Zhenya Huang
Publications
MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research
Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition. In this paper, we propose MathCoPilot, a human-in-the-loop system that embodies a new human--AI symbiotic paradigm for mathematical research, in which the mathematician steers the high-level mathematical direction while AI agents carry out the detailed formalization and proof work under continuous human guidance. MathCoPilot unifies three core capabilities: (1) an interactive workbench where the mathematician and AI agents collaborate through a living proof blueprint that decomposes a proof into navigable steps the human can directly inspect, direct, and refine; (2) automated proving skill orchestration with adaptive knowledge base search and Lean-integrated iterative verification; and (3) topic-driven paper retrieval and automated formalization into a verified Lean knowledge base. Using MathCoPilot, we systematically compare four state-of-the-art LLMs, including Gemini~3.1~Pro, GPT-5.4, and Claude~Opus~4.7, on a FormalMATH subset and on two real PDE theorems requiring deep domain expertise, evaluating their ability to produce verified Lean~4 proofs and to identify errors in deliberately incorrect proofs. Our results show that while current models can handle undergraduate-level problems with high success rates under favorable autoformalization conditions, substantial challenges remain for domain-specific theorems requiring genuine mathematical understanding.
UniCog: Uncovering Cognitive Abilities of LLMs through Latent Mind Space Analysis
A growing body of research suggests that the cognitive processes of large language models (LLMs) differ fundamentally from those of humans. However, existing interpretability methods remain limited in explaining how cognitive abilities are engaged during LLM reasoning. In this paper, we propose UniCog, a unified framework that analyzes LLM cognition via a latent mind space. Formulated as a latent variable model, UniCog encodes diverse abilities from dense model activations into sparse, disentangled latent dimensions. Through extensive analysis on six advanced LLMs, including DeepSeek-V3.2 and GPT-4o, we reveal a Pareto principle of LLM cognition, where a shared reasoning core is complemented by ability-specific signatures. Furthermore, we discover that reasoning failures often manifest as anomalous intensity in latent activations. These findings opens a new paradigm in LLM analysis, providing a cognition grounded view of reasoning dynamics. Finally, leveraging these insights, we introduce a latent-informed candidate prioritization strategy, which improves reasoning performance by up to 7.5% across challenging benchmarks. Our code is available at https://github.com/milksalute/unicog.