Yu-Xiang Wang
Publications
Learnable Chernoff Baselines for Inference-Time Alignment
We study inference-time reward-guided alignment for generative models. Existing methods often rely on either architecture-specific adaptations or computationally costly inference procedures. We introduce Learnable Chernoff Baselines (LCBs) as a method for efficiently and approximately sampling from the exponentially tilted kernels that arise from KL-regularized reward alignment. Using only black-box sampling access to the pretrained model, LCBs implement a form of rejection sampling with adaptively selected acceptance probabilities, which allows fine-grained control over inference-compute scaling. We establish total-variation guarantees to the ideal aligned model, and demonstrate in both continuous and discrete diffusion settings that LCB sampling closely matches ideal rejection sampling while using substantially fewer queries to the pretrained model.
ConvexBench: Can LLMs Recognize Convex Functions?
Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with convexity. We introduce \cb, a scalable and mechanically verifiable benchmark for testing \textit{whether LLMs can identify the convexity of a symbolic objective under deep functional composition.} Experiments on frontier LLMs reveal a sharp compositional reasoning gap: performance degrades rapidly with increasing depth, dropping from an F1-score of $1.0$ at depth $2$ to approximately $0.2$ at depth $100$. Inspection of models' reasoning traces indicates two failure modes: \textit{parsing failure} and \textit{lazy reasoning}. To address these limitations, we propose an agentic divide-and-conquer framework that (i) offloads parsing to an external tool to construct an abstract syntax tree (AST) and (ii) enforces recursive reasoning over each intermediate sub-expression with focused context. This framework reliably mitigates deep-composition failures, achieving substantial performance improvement at large depths (e.g., F1-Score $= 1.0$ at depth $100$).
ConvexBench: Can LLMs Recognize Convex Functions?
Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with convexity. We introduce \cb, a scalable and mechanically verifiable benchmark for testing \textit{whether LLMs can identify the convexity of a symbolic objective under deep functional composition.} Experiments on frontier LLMs reveal a sharp compositional reasoning gap: performance degrades rapidly with increasing depth, dropping from an F1-score of $1.0$ at depth $2$ to approximately $0.2$ at depth $100$. Inspection of models' reasoning traces indicates two failure modes: \textit{parsing failure} and \textit{lazy reasoning}. To address these limitations, we propose an agentic divide-and-conquer framework that (i) offloads parsing to an external tool to construct an abstract syntax tree (AST) and (ii) enforces recursive reasoning over each intermediate sub-expression with focused context. This framework reliably mitigates deep-composition failures, achieving substantial performance improvement at large depths (e.g., F1-Score $= 1.0$ at depth $100$).