On convex decision regions in deep network representations

TL;DR

This paper investigates the convexity of concept regions in deep neural network representations, proposing tools to measure it and showing its prevalence and importance for generalization and fine-tuning performance.

Contribution

It introduces methods to quantify convexity in neural representations and demonstrates its robustness and significance across various domains and training stages.

Findings

Convexity is widespread in neural representations across domains.

Fine-tuning generally increases convexity of label regions.

Pretraining convexity predicts fine-tuning success.

Abstract

Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human representations. Convexity of object regions in conceptual spaces is argued to promote generalizability, few-shot learning, and interpersonal alignment. Based on these insights, we investigate the notion of convexity of concept regions in machine-learned latent spaces. We develop a set of tools for measuring convexity in sampled data and evaluate emergent convexity in layered representations of state-of-the-art deep networks. We show that convexity is robust to basic re-parametrization and, hence, meaningful as a quality of machine-learned latent spaces. We find that approximate convexity is pervasive in neural representations in multiple application domains, including models of images, audio, human activity, text, and medical images. Generally, we observe that fine-tuning increases the convexity of label regions. We find evidence that pretraining convexity of class label regions predicts subsequent fine-tuning performance.