arXiv subjects

Yuejie Chi

Publications and source records attributed to Yuejie Chi.

At least 19 recordsLinked to original sources

arXiv2026

Robust Average-Reward Markov Decision Processes: Minimax-Optimal Learning via Plug-in Reductions

Distributionally robust Markov decision processes provide a principled framework for sequential decision making under model uncertainty. We study how many samples are necessary and sufficient to learn an $\varepsilon$-optimal robust policy under the average-reward criterion. A generative model provides samples from the nominal transition kernel, whereas policy performance is evaluated over $(s,a)$-rectangular total-variation uncertainty sets of radius at most $σ$. Let $H_0$ and $H_σ$ denote the nominal and robust optimal bias spans, respectively. We identify $σH_0$ as the perturbation scale separating high- and low-tolerance regimes. Our matching upper and lower bounds show that, up to logarithmic factors, the minimax total sample complexity is $$ NSA \asymp \frac{SA}{\varepsilon^2}\begin{cases} \min\{H_0,H_σ\}, & \varepsilon\gtrsimσH_0,\\ \min\{H_0,H_σ\}+σH_σ^2, & \varepsilon\lesssimσH_0. \end{cases} $$ Here $S$ and $A$ are the numbers of states and actions, and $N$ is the number of samples per state-action pair. The sample complexity consists of a linear-span term that resembles the nominal AMDP results and a robustness-specific term that appears only in the low-tolerance regime. We attain these rates using reduction-based plug-in procedures that select the reduction---nominal or robust---and its discount factor: a span-informed procedure that makes these choices using known span parameters, and a span-agnostic procedure that calibrates both choices from data.

cs.LG↗

arXiv2026

On the Emergence of Implicit Curriculum in RLVR Learning Dynamics

Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier to extended reasoning. To understand this, we develop a theory of the training dynamics of RLVR for transformers on compositional reasoning tasks. Our theory shows that mixed-difficulty training naturally induces an implicit curriculum: without any explicit schedule, easier problems become learnable first and shape the frontier for harder ones, creating a learning progression from easy to hard during optimization. The effectiveness of this curriculum is governed by the smoothness of the difficulty spectrum. When the spectrum is smooth, training dynamics enter a well-behaved relay regime, in which persistent gradient signals on easier problems make slightly harder ones tractable and keep training at the edge of competence. When the spectrum contains abrupt discontinuities, training undergoes grokking-type phase transitions with prolonged plateaus before progress recurs. As a technical contribution, our analysis develops and adapts techniques from Fourier analysis on finite groups to our setting. We validate the predicted mechanisms empirically via controlled synthetic experiments and real-model RLVR runs.

cs.LG↗

arXiv2026

Agentic Transformers Provably Learn to Search via Reinforcement Learning

Tree search is a central abstraction behind many language-agent reasoning and decision-making tasks: agents must explore actions, remember failures, and backtrack toward promising alternatives. Yet, we lack a theoretical understanding of how transformer-based policies acquire such search capabilities from the training dynamics of reinforcement learning (RL). We study this question in a stochastic $k$-ary tree environment, where an agentic transformer observes only its trajectory history through interaction and receives a terminal reward for reaching a hidden leaf goal node. We first construct a two-head transformer that implements randomized depth-first search (DFS): one head tracks previous actions, while the other detects failure outcomes and triggers backtracking. We then analyze the training dynamics of policy gradient under a depth-wise curriculum, showing that this same DFS mechanism emerges in stages from sparse reinforcement feedback without expert demonstrations. The resulting policy exhibits depth generalization: after training only on depth-$1$ and depth-$2$ trees, it succeeds on deeper full trees. We further show that, under imbalanced goal distributions, discounting the return leads to a ranked DFS policy that prioritizes higher-probability branches. Overall, our results identify a mechanistic normal form for transformer-based search, in which attention heads specialize and cooperate to extract decision-relevant traces from context and convert them into agentic action selection via RL training.

cs.LG↗

arXiv2026

Multimodal Diffusion to Mutually Enhance Polarized Light and Low Resolution EBSD Data

