The remarkable empirical performance of distributional reinforcement learning (RL) has garnered increasing attention to understanding its theoretical advantages over classical RL. By decomposing the categorical distributional loss commonly employed in distributional RL, we find that the potential superiority of distributional RL can be attributed to a derived distribution-matching entropy regularization. This less-studied entropy regularization aims to capture additional knowledge of return distribution beyond only its expectation, contributing to an augmented reward signal in policy optimization. In contrast to the vanilla entropy regularization in MaxEnt RL, which explicitly encourages exploration by promoting diverse actions, the novel entropy regularization derived from categorical distributional loss implicitly updates policies to align the learned policy with (estimated) environmental uncertainty. Finally, extensive experiments verify the significance of this uncertainty-aware regularization from distributional RL on the empirical benefits over classical RL. Our study offers an innovative exploration perspective to explain the intrinsic benefits of distributional learning in RL.

Trust in a decision-making system requires both safety guarantees and the ability to interpret and understand its behavior. This is particularly important for learned systems, whose decision-making processes are often highly opaque. Shielding is a prominent model-based technique for enforcing safety in reinforcement learning. However, because shields are automatically synthesized using rigorous formal methods, their decisions are often similarly difficult for humans to interpret. Recently, decision trees became customary to represent controllers and policies.

Humans can efficiently extract knowledge and learn skills from the videos within only a few trials and errors. However, it poses a big challenge to replicate this learning process for autonomous agents, due to the complexity of visual input, the absence of action or reward signals, and the limitations of interaction steps. In this paper, we propose a novel, unsupervised, and sample-efficient framework to achieve imitation learning from videos (ILV), named Behavior Cloning from Videos via Latent Representations (BCV-LR). BCV-LR extracts action-related latent features from high-dimensional video inputs through self-supervised tasks, and then leverages a dynamics-based unsupervised objective to predict latent actions between consecutive frames. The pre-trained latent actions are fine-tuned and efficiently aligned to the real action space online (with collected interactions) for policy behavior cloning. The cloned policy in turn enriches the agent experience for further latent action finetuning, resulting in an iterative policy improvement that is highly sample-efficient. We conduct extensive experiments on a set of challenging visual tasks, including both discrete control and continuous control. BCV-LR enables effective (even expert-level on some tasks) policy performance with only a few interactions, surpassing state-of-the-art ILV baselines and reinforcement learning methods (provided with environmental rewards) in terms of sample efficiency across 24/28 tasks. To the best of our knowledge, this work for the first time demonstrates that videos can support extremely sample-efficient visual policy learning, without the need to access any other expert supervision.

Today's deep learning architectures are primarily based on perceptron models, which do not capture the oscillatory dynamics characteristic of biological neural activity. Although oscillatory systems have recently gained attention for their closer resemblance to neural behavior, they often lack a structured mechanism to represent rich spatio-temporal dynamics in a controllable and interpretable manner. In this paper, we propose a bio-inspired oscillatory state system (BioOSS), a 2D topographically organized oscillatory state-space model designed to generate diverse oscillation-driven spatio-temporal patterns. BioOSS comprises two coupled state components: punits that represent membrane-potential-like variables inspired by pyramidal-cell activity, and o units that act as velocity-like latent states controlling phase, time scales, and damping. The model incorporates trainable parameters for damping and effective oscillation rates, enabling flexible adaptation to task-specific temporal structures while remaining efficient for long-sequence learning via scanfriendly diagonal dynamics. We evaluate BioOSS on both synthetic and real-world tasks, demonstrating superior performance and enhanced interpretability compared to alternative architectures.

While recent advancements in generative modeling have significantly improved text-image alignment, some residual misalignment between text and image representations still remains. Some approaches address this issue by fine-tuning models in terms of preference optimization, etc., which require tailored datasets. Orthogonal to these methods, we revisit the challenge from the perspective of representation alignment--an approach that has gained popularity with the success of REPresentation Alignment (REPA) [46]. We first argue that conventional text-to-image (T2I) diffusion models, typically trained on paired image and text data (i.e., positive pairs) by minimizing score matching or flow matching losses, is suboptimal from the standpoint of representation alignment.

This work establishes that sparse Bayesian neural networks achieve optimal posterior contraction rates over anisotropic Besov spaces and their hierarchical compositions. These structures reflect the intrinsic dimensionality of the underlying function, thereby mitigating the curse of dimensionality. Our analysis shows that Bayesian neural networks equipped with either sparse or continuous shrinkage priors attain the optimal rates which are dependent on the intrinsic dimension of the true structures. Moreover, we show that these priors enable rate adaptation, allowing the posterior to contract at the optimal rate even when the smoothness level of the true function is unknown. The proposed framework accommodates a broad class of functions, including additive and multiplicative Besov functions as special cases. These results advance the theoretical foundations of Bayesian neural networks and provide rigorous justification for their practical effectiveness in high-dimensional, structured estimation problems.

Large language models (LLMs) have demonstrated remarkable reasoning capabilities through test-time scaling approaches, particularly when fine-tuned with chain-of-thought (CoT) data distilled from more powerful large reasoning models (LRMs). However, these reasoning chains often contain verbose elements that mirror human problem-solving, categorized as progressive reasoning (the essential solution development path) and functional elements (verification processes, alternative solution approaches, and error corrections). While progressive reasoning is crucial, the functional elements significantly increase computational demands during test-time inference. We introduce PIR (Perplexity-based Importance Refinement), a principled framework that quantitatively evaluates the importance of each reasoning step based on its impact on answer prediction confidence. PIR systematically identifies and selectively prunes only low-importance functional steps while preserving progressive reasoning components, creating optimized training data that maintains the integrity of the core solution path while reducing verbosity. Models fine-tuned on PIR-optimized data exhibit superior test-time scaling properties, generating more concise reasoning chains while achieving improved accuracy (+0.9% to +6.6%) with significantly reduced token usage (-3% to -41%) across challenging reasoning benchmarks (AIME, AMC, and GPQA Diamond). Our approach demonstrates strong generalizability across different model sizes, data sources, and token budgets, offering a practical solution for deploying reasoningcapable LLMs in scenarios where efficient test-time scaling, response time, and computational efficiency are valuable constraints. Code and dataset are available at the LIMOPro.

Recent studies have uncovered an interesting phenomenon: unimodal foundation models tend to learn convergent representations, regardless of differences in architecture, training objectives, or data modalities. However, these representations are essentially internal abstractions of samples that characterize samples independently, leading to limited expressiveness. In this paper, we propose The Indra Representation Hypothesis, inspired by the philosophical metaphor of Indra's Net. We argue that representations from unimodal foundation models are converging to implicitly reflect a shared relational structure underlying reality, akin to the relational ontology of Indra's Net.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of'flows' - one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

We study the problem of differentially private second moment estimation and present a new algorithm that achieve strong privacy-utility trade-offs even for worst-case inputs under subsamplability assumptions on the data. We call an input (m,α,β)-subsamplable if a random subsample of size m(or larger) preserves w.p 1 β the spectral structure of the original second moment matrix up to a multiplicative factor of 1 α. Building upon subsamplability, we give a recursive algorithmic framework similar to Kamath et al. (2019) that abides zero-Concentrated Differential Privacy (zCDP) while preserving w.h.p the accuracy of the second moment estimation upto an arbitrary factor of (1 γ). We then show how to apply our algorithm to approximate the second moment matrix of a distribution D, even when a noticeable fraction of the input are outliers.