Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib’s definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework. We introduce TaoAnalysisBench, an undergraduate-level benchmark derived from the exercises and definitional frameworks given in Terence Tao’s Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoAnalysisBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of 2.18x on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoAnalysisBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.

Large language models (LLMs) are increasingly adept at solving complex problems, such as mathematical reasoning and automatic evaluation. However, performance often degrades when prompts intertwine task instructions with rigid formatting requirements. This entanglement creates competing goals for the model, hindering its reasoning capabilities. To address this, we introduce Deco-G, a decoding framework that explicitly decouples format adherence from problem solving. Deco-G delegates format adherence to a separate Format Estimation Module (FEM), which performs probabilistic lookahead to estimate future format compliance rate and reweighs token probabilities, allowing the LLM to focus solely on task resolution. To make this approach both practical and efficient, we introduce three key innovations: instruction-aware distillation, a flexible trie-building algorithm, and HMM state pruning. Experiments across mathematical reasoning, event argument extraction, and LLM-as-a-judge demonstrate that Deco-G constantly gains over prompting or structured generation baselines, with guaranteed format compliance.

While large language models have proven effective in a huge range of downstream applications, they often generate text that is problematic or lacks a desired attribute. In this paper, we introduce Reward-Augmented Decoding (RAD), a text generation procedure that uses a small unidirectional reward model to encourage a language model to generate text that has certain properties. Specifically, RAD uses the reward model to score generations as they are produced and rescales sampling probabilities to favor high-reward tokens. By using a unidirectional reward model, RAD can cache activations from prior generation steps to decrease computational overhead. Through experiments on generating non-toxic and sentiment-controlled text, we demonstrate that RAD performs best among methods that change only the generation procedure and matches the performance of state-of-the-art methods that involve re-training the language model. We further validate that RAD is effective on very large language models while incurring a minimal computational overhead.