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

arXiv: https://arxiv.org/abs/2302.12715 · HTML: https://mlsanity.com/paper/2302.12715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 60 references that are in the map.
- First posted on arXiv 24 Feb 2023.

## Builds on (most cited first, 17 of 17)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [Why Do Pretrained Language Models Help in Downstream Tasks? An Analysis of Head and Prompt Tuning](https://mlsanity.com/paper/2106.09226/) (2021)
- [How to Understand Masked Autoencoders](https://mlsanity.com/paper/2202.03670/) (2022)
- [Simple, Efficient, and Neural Algorithms for Sparse Coding](https://mlsanity.com/paper/1503.00778/) (2015)
- [New Algorithms for Learning Incoherent and Overcomplete Dictionaries](https://mlsanity.com/paper/1308.6273/) (2013)
- [Towards Understanding Why Mask-Reconstruction Pretraining Helps in Downstream Tasks](https://mlsanity.com/paper/2206.03826/) (2022)
- [Sparse and spurious: dictionary learning with noise and outliers](https://mlsanity.com/paper/1407.5155/) (2014)
- [More Algorithms for Provable Dictionary Learning](https://mlsanity.com/paper/1401.0579/) (2014)
- [Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals](https://mlsanity.com/paper/1807.03182/) (2018)
- [Recovery and Generalization in Over-Realized Dictionary Learning](https://mlsanity.com/paper/2006.06179/) (2020)

## Abstract (arXiv)

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.