Rabat, Morocco. It has been extended with a formal proof on PAC-bounds, and the discussion and analysis of a similar approach has been moved from the appendix and now has a full dedicated section. State machine models are models that simulate the behavior of discrete event systems, capable of representing systems such as software systems, network interactions, and control systems, and have been researched extensively. The nature of most learning algorithms however is the assumption that all data be available at the beginning of the algorithm, and little research has been done in learning state machines from streaming data. In this paper, we want to close this gap further by presenting a generic method for learning state machines from data streams, as well as a merge heuristic that uses sketches to account for incomplete prefix trees. We implement our approach in an open-source state merging library and compare it with existing methods. We show the effectiveness of our approach with respect to run-time, memory consumption, and quality of results on a well known open dataset. Additionally, we provide a formal analysis of our algorithm, showing that it is capable of learning within the PAC framework, and show a theoretical improvement to increase run-time, without sacrificing correctness of the algorithm in larger sample sizes.

State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.

A probability forecast or probabilistic classifier is reliable or calibrated if the predicted probabilities are matched by ex post observed frequencies, as examined visually in reliability diagrams. The classical binning and counting approach to plotting reliability diagrams has been hampered by a lack of stability under unavoidable, ad hoc implementation decisions. Here we introduce the CORP approach, which generates provably statistically Consistent, Optimally binned, and Reproducible reliability diagrams in an automated way. CORP is based on non-parametric isotonic regression and implemented via the Pool-adjacent-violators (PAV) algorithm - essentially, the CORP reliability diagram shows the graph of the PAV- (re)calibrated forecast probabilities. The CORP approach allows for uncertainty quantification via either resampling techniques or asymptotic theory, furnishes a new numerical measure of miscalibration, and provides a CORP based Brier score decomposition that generalizes to any proper scoring rule. We anticipate that judicious uses of the PAV algorithm yield improved tools for diagnostics and inference for a very wide range of statistical and machine learning methods.

We study reinforcement learning with function approximation for large-scale Partially Observable Markov Decision Processes (POMDPs) where the state space and observation space are large or even continuous. Particularly, we consider Hilbert space embeddings of POMDP where the feature of latent states and the feature of observations admit a conditional Hilbert space embedding of the observation emission process, and the latent state transition is deterministic. Under the function approximation setup where the optimal latent state-action Q-function is linear in the state feature, and the optimal Q-function has a gap in actions, we provide a computationally and statistically efficient algorithm for finding the exact optimal policy. We show our algorithm's computational and statistical complexities scale polynomially with respect to the horizon and the intrinsic dimension of the feature on the observation space. Furthermore, we show both the deterministic latent transitions and gap assumptions are necessary to avoid statistical complexity exponential in horizon or dimension. Since our guarantee does not have an explicit dependence on the size of the state and observation spaces, our algorithm provably scales to large-scale POMDPs.

Continuous latent variables (LVs) are a key ingredient of many generative models, as they allow modelling expressive mixtures with an uncountable number of components. In contrast, probabilistic circuits (PCs) are hierarchical discrete mixtures represented as computational graphs composed of input, sum and product units. Unlike continuous LV models, PCs provide tractable inference but are limited to discrete LVs with categorical (i.e. unordered) states. We bridge these model classes by introducing probabilistic integral circuits (PICs), a new language of computational graphs that extends PCs with integral units representing continuous LVs. In the first place, PICs are symbolic computational graphs and are fully tractable in simple cases where analytical integration is possible. In practice, we parameterise PICs with light-weight neural nets delivering an intractable hierarchical continuous mixture that can be approximated arbitrarily well with large PCs using numerical quadrature. On several distribution estimation benchmarks, we show that such PIC-approximating PCs systematically outperform PCs commonly learned via expectation-maximization or SGD.

Purpose. Patients with advanced cancer may undergo multiple lines of treatment, switching therapies as their disease progresses. Motivated by a study of metastatic prostate cancer, we develop a microsimulation framework to study therapy sequence. Methods. We propose a discrete-time state transition model to study two lines of anti-cancer therapy. Based on digitized published progression-free survival (PFS) and overall survival (OS) curves, we infer event types (progression or death), and estimate transition probabilities using cumulative incidence functions with competing risks. Our model incorporates within-patient dependence over time, such that response to first-line therapy informs subsequent event probabilities. Parameters governing the degree of within-patient dependence can be used to calibrate the model-based results to those of a target trial. We demonstrate these methods in a study of two therapy sequences for metastatic prostate cancer, where Docetaxel (DCT) and Abiraterone Acetate (AA) are both appropriate for use in either first or second line treatment. We assess costs, Quality-Adjusted Life Years (QALYs) and Incremental Cost Effectiveness Ratio (ICER) for two treatment strategies: DCT then AA vs AA then DCT. Results. Using digitized survival curves from relevant clinical trials, we identified 8.6-13.9% of PFS times that should be categorized as deaths, allowing for estimation of cumulative incidence functions. Models assuming within-patient independence overestimated OS time, corrected with our calibration approach. Correction resulted in meaningful changes in the difference in QALYs between treatment strategies (0.07 vs 0.15) and the ICER (-\76,836/QALY vs -21,030/QALY). Conclusions. Microsimulation models can be successfully used to study cost-effectiveness of therapy sequences, taking care to account correctly for within-patient dependence.

Large language model (LLM)-based multi-agent systems enable expressive agent reasoning but are expensive to scale and poorly calibrated for timestep-aligned state-transition simulation, while classical agent-based models (ABMs) offer interpretability but struggle to integrate rich individual-level signals and non-stationary behaviors. We propose PhysicsAgentABM, which shifts inference to behaviorally coherent agent clusters: state-specialized symbolic agents encode mechanistic transition priors, a multimodal neural transition model captures temporal and interaction dynamics, and uncertainty-aware epistemic fusion yields calibrated cluster-level transition distributions. Individual agents then stochastically realize transitions under local constraints, decoupling population inference from entity-level variability. We further introduce ANCHOR, an LLM agent-driven clustering strategy based on cross-contextual behavioral responses and a novel contrastive loss, reducing LLM calls by up to 6-8 times. Experiments across public health, finance, and social sciences show consistent gains in event-time accuracy and calibration over mechanistic, neural, and LLM baselines. By re-architecting generative ABM around population-level inference with uncertainty-aware neuro-symbolic fusion, PhysicsAgentABM establishes a new paradigm for scalable and calibrated simulation with LLMs.

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the L_{12} bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

The performance of autonomous Web GUI agents heavily relies on the quality and quantity of their training data. However, a fundamental bottleneck persists: collecting interaction trajectories from real-world websites is expensive and difficult to verify. The underlying state transitions are hidden, leading to reliance on inconsistent and costly external verifiers to evaluate step-level correctness. To address this, we propose AutoWebWorld, a novel framework for synthesizing controllable and verifiable web environments by modeling them as Finite State Machines (FSMs) and use coding agents to translate FSMs into interactive websites. Unlike real websites, where state transitions are implicit, AutoWebWorld explicitly defines all states, actions, and transition rules. This enables programmatic verification: action correctness is checked against predefined rules, and task success is confirmed by reaching a goal state in the FSM graph. AutoWebWorld enables a fully automated search-and-verify pipeline, generating over 11,663 verified trajectories from 29 diverse web environments at only $0.04 per trajectory. Training on this synthetic data significantly boosts real-world performance. Our 7B Web GUI agent outperforms all baselines within 15 steps on WebVoyager. Furthermore, we observe a clear scaling law: as the synthetic data volume increases, performance on WebVoyager and Online-Mind2Web consistently improves.