In spite of the utility of 3-D electron back-scattered diffraction (EBSD) microscopy, the data collection process can be time-consuming with serial-sectioning. Hence, it is natural to look at other modalities, such as polarized light (PL) data, to accelerate EBSD data collection, supplemented with shared information. Complementarily, features in chaotic PL data could even be enriched with a handful of EBSD measurements. To inherently learn the complex dynamics between EBSD and PL to solve these inverse problems, we use an unconditional multimodal diffusion model, motivated by progress in diffusion models for inverse problems. Although trained solely on synthetic data once, our model has strong generalizable capabilities on real data which can be low-resolution, noisy, corrupted, and misregistered. With inference-time scaling, we show gains in performance on a variety of objectives including grain boundary prediction, super-resolution, and denoising. With our model, we demonstrate that there is little difference from full resolution performance with only 25% (1/4 the resolution) of EBSD data and corrupted PL data.

eess.IV↗

arXiv2026

Feynman: Knowledge-Infused Diagramming Agent for Scalable Visual Designs

Visual design is an essential application of state-of-the-art multi-modal AI systems. Improving these systems requires high-quality vision-language data at scale. Despite the abundance of internet image and text data, knowledge-rich and well-aligned image-text pairs are rare. In this paper, we present a scalable diagram generation pipeline built with our agent, Feynman. To create diagrams, Feynman first enumerates domain-specific knowledge components (''ideas'') and performs code planning based on the ideas. Given the plan, Feynman translates ideas into simple declarative programs and iterates to receives feedback and visually refine diagrams. Finally, the declarative programs are rendered by the Penrose diagramming system. The optimization-based rendering of Penrose preserves the visual semantics while injecting fresh randomness into the layout, thereby producing diagrams with visual consistency and diversity. As a result, Feynman can author diagrams along with grounded captions with very little cost and time. Using Feynman, we synthesized a dataset with more than 100k well-aligned diagram-caption pairs. We also curate a visual-language benchmark, Diagramma, from freshly generated data. Diagramma can be used for evaluating the visual reasoning capabilities of vision-language models. We plan to release the dataset, benchmark, and the full agent pipeline as an open-source project.

cs.LG↗

arXiv2026

Diffusion Controller: Framework, Algorithms and Parameterization

Controllable diffusion generation often relies on various heuristics that are seemingly disconnected without a unified understanding. We bridge this gap with Diffusion Controller (DiffCon), a unified control-theoretic view that casts reverse diffusion sampling as state-only stochastic control within (generalized) linearly-solvable Markov Decision Processes (LS-MDPs). Under this framework, control acts by reweighting the pretrained reverse-time transition kernels, balancing terminal objectives against an $f$-divergence cost. From the resulting optimality conditions, we derive practical reinforcement learning methods for diffusion fine-tuning: (i) f-divergence-regularized policy-gradient updates, including a PPO-style rule, and (ii) a regularizer-determined reward-weighted regression objective with a minimizer-preservation guarantee under the Kullback-Leibler (KL) divergence. The LS-MDP framework further implies a principled model form: the optimal score decomposes into a fixed pretrained baseline plus a lightweight control correction, motivating a side-network parameterization conditioned on exposed intermediate denoising outputs, enabling effective gray-box adaptation with a frozen backbone. Experiments on Stable Diffusion v1.4 across supervised and reward-driven finetuning show consistent gains in preference-alignment win rates and improved quality-efficiency trade-offs versus gray-box baselines and even the parameter-efficient white-box adapter LoRA.

cs.LG↗

arXiv2026

Scalable LLM Reasoning Acceleration with Low-rank Distillation

Due to long generations, large language model (LLM) math reasoning demands significant computational resources and time. While many existing efficient inference methods have been developed with excellent performance preservation on language tasks, they often severely degrade math performance. In this paper, we propose Caprese, a resource-efficient distillation method to recover lost capabilities from deploying efficient inference methods, focused primarily in feedforward blocks. With original weights unperturbed, roughly 1% of additional parameters, and only 20K synthetic training samples, we are able to recover much if not all of the reasoning capabilities lost from efficient inference for thinking LLMs and without harm to language tasks for instruct LLMs. Moreover, Caprese slashes the number of active parameters (~2B cut for Gemma 2 9B and Llama 3.1 8B) and integrates cleanly into existing model layers to reduce latency (>16% time-to-next-token reduction) while encouraging response brevity (up to 8.5% fewer tokens).

