Winner-Take-All bottlenecks enforce disentangled symbolic representations in multi-task learning

TL;DR

This paper demonstrates that winner-take-all (WTA) bottlenecks in deep neural networks can enforce the extraction of symbolic, disentangled categorical features, improving interpretability and generalization in multi-task learning.

Contribution

The authors prove that WTA bottlenecks can produce highly symbolic representations of categorical features and empirically validate this in neural network architectures beyond theoretical assumptions.

Findings

WTA bottlenecks enforce symbolic, disentangled representations.

Empirical results show improved generalization with WTA-induced features.

Symbolic representations emerge even outside strict theoretical conditions.

Abstract

Winner-take-all (WTA) networks constitute a central circuit motif in cortical networks of the brain. In addition, WTA-like activations are abundant in modern deep learning models in the form of the softmax activation for example in attention layers of transformers. While their role in the extraction of latent factors has been studied for relatively simple generative models, their role in the context of highly non-linearly entangled latent factors has remained elusive. In this article, we show that a WTA bottleneck within a deep neural network can enforce under certain well-defined conditions the extraction of categorical latent factors of the data in a multi-task learning setup. In particular, we prove that the representation that emerges in the WTA bottleneck is highly symbolic, where a single neuron or a population of neurons encodes the presence of a single abstract feature such as a specific object, color, or position. We furthermore show empirically on two datasets, that this also holds for architectures and setups that do not fully comply with the assumptions of our theorem and demonstrate the advantages of the acquired symbolic representation for generalization. Our proposed model provides insights into the generalization capabilities of deep neural networks with WTA-like components and may serve as an interface between symbolic and subsymbolic AI systems.