Sizhe Tang
Publications
The Topology of Ill-Posed Questions: Persistent Homology for Detection and Steering in LLMs
Ill-posed questions, including ambiguous, underspecified, or contradictory queries, may admit no valid answer or multiple plausible answers, posing a challenge for large language models (LLMs). Existing approaches largely analyze ill-posedness through model outputs and often focus on specific subclasses. We investigate whether diverse sources of ill-posedness can be represented within a unified topology of LLM internal states and whether this structure can be used to steer response behavior. We model the contextual hidden states of prompt tokens at each transformer layer as a point cloud and characterize its geometry using finite zero-dimensional persistent homology. Each layer is summarized by three compact descriptors: mean finite lifetime, normalized lifetime entropy, and largest-lifetime concentration. Concatenating these descriptors across layers yields a topology representation of the question. We further introduce topology-conditioned activation steering, which retrieves topologically similar examples and constructs query-specific activation interventions that encourage source-aware clarification or abstention. Across three open-weight LLMs, topology features consistently outperform prompt-based and pooled-hidden-state baselines for ill-posedness classification, improving average accuracy from \(67.4\%\) to \(78.9\%\) on AmbigQA, from \(79.9\%\) to \(88.5\%\) on SituatedQA, and from \(57.6\%\) to \(69.6\%\) on CLAMBER 9-way classification. Topology-conditioned steering increases the average total acceptable response rate from \(61.4\%\) to \(70.6\%\) and grounded acceptable responses from \(11.9\%\) to \(16.4\%\). These results show that persistent homology provides both an interpretable representation of ill-posedness and an effective mechanism for targeted response steering.
Reason in Chains, Learn in Trees: Self-Rectification and Grafting for Multi-turn Agent Policy Optimization
Reinforcement learning for Large Language Model agents is often hindered by sparse rewards in multi-step reasoning tasks. Existing approaches like Group Relative Policy Optimization treat sampled trajectories as independent chains, assigning uniform credit to all steps in each chain and ignoring the existence of critical steps that may disproportionally impact reasoning outcome. In this paper, we propose T-STAR(Tree-structured Self-Taught Agent Rectification), a framework that recovers the latent correlated reward structure across seemingly independent trajectories. Specifically, we consolidate trajectories into a unified Cognitive Tree by identifying and merging functionally similar steps/nodes. It enables an Introspective Valuation mechanism that back-propagates trajectory-level rewards through the tree to obtain a new notion of variance-reduced relative advantage at step-level. Using the Cognitive Tree, we also develop In-Context Thought Grafting to synthesize corrective reasoning by contrasting successful and failed branches at critical divergence points/steps. Our proposed Surgical Policy Optimization then capitalizes on the rich policy gradient information concentrated at these critical points/steps through a Bradley-Terry type of surgical loss. Extensive experiments across embodied, interactive, reasoning, and planning benchmarks demonstrate that T-STAR achieves consistent improvements over strong baselines, with gains most pronounced on tasks requiring extended reasoning chains.
IntentScore: Intent-Conditioned Action Evaluation for Computer-Use Agents
Computer-Use Agents (CUAs) leverage large language models to execute GUI operations on desktop environments, yet they generate actions without evaluating action quality, leading to irreversible errors that cascade through subsequent steps. We propose IntentScore, a plan-aware reward model that learns to score candidate actions from 398K offline GUI interaction steps spanning three operating systems. IntentScore trains with two complementary objectives: contrastive alignment for state-action relevance and margin ranking for action correctness. Architecturally, it embeds each candidate's planning intent in the action encoder, enabling discrimination between candidates with similar actions but different rationales. IntentScore achieves 97.5% pairwise discrimination accuracy on held-out evaluation. Deployed as a re-ranker for Agent S3 on OSWorld, an environment entirely unseen during training, IntentScore improves task success rate by 6.9 points, demonstrating that reward estimation learned from heterogeneous offline trajectories generalizes to unseen agents and task distributions.
Cochain Perspectives on Temporal-Difference Signals for Learning Beyond Markov Dynamics
Non-Markovian dynamics are commonly found in real-world environments due to long-range dependencies, partial observability, and memory effects. The Bellman equation that is the central pillar of Reinforcement learning (RL) becomes only approximately valid under Non-Markovian. Existing work often focus on practical algorithm designs and offer limited theoretical treatment to address key questions, such as what dynamics are indeed capturable by the Bellman framework and how to inspire new algorithm classes with optimal approximations. In this paper, we present a novel topological viewpoint on temporal-difference (TD) based RL. We show that TD errors can be viewed as 1-cochain in the topological space of state transitions, while Markov dynamics are then interpreted as topological integrability. This novel view enables us to obtain a Hodge-type decomposition of TD errors into an integrable component and a topological residual, through a Bellman-de Rham projection. We further propose HodgeFlow Policy Search (HFPS) by fitting a potential network to minimize the non-integrable projection residual in RL, achieving stability/sensitivity guarantees. In numerical evaluations, HFPS is shown to significantly improve RL performance under non-Markovian.
Agent Alpha: Tree Search Unifying Generation, Exploration and Evaluation for Computer-Use Agents
While scaling test-time compute through trajectory-level sampling has significantly improved Graphical User Interface (GUI) agents, the lack of regressive ability prevents the reuse of partial successes and the recovery from early missteps. In this paper, we introduce Agent Alpha, a unified framework that synergizes generation, exploration, and evaluation through step-level Monte Carlo Tree Search (MCTS). It enables active modeling or exploiting structures of the planning space. By integrating alpha-UCT guided search into the interaction loop, Agent Alpha enables deliberate planning, facilitating early pruning of suboptimal branches and efficient prefix reuse. We also employ comparison-driven evaluation to mitigate absolute scoring biases and diversity-constrained expansion to maintain a compact, informative search space. Regret bound of alpha-UCT is analyzed. On the OSWorld benchmark, Agent Alpha achieves a state-of-the-art success rate of $\sim 77\%$, significantly outperforming trajectory-level baselines under equivalent compute.