Topological Active Inference for Task Disambiguation

In open-ended domains, natural language instructions are often \textit{underspecified}, mapping to multiple valid yet functionally distinct latent intents. Although Large Language Models (LLMs) excel at generation, their interactive disambiguation remains limited by *semantic blindness*: they may spend clarification turns distinguishing superficial syntactic variants rather than resolving substantive intent differences. We propose *Topological Active Inference* (TAI), a geometric framework that recasts task disambiguation as *intent-manifold contraction*. TAI uses *Persistent Homology* to recover persistent intent clusters from sampled solutions, filtering short-lived syntactic variations while preserving robust semantic structure under mild separability assumptions. It then synthesizes clarifying questions as semantic separators and selects them with *Topological Expected Information Gain* (TEIG), which optimizes uncertainty reduction over intent clusters rather than individual candidates. This reduces the effective hypothesis space from $N$ sampled solutions to $K$ latent intents and yields logarithmic interaction complexity $\mathcal{O}(\log K)$ under balanced-split conditions. Experiments across code, visualization, and navigation tasks show that TAI resolves user intent with fewer turns and remains robust to noisy feedback, and smaller model scales.

People often give AI assistants instructions that are incomplete or ambiguous. For example, a user may ask an assistant to “analyze this data” or “write a solution” without specifying the exact goal, format, constraints, or preferred approach. In such cases, an AI system may choose one possible interpretation too early and produce an answer that looks reasonable but does not match what the user actually wanted. This paper proposes TAI, a method that helps AI assistants clarify ambiguous tasks more effectively. Instead of treating every possible answer as completely separate, TAI groups possible answers according to their underlying meaning. It then asks clarification questions that separate genuinely different user intentions, rather than wasting questions on small wording or formatting differences. Experiments on coding, visualization, and navigation tasks show that TAI can identify the user’s intent with fewer interaction turns than standard methods. It is also more reliable when user feedback is noisy or uncertain, and it remains useful even with smaller language models. Overall, this work aims to make AI assistants better at asking the right questions before acting, reducing misunderstandings and improving reliability in interactive use.