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated with a discounted infinite horizon planning task varies continuously with respect to our metric distances.

Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

A key challenge in training Vision-Language Model (VLM) agents, compared to Language Model (LLM) agents, lies in the shift from textual states to complex visual observations. This transition introduces partial observability and demands robust world modeling. We ask: Can VLM agents construct internal world models through explicit visual state reasoning? To address this question, we architecturally enforce and reward the agent's reasoning process via reinforcement learning (RL), formulating it as a Partially Observable Markov Decision Process (POMDP). We find that decomposing the agent's reasoning into State Estimation ("what is the current state?") and Transition Modeling ("what comes next?") is critical for success, as demonstrated through five reasoning strategies. Our investigation into how agents represent internal beliefs reveals that the optimal representation is task-dependent: Natural Language excels at capturing semantic relationships in general tasks, while Structured formats are indispensable for precise manipulation and control. Building on these insights, we design a World Modeling Reward that provides dense, turn-level supervision for accurate state prediction, and introduce Bi-Level General Advantage Estimation (Bi-Level GAE) for turn-aware credit assignment. Through this form of visual state reasoning, a 3B-parameter model achieves a score of 0.82 across five diverse agent benchmarks, representing a 3times improvement over its untrained counterpart (0.21) and outperforming proprietary reasoning models such as GPT-5 (0.75), Gemini 2.5 Pro (0.67) and Claude 4.5 (0.62). All experiments are conducted within our VAGEN framework, a scalable system for training and analyzing multi-turn VLM agents in diverse visual environments. Code and data are publicly available at https://vagen-ai.github.io.

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are probabilistic models, and may be expressed in the language of graphical models with random variables whose values are complex data types such as strings. Cases with control flow and dynamic structure require techniques from probabilistic programming, which allow implementing disparate model structures and inference strategies in a unified language. We formalize several existing techniques from this perspective, including scratchpads / chain of thought, verifiers, STaR, selection-inference, and tool use. We refer to the resulting programs as language model cascades.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

We present Probabilistic Structure Integration (PSI), a system for learning richly controllable and flexibly promptable world models from data. PSI consists of a three-step cycle. The first step, Probabilistic prediction, involves building a probabilistic graphical model Psi of the data, in the form of a random-access autoregressive sequence model. Psi supports a complete set of learned conditional distributions describing the dependence of any variables in the data on any other set of variables. In step 2, Structure extraction, we show how to extract underlying low-dimensional properties in the data, corresponding to a diverse set of meaningful "intermediate structures", in a zero-shot fashion via causal inference on Psi. Step 3, Integration, completes the cycle by converting these structures into new token types that are then continually mixed back into the training diet as conditioning signals and prediction targets. Each such cycle augments the capabilities of Psi, both allowing it to model the underlying data better, and creating new control handles -- akin to an LLM-like universal prompting language. We train an instance of Psi on 1.4 trillion tokens of internet video data; we use it to perform a variety of useful video prediction and understanding inferences; we extract state-of-the-art optical flow, self-supervised depth and object segmentation; and we use these structures to support a full cycle of predictive improvements.

Auto-bidding plays a crucial role in facilitating online advertising by automatically providing bids for advertisers. Reinforcement learning (RL) has gained popularity for auto-bidding. However, most current RL auto-bidding methods are modeled through the Markovian Decision Process (MDP), which assumes the Markovian state transition. This assumption restricts the ability to perform in long horizon scenarios and makes the model unstable when dealing with highly random online advertising environments. To tackle this issue, this paper introduces AI-Generated Bidding (AIGB), a novel paradigm for auto-bidding through generative modeling. In this paradigm, we propose DiffBid, a conditional diffusion modeling approach for bid generation. DiffBid directly models the correlation between the return and the entire trajectory, effectively avoiding error propagation across time steps in long horizons. Additionally, DiffBid offers a versatile approach for generating trajectories that maximize given targets while adhering to specific constraints. Extensive experiments conducted on the real-world dataset and online A/B test on Alibaba advertising platform demonstrate the effectiveness of DiffBid, achieving 2.81% increase in GMV and 3.36% increase in ROI.

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.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to break down complex problems into interpretable intermediate steps, significantly enhancing model transparency and performance in reasoning tasks. However, conventional CoT methods rely on heuristic sampling without structured modeling of reasoning transitions, constraining their ability to systematically explore and discover diverse and effective reasoning trajectories. In this work, we introduce CTRLS, a framework that formulates CoT reasoning as a Markov decision process (MDP) with latent state transitions, enabling principled and state-aware exploration via distributional reinforcement learning. By modelling reasoning actions as explicit probability distributions in latent space, our approach explicitly models epistemic uncertainty, facilitating robust exploration of the reasoning space. As part of our framework, we introduce an on-policy reinforcement learning strategy incorporating epsilon-greedy exploration and entropy-based regularization to iteratively refine latent state transitions without requiring additional fine-tuning of the underlying LLM. Theoretical analyses provide evidence lower bounds (ELBO), theoretically grounding our transition-aware modeling of latent reasoning dynamics. Further experiments demonstrate improvements in reasoning accuracy, diversity, and exploration efficiency across benchmark reasoning tasks.

To enable Large Language Models (LLMs) to function as conscious agents with generalizable reasoning capabilities, it is crucial that they possess the reasoning ability to comprehend situational changes (transitions) in distribution triggered by environmental factors or actions from other agents. Despite its fundamental significance, this ability remains underexplored due to the complexity of modeling infinite possible changes in an event and their associated distributions, coupled with the lack of benchmark data with situational transitions. Addressing these gaps, we propose a novel formulation of reasoning with distributional changes as a three-step discriminative process, termed as MetAphysical ReaSoning. We then introduce the first-ever benchmark, MARS, comprising three tasks corresponding to each step. These tasks systematically assess LLMs' capabilities in reasoning the plausibility of (i) changes in actions, (ii) states caused by changed actions, and (iii) situational transitions driven by changes in action. Extensive evaluations with 20 (L)LMs of varying sizes and methods indicate that all three tasks in this process pose significant challenges, even for state-of-the-art LLMs and LMs after fine-tuning. Further analyses reveal potential causes for the underperformance of LLMs and demonstrate that pre-training them on large-scale conceptualization taxonomies can potentially enhance their metaphysical reasoning capabilities. Our data and models are publicly accessible at https://github.com/HKUST-KnowComp/MARS.

We formalize a transfinite Phi process that treats all possibility embeddings as operators on structured state spaces including complete lattices, Banach and Hilbert spaces, and orthomodular lattices. We prove a determinization lemma showing that lifting to sets or distributions yields a deterministic global dynamic, an ordinal stabilization theorem sending operator transforms to the fixed subspace by stage omega under normal spectral contraction, and a product of Riesz projections theorem for commuting layers. We establish a compositionality law for lifted maps, show closure of Phi packings, and present a quantitative application to sensory depletion that models tissue removal as a projection and derives strict decreases in the attainable fixed point under minimal monotonicity and positivity assumptions. We also state measurable conditions for probabilistic lifts, give explicit non normal and non commuting counterexamples, and provide finite dimensional and stochastic witnesses together with per theorem scope tables and a small reproducible code appendix.