cs.CL↗

arXiv2026

Generalized Parallel Scaling with Interdependent Generations

Parallel LLM inference scaling involves sampling a set of $N>1$ responses for a single input prompt. However, these $N$ parallel responses tend to be generated independently from each other, partitioning compute resources and leaving potentially useful information in one generation untapped by others. This is in contrast to response length scaling where past computation is used in all future steps. For higher quality responses and response sets, we propose Bridge to generate interdependent responses in parallel by rethinking batched LLM hidden states as holistic tensors rather than independent slices. With only a small amount (2.8%-5.1%) of new parameters, Bridge improves the relative mean accuracy gains from reinforcement learning with verifiable rewards by up to 39% and boosts consistency of correct responses. Trained once, Bridge scales to any generation width, all with greater performance than independent generations, unlocking a more general mode of parallel scaling that effectively leverages information between sequences, compatible with any post-generation aggregation technique.

cs.AI↗

arXiv2026

A Multi-Token Coordinate Descent Method for Semi-Decentralized Vertical Federated Learning

Most federated learning (FL) methods use a client-server scheme, where clients communicate only with a central server. However, this scheme is prone to bandwidth bottlenecks at the server and has a single point of failure. In contrast, in a (fully) decentralized approach, clients communicate directly with each other, dispensing with the server and mitigating these issues. Yet, as the client network grows larger and sparser, the convergence of decentralized methods slows down, even failing to converge if the network is disconnected. This work addresses this gap between client-server and decentralized schemes, focusing on the vertical FL setup, where clients hold different features of the same samples. We propose multi-token coordinate descent (MTCD), a flexible semi-decentralized method for vertical FL that can exploit both client-server and client-client links. By selecting appropriate hyperparameters, MTCD recovers the client-sever and decentralized schemes as special cases. In fact, its decentralized instance is itself a novel method of independent interest. Yet, by controlling the degree of dependency on client-server links, MTCD can also explore a spectrum of schemes ranging from client-server to decentralized. We prove that, for sufficiently large batch sizes, MTCD converges at an $\mathcal{O}(1/T)$ rate for nonconvex objectives when the tokens roam across disjoint subsets of clients. To capture the aforementioned drawbacks of the client-server scheme succinctly, we model the relative impact of using client-server versus client-client links as the ratio of their "costs", which depends on the application. This allows us to demonstrate, both analytically and empirically, that by tuning the degree of dependency on the server, the semi-decentralized instances of MTCD can outperform both client-server and decentralized approaches across a range of applications.

cs.LG↗

arXiv2026

Provably Efficient and Agile Randomized Q-Learning

While Bayesian-based exploration often demonstrates superior empirical performance compared to bonus-based methods in model-based reinforcement learning (RL), its theoretical understanding remains limited for model-free settings. Existing provable algorithms either suffer from computational intractability or rely on stage-wise policy updates which reduce responsiveness and slow down the learning process. In this paper, we propose a novel variant of Q-learning algorithm, refereed to as RandomizedQ, which integrates sampling-based exploration with agile, step-wise, policy updates, for episodic tabular RL. We establish an $\widetilde{O}(\sqrt{H^5SAT})$ regret bound, where $S$ is the number of states, $A$ is the number of actions, $H$ is the episode length, and $T$ is the total number of episodes. In addition, we present a logarithmic regret bound under a mild positive sub-optimality condition on the optimal Q-function. Empirically, RandomizedQ exhibits outstanding performance compared to existing Q-learning variants with both bonus-based and Bayesian-based exploration on standard benchmarks.

cs.LG↗

arXiv2026

Achieving Logarithmic Regret in KL-Regularized Zero-Sum Markov Games

Reverse Kullback-Leibler (KL) divergence-based regularization with respect to a fixed reference policy is widely used in modern reinforcement learning to preserve the desired traits of the reference policy and sometimes to promote exploration (using uniform reference policy, known as entropy regularization). Beyond serving as a mere anchor, the reference policy can also be interpreted as encoding prior knowledge about good actions in the environment. In the context of alignment, recent game-theoretic approaches have leveraged KL regularization with pretrained language models as reference policies, achieving notable empirical success in self-play methods. Despite these advances, the theoretical benefits of KL regularization in game-theoretic settings remain poorly understood. In this work, we develop and analyze algorithms that provably achieve improved sample efficiency under KL regularization. We study both two-player zero-sum matrix games and Markov games: for matrix games, we propose OMG, an algorithm based on best response sampling with optimistic bonuses, and extend this idea to Markov games through the algorithm SOMG, which also uses best response sampling and a novel concept of superoptimistic bonuses. Both algorithms achieve a logarithmic regret in $T$ that scales inversely with the KL regularization strength $β$ in addition to the traditional $\widetilde{\mathcal{O}}(\sqrt{T})$ regret without the $β^{-1}$ dependence.

