Topological Signal in Learned Odor Embeddings Under Baseline and Utility Controls

An audit of whether first-homology (H1) persistent topology in the Principal Odor Map (POM) is reproducible, representation-specific, and practically useful. Persistent homology has become a tempting way to assign geometric meaning to learned molecular representations, but the existence of topological signal does not by itself imply that a representation captures uniquely informative structure. We evaluate H1 signal in fixed OpenPOM embeddings across a curated 4,983-row GoodScents/Leffingwell table, a broader 5,862-row GS/LF table, and a 1,600-molecule non-overlap subset, using repeated subsampling and matched null models. Across repeated direct subsamples, POM showed robust signal above matched nulls on all datasets, with top-1 signal-to-null ratios of 1.41–1.68 on the curated table and 1.42–1.56 on the non-overlap subset. The same Euclidean result stayed above null for all 10 released OpenPOM ensemble checkpoints (mean 1.52, range 1.42–1.68). Paper-matched Morgan bit fingerprints were at least as strong and often stronger, reaching direct top-1 ratios of 2.44–2.93 on the curated table and 3.02–4.02 on the non-overlap subset. Landmark distance-matrix analyses preserved the same qualitative caution: POM's H1 signal is real, but robust topology is not uniquely favorable to POM relative to strong chemical baselines. An important interpretive detail runs through the whole study: POM is a 256-dimensional dense representation while the strongest fingerprint baselines are 2,048-dimensional sparse encodings of explicit substructure content. That asymmetry makes the comparison not a clean scoreboard. A compressed learned space that retains robust topology under that bottleneck is noteworthy, but the fact that a sparser high-dimensional fingerprint shows stronger raw signal does not automatically imply it contains more odor-relevant structure. The results are better read as evidence that compressed learned odor spaces can preserve nontrivial topology than as evidence that POM has topological superiority. A utility analysis tested whether local topology features add explanatory value beyond local geometry for neighborhood-level odor-label prediction. Gains were modest and target-dependent: the largest POM improvement was ΔR² = +0.048 (neighbor-label entropy, curated table, cosine) but non-POM representations sometimes matched or exceeded POM on the non-overlap subset. Topology can add utility, but not universally and not uniquely to POM. The contribution is analytical rather than mechanistic: a reproducible comparison pipeline, stress-tested across datasets and checkpoints, with explicit statements of what the evidence does and does not justify. The work supports topological data analysis as a useful audit of learned odor representations while arguing against strong claims that current odor embeddings exhibit uniquely informative topology. Supports: reproducible H1 signal in POM across datasets; Euclidean stability across all 10 OpenPOM ensemble checkpoints; landmark-route agreement with direct analyses; modest utility gains from topology features in some settings. Not necessarily support: topological uniqueness of POM relative to sparse chemical baselines; interpretability of detected loops as perceptual dimensions; broad practical utility for molecular design; a clean separation of "odor-relevant structure preserved under compression" from "raw combinatorial structure retained by sparse encodings." This Zenodo archive contains the manuscript PDF, the analysis code (github.com/Obiohagwu/odor-topology, frozen at submission), and the CSV/JSON analysis reports that the figures are generated from. The companion preprint is on ChemRxiv. Keywords: persistent homology, topological data analysis, Principal Odor Map, POM, OpenPOM, Morgan fingerprints, molecular representations, chemosensory machine learning, representation auditing, Ripser.