# Hiding Data Helps: On the Benefits of Masking for Sparse Coding

## TL;DR

This paper demonstrates that masking strategies in sparse coding can improve dictionary recovery in noisy, over-realized settings, offering both theoretical insights and empirical benefits over traditional methods.

## Contribution

It introduces a novel masking-based objective for sparse coding that enhances dictionary recovery in noisy, over-realized regimes, supported by theoretical analysis and experiments.

## Key findings

- Standard dictionary learning fails in noisy over-realized settings.
- The proposed masking objective achieves better recovery as signal increases.
- Empirical results show improved performance over traditional reconstruction methods.

## Abstract

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.