Language environments such as web browsers, code terminals, and interactive simulations emit raw text rather than states, and provide none of the runtime structure that MDP analysis requires. No explicit state space, no observation-to-state mapping, no certified transitions, and no termination criterion. We introduce the State-Centric Decision Process (SDP), a runtime framework that constructs these missing inputs by having the agent build them, predicate by predicate, as it acts. At each step the agent commits to a natural-language predicate describing how the world should look, takes an action to make it true, and checks the observation against it. Predicates that pass become certified states, and the resulting trajectory carries the four objects language environments do not provide, namely a task-induced state space, an observation-to-state mapping, certified transitions, and a termination criterion. We evaluate SDP on five benchmarks spanning planning, scientific exploration, web reasoning, and multi-hop question answering. SDP achieves the best training-free results on all five, with the advantage widening as the horizon grows. The certified trajectories additionally support analyses unavailable to reactive agents, including per-predicate credit assignment, failure localization, partial-progress measurement, and modular operator replacement.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Transition state (TS) structures define the critical geometries and energy barriers underlying chemical reactivity, yet their fleeting nature renders them experimentally elusive and drives the reliance on costly, high-throughput density functional theory (DFT) calculations. Here, we introduce TS-GEN, a conditional flow-matching generative model that maps samples from a simple Gaussian prior directly to transition-state saddle-point geometries in a single, deterministic pass. By embedding both reactant and product conformations as conditioning information, TS-GEN learns to transport latent noise to true TS structures via an optimal-transport path, effectively replacing the iterative optimization common in nudged-elastic band or string-method algorithms. TS-GEN delivers unprecedented accuracy, achieving a root-mean-square deviation of 0.004 mathring{A} (vs. 0.103 mathring{A} for prior state-of-the-art) and a mean barrier-height error of 1.019 {rm kcal/mol} (vs. 2.864 {rm kcal/mol}), while requiring only 0.06 {rm s} GPU time per inference. Over 87% of generated TSs meet chemical-accuracy criteria (<1.58 {rm kcal/mol} error), substantially outpacing existing methods. TS-GEN also exhibits strong transferability to out-of-distribution reactions from a larger database. By uniting sub-angstrom precision, sub-second speed, and broad applicability, TS-GEN will be highly useful for high-throughput exploration of complex reaction networks, paving the way to the exploration of novel chemical reaction mechanisms.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

State space models (SSM) have been widely applied for the analysis and visualization of large sequential datasets. Sequential Monte Carlo (SMC) is a very popular particle-based method to sample latent states from intractable posteriors. However, SSM is significantly influenced by the choice of the proposal. Recently Hamiltonian Monte Carlo (HMC) sampling has shown success in many practical problems. In this paper, we propose an SMC augmented by HMC (HSMC) for inference and model learning of nonlinear SSM, which can exempt us from learning proposals and reduce the model complexity significantly. Based on the measure preserving property of HMC, the particles directly generated by transition function can approximate the posterior of latent states arbitrarily well. In order to better adapt to the local geometry of latent space, the HMC is conducted on Riemannian manifold defined by a positive definite metric. In addition, we show that the proposed HSMC method can improve SSMs realized by both Gaussian Processes (GP) and Neural Network (NN).

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to random variables are discussed, including the approach based on completions in a Polish space. We apply the theory to the study of stochastic dynamical systems in discrete-time, and give a brief exposition of the Wiener process as a foundation for stochastic differential equations. The theory is based within the framework of type-two effectivity, so has an explicit direct link with Turing computation, and is expressed in a system of computable types and operations, so has a clean mathematical description.

This monograph attempts a theory of every 'thing' that can be distinguished from other things in a statistical sense. The ensuing statistical independencies, mediated by Markov blankets, speak to a recursive composition of ensembles (of things) at increasingly higher spatiotemporal scales. This decomposition provides a description of small things; e.g., quantum mechanics - via the Schrodinger equation, ensembles of small things - via statistical mechanics and related fluctuation theorems, through to big things - via classical mechanics. These descriptions are complemented with a Bayesian mechanics for autonomous or active things. Although this work provides a formulation of every thing, its main contribution is to examine the implications of Markov blankets for self-organisation to nonequilibrium steady-state. In brief, we recover an information geometry and accompanying free energy principle that allows one to interpret the internal states of something as representing or making inferences about its external states. The ensuing Bayesian mechanics is compatible with quantum, statistical and classical mechanics and may offer a formal description of lifelike particles.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

We consider finite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we propose a new formulation, Bayesian risk Markov Decision Process (BR-MDP), to address parameter uncertainty in MDPs, where a risk functional is applied in nested form to the expected total cost with respect to the Bayesian posterior distribution of the unknown parameters. The proposed formulation provides more flexible risk attitutes towards parameter uncertainty and takes into account the availability of data in future times stages. To solve the proposed formulation with the conditional value-at-risk (CVaR) risk functional, we propose an efficient approximation algorithm by deriving an analytical approximation of the value function and utilizing the convexity of CVaR. We demonstrate the empirical performance of the BR-MDP formulation and proposed algorithms on a gambler's betting problem and an inventory control problem.

Accurately predicting the future would be an important milestone in the capabilities of artificial intelligence. However, research on the ability of large language models to provide probabilistic predictions about future events remains nascent. To empirically test this ability, we enrolled OpenAI's state-of-the-art large language model, GPT-4, in a three-month forecasting tournament hosted on the Metaculus platform. The tournament, running from July to October 2023, attracted 843 participants and covered diverse topics including Big Tech, U.S. politics, viral outbreaks, and the Ukraine conflict. Focusing on binary forecasts, we show that GPT-4's probabilistic forecasts are significantly less accurate than the median human-crowd forecasts. We find that GPT-4's forecasts did not significantly differ from the no-information forecasting strategy of assigning a 50% probability to every question. We explore a potential explanation, that GPT-4 might be predisposed to predict probabilities close to the midpoint of the scale, but our data do not support this hypothesis. Overall, we find that GPT-4 significantly underperforms in real-world predictive tasks compared to median human-crowd forecasts. A potential explanation for this underperformance is that in real-world forecasting tournaments, the true answers are genuinely unknown at the time of prediction; unlike in other benchmark tasks like professional exams or time series forecasting, where strong performance may at least partly be due to the answers being memorized from the training data. This makes real-world forecasting tournaments an ideal environment for testing the generalized reasoning and prediction capabilities of artificial intelligence going forward.

Understanding transition pathways between two meta-stable states of a molecular system is crucial to advance drug discovery and material design. However, unbiased molecular dynamics (MD) simulations are computationally infeasible because of the high energy barriers that separate these states. Although recent machine learning techniques are proposed to sample rare events, they are often limited to simple systems and rely on collective variables (CVs) derived from costly domain expertise. In this paper, we introduce a novel approach that trains diffusion path samplers (DPS) to address the transition path sampling (TPS) problem without requiring CVs. We reformulate the problem as an amortized sampling from the transition path distribution by minimizing the log-variance divergence between the path distribution induced by DPS and the transition path distribution. Based on the log-variance divergence, we propose learnable control variates to reduce the variance of gradient estimators and the off-policy training objective with replay buffers and simulated annealing techniques to improve sample efficiency and diversity. We also propose a scale-based equivariant parameterization of the bias forces to ensure scalability for large systems. We extensively evaluate our approach, termed TPS-DPS, on a synthetic system, small peptide, and challenging fast-folding proteins, demonstrating that it produces more realistic and diverse transition pathways than existing baselines.

