Skill assessment from video entails rating the quality of a person's physical performance and explaining what could be done better. Today's models specialize for an individual sport, and suffer from the high cost and scarcity of expert-level supervision across the long tail of sports. Towards closing that gap, we explore transferable video representations for skill assessment. Our CrossTrainer approach discovers skill-attributes--such as balance, control, and hand positioning--whose meaning transcends the boundaries of any given sport, then trains a multimodal language model to generate actionable feedback for a novel video, e.g., "lift hands more to generate more power" as well as its proficiency level, e.g., early expert. We validate the new model on multiple datasets for both cross-sport (transfer) and intra-sport (in-domain) settings, where it achieves gains up to 60% relative to the state of the art. By abstracting out the shared behaviors indicative of human skill, the proposed video representation generalizes substantially better than an array of existing techniques, enriching today's multimodal large language models.

As models grow larger and training them becomes expensive, it becomes increasingly important to scale training recipes not just to larger models and more data, but to do so in a compute-optimal manner that extracts maximal performance per unit of compute. While such scaling has been well studied for language modeling, reinforcement learning (RL) has received less attention in this regard. In this paper, we investigate compute scaling for online, value-based deep RL. These methods present two primary axes for compute allocation: model capacity and the update-to-data (UTD) ratio. Given a fixed compute budget, we ask: how should resources be partitioned across these axes to maximize data efficiency? Our analysis reveals a nuanced interplay between model size, batch size, and UTD. In particular, we identify a phenomenon we call TD-overfitting: increasing the batch quickly harms Q-function accuracy for small models, but this effect is absent in large models, enabling effective use of large batch size at scale. We provide a mental model for understanding this phenomenon and build guidelines for choosing batch size and UTD to optimize compute usage. Our findings provide a grounded starting point for compute-optimal scaling in deep RL, mirroring studies in supervised learning but adapted to TD learning.

Modern LLMs are increasingly deep, and depth correlates with performance, albeit with diminishing returns. However, do these models use their depth efficiently? Do they compose more features to create higher-order computations that are impossible in shallow models, or do they merely spread the same kinds of computation out over more layers? To address these questions, we analyze the residual stream of the Llama 3.1, Qwen 3, and OLMo 2 family of models. We find: First, comparing the output of the sublayers to the residual stream reveals that layers in the second half contribute much less than those in the first half, with a clear phase transition between the two halves.

We consider the problem of diversity maximization from the perspective of individual fairness: given a set $P$ of $n$ points in a metric space, we aim to extract a subset $S$ of size $k$ from $P$ so that (1) the diversity of $S$ is maximized and (2) $S$ is \emph{individually fair} in the sense that every point in $P$ has at least one of its $\frac{n}{k}$-nearest neighbors as its ``representative'' in $S$. We propose $\left(O(1), 3\right)$-bicriteria approximation algorithms for the individually fair variants of the three most common diversity maximization problems, namely, max-min diversification, max-sum diversification, and sum-min diversification. Specifically, the proposed algorithms provide a set of points where every point in the dataset finds a point within a distance at most $3$ times its distance to its $\frac{n}{k}$-nearest neighbor while achieving a diversity value at most $O(1)$ times lower than the optimal solution. Numerical experiments on real-world and synthetic datasets demonstrate that the proposed algorithms generate solutions that are individually fairer than those produced by unconstrained algorithms and incur only modest losses in diversity.

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies, remains challenging. Existing methods often rely on soft penalties or architectural biases that fail to guarantee hard constraints. In this work, we propose Physics-Constrained Flow Matching (PCFM), a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models. PCFM continuously guides the sampling process through physics-based corrections applied to intermediate solution states, while remaining aligned with the learned flow and satisfying physical constraints. Empirically, PCFM outperforms both unconstrained and constrained baselines on a range of PDEs, including those with shocks, discontinuities, and sharp features, while ensuring exact constraint satisfaction at the final solution. Our method provides a flexible framework for enforcing hard constraints in both scientific and general-purpose generative models, especially in applications where constraint satisfaction is essential.

Robotic manipulation systems benefit from complementary sensing modalities, where each provides unique environmental information. Point clouds capture detailed geometric structure, while RGB images provide rich semantic context. Current point cloud methods struggle to capture fine-grained detail, especially for complex tasks, which RGB methods lack geometric awareness, which hinders their precision and generalization. We introduce PointMapPolicy, a novel approach that conditions diffusion policies on structured grids of points without downsampling. The resulting data type makes it easier to extract shape and spatial relationships from observations, and can be transformed between reference frames. Yet due to their structure in a regular grid, we enable the use of established computer vision techniques directly to 3D data. Using xLSTM as a backbone, our model efficiently fuses the point maps with RGB data for enhanced multi-modal perception. Through extensive experiments on the RoboCasa and CALVIN benchmarks and real robot evaluations, we demonstrate that our method achieves state-of-the-art performance across diverse manipulation tasks.

Reinforcement learning from human feedback (RLHF) has demonstrated remarkable effectiveness in aligning large language models (LLMs) with human preferences. Many existing alignment approaches rely on the Bradley-Terry (BT) model assumption, which assumes the existence of a ground-truth reward for each prompt-response pair. However, this assumption can be overly restrictive when modeling complex human preferences. In this paper, we drop the BT model assumption and study LLM alignment under general preferences, formulated as a two-player game. Drawing on theoretical insights from learning in games, we integrate optimistic online mirror descent into our alignment framework to approximate the Nash policy. Theoretically, we demonstrate that our approach achieves an $\mathcal{O}(T^{-1})$ bound on the duality gap, improving upon the previous $\mathcal{O}(T^{-1/2})$ result. Meanwhile, it enjoys a linear convergence rate in the last iterate, a property not achieved by previous methods. More importantly, we implement our method and show through experiments that it outperforms state-of-the-art RLHF algorithms across multiple representative benchmarks.

Motion in the real world takes place in 3D space. Existing Frame Interpolation methods often estimate global receptive fields in 2D frame space. Due to the limitations of 2D space, these global receptive fields are limited, which makes it difficult to match object correspondences between frames, resulting in sub-optimal performance when handling large-motion scenarios. In this paper, we introduce a novel pipeline for exploring object correspondences based on differential surface theory. The differential surface coordinate system provides a better representation of the real world, enabling effective exploration of object correspondences. Specifically, the pipeline first transforms an input pair of video frames from the image coordinate system to the differential surface coordinate system. Subsequently, within this coordinate system, object correspondences are explored based on surface geometric properties and the surface uniqueness theorem.

Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To counteract the degradation in convergence associated with compressed communication, error feedback schemes---most notably EF and EF21---were introduced. In this work, we provide a tight analysis of both of these methods. Specifically, we find the Lyapunov function that yields the best possible convergence rate for each method---with matching lower bounds. This principled approach yields sharp performance guarantees and enables a rigorous, apples-to-apples comparison between EF, EF21, and compressed gradient descent. Our analysis is carried out in the simplified single-agent setting, which allows for clean theoretical insights and fair comparison of the underlying mechanisms.

Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by the Andrews--Curtis conjecture, we analyze how reinforcement learning agents handle problems of varying hardness. We also address many mathematical questions as a part of our study. Notably, we demonstrate the length reducibility of all but two presentations in the Akbulut--Kirby series (1981), and resolve various potential counterexamples in the Miller--Schupp series (1991), including three infinite subfamilies.