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Optical Recording of Suprathreshold Neural Activity with Single-cell and Single-spike Resolution

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Shot-noise-limited performance of optical neural networks.

M M Hayat¹, B A Saleh, J A Gubner

¹Dept. of Electr. and Comput. Eng., Wisconsin Univ., Madison, WI.

IEEE Transactions on Neural Networks

|January 1, 1996

Summary

We analyzed neural network performance using shot-noise models, finding that reducing computing and weight-recording noise significantly lowers error probability. Optimal performance is achieved by carefully selecting nonlinearity thresholds.

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Area of Science:

Computational neuroscience
Information theory
Machine learning

Background:

Neural networks, including optical and biological systems, often exhibit performance limitations due to noise.
Shot-noise processes, stemming from the particle nature of signals and weight recording, are a key source of this noise.

Purpose of the Study:

To develop a theoretical framework for calculating the average probability of error in multistage and recurrent neural networks operating under shot-noise conditions.
To identify key noise parameters and their impact on network performance.

Main Methods:

Modeling neural network weights and signals using shot-noise processes.
Developing a theory to compute the average probability of error.
Analyzing the influence of computing-noise and weight-recording-noise parameters.
Utilizing large deviations theory to determine error decay rates.
Investigating performance optimization through nonlinearity threshold selection.

Main Results:

The probability of error is expressed in terms of the computing-noise and weight-recording-noise parameters.
Error probability decreases with increasing noise parameters, saturating at a level determined by the other parameter.
Increasing both noise parameters leads to exponentially fast error reduction.
Performance optimization is possible via selective nonlinearity threshold adjustments.
In recurrent networks, error initially increases with iterations before saturating.

Conclusions:

The study provides a quantitative understanding of shot-noise effects on neural network performance.
Noise parameters critically influence error rates, with trade-offs between computing and recording noise.
Optimizing network design requires careful consideration of noise sources and nonlinearity settings.