Identifying transition states (TSs) on potential energy surfaces is a central computational bottleneck in mechanistic studies of catalytic materials. A TS search is not a single calculation but a long-horizon, multi-step workflow of atomistic simulations with delayed, asynchronous feedback and heterogeneous failure modes that require a joint multimodal analysis of scalar convergence diagnostics and atomic geometries along the reaction path. To address this challenge, we propose TSAgent, an agentic workflow that automates TS search directly at the density functional theory (DFT) level of quantum chemical accuracy. TSAgent operates through a persistent plan-execute-analyze-replan loop, continuously adapting its strategy based on convergence diagnostics and geometric feedback without human intervention. We evaluate TSAgent on a diverse 100-example subset of the OC20NEB heterogeneous catalysis benchmark, where it successfully locates TSs with 83% accuracy. In a direct comparison against expert DFT practitioners on 10 held-out examples, TSAgent achieves a 70% success rate compared to a human-expert average of 73 +/- 12%. Finally, TSAgent independently reproduces Bronsted-Evans-Polanyi scaling relationships for NH3 dissociation on metal and single-atom alloy surfaces from a published heterogeneous catalysis study, demonstrating that its utility extends beyond curated benchmarks to real scientific investigations.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

We consider infinite-horizon Markov Decision Processes where parameters, such as transition probabilities, are unknown and estimated from data. The popular distributionally robust approach to addressing the parameter uncertainty can sometimes be overly conservative. In this paper, we utilize the recently proposed formulation, Bayesian risk Markov Decision Process (BR-MDP), to address parameter (or epistemic) uncertainty in MDPs. To solve the infinite-horizon BR-MDP with a class of convex risk measures, we propose a computationally efficient approach called approximate bilevel difference convex programming (ABDCP). The optimization is performed offline and produces the optimal policy that is represented as a finite state controller with desirable performance guarantees. We also demonstrate the empirical performance of the BR-MDP formulation and the proposed algorithm.

Recent video generation models are increasingly framed as world models. Many physical processes can unfold in more than one valid way. Therefore, a world model should reproduce not only a plausible trajectory, but also the distribution of possible behaviors under the same initial observation and action. We call this distribution-level requirement probabilistic alignment. However, existing evaluations largely assess individual-video plausibility and do not test whether repeated generations recover the correct distribution. This raises a central question: how far are current video generators from probabilistically aligned world modeling? To answer it, we formalize probabilistic alignment as a distributional criterion for world models and introduce PAWBench, a benchmark for evaluating video generators as stochastic samplers of world dynamics. We further introduce PAWEval, an outcome-level protocol that converts repeated video rollouts into empirical distributions over possible physical behaviors. Across 50 scenarios and eleven current systems, no model consistently matches the reference probabilities while recovering the range of valid behaviors. Having established this gap, we test whether language prompts, initial noise sampling, or model training can reshape the model's predictive distribution. We believe our work can serve as a foundation for future efforts to move towards probabilistically aligned world modeling.

Counterfactual explanations are attracting significant attention due to the flourishing applications of machine learning models in consequential domains. A counterfactual plan consists of multiple possibilities to modify a given instance so that the model's prediction will be altered. As the predictive model can be updated subject to the future arrival of new data, a counterfactual plan may become ineffective or infeasible with respect to the future values of the model parameters. In this work, we study the counterfactual plans under model uncertainty, in which the distribution of the model parameters is partially prescribed using only the first- and second-moment information. First, we propose an uncertainty quantification tool to compute the lower and upper bounds of the probability of validity for any given counterfactual plan. We then provide corrective methods to adjust the counterfactual plan to improve the validity measure. The numerical experiments validate our bounds and demonstrate that our correction increases the robustness of the counterfactual plans in different real-world datasets.

The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its ability to answer questions pertaining to probability through the use of multiple-choice questions (MCQs). However, this paradigm, which we refer to as explicit probabilistic reasoning, has been shown in the literature to yield significant limitations (e.g., sensitivity to answer ordering). In this work, we introduce an alternative approach, named implicit probabilistic reasoning, which evaluates the models' ability to integrate probabilistic reasoning into their text generation process. To achieve this, we rephrase MCQs as text-completion scenarios with a determined set of outcomes and compare the model's next-token probability assignments to the true likelihood of the outcomes. In line with previous work, we find that models exhibit solid performance in their explicit probabilistic reasoning (i.e., answers to MCQs). However, during text completion (i.e., implicit probabilistic reasoning), where the same information must be taken into account to generate text, the models' predictions often significantly diverge from the known ground truth. For instance, our evaluation method reveals that implicit probabilistic reasoning is improperly influenced by many factors, such as independent prior events, partial observations about a result, or statistical background information. All of these issues can cause erroneous results to be produced in text generation, which are not detected by conventional MCQ-based evaluation.

Probabilistic forecasting estimates the likelihood of uncertain future events. To improve LLM forecasting, existing methods typically learn from binary outcomes to output verbalized forecasts. However, while aggregated human forecasts contain rich information in both the crowd probability estimate and the degree of agreement among forecasters, how to utilize these signals remains underexplored. To address this, we propose the Beta-Bernoulli Calibrator (BBC), which converts an initial point estimate forecast from any model into a distribution over event likelihood, using supervision from both binary outcomes and human forecasts. BBC models event likelihood p sim Beta(α, β) and outcome y sim Bernoulli(p), with the mean as the calibrated point forecast and the variance as the epistemic uncertainty. Our results show that BBC generally provides better calibrated and more accurate forecasts than both traditional post-hoc calibration methods and models fine-tuned specifically for forecasting, while remaining lightweight and having good generalization. We also show that the epistemic uncertainty captured by BBC is a more reliable predictor of forecasting error than verbalized confidence.

From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Markov kernels) gives a nice framework for conceptualization and analysis of many aspects of machine learning. Using categorical methods, we construct models for parametric and nonparametric Bayesian reasoning on function spaces, thus providing a basis for the supervised learning problem. In particular, stochastic processes are arrows to these function spaces which serve as prior probabilities. The resulting inference maps can often be analytically constructed in this symmetric monoidal weakly closed category. We also show how to view general stochastic processes using functor categories and demonstrate the Kalman filter as an archetype for the hidden Markov model.

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical instabilities along class-separating directions, but practical methods to detect and exploit these windows in trained models are still limited. We show that tracking the class-conditional entropy of a latent semantic variable given the noisy state provides a reliable signature of these transition regimes. By restricting the entropy to semantic partitions, the entropy can furthermore resolve semantic decisions at different levels of abstraction. We analyze this behavior in high-dimensional Gaussian mixture models and show that the entropy rate concentrates on the same logarithmic time scale as the speciation symmetry-breaking instability previously identified in variance-preserving diffusion. We validate our method on EDM2-XS and Stable Diffusion 1.5, where class-conditional entropy consistently isolates the noise regimes critical for semantic structure formation. Finally, we use our framework to quantify how guidance redistributes semantic information over time. Together, these results connect information-theoretic and statistical physics perspectives on diffusion and provide a principled basis for time-localized control.

