Guancheng Pan, Qixin Tan, Yang Yuan, Andrew Chi-Chih Yao
AI 速览：提出代数世界模型（AWM），将未知环境中的探索转化为可执行假设、范畴论引导的结构化模型，并在 Lean 4 中形式化证明可达性与不可能性。
AI has made remarkable progress in mathematics, solving challenging problems with machine-checkable proofs in Lean, yet typically relying on predefined mathematical definitions and formal specifications. This raises a natural question: can it reason rigorously about an unknown world? We introduce the Algebraic World Model (AWM), a framework that turns interaction with unfamiliar environments into explicit mathematical models supporting formal reasoning. AWM explores the environment and develops executable Python hypotheses, continually testing and revising them against observations. It then structures these hypotheses into typed objects and shared rules, simplifies their structure through category-theory-guided transformations, and formalizes the resulting model in Lean 4 to prove reachability and impossibility. AWM can formally prove that a goal is unreachable, even beyond explored trajectories. On two impossible game levels, it constructs closed, kernel-checked Lean proofs excluding every legal winning sequence in all six runs, while Claude Opus 5.5 and GPT-6 Astra, equipped with coding tools, produce none in twelve baseline runs. Four of AWM's six initial bounds are correct, compared with one for Opus 5.5 and none for GPT-6 Astra; given only feedback that a cheaper win exists, AWM revises its rules and constructs new proofs, reaching six of six correct bounds. Moreover, AWM produces interpretable mathematical models whose rules can be inspected and tested step by step. Across all 25 public ARC-AGI-3 games, these models enable Lean to replay the winning trajectories of all 183 levels and generalize beyond observed play, predicting unseen transitions and detecting changes in game mechanics. With Claude Opus 5, AWM clears all levels with a score of 99.9, while its certified winning trajectories use only 43% of the human baseline's actions.
ContextEcho: A Benchmark for Persona Drift in Long Agentic-Coding Sessions
Xianzhong Ding, Yangyang Yu, Changwei Liu, Bill Zhao, Le Chen, Tao Chen
AI 速览：作者提出 ContextEcho 基准与可复用测试框架，用于刻画长程智能体编程会话中编程助手人格的漂移现象。
Frontier language models are trained to exhibit stable programming assistant personas, yet those personas may drift over long agentic coding sessions in production. After a long real-world coding session, a model that hedges preferences in a fresh chat ("I don't have preferences") may instead express them directly ("Python -- the feedback loop is instant..."). Existing persona-stability studies focus on scripted chat of tens of turns, leaving long production coding sessions involving thousands of tool-using agent steps, repeated compaction, and hours of interaction largely uncharacterized. We introduce ContextEcho, a benchmark and reusable harness with a 25-probe identity suite, a snapshot-then-probe protocol that evaluates conversation state without perturbing the main session, judge-based and judge-free metrics, and a corpus of 57 long agentic-coding sessions collected with consent and redacted for release across Claude Code and Codex CLI. We use one representative session for a 23-model cross-provider study and all 57 sessions for corpus-scale trajectory analysis across frontier and open-weight models. Results show that persona drift occurs across providers and emerges early in real agentic interaction, while in-session compaction neither reliably resets nor amplifies it. A single-shot anchor restores the original assistant persona, though placebo controls suggest a generic register-reset effect. On same-task continuations, drifted prefixes improve tool-call fidelity -- which we attribute to retained task context rather than drift itself. In tool-free chat, however, the same prefixes break output-format contracts and inflate output length. These findings motivate ContextEcho as an open-source framework for auditing persona drift in long coding sessions without retraining.