Modern generative models, such as neural ordinary differential equations (neural ODEs) [4], transformers [25], and diffusion models [22], have demonstrated remarkable ability to learn and generate samples from complex, high-dimensional probability distributions. These architectures have achieved broad success in scientific computing, image processing, and data science, offering scalable frameworks for data-driven modeling. However, training and sampling in such spaces remain expensive and highly sensitive to architectural and optimization choices. Despite these advances, the curse of dimensionality continues to present a fundamental challenge in many real-world applications. Fortunately, numerous problems in scientific computing exhibit intrinsic structures, such as sparsity, low-rank representations, or approximate invariances, that can be interpreted as prior information about the underlying data or operators. Leveraging such priors within generative models offers a promising avenue to improve both computational efficiency and generalization. A classical way to incorporate prior information, such as sparsity or piecewise regularity, is through Bayesian modeling, where the posterior combines a prior distribution encoding structural knowledge with a likelihood function derived from observations.

In this work, we present the first finite-time analysis of the Q-learning algorithm under time-varying learning policies (i.e., on-policy sampling) with minimal assumptions -- specifically, assuming only the existence of a policy that induces an irreducible Markov chain over the state space. We establish a last-iterate convergence rate for $\mathbb{E}[\|Q_k - Q^*\|_\infty^2]$, implying a sample complexity of order $O(1/ε^2)$ for achieving $\mathbb{E}[\|Q_k - Q^*\|_\infty] \le ε$, matching that of off-policy Q-learning but with a worse dependence on exploration-related parameters. We also derive an explicit rate for $\mathbb{E}[\|Q^{π_k} - Q^*\|_\infty^2]$, where $π_k$ is the learning policy at iteration $k$. These results reveal that on-policy Q-learning exhibits weaker exploration than its off-policy counterpart but enjoys an exploitation advantage, as its policy converges to an optimal one rather than remaining fixed. Numerical simulations corroborate our theory. Technically, the combination of time-varying learning policies (which induce rapidly time-inhomogeneous Markovian noise) and the minimal assumption on exploration presents significant analytical challenges. To address these challenges, we employ a refined approach that leverages the Poisson equation to decompose the Markovian noise corresponding to the lazy transition matrix into a martingale-difference term and residual terms. To control the residual terms under time inhomogeneity, we perform a sensitivity analysis of the Poisson equation solution with respect to both the Q-function estimate and the learning policy. These tools may further facilitate the analysis of general reinforcement learning algorithms with rapidly time-varying learning policies -- such as single-timescale actor--critic methods and learning-in-games algorithms -- and are of independent interest.

Latent-variable energy-based models (LV-EBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood training as a saddle problem over distributions on the latent and joint manifolds and view the inner updates as coupled Wasserstein gradient flows. The resulting algorithm alternates overdamped Langevin updates for a joint negative pool and for conditional latent particles with stochastic parameter ascent, requiring no discriminator or auxiliary networks. We prove existence and convergence under standard smoothness and dissi-pativity assumptions, with decay rates in KL divergence and Wasserstein-2 distance. The saddle-point view further yields an ELBO strictly tighter than bounds obtained with restricted amortized posteriors. Our method is evaluated on numerical approximations of physical systems and performs competitively against comparable approaches.

Conflicting experiments disagree on whether the titanium-vanadium (Ti-V) binary alloy exhibits a body-centred cubic (BCC) miscibility gap or remains completely soluble. A leading hypothesis attributes the miscibility gap to oxygen contamination during alloy preparation. To resolve this disagreement, we use an ab initio + machine-learning workflow that couples an actively-trained Moment Tensor Potential with Bayesian inference of free energy surface. This workflow enables construction of the Ti-V phase diagram across the full composition range with systematically reduced statistical and finite-size errors. The resulting diagram reproduces all experimental features, demonstrating the robustness of our approach, and clearly favors the variant with a BCC miscibility gap terminating at T = 980 K and c = 0.67. Because our simulations model a perfectly oxygen-free Ti-V system, the observed gap cannot originate from impurity effects, in contrast to recent CALPHAD reassessments.

Autonomous vehicles (AV) offer a cost-effective solution for scientific missions such as underwater tracking. Recently, reinforcement learning (RL) has emerged as a powerful method for controlling AVs in complex marine environments. However, scaling these techniques to a fleet--essential for multi-target tracking or targets with rapid, unpredictable motion--presents significant computational challenges. Multi-Agent Reinforcement Learning (MARL) is notoriously sample-inefficient, and while high-fidelity simulators like Gazebo's LRAUV provide 100x faster-than-real-time single-robot simulations, they offer no significant speedup for multi-vehicle scenarios, making MARL training impractical. To address these limitations, we propose an iterative distillation method that transfers high-fidelity simulations into a simplified, GPU-accelerated environment while preserving high-level dynamics. This approach achieves up to a 30,000x speedup over Gazebo through parallelization, enabling efficient training via end-to-end GPU acceleration. Additionally, we introduce a novel Transformer-based architecture (TransfMAPPO) that learns multi-agent policies invariant to the number of agents and targets, significantly improving sample efficiency. Following large-scale curriculum learning conducted entirely on GPU, we perform extensive evaluations in Gazebo, demonstrating that our method maintains tracking errors below 5 meters over extended durations, even in the presence of multiple fast-moving targets. This work bridges the gap between large-scale MARL training and high-fidelity deployment, providing a scalable framework for autonomous fleet control in real-world sea missions.

