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Neurons as Detectors of Coherent Sets in Sensory Dynamics
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Proposes that sensory neurons act as detectors of coherent sets, computing membership via the sign of subdominant singular functions of the stochastic Koopman operator, derived analytically for saddle-point Ornstein–Uhlenbeck dynamics and estimated via past–future CCA.
Problem
How single sensory neurons could compactly represent temporally correlated stimulus dynamics and explain temporal receptive fields, rectification (ON/OFF), and predictive vs. retrospective neuron classes.
Approach
Neurons are modeled as self-supervised learners that detect coherent sets via subdominant singular functions of the stochastic Koopman operator; for OU processes these reduce to linear projections onto singular vectors of the whitened finite-time transition matrix, which act as temporal filters, with left vectors giving predictive and right vectors giving retrospective neurons.
Key results
- For multivariate OU processes the subdominant SKO singular function reduces to a linear projection onto a singular vector of the whitened transition matrix, providing an analytic account of temporal filters.
- In analysis of 204 rat olfactory bulb TCs/MCs, approximately half were orthogonal to decaying exponentials (predictive), about 4% orthogonal to growing exponentials (retrospective), and about one-third to both.
- Of 1345 retinal ganglion cells, the majority were predictive while about 1% were retrospective.
Surprising findings
- Retrospective neurons are rare in the retinal ganglion cell dataset (about 1%) and in the olfactory bulb dataset (about 4%).
- Approximately one-third of olfactory bulb cells were orthogonal to both growing and decaying exponentials, suggesting higher-dimensional dynamics.
Limitations
- Analytic results are derived for 2D saddle-point OU dynamics; correspondence may not extend to higher dimensions or multiple unstable directions.
- Extension to unstable modes and reference measures remains open.
- Nonlinear extension relies on Galerkin projection with a lag-vector basis and is not rigorously established.
Experimental setup
Datasets: dead leaves natural image model stimulus rat olfactory bulb tufted/mitral cell temporal receptive fields (204 cells) dissociated vertebrate retina RGC temporal receptive fields (1345 cells) salamander retinal bipolar cell flash response
Metrics: cosine similarity with exponentials canonical correlations fraction of cells orthogonal to growing/decaying exponential
Baselines: VAMPnets slow feature analysis predictive coding models lattice filter model of visual pathway
Builds on: information bottleneck slow feature analysis VAMP Galerkin approximation of the Koopman operator
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