Theory research

The frontier

Polylogarithmic Nash regret achieved for any finite matrix game

The authors study Nash regret minimization in unknown finite matrix games with bandit payoff feedback and observed opponent actions. They develop Optimistic Payoff Balancing (OPB), which achieves instance-dependent O(log^2 T) Nash regret against arbitrary adaptive opponents, including games with nonunique equilibria. This resolves the open problem posed by Maiti et al. (2025), extending their polylogarithmic guarantee from 2x2 games to arbitrary finite dimensions.

Yuheng Zhang

Language models

Effective depth shows transformer layers are redundantly correlated

Gahtan et al. introduce effective depth, a scalar that treats a transformer's residual stream as a discrete-time process and measures how representation similarity decays with layer distance. Across 16 decoder-only LLMs, they find that effective depth is almost always below a closed-form reference that assumes maximally diverse orthogonal updates, suggesting that residual updates are strongly correlated.

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Efficiency & systems

Mentored decoding can trade small distribution shifts for better predictions

Tran-Thien and Nock formalize mentored decoding, in which a fast draft model’s tokens are accepted while the resulting distribution remains within a chosen distance of a larger target model. Their analysis shows how this controlled deviation can increase draft acceptance and, under boosting-style conditions, produce predictions better than the target’s rather than merely approximate it.

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Theory

Finite probe sets identify neural networks, but hidden activations make them far more informative

Sarangi et al. study when finite probe evaluations of a neural network suffice for learning neural functionals. They prove identification and universality results, show hidden-layer probes are strictly more informative than final-output probes, and introduce HiddenProbe, which achieves state-of-the-art performance on MLP and Transformer benchmarks.

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Reinforcement learning

Three diffusion RL methods unified as divergence-constrained reward maximizers

A unified theoretical framework reveals that three prominent regression-based diffusion reinforcement learning methods—DiffusionNFT, FlowAWR, and RAM—are each solutions to a divergence-constrained reward-maximization problem, differing only in the convex generator defining the constraint. The authors identify approximations in prior work and propose DiffusionRFT, which uses an exact sparsemax projection, leading to faster convergence, more stable training, and top performance.

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Theory

Unmodified posterior sampling achieves minimax regret in reinforcement learning

Goo and Hong prove that exact vanilla posterior sampling for reinforcement learning (PSRL) is minimax optimal in leading-order Bayesian regret for finite-horizon time-inhomogeneous tabular MDPs with unknown stochastic rewards, achieving the rate Õ(√(SAH³K)). They extend the same proof principle to linear-mixture MDPs, obtaining Õ(d√(H³K)). The key technical advance is a method to decouple the posterior-sampled model from its own continuation value using a common empirical transition reference and a Bellman-based variance argument.

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Language models

Geometry-aware LoRA optimization improves convergence across supervised and reinforcement learning

Ding, Zazo and Hensman introduce Rotated Manifold Optimization, or RoM, an optimizer designed around a symmetry in low-rank adaptation: many pairs of LoRA factors represent exactly the same weight update. Across supervised fine-tuning and reinforcement learning experiments, RoM converged faster and reached lower held-out loss than the compared LoRA optimizers, while producing better or comparable downstream performance.

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