Learning Regularities from Data using Spiking Functions: A Theory

TL;DR

This paper introduces a new theoretical framework based on spiking functions to explicitly identify and represent data regularities, addressing limitations of traditional neural networks' implicit feature encoding.

Contribution

It defines regularities mathematically using spiking functions and information theory, proposing a method to discover and encode the most concise and informative data regularities.

Findings

Theoretically characterizes regularities as concise data features.

Defines optimal spiking functions that capture maximum information.

Proposes a practical approach to find these optimal functions.

Abstract

Deep neural networks trained in an end-to-end manner are proven to be efficient in a wide range of machine learning tasks. However, there is one drawback of end-to-end learning: The learned features and information are implicitly represented in neural network parameters, which cannot be used as regularities, concepts or knowledge to explicitly represent the data probability distribution. To resolve this issue, we propose in this paper a new machine learning theory, which defines in mathematics what are regularities. Briefly, regularities are concise representations of the non-random features, or 'non-randomness' in the data probability distribution. Combining this with information theory, we claim that regularities can also be regarded as a small amount of information encoding a large amount of information. Our theory is based on spiking functions. That is, if a function can react to, or spike on specific data samples more frequently than random noise inputs, we say that such a function discovers non-randomness from the data distribution. Also, we say that the discovered non-randomness is encoded into regularities if the function is simple enough. Our theory also discusses applying multiple spiking functions to the same data distribution. In this process, we claim that the 'best' regularities, or the optimal spiking functions, are those who can capture the largest amount of information from the data distribution, and then encode the captured information in the most concise way. Theorems and hypotheses are provided to describe in mathematics what are 'best' regularities and optimal spiking functions. Finally, we propose a machine learning approach, which can potentially obtain the optimal spiking functions regarding the given dataset in practice.