HTCE: Homeomorphism-inspired Topological Cross-Scene Experience Canonicalization and Reuse for Object Navigation

Abstract

As embodied agents perform object-goal navigation across residential environments, they accumulate successful experiences whose semantic structure recurs across scenes even when geometric trajectories do not. Reusing such experience is challenging because differences in region naming and observation granularity produce distinct graph representations of similar approaches, while meaningful differences in anchors, branches, and endpoints must stay distinguishable. We introduce HTCE, a homeomorphism-inspired topological framework that canonicalizes and reuses navigation experience. Feature and topology subdivisions characterize representational variations, and their semantically constrained reductions produce comparable semantic sequences and structural signatures while preserving semantic anchors, branching relations, and navigation endpoints. HTCE then retrieves historical successful approaches through subdivision-aware matching as guidance for a frozen vision-language policy. Canonicalization compresses the experience index losslessly, merging 17.7--23.6\% of distinct stored route descriptions while retaining full task performance. Under a single frozen vision-language backbone shared by all compared systems, HTCE attains the best SR and SPL in every setting---59.9\%/31.8\% on HM3D v0.1, 71.0\%/31.5\% on HM3D v0.2, and 46.6\%/16.6\% on MP3D---with SR gains of up to 4.9 points and structured retrieval contributing up to 2.8 SPL points. The code is available in https://github.com/startracker0/htce.git