Synergies between Disentanglement and Sparsity: Generalization and Identifiability in Multi-Task Learning

TL;DR

This paper demonstrates that combining disentangled representations with sparse predictors enhances generalization in multi-task learning, supported by theoretical identifiability results and practical algorithms with competitive few-shot classification performance.

Contribution

It provides a new theoretical identifiability result linking sparsity and disentanglement, and proposes a practical sparsity-promoting optimization method for learning disentangled representations.

Findings

Sparse predictors improve generalization in multi-task learning.

Theoretical conditions for disentanglement with sparse predictors are established.

The proposed method achieves competitive few-shot classification results.

Abstract

Although disentangled representations are often said to be beneficial for downstream tasks, current empirical and theoretical understanding is limited. In this work, we provide evidence that disentangled representations coupled with sparse base-predictors improve generalization. In the context of multi-task learning, we prove a new identifiability result that provides conditions under which maximally sparse base-predictors yield disentangled representations. Motivated by this theoretical result, we propose a practical approach to learn disentangled representations based on a sparsity-promoting bi-level optimization problem. Finally, we explore a meta-learning version of this algorithm based on group Lasso multiclass SVM base-predictors, for which we derive a tractable dual formulation. It obtains competitive results on standard few-shot classification benchmarks, while each task is using only a fraction of the learned representations.