Topological Active Inference for Task Disambiguation

In open-ended domains, natural language instructions are often 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.