Temporal Point Processes (TPP) are probabilistic generative frameworks. They model discrete event sequences localized in continuous time. Generally, real-life events reveal descriptive information, known as marks. Marked TPPs model time and marks of the event together for practical relevance. Conditioned on past events, marked TPPs aim to learn the joint distribution of the time and the mark of the next event. For simplicity, conditionally independent TPP models assume time and marks are independent given event history. They factorize the conditional joint distribution of time and mark into the product of individual conditional distributions. This structural limitation in the design of TPP models hurt the predictive performance on entangled time and mark interactions. In this work, we model the conditional inter-dependence of time and mark to overcome the limitations of conditionally independent models. We construct a multivariate TPP conditioning the time distribution on the current event mark in addition to past events. Besides the conventional intensity-based models for conditional joint distribution, we also draw on flexible intensity-free TPP models from the literature. The proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks. Our experimentation on various datasets with multiple evaluation metrics highlights the merit of the proposed approach.

Large language model post-training methods such as supervised fine-tuning (SFT), reinforcement learning (RL), and distillation are often analyzed through their loss functions: maximum likelihood, policy gradients, forward KL, reverse KL, or related objective-level variants. We study a complementary factor: the state distribution on which supervision is applied. For an autoregressive policy, a state is a prompt plus generated prefix. SFT trains on fixed dataset states, while RL and on-policy distillation (OPD) train on states induced by the current learner. We formalize post-training as state-distribution shaping and run a controlled smallscale study using Qwen3-0.6B-Base on GSM8K, with TruthfulQA and MMLU as retention evaluations. Our results show three phenomena. First, a mild SFT run improves GSM8K with little forgetting, while a stress SFT run causes substantial retention loss. Second, OPD from a degraded SFT teacher surpasses that teacher on GSM8K, TruthfulQA, and MMLU, despite using the teacher as its only supervision source. Third, a lightweight on-policy RL run improves GSM8K while preserving retention. These results support a state-centric view of post-training: the source and locality of training states can be as important as the form of the supervision signal.

Probabilistic circuits (PCs) are models that allow exact and tractable probabilistic inference. In contrast to neural networks, they are often assumed to be well-calibrated and robust to out-of-distribution (OOD) data. In this paper, we show that PCs are in fact not robust to OOD data, i.e., they don't know what they don't know. We then show how this challenge can be overcome by model uncertainty quantification. To this end, we propose tractable dropout inference (TDI), an inference procedure to estimate uncertainty by deriving an analytical solution to Monte Carlo dropout (MCD) through variance propagation. Unlike MCD in neural networks, which comes at the cost of multiple network evaluations, TDI provides tractable sampling-free uncertainty estimates in a single forward pass. TDI improves the robustness of PCs to distribution shift and OOD data, demonstrated through a series of experiments evaluating the classification confidence and uncertainty estimates on real-world data.

Reinforcement learning (RL) has become a standard paradigm for post-training and aligning Large Language Models (LLMs), yet recent evidence suggests it faces a persistent "capability ceiling": unlike classical RL systems that discover novel strategies, RL for LLMs often acts as a mere refiner of patterns already latent in pre-trained weights. In this work, we identify a fundamental structural bottleneck: while classical RL relies on compact, informative Markov states, current LLM post-training formulations are tethered to an ever-expanding history of actions. We revisit a classical principle long central to RL yet absent from LLM post-training: explicit Markov states. Theoretically, we provide rigorous guarantees demonstrating that leveraging estimated Markov states can significantly reduce sample complexity. Empirically, we show that introducing Markov states consistently breaks the performance boundaries of standard RL post-training across a suite of complex logic puzzles. Our findings suggest that moving beyond "history-as-state" modeling in favor of structured Markovian representations is essential for unlocking open-ended discovery and genuinely new reasoning capabilities in Generative AI.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

On-policy distillation (OPD) provides teacher supervision on states visited by the student, reducing the distribution gap between training and inference. However, in multi-turn agentic tasks, student deviations may accumulate over time, gradually moving the trajectory away from states where teacher guidance remains effective. Our quantitative analysis further shows that high-disagreement states offer promising opportunities for teacher guidance, but determining whether such guidance is beneficial requires examining its effect on subsequent student trajectories. We propose FutureBridge-OPD (FTB), which executes a short teacher bridge at a high disagreement state and uses the resulting student continuation to assess whether the bridge increases the density of positive distillation signals relative to the teacher. On ALFWorld, WebShop, and ScienceWorld, under the main Qwen3-32B teacher to Qwen3-1.7B student setting, FTB outperforms vanilla OPD and TCOD by an average of 16.6 and 7.6 points, respectively, and remains effective across student scales and teacher settings. Our code is publicly available at https://github.com/ChenChiShui/FutureBridge-OPD.

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval. Empirically, RADD is up to 3.5 times faster while achieving similar performance with the strongest baseline. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at https://github.com/ML-GSAI/RADD.

Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for such robust policies is a notoriously difficult problem, related to the so-called dynamic model of transition function uncertainty, where the environment dynamics are allowed to change at each time step. But in practical cases, one is rather interested in robustness to a span of static transition models throughout interaction episodes. The static model is known to be harder to solve than the dynamic one, and seminal algorithms, such as robust value iteration, as well as most recent works on deep robust RL, build upon the dynamic model. In this work, we propose to revisit the static model. We suggest an analysis of why solving the static model under some mild hypotheses is a reasonable endeavor, based on an equivalence with the dynamic model, and formalize the general intuition that robust MDPs can be solved by tackling a series of static problems. We introduce a generic meta-algorithm called IWOCS, which incrementally identifies worst-case transition models so as to guide the search for a robust policy. Discussion on IWOCS sheds light on new ways to decouple policy optimization and adversarial transition functions and opens new perspectives for analysis. We derive a deep RL version of IWOCS and demonstrate it is competitive with state-of-the-art algorithms on classical benchmarks.

The general sequential decision-making problem, which includes Markov decision processes (MDPs) and partially observable MDPs (POMDPs) as special cases, aims at maximizing a cumulative reward by making a sequence of decisions based on a history of observations and actions over time. Recent studies have shown that the sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs). Despite these advancements, existing approaches typically involve oracles or steps that are computationally intractable. On the other hand, the upper confidence bound (UCB) based approaches, which have served successfully as computationally efficient methods in bandits and MDPs, have not been investigated for more general PSRs, due to the difficulty of optimistic bonus design in these more challenging settings. This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. We further characterize the sample complexity bounds for our designed UCB-type algorithms for both online and offline PSRs. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.

This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the study of Schrodinger operators on multidimensional integer lattice, to characterize the evolution of continuous time quantum walks. Extending this framework, we develop a probabilistic method to represent discrete time quantum walks on an infinite integer line, bypassing the locality constraints that typically inhibit direct application of Molchanov formula. The validity of our representation is empirically confirmed through a benchmark analysis of the Hadamard walk, demonstrating high fidelity with traditional unitary evolution. Our results suggest that this probabilistic lens offer a powerful alternative for learning multidimensional quantum walks and provides new analytical pathways for investigating quantum systems via classical stochastic processes.

Understanding and predicting how social beliefs evolve in response to events -- from policy changes to scientific breakthroughs -- remains a fundamental challenge in social science. Given LLMs' commonsense knowledge and social intelligence, we ask: Can LLMs model the dynamics of social beliefs following social events? In this work, we introduce the concept of the Social World Model (SWM), a general framework designed to capture how social beliefs evolve in response to major events. SWM learns state-transition functions for social beliefs by mining temporal patterns in social data and optimizing the evidence lower bound, without the need for explicit human annotations linking events to belief shifts, or for expensive census data. To evaluate SWM, we introduce a benchmark, SWM-bench, derived from real-world prediction markets, specifically Kalshi and Polymarket. SWM-bench includes over 12k data points for social belief prediction tasks spanning diverse domains such as politics, finance, and cryptocurrency. Our experimental results show that SWM significantly outperforms time-series foundation models, achieving state-of-the-art results on Kalshi data and demonstrating competitive performance on Polymarket data, while offering interpretable insights into the underlying mechanisms of social belief dynamics.