Speech summarization has become an essential tool for efficiently managing and accessing the growing volume of spoken and audiovisual content. However, despite its increasing importance, speech summarization remains loosely defined. The field intersects with several research areas, including speech recognition, text summarization, and specific applications like meeting summarization. This survey not only examines existing datasets and evaluation protocols, which are crucial for assessing the quality of summarization approaches, but also synthesizes recent developments in the field, highlighting the shift from traditional systems to advanced models like fine-tuned cascaded architectures and end-to-end solutions. In doing so, we surface the ongoing challenges, such as the need for realistic evaluation benchmarks, multilingual datasets, and long-context handling.

Large language models (LLMs) are moving beyond static uses and are now powering agents that learn continually during their interaction with external environments. For example, agents can learn reusable skills while navigating web pages or toggling new tools. However, existing methods for skill learning often create skills that are over-specialized to a single website and fail to generalize. We introduce PolySkill, a new framework that enables agents to learn generalizable and compositional skills. The core idea, inspired by polymorphism in software engineering, is to decouple a skill's abstract goal (what it accomplishes) and its concrete implementation (how it is executed). Experiments show that our method (1) improves skill reuse by 1.7x on seen websites and (2) boosts success rates by up to 9.4% on Mind2Web and 13.9% on unseen websites, while reducing steps by over 20%. (3) In self-exploration settings without specified tasks, our framework improves the quality of proposed tasks and enables agents to learn generalizable skills that work across different sites. By enabling the agent to identify and refine its own goals, the PolySkill enhances the agent's ability to learn a better curriculum, leading to the acquisition of more generalizable skills compared to baseline methods. This work provides a practical path toward building agents capable of continual learning in adaptive environments. Our findings show that separating a skill's goal from its execution is a crucial step toward developing autonomous agents that can learn and generalize across the open web continuously.

For an AI's training process to successfully impart a desired goal, it is important that the AI does not attempt to resist the training. However, partially learned goals will often incentivize an AI to avoid further goal updates, as most goals are better achieved by an AI continuing to pursue them. We say that a goal is corrigible if it does not incentivize taking actions that avoid proper goal updates or shutdown. In addition to convergence in training, corrigibility also allows for correcting mistakes and changes in human preferences, which makes it a crucial safety property. Despite this, the existing literature does not include specifications for goals that are both corrigible and competitive with non-corrigible alternatives. We provide a formal definition for corrigibility, then introduce a transformation that constructs a corrigible version of any goal that can be made corrigible, without sacrificing performance. This is done by myopically eliciting predictions of reward conditional on costlessly preventing updates, which then also determine the reward when updates are accepted. The transformation can be modified to recursively extend corrigibility to any new agents created by corrigible agents, and to prevent agents from deliberately modifying their goals. Two gridworld experiments demonstrate that these corrigible goals can be learned effectively, and that they lead to the desired behavior.

Feature learning (FL), where neural networks adapt their internal representations during training, remains poorly understood. Using methods from statistical physics, we derive a tractable, self-consistent mean-field (MF) theory for the Bayesian posterior of two-layer non-linear networks trained with stochastic gradient Langevin dynamics (SGLD). At infinite width, this theory reduces to kernel ridge regression, but at finite width it predicts a symmetry breaking phase transition where networks abruptly align with target functions. While the basic MF theory provides theoretical insight into the emergence of FL in the finite-width regime, semi-quantitatively predicting the onset of FL with noise or sample size, it substantially underestimates the improvements in generalisation after the transition. We trace this discrepancy to a key mechanism absent from the plain MF description: \textit{self-reinforcing input feature selection}. Incorporating this mechanism into the MF theory allows us to quantitatively match the learning curves of SGLD-trained networks and provides mechanistic insight into FL.

We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can diverge under interventions, so observational adequacy alone cannot guarantee interventional competence. We begin by laying foundations, definitions of knowledge, learning, intelligence, counterfactual competence and AGI, and then analyze the limits of observational learning that motivate an error centric shift. We recast the problem as three questions about how explicit and implicit errors evolve under an agent's actions, which errors are unreachable within a fixed hypothesis space, and how conjecture and criticism expand that space. From these questions we propose Causal Mechanics, a mechanisms first program in which hypothesis space change is a first class operation and probabilistic structure is used when useful rather than presumed. We advance structural principles that make error discovery and correction tractable, including a differential Locality and Autonomy Principle for modular interventions, a gauge invariant form of Independent Causal Mechanisms for separability, and the Compositional Autonomy Principle for analogy preservation, together with actionable diagnostics. The aim is a scaffold for systems that can convert unreachable errors into reachable ones and correct them.