cs.LG↗

arXiv2026

Preconditioning Benefits of Spectral Orthogonalization in Muon

The Muon optimizer, a matrix-structured algorithm that leverages spectral orthogonalization of gradients, is a milestone in the pretraining of large language models. However, the underlying mechanisms of Muon -- particularly the role of gradient orthogonalization -- remain poorly understood, with very few works providing end-to-end analyses that rigorously explain its advantages in concrete applications. We take a step by studying the effectiveness of a simplified variant of Muon through two case studies: matrix factorization, and in-context learning of linear transformers. For both problems, we prove that simplified Muon converges linearly with iteration complexities independent of the relevant condition number, provably outperforming gradient descent and Adam. Our analysis reveals that the Muon dynamics decouple into a collection of independent scalar sequences in the spectral domain, each exhibiting similar convergence behavior. Our theory formalizes the preconditioning effect induced by spectral orthogonalization, offering insight into Muon's effectiveness in these matrix optimization problems and potentially beyond.

cs.LG↗

arXiv2026

Sample Complexity of Average-Reward Q-Learning: From Single-agent to Federated Reinforcement Learning

Average-reward reinforcement learning offers a principled framework for long-term decision-making by maximizing the mean reward per time step. Although Q-learning is a widely used model-free algorithm with established sample complexity in discounted and finite-horizon Markov decision processes (MDPs), its theoretical guarantees for average-reward settings remain limited. This work studies a simple but effective Q-learning algorithm for average-reward MDPs with finite state and action spaces under the weakly communicating assumption, covering both single-agent and federated scenarios. For the single-agent case, we show that Q-learning with carefully chosen parameters achieves sample complexity $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{\varepsilon^3}\right)$, where $\|h^{\star}\|_{\mathsf{sp}}$ is the span norm of the bias function, improving previous results by at least a factor of $\frac{\|h^{\star}\|_{\mathsf{sp}}^2}{\varepsilon^2}$. In the federated setting with $M$ agents, we prove that collaboration reduces the per-agent sample complexity to $\widetilde{O}\left(\frac{|\mathcal{S}||\mathcal{A}|\|h^{\star}\|_{\mathsf{sp}}^3}{M\varepsilon^3}\right)$, with only $\widetilde{O}\left(\frac{\|h^{\star}\|_{\mathsf{sp}}}{\varepsilon}\right)$ communication rounds required. These results establish the first federated Q-learning algorithm for average-reward MDPs, with provable efficiency in both sample and communication complexity.

stat.ML↗

arXiv2026

Polynomial Convergence of Riemannian Diffusion Models

Diffusion models have demonstrated remarkable empirical success in the recent years and are considered one of the state-of-the-art generative models in modern AI. These models consist of a forward process, which gradually diffuses the data distribution to a noise distribution spanning the whole space, and a backward process, which inverts this transformation to recover the data distribution from noise. Most of the existing literature assumes that the underlying space is Euclidean. However, in many practical applications, the data are constrained to lie on a submanifold of Euclidean space. Addressing this setting, De Bortoli et al. (2022) introduced Riemannian diffusion models and proved that using an exponentially small step size yields a small sampling error in the Wasserstein distance, provided the data distribution is smooth and strictly positive, and the score estimate is $L_\infty$-accurate. In this paper, we greatly strengthen this theory by establishing that, under $L_2$-accurate score estimate, a {\em polynomially small stepsize} suffices to guarantee small sampling error in the total variation distance, without requiring smoothness or positivity of the data distribution. Our analysis only requires mild and standard curvature assumptions on the underlying manifold. The main ingredients in our analysis are Li-Yau estimate for the log-gradient of heat kernel, and Minakshisundaram-Pleijel parametrix expansion of the perturbed heat equation. Our approach opens the door to a sharper analysis of diffusion models on non-Euclidean spaces.