When an LLM agent reads a confidential file, then writes a summary, then emails it externally, no single step is unsafe, but the sequence is a data leak. We call this safety drift: individually safe actions compounding into violations. Prior work has measured this problem; we predict it. SafetyDrift models agent safety trajectories as absorbing Markov chains, computing the probability that a trajectory will reach a violation within a given number of steps via closed form absorption analysis. A consequence of the monotonic state design is that every agent will eventually violate safety if left unsupervised (absorption probability 1.0 from all states), making the practical question not if but when, and motivating our focus on finite horizon prediction. Across 357 traces spanning 40 realistic tasks in four categories, we discover that "points of no return" are sharply task dependent: in communication tasks, agents that reach even a mild risk state have an 85% chance of violating safety within five steps, while in technical tasks the probability stays below 5% from any state. A lightweight monitor built on these models detects 94.7% of violations with 3.7 steps of advance warning at negligible computational cost, outperforming both keyword matching (44.7% detection, 55.9% false positive rate) and per step LLM judges (52.6% detection, 38.2% false positive rate) while running over 60,000x faster.

In this paper, we propose feedback designs for manipulating a quantum state to a target state by performing sequential measurements. In light of Belavkin's quantum feedback control theory, for a given set of (projective or non-projective) measurements and a given time horizon, we show that finding the measurement selection policy that maximizes the probability of successful state manipulation is an optimal control problem for a controlled Markovian process. The optimal policy is Markovian and can be solved by dynamical programming. Numerical examples indicate that making use of feedback information significantly improves the success probability compared to classical scheme without taking feedback. We also consider other objective functionals including maximizing the expected fidelity to the target state as well as minimizing the expected arrival time. The connections and differences among these objectives are also discussed.

Chemical reaction networks can undergo nonequilibrium phase transitions upon variation of external control parameters like the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the entropy production and its critical fluctuations within the Schlögl model. Numerical simulations show that the corresponding diffusion coefficient diverges at the critical point as a function of system size. In the vicinity of the critical point, the diffusion coefficient follows a scaling form. We develop an analytical approach based on the chemical Langevin equation and van Kampen's system size expansion that yields the corresponding exponents in the monostable regime. In the bistable regime, we rely on a two-state approximation in order to analytically describe the critical behavior.

It is a notable trend to use Large Language Models (LLMs) to tackle complex tasks, e.g., tasks that require a sequence of actions and dynamic interaction with tools and external environments. In this paper, we propose StateFlow, a novel LLM-based task-solving paradigm that conceptualizes complex task-solving processes as state machines. In StateFlow, we distinguish between "process grounding" (via state and state transitions) and "sub-task solving" (through actions within a state), enhancing control and interpretability of the task-solving procedure. A state represents the status of a running process. The transitions between states are controlled by heuristic rules or decisions made by the LLM, allowing for a dynamic and adaptive progression. Upon entering a state, a series of actions is executed, involving not only calling LLMs guided by different prompts, but also the utilization of external tools as needed. Our results show that StateFlow significantly enhances LLMs' efficiency. For instance, StateFlow achieves 13% and 28% higher success rates compared to ReAct in InterCode SQL and ALFWorld benchmark, with 5x and 3x less cost respectively. We also show that StateFlow can be combined with iterative refining methods like Reflexion to further improve performance.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Along the way initiated by Carleo and Troyer [1], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of discrete events in continuous time, by constructing a neurally self-modulating multivariate point process in which the intensities of multiple event types evolve according to a novel continuous-time LSTM. This generative model allows past events to influence the future in complex and realistic ways, by conditioning future event intensities on the hidden state of a recurrent neural network that has consumed the stream of past events. Our model has desirable qualitative properties. It achieves competitive likelihood and predictive accuracy on real and synthetic datasets, including under missing-data conditions.

Generative Flow Networks or GFlowNets are related to Monte-Carlo Markov chain methods (as they sample from a distribution specified by an energy function), reinforcement learning (as they learn a policy to sample composed objects through a sequence of steps), generative models (as they learn to represent and sample from a distribution) and amortized variational methods (as they can be used to learn to approximate and sample from an otherwise intractable posterior, given a prior and a likelihood). They are trained to generate an object x through a sequence of steps with probability proportional to some reward function R(x) (or exp(-E(x)) with E(x) denoting the energy function), given at the end of the generative trajectory. Like for other RL settings where the reward is only given at the end, the efficiency of training and credit assignment may suffer when those trajectories are longer. With previous GFlowNet work, no learning was possible from incomplete trajectories (lacking a terminal state and the computation of the associated reward). In this paper, we consider the case where the energy function can be applied not just to terminal states but also to intermediate states. This is for example achieved when the energy function is additive, with terms available along the trajectory. We show how to reparameterize the GFlowNet state flow function to take advantage of the partial reward already accrued at each state. This enables a training objective that can be applied to update parameters even with incomplete trajectories. Even when complete trajectories are available, being able to obtain more localized credit and gradients is found to speed up training convergence, as demonstrated across many simulations.

Automated evaluation of free-form outputs from large language models (LLMs) is challenging because many distinct answers can be equally valid. A common practice is to use LLMs themselves as judges, but the theoretical properties of this approach are not yet well understood. We show that a geometric framework that represents both judges and candidates as points on a probability simplex can provide helpful insight on what is or is not identifiable using LLM judges. Our theoretical analysis uncovers a "phase transition" in ranking identifiability: for binary scoring systems, true rankings are identifiable even with weak judges under mild assumptions, while rankings become non-identifiable for three or more scoring levels even with infinite data, absent additional prior knowledge. This non-identifiability highlights how uncertainty in rankings stems from not only aleatoric uncertainty (i.e., inherent stochasticity in the data) but also epistemic uncertainty regarding which assumptions hold, an aspect that has received limited attention until now. To integrate both types of uncertainty, we use Bayesian inference to encode assumptions as priors and conduct sensitivity analysis of ranking estimates and credible intervals. Empirical evaluations across multiple benchmarks demonstrate that Bayesian inference yields more accurate rankings and substantially improves coverage rates. These results underscore the importance of taking a more holistic approach to uncertainty quantification when using LLMs as judges.

Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via either Monte Carlo or expectation-maximization methods. In this work we introduce an alternative, variational inference algorithm for Markov jump processes which relies on neural ordinary differential equations, and is trainable via back-propagation. Our methodology learns neural, continuous-time representations of the observed data, that are used to approximate the initial distribution and time-dependent transition probability rates of the posterior Markov jump process. The time-independent rates of the prior process are in contrast trained akin to generative adversarial networks. We test our approach on synthetic data sampled from ground-truth Markov jump processes, experimental switching ion channel data and molecular dynamics simulations. Source code to reproduce our experiments is available online.

