Summary of The Implicit Bias Of Heterogeneity Towards Invariance: a Study Of Multi-environment Matrix Sensing, by Yang Xu et al.
The Implicit Bias of Heterogeneity towards Invariance: A Study of Multi-Environment Matrix Sensing
by Yang Xu, Yihong Gu, Cong Fang
First submitted to arxiv on: 3 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper explores how Stochastic Gradient Descent (SGD) can learn invariant solutions through standard training procedures. Invariance learning involves distinguishing core relations that remain consistent across varying environments, ensuring predictions are safe, robust, and fair. The authors show that implicit bias in SGD drives the model towards an invariant solution, calling this phenomenon “implicit invariance learning.” They theoretically investigate a multi-environment low-rank matrix sensing problem, where they demonstrate that using large step size and large-batch SGD sequentially in each environment can prevent learning spurious signals. This approach reaches an invariant solution after certain iterations, whereas pooled SGD over all data would learn both invariant and spurious signals. The authors’ findings reveal another implicit bias resulting from the symbiosis between data heterogeneity and modern algorithms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary SGD models are usually expected to adapt to changing environments by learning what stays the same. Researchers found that this “invariance learning” can happen naturally when using standard training procedures, even without special algorithms or rules. They studied how SGD handles different types of data in various settings and discovered that it’s drawn to finding consistent patterns across all scenarios. This means that models trained with large step sizes and batches in each environment are less likely to pick up on random variations and more likely to focus on underlying truths. |
Keywords
* Artificial intelligence * Stochastic gradient descent