cs.LG↗

arXiv2026

Beyond Expectations: Learning with Stochastic Dominance Made Practical

Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying uncertainty, in contrast to simply resorting to the expectations. Despite theoretical appeal, the application of stochastic dominance in machine learning has been scarce, due to the following challenges: $\textbf{i)}$, the original concept of stochastic dominance only provides a $\textit{partial order}$, and therefore, is not amenable to serve as a general optimality criterion; and $\textbf{ii)}$, an efficient computational recipe remains lacking due to the continuum nature of evaluating stochastic dominance. In this work, we make the first attempt towards establishing a general framework of learning with stochastic dominance. We first generalize the stochastic dominance concept to enable feasible comparisons between any arbitrary pair of random variables. We next develop a simple and computationally efficient approach for finding the optimal solution in terms of stochastic dominance, which can be seamlessly plugged into many learning tasks. Numerical experiments demonstrate that the proposed method achieves comparable performance as standard risk-neutral strategies and obtains better trade-offs against risk across a variety of applications including supervised learning, reinforcement learning, and portfolio optimization.

cs.LG↗

arXiv2025

The Power of Preconditioning in Overparameterized Low-Rank Matrix Sensing

We propose $\textsf{ScaledGD($λ$)}$, a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, $\textsf{ScaledGD($λ$)}$ starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, $\textsf{ScaledGD($λ$)}$ is remarkably robust to ill-conditioning compared to vanilla gradient descent ($\textsf{GD}$) even with overprameterization. Specifically, we show that, under the Gaussian design, $\textsf{ScaledGD($λ$)}$ converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla $\textsf{GD}$ which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

cs.LG↗

arXiv2025

Multi-head Transformers Provably Learn Symbolic Multi-step Reasoning via Gradient Descent

Transformers have demonstrated remarkable capabilities in multi-step reasoning tasks. However, understandings of the underlying mechanisms by which they acquire these abilities through training remain limited, particularly from a theoretical standpoint. This work investigates how transformers learn to solve symbolic multi-step reasoning problems through chain-of-thought processes, focusing on path-finding in trees. We analyze two intertwined tasks: a backward reasoning task, where the model outputs a path from a goal node to the root, and a more complex forward reasoning task, where the model implements two-stage reasoning by first identifying the goal-to-root path and then reversing it to produce the root-to-goal path. Our theoretical analysis, grounded in the dynamics of gradient descent, shows that trained one-layer transformers can provably solve both tasks with generalization guarantees to unseen trees. In particular, our multi-phase training dynamics for forward reasoning elucidate how different attention heads learn to specialize and coordinate autonomously to solve the two subtasks in a single autoregressive path. These results provide a mechanistic explanation of how trained transformers can implement sequential algorithmic procedures. Moreover, they offer insights into the emergence of reasoning abilities, suggesting that when tasks are structured to take intermediate chain-of-thought steps, even shallow multi-head transformers can effectively solve problems that would otherwise require deeper architectures.

cs.LG↗

arXiv2025

Transformers Provably Learn Chain-of-Thought Reasoning with Length Generalization

The ability to reason lies at the core of artificial intelligence (AI), and challenging problems usually call for deeper and longer reasoning to tackle. A crucial question about AI reasoning is whether models can extrapolate learned reasoning patterns to solve harder tasks with longer chain-of-thought (CoT). In this work, we present a theoretical analysis of transformers learning on synthetic state-tracking tasks with gradient descent. We mathematically prove how the algebraic structure of state-tracking problems governs the degree of extrapolation of the learned CoT. Specifically, our theory characterizes the length generalization of transformers through the mechanism of attention concentration, linking the retrieval robustness of the attention layer to the state-tracking task structure of long-context reasoning. Moreover, for transformers with limited reasoning length, we prove that a recursive self-training scheme can progressively extend the range of solvable problem lengths. To our knowledge, we provide the first optimization guarantee that constant-depth transformers provably learn $\mathsf{NC}^1$-complete problems with CoT, significantly going beyond prior art confined in $\mathsf{TC}^0$, unless the widely held conjecture $\mathsf{TC}^0 \neq \mathsf{NC}^1$ fails. Finally, we present a broad set of experiments supporting our theoretical results, confirming the length generalization behaviors and the mechanism of attention concentration.

cs.LG↗