Hyperbolic Odor-Space

Hyperbolic odor-space is the geometric model underlying Combinatorial Scent Mereology (CSM). The idea: human olfactory perception is structured by a hyperbolic manifold — a space of negative curvature — rather than by a Euclidean feature space.

Olfactory receptor binding patterns form branching similarity hierarchies that embed naturally in negatively curved space (Haddad et al., 2008). Tree-like metric graphs embed quasi-isometrically in hyperbolic spaces, a consequence of Mikhail Gromov’s work on hyperbolic groups (Gromov, 1987). This means distances in the OR binding landscape grow exponentially from any reference point, consistent with psychophysical data showing non-metric similarity judgments and triangle inequality violations (Haddad et al., 2010; Keller et al., 2017).

See Combinatorial Scent Mereology in the biology module for the full mathematical treatment.

Related concepts

• Combinatorial Scent Mereology — the full framework treating odor percepts as mereological composites within this hyperbolic space

Gromov, M. (1987). Hyperbolic Groups. In Essays in Group Theory (pp. 75–263). Springer.

Haddad, R., Khan, R., Takahashi, Y. K., Mori, K., Harel, D., & Bhatt, D. (2008). A Metric for Odorant Comparison. Nature Methods, 5(5), 425–429.

Haddad, R., Weiss, T., Khan, R., Nadler, B., Mandairon, N., Bensafi, M., Schneidman, E., Bhatt, D., Harel, D., & Sobel, N. (2010). Global Features of Neural Activity in the Olfactory System Form a Parallel Code That Predicts Olfactory Behavior and Perception. Proceedings of the National Academy of Sciences, 107(29), 12940–12945.

Keller, A., Gerkin, R. C., Guan, Y., Dhurandhar, A., Turu, G., Szalai, B., Mainland, J. D., Ihara, Y., Yu, C. W., Wolfinger, R., & others. (2017). Predicting Human Olfactory Perception from Chemical Features of Odor Molecules. Science, 355(6327), 820–826.