Scientific discovery is not only answer generation but revision of the representational regime in which evidence, artifacts, operations, and verifiers are typed. We develop a category-theoretic account of agentic discovery for materials science. In a fixed regime b with schema category S_b, the system state is a copresheaf I_t: S_b -> Set, and provenance is the category of elements \int_{S_b} I_t. Fixed-regime operation is an update on such states, endofunctorial only when provenance-preserving refinements are specified and preserved. Discovery is instead a verified regime transition u: S_b -> S_b': old artifacts are preserved, transported by the left Kan extension Lan_u I_t, and compared with the post-transition state to identify residual content beyond functorial transport. This separates retrieval, search, and discovery without subjective novelty. We instantiate the framework in two systems. In Builder/Breaker, a protein-mechanics world model is revised under a Minimum Description Length gate; the accepted law expresses within-chain flexibility as all-mode elastic compliance conditioned by slow collective-mode participation, or mode-conditioned compliance. In CategoryScienceClaw, typed skills, artifacts, open needs, workflow mutation, gates, stress tests, and public discourse become a proof-carrying knowledge-computation graph. A fiber-network example records candidate models, rejected alternatives, an AIC gate, perturbation tests, and an accepted orientation-tensor anisotropic stiffness surrogate over an isotropic fiber-count descriptor. Together, the cases show how category theory can be both a mathematical language for discovery and an engineering specification for self-revising AI discovery systems.

Despite strong capabilities in data understanding and decision-making, autonomous data science agents still heavily rely on trial-and-error workflows that involve expensive computation. This bottleneck motivates models that can anticipate the effects of data science operations before real execution. In this paper, we introduce the concept of Data Science World Model, which model the data science execution environment by predicting environment state transitions conditioned on current workflow states and candidate operations. We further propose DSWorld, a practical framework that combines structured state construction, cost-aware routing, lightweight real execution, and an LLM-based simulator for expensive operations. To support training, we construct an 8K-scale transition trajectory dataset and introduce Reflective World Model Optimization, an error-aware reinforcement learning strategy for improving transition prediction. Experiments show that DSWorld accelerates RL-based agent training by approximately 14times and search-based inference by approximately 3-6times while maintaining competitive performance, and outperforms the strongest LLM baseline by 35.6% on transition prediction tasks. The code is available at https://anonymous.4open.science/r/DSWorld.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

Online Surgical Phase Recognition (SPR) models can reach high frame-wise accuracy, yet their predictions often lack temporal stability, fragmenting workflow understanding and reducing the reliability of downstream assistance. We show that this instability is not random noise but arises from two mechanisms: early misclassifications corrupt temporal feature states and propagate forward to form error cascades, and phase transitions follow evidence-accumulation dynamics whereas most online SPR systems rely on memoryless frame-wise decisions, making them sensitive to transient confidence fluctuations. We propose a unified Train-Inference-Evaluation framework that explicitly stabilizes temporal inference dynamics using model-agnostic, plug-and-play components. For training, the Temporal Error-Cascade (TEC) loss suppresses error onset and mitigates forward error propagation by stabilizing temporal feature evolution. For inference, the Evidence-Gated Transition Predictor (EGTP) enforces evidence-driven state transitions, allowing phase changes only when accumulated evidence exceeds a confidence boundary. For evaluation, we introduce the Temporal Fragmentation Index (TFI), a reliability-aware metric that quantifies instability-induced temporal disagreement beyond conventional frame-wise and token-based measures. Experiments on Cholec80 and AutoLaparo across three representative backbones show that the proposed framework substantially improves temporal stability and reduces prediction fragmentation, while maintaining or modestly improving frame-wise performance.

Image generation models now produce high-quality static images, yet their ability to represent how a visual world changes over time remains poorly understood. Practical workflows such as storyboarding, step-by-step illustration, reference-guided editing, and video previsualization require models to preserve identities, objects, spatial relations, and causal order across multiple visual states. Existing evaluations largely measure single-image correctness, compositional alignment, or video quality, leaving open whether an image model can coherently imagine a temporally ordered process. We introduce ImageTime, a diagnostic benchmark that uses spatiotemporal consistency as a behavioral probe of visual world modeling in image generation. Given an action instruction, and optionally a reference image specifying the initial state, a model must generate one image containing four ordered key states: initial state, action onset, transition state, and final state. This four-keyframe protocol is more temporally demanding than single-image generation while avoiding the confounds of dense video dynamics. ImageTime organizes tasks with a progressive capability hierarchy and decomposes each scenario into stage-wise state predicates, cross-frame temporal constraints, and forbidden causal violations. GPT-5.5 scores all generated images under a structured VLM-as-judge protocol, producing interpretable capability scores, diagnostic subscores, and failure labels. Through multi-family benchmarking, ImageTime reveals where current image generation systems succeed, fail, and drift when asked to maintain coherent visual world states over time.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

We provide an optimization-based framework to perform counterfactual analysis in a dynamic model with hidden states. Our framework is grounded in the ``abduction, action, and prediction'' approach to answer counterfactual queries and handles two key challenges where (1) the states are hidden and (2) the model is dynamic. Recognizing the lack of knowledge on the underlying causal mechanism and the possibility of infinitely many such mechanisms, we optimize over this space and compute upper and lower bounds on the counterfactual quantity of interest. Our work brings together ideas from causality, state-space models, simulation, and optimization, and we apply it on a breast cancer case study. To the best of our knowledge, we are the first to compute lower and upper bounds on a counterfactual query in a dynamic latent-state model.

Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs demonstrate outstanding performance across a diverse set of domains, at a reduced training and inference cost compared to attention-based transformers. Recent developments show that if the linear recurrence powering SSMs allows for multiplicative interactions between inputs and hidden states (e.g. GateLoop, Mamba, GLA), then the resulting architecture can surpass in both in accuracy and efficiency attention-powered foundation models trained on text, at scales of billion parameters. In this paper, we give theoretical grounding to this recent finding using tools from Rough Path Theory: we show that when random linear recurrences are equipped with simple input-controlled transitions (selectivity mechanism), then the hidden state is provably a low-dimensional projection of a powerful mathematical object called the signature of the input -- capturing non-linear interactions between tokens at distinct timescales. Our theory not only motivates the success of modern selective state-space models such as Mamba but also provides a solid framework to understand the expressive power of future SSM variants.

We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties like exchangeability of conditions. Conditioning on equality of continuous random variables is nontrivial, as the exact observation may have probability zero; this is Borel's paradox. Using categorical formulations of conditional probability, we show that the good properties of our language are not particular to Gaussians, but can be derived from universal properties, thus generalizing to wider settings. We define the Cond construction, which internalizes conditioning as a morphism, providing general compositional semantics for probabilistic programming with exact conditioning.

We propose MDP-GapE, a new trajectory-based Monte-Carlo Tree Search algorithm for planning in a Markov Decision Process in which transitions have a finite support. We prove an upper bound on the number of calls to the generative models needed for MDP-GapE to identify a near-optimal action with high probability. This problem-dependent sample complexity result is expressed in terms of the sub-optimality gaps of the state-action pairs that are visited during exploration. Our experiments reveal that MDP-GapE is also effective in practice, in contrast with other algorithms with sample complexity guarantees in the fixed-confidence setting, that are mostly theoretical.

Chain-of-Thought (CoT) prompting enables complex reasoning in large language models (LLMs), including applications in information retrieval (IR). However, it often leads to overthinking, where models produce excessively long and semantically redundant traces with little or no benefit. We identify two key challenges in IR: redundant trajectories that revisit similar states and misguided reasoning that diverges from user intent. To address these, we propose State Machine Reasoning (SMR), a transition-based reasoning framework composed of discrete actions (Refine, Rerank, Stop) that support early stopping and fine-grained control. Experiments on the BEIR and BRIGHT benchmarks show that SMR improves retrieval performance (nDCG@10) by 3.4% while reducing token usage by 74.4%. It generalizes across LLMs and retrievers without requiring task-specific tuning, offering a practical alternative to conventional CoT reasoning. The code and details are available at https://github.com/ldilab/SMR.

