12 papers
Non-Commutative Lie-Algebraic State-Space Models: Finite-Division Variety Laws, Semidirect Cascades, and Gradient Saddle Escape
Zeyu Jia
Structured state-space models (SSMs) achieve linear-time inference and logarithmic-time parallel training via associative scans, yet homogeneous diagonal transitions generate solva…
Port-Hamiltonian Latent Deliberation: Mitigating the Deliberation Drift Cliff in Test-Time Compute Scaling
Zeyu Jia
Test-time compute scaling has emerged as a cornerstone of advanced machine reasoning, yet performing iterative deliberation directly within continuous latent representation spaces…
Fixed-Capacity Causal Models with Parallel Recovery for GPU Lossless Compression
Zeyu Jia
GPU compression needs both dense complete frames and inexpensive checked recovery. We compare three causal representations under the same 512-row model budget, select before encodi…
Beyond Embedding Transfer: Component Roles in Grokking Transfer and Stability
Zeyu Jia
Warm-start transfer can make algorithmic tasks generalize rapidly, yet it is unclear which model components provide the gain and whether that gain remains stable under continued op…
A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity
Zeyu Jia, Yury Polyanskiy, Alexander Rakhlin
We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class…
Outcome-Based Online Reinforcement Learning: Algorithms and Fundamental Limits
Fan Chen, Zeyu Jia, Alexander Rakhlin +1
Reinforcement learning with outcome-based feedback faces a fundamental challenge: when rewards are only observed at trajectory endpoints, how do we assign credit to the right actio…
Trajectory Bellman Residual Minimization: A Simple Value-Based Method for LLM Reasoning
Yurun Yuan, Fan Chen, Zeyu Jia +2
Policy-based methods currently dominate reinforcement learning (RL) pipelines for large language model (LLM) reasoning, leaving value-based approaches largely unexplored. We revisi…
Do We Need to Verify Step by Step? Rethinking Process Supervision from a Theoretical Perspective
Zeyu Jia, Alexander Rakhlin, Tengyang Xie
As large language models have evolved, it has become crucial to distinguish between process supervision and outcome supervision -- two key reinforcement learning approaches to comp…
On the Minimax Regret of Sequential Probability Assignment via Square-Root Entropy
Zeyu Jia, Yury Polyanskiy, Alexander Rakhlin
We study the problem of sequential probability assignment under logarithmic loss, both with and without side information. Our objective is to analyze the minimax regret -- a notion…
How Does Variance Shape the Regret in Contextual Bandits?
Zeyu Jia, Jian Qian, Alexander Rakhlin +1
We consider realizable contextual bandits with general function approximation, investigating how small reward variance can lead to better-than-minimax regret bounds. Unlike in mini…
Offline Reinforcement Learning: Role of State Aggregation and Trajectory Data
Zeyu Jia, Alexander Rakhlin, Ayush Sekhari +1
We revisit the problem of offline reinforcement learning with value function realizability but without Bellman completeness. Previous work by Xie and Jiang (2021) and Foster et al.…
When is Agnostic Reinforcement Learning Statistically Tractable?
Zeyu Jia, Gene Li, Alexander Rakhlin +2
We study the problem of agnostic PAC reinforcement learning (RL): given a policy class , how many rounds of interaction with an unknown MDP (with a potentially large state and a…