Sparse input representations explain odor discrimination in complex, concentration-varying mixtures

In natural environments, animals must detect behaviorally relevant odors despite variability in both odor mixture composition and stimulus intensity. Although mice can identify salient odors embedded in complex mixtures, how target concentration and background complexity jointly constrain discrimination remains unclear. We trained mice in a two-alternative forced choice task to identify target odors embedded in mixtures containing up to 16 background components. After performance stabilized, we systematically varied target odor concentration. Discrimination accuracy declined with decreasing target concentration but showed little additional dependence on background complexity. Using a biophysically grounded model of olfactory bulb glomerular responses, we show that linear decoding reproduces behavioral performance when intrinsic neural noise dominates over background-driven variability. Manifold capacity analysis revealed that neural representations remain efficiently structured for odor discrimination despite variation in background complexity. These results define a noise-limited regime of olfactory discrimination in which target detectability is primarily constrained by neural sensitivity rather than background interference.