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Linear readout of object manifolds.

SueYeon Chung^1,2, Daniel D Lee³, Haim Sompolinsky^2,4,5

¹Program in Applied Physics, School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.

Physical Review. E

|July 15, 2016

Summary

Sensory systems represent objects using continuous manifolds. This study reveals how neural representation geometry, specifically manifold dimensionality, size, and shape, impacts invariant object decoding by perceptron networks.

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Area of Science:

Computational neuroscience
Sensory processing
Machine learning

Background:

Neuronal responses exhibit sensitivity to physical object features like location and intensity, leading to continuous manifold representations.
Understanding how sensory information is decoded invariantly by downstream neural networks is a key challenge.

Purpose of the Study:

To develop a theoretical framework characterizing the capacity of linear readout networks (perceptrons) for invariant object classification.
To investigate how the geometric properties of neural representations influence decoding performance.

Main Methods:

Theoretical analysis of perceptron capacity.
Mathematical modeling of object manifolds in neural representations.
Simulations to evaluate decoding performance based on manifold geometry.

Main Results:

The readout capacity of a perceptron is fundamentally determined by the dimensionality, size, and shape of the object manifolds.
Specific manifold geometries can enhance or limit the ability of linear decoders to achieve invariant object recognition.

Conclusions:

The geometry of neural representations plays a critical role in the efficiency and invariance of object decoding.
This work provides insights into the design principles for neural systems that support robust object recognition.