Rui Yuan

Rui Yuan, Mykola Khandoga, Vinay Kumar Sankarapu

Policy optimization methods like Group Relative Policy Optimization (GRPO) and its variants have achieved strong results on mathematical reasoning and code generation tasks. Despite extensive exploration of reward processing strategies and training dynamics, all existing group-based methods exclusively use KL divergence for policy regularization, leaving the choice of divergence function unexplored. We introduce Group-Based Mirror Policy Optimization (GBMPO), a framework that extends group-based policy optimization to flexible Bregman divergences, including hand-designed alternatives (L2 in probability space) and learned neural mirror maps. On GSM8K mathematical reasoning, hand-designed ProbL2-GRPO achieves 86.7% accuracy, improving +5.5 points over the Dr. GRPO baseline. On MBPP code generation, neural mirror maps reach 60.1-60.8% pass@1, with random initialization already capturing most of the benefit. While evolutionary strategies meta-learning provides marginal accuracy improvements, its primary value lies in variance reduction ($\pm$0.2 versus $\pm$0.6) and efficiency gains (15% shorter responses on MBPP), suggesting that random initialization of neural mirror maps is sufficient for most practical applications. These results establish divergence choice as a critical, previously unexplored design dimension in group-based policy optimization for LLM reasoning.

Shifeng Xie, Rui Yuan, Simone Rossi et al.

In-context learning (ICL) in large language models (LLMs) is a striking phenomenon, yet its underlying mechanisms remain only partially understood. Previous work connects linear self-attention (LSA) to gradient descent (GD), this connection has primarily been established under simplified conditions with zero-mean Gaussian priors and zero initialization for GD. However, subsequent studies have challenged this simplified view by highlighting its overly restrictive assumptions, demonstrating instead that under conditions such as multi-layer or nonlinear attention, self-attention performs optimization-like inference, akin to but distinct from GD. We investigate how multi-head LSA approximates GD under more realistic conditions specifically when incorporating non-zero Gaussian prior means in linear regression formulations of ICL. We first extend multi-head LSA embedding matrix by introducing an initial estimation of the query, referred to as the initial guess. We prove an upper bound on the number of heads needed for ICL linear regression setup. Our experiments confirm this result and further observe that a performance gap between one-step GD and multi-head LSA persists. To address this gap, we introduce yq-LSA, a simple generalization of single-head LSA with a trainable initial guess yq. We theoretically establish the capabilities of yq-LSA and provide experimental validation on linear regression tasks, thereby extending the theory that bridges ICL and GD. Finally, inspired by our findings in the case of linear regression, we consider widespread LLMs augmented with initial guess capabilities, and show that their performance is improved on a semantic similarity task.

Zhe Huang, Simone Rossi, Rui Yuan et al.

Transformers have become a standard architecture in machine learning, demonstrating strong in-context learning (ICL) abilities that allow them to learn from the prompt at inference time. However, uncertainty quantification for ICL remains an open challenge, particularly in noisy regression tasks. This paper investigates whether ICL can be leveraged for distribution-free uncertainty estimation, proposing a method based on conformal prediction to construct prediction intervals with guaranteed coverage. While traditional conformal methods are computationally expensive due to repeated model fitting, we exploit ICL to efficiently generate confidence intervals in a single forward pass. Our empirical analysis compares this approach against ridge regression-based conformal methods, showing that conformal prediction with in-context learning (CP with ICL) achieves robust and scalable uncertainty estimates. Additionally, we evaluate its performance under distribution shifts and establish scaling laws to guide model training. These findings bridge ICL and conformal prediction, providing a theoretically grounded and new framework for uncertainty quantification in transformer-based models.