Learning Hierarchically Structured Concepts

TL;DR

This paper presents a biologically plausible neural network model for recognizing and learning hierarchically structured concepts, providing formal proofs of its capabilities and limitations, including noise robustness and layer-depth requirements.

Contribution

It introduces a general framework for hierarchical concept recognition and learning, with formal analysis of Oja's rule and layer-depth bounds.

Findings

Neural networks can recognize hierarchical concepts even with noise.

Oja's rule effectively supports learning in the proposed model.

Recognition depth requires a corresponding number of network layers.

Abstract

We study the question of how concepts that have structure get represented in the brain. Specifically, we introduce a model for hierarchically structured concepts and we show how a biologically plausible neural network can recognize these concepts, and how it can learn them in the first place. Our main goal is to introduce a general framework for these tasks and prove formally how both (recognition and learning) can be achieved. We show that both tasks can be accomplished even in presence of noise. For learning, we analyze Oja's rule formally, a well-known biologically-plausible rule for adjusting the weights of synapses. We complement the learning results with lower bounds asserting that, in order to recognize concepts of a certain hierarchical depth, neural networks must have a corresponding number of layers.