We present the Bayesian Linguistic Forecaster (BLF), an agentic system for binary forecasting that achieves state-of-the-art performance on the ForecastBench benchmark. The system is built on three ideas. (1) Linguistic belief state: a semi-structured representation combining numerical probability estimates with natural-language evidence summaries, updated by the LLM at each step of an iterative tool-use loop. This contrasts with the common approach of appending all retrieved evidence to an ever-growing, unstructured context. (2) Hierarchical multi-trial aggregation: running K independent trials and combining them using logit-space averaging shrinkage with a data-dependent prior. (3) Hierarchical calibration: Platt scaling with a hierarchical prior, which avoids over-shrinking extreme predictions for sources with skewed base rates. On 400 questions from the ForecastBench leaderboard, BLF outperforms all the top public methods, including Cassi, GPT-5, Grok~4.20, and Foresight-32B. Careful ablation studies, using mixed effects analysis to control for question variability (which accounts for 62\% of the variance in performance), reveals that all 3 components contribute to the overall gains, but some components matter more than others, depending on the base LLM, and the setting (e.g.\ with or without a crowd prior). All our experiments are based on a robust back-testing framework which we develop, which has a leakage rate below 1.5\%, and may be of independent interest.

The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent's current understanding of the dynamics of the system, drastically reducing the computational costs. We extensively evaluate our method by measuring the agent's performance in terms of environment exploration, for continuous tasks, and looking at the game scores achieved, for video games. Our model is computationally cheap and compares positively with current state-of-the-art methods on several problems. We also investigate the effects caused by stochasticity in the environment, which is often a failure case for curiosity-driven agents. In this regime, the results suggest that our approach is resilient to stochastic transitions.

In this paper, we discuss that an observable-based single-system Copenhagen and entanglement-based two-system von Neumann measurement protocols in quantum theory can be made equivalent by considering the second part of the two-system scheme to be a Dirac-type negative sea filling up the first system. Based on this equivalence, and by considering the universe as a computational process, the choice of the apparatus state in the two-system protocol can be identified with the choice of the observable in the single-system scheme as negative sea filling up the observable universe. In particular, the measuring party's state is considered to be evolving backwards in time to the big bang as a nondeterministic computational process, which chooses the acceptable path as a time-reversal process of irreversible computation. The suggested model proposes that the prepared microstate of the universe, or reality, corresponds to the observer's choice, therefore, subjective reality. Thus, this effectively provides a specific description of the subjective universe model previously proposed, which is based on the symmetry breakdown between the Schrodinger and the Heisenberg pictures of quantum theory.

Quantum algorithms for probing ground-state properties of quantum systems require good initial states. Projection-based methods such as eigenvalue filtering rely on inputs that have a significant overlap with the low-energy subspace, which can be challenging for large, strongly-correlated systems. This issue has motivated the study of physically-inspired dynamical approaches such as thermodynamic cooling. In this work, we introduce a ground-state preparation algorithm based on the simulation of quantum dynamics. Our main insight is to transform the Hamiltonian by a shifted sign function via quantum signal processing, effectively mapping eigenvalues into positive and negative subspaces separated by a large gap. This automatically ensures that all states within each subspace conserve energy with respect to the transformed Hamiltonian. Subsequent time-evolution with a perturbed Hamiltonian induces transitions to lower-energy states while preventing unwanted jumps to higher energy states. The approach does not rely on a priori knowledge of energy gaps and requires no additional qubits to model a bath. Furthermore, it makes mathcal{O}(d^{,3/2}/epsilon) queries to the time-evolution operator of the system and mathcal{O}(d^{,3/2}) queries to a block-encoding of the perturbation, for d cooling steps and an epsilon-accurate energy resolution. Our results provide a framework for combining quantum signal processing and Hamiltonian simulation to design heuristic quantum algorithms for ground-state preparation.

One of the predominant methods for training world models is autoregressive prediction in the output space of the next element of a sequence. In Natural Language Processing (NLP), this takes the form of Large Language Models (LLMs) predicting the next token; in Computer Vision (CV), this takes the form of autoregressive models predicting the next frame/token/pixel. However, this approach differs from human cognition in several respects. First, human predictions about the future actively influence internal cognitive processes. Second, humans naturally evaluate the plausibility of predictions regarding future states. Based on this capability, and third, by assessing when predictions are sufficient, humans allocate a dynamic amount of time to make a prediction. This adaptive process is analogous to System 2 thinking in psychology. All these capabilities are fundamental to the success of humans at high-level reasoning and planning. Therefore, to address the limitations of traditional autoregressive models lacking these human-like capabilities, we introduce Energy-Based World Models (EBWM). EBWM involves training an Energy-Based Model (EBM) to predict the compatibility of a given context and a predicted future state. In doing so, EBWM enables models to achieve all three facets of human cognition described. Moreover, we developed a variant of the traditional autoregressive transformer tailored for Energy-Based models, termed the Energy-Based Transformer (EBT). Our results demonstrate that EBWM scales better with data and GPU Hours than traditional autoregressive transformers in CV, and that EBWM offers promising early scaling in NLP. Consequently, this approach offers an exciting path toward training future models capable of System 2 thinking and intelligently searching across state spaces.

Probability estimation models play an important role in various fields, such as weather forecasting, recommendation systems, and sports analysis. Among several models estimating probabilities, it is difficult to evaluate which model gives reliable probabilities since the ground-truth probabilities are not available. The win probability estimation model for esports, which calculates the win probability under a certain game state, is also one of the fields being actively studied in probability estimation. However, most of the previous works evaluated their models using accuracy, a metric that only can measure the performance of discrimination. In this work, we firstly investigate the Brier score and the Expected Calibration Error (ECE) as a replacement of accuracy used as a performance evaluation metric for win probability estimation models in esports field. Based on the analysis, we propose a novel metric called Balance score which is a simple yet effective metric in terms of six good properties that probability estimation metric should have. Under the general condition, we also found that the Balance score can be an effective approximation of the true expected calibration error which has been imperfectly approximated by ECE using the binning technique. Extensive evaluations using simulation studies and real game snapshot data demonstrate the promising potential to adopt the proposed metric not only for the win probability estimation model for esports but also for evaluating general probability estimation models.

Two common approaches to sequential decision-making are AI planning (AIP) and reinforcement learning (RL). Each has strengths and weaknesses. AIP is interpretable, easy to integrate with symbolic knowledge, and often efficient, but requires an up-front logical domain specification and is sensitive to noise; RL only requires specification of rewards and is robust to noise but is sample inefficient and not easily supplied with external knowledge. We propose an integrative approach that combines high-level planning with RL, retaining interpretability, transfer, and efficiency, while allowing for robust learning of the lower-level plan actions. Our approach defines options in hierarchical reinforcement learning (HRL) from AIP operators by establishing a correspondence between the state transition model of AI planning problem and the abstract state transition system of a Markov Decision Process (MDP). Options are learned by adding intrinsic rewards to encourage consistency between the MDP and AIP transition models. We demonstrate the benefit of our integrated approach by comparing the performance of RL and HRL algorithms in both MiniGrid and N-rooms environments, showing the advantage of our method over the existing ones.

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about ``planning as inference''? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that, just like all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, planning corresponds exactly to a different set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored-state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition.