Neurons as Detectors of Coherent Sets in Sensory Dynamics
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918179684483072 |
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| author | Pughe-Sanford, Joshua L. Ding, Xuehao Moore, Jason J. Sengupta, Anirvan M. Epstein, Charles Greengard, Philip Chklovskii, Dmitri B. |
| author_facet | Pughe-Sanford, Joshua L. Ding, Xuehao Moore, Jason J. Sengupta, Anirvan M. Epstein, Charles Greengard, Philip Chklovskii, Dmitri B. |
| contents | We model sensory streams as observations from high-dimensional stochastic dynamical systems and conceptualize sensory neurons as self-supervised learners of compact representations of such dynamics. From prior experience, neurons learn coherent sets-regions of stimulus state space whose trajectories evolve cohesively over finite times-and assign membership indices to new stimuli. Coherent sets are identified via spectral clustering of the stochastic Koopman operator (SKO), where the sign pattern of a subdominant singular function partitions the state space into minimally coupled regions. For multivariate Ornstein-Uhlenbeck processes, this singular function reduces to a linear projection onto the dominant singular vector of the whitened state-transition matrix. Encoding this singular vector as a receptive field enables neurons to compute membership indices via the projection sign in a biologically plausible manner. Each neuron detects either a predictive coherent set (stimuli with common futures) or a retrospective coherent set (stimuli with common pasts), suggesting a functional dichotomy among neurons. Since neurons lack access to explicit dynamical equations, the requisite singular vectors must be estimated directly from data, for example, via past-future canonical correlation analysis on lag-vector representations-an approach that naturally extends to nonlinear dynamics. This framework provides a novel account of neuronal temporal filtering, the ubiquity of rectification in neural responses, and known functional dichotomies. Coherent-set clustering thus emerges as a fundamental computation underlying sensory processing and transferable to bio-inspired artificial systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26955 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neurons as Detectors of Coherent Sets in Sensory Dynamics Pughe-Sanford, Joshua L. Ding, Xuehao Moore, Jason J. Sengupta, Anirvan M. Epstein, Charles Greengard, Philip Chklovskii, Dmitri B. Neurons and Cognition We model sensory streams as observations from high-dimensional stochastic dynamical systems and conceptualize sensory neurons as self-supervised learners of compact representations of such dynamics. From prior experience, neurons learn coherent sets-regions of stimulus state space whose trajectories evolve cohesively over finite times-and assign membership indices to new stimuli. Coherent sets are identified via spectral clustering of the stochastic Koopman operator (SKO), where the sign pattern of a subdominant singular function partitions the state space into minimally coupled regions. For multivariate Ornstein-Uhlenbeck processes, this singular function reduces to a linear projection onto the dominant singular vector of the whitened state-transition matrix. Encoding this singular vector as a receptive field enables neurons to compute membership indices via the projection sign in a biologically plausible manner. Each neuron detects either a predictive coherent set (stimuli with common futures) or a retrospective coherent set (stimuli with common pasts), suggesting a functional dichotomy among neurons. Since neurons lack access to explicit dynamical equations, the requisite singular vectors must be estimated directly from data, for example, via past-future canonical correlation analysis on lag-vector representations-an approach that naturally extends to nonlinear dynamics. This framework provides a novel account of neuronal temporal filtering, the ubiquity of rectification in neural responses, and known functional dichotomies. Coherent-set clustering thus emerges as a fundamental computation underlying sensory processing and transferable to bio-inspired artificial systems. |
| title | Neurons as Detectors of Coherent Sets in Sensory Dynamics |
| topic | Neurons and Cognition |
| url | https://arxiv.org/abs/2510.26955 |