Learning the Pseudoinverse Solution to Network Weights

TL;DR

This paper introduces an online, biologically plausible, and memory-efficient method for computing the pseudoinverse in neural networks, suitable for adaptive learning from non-stationary data streams.

Contribution

It proposes a novel incremental pseudoinverse computation method that is biologically plausible and adaptable for real-time learning in neural networks.

Findings

The method is more memory-efficient than SVD-based pseudoinverse computation.

It enables online, adaptive learning suitable for non-stationary data streams.

The approach aligns with biological plausibility in neural network learning.

Abstract

The last decade has seen the parallel emergence in computational neuroscience and machine learning of neural network structures which spread the input signal randomly to a higher dimensional space; perform a nonlinear activation; and then solve for a regression or classification output by means of a mathematical pseudoinverse operation. In the field of neuromorphic engineering, these methods are increasingly popular for synthesizing biologically plausible neural networks, but the "learning method" - computation of the pseudoinverse by singular value decomposition - is problematic both for biological plausibility and because it is not an online or an adaptive method. We present an online or incremental method of computing the pseudoinverse, which we argue is biologically plausible as a learning method, and which can be made adaptable for non-stationary data streams. The method is significantly more memory-efficient than the conventional computation of pseudoinverses by singular value decomposition.