Summary of A Convex Relaxation Approach to Generalization Analysis For Parallel Positively Homogeneous Networks, by Uday Kiran Reddy Tadipatri et al.
A Convex Relaxation Approach to Generalization Analysis for Parallel Positively Homogeneous Networks
by Uday Kiran Reddy Tadipatri, Benjamin D. Haeffele, Joshua Agterberg, René Vidal
First submitted to arxiv on: 5 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Signal Processing (eess.SP); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Our paper proposes a framework for deriving generalization bounds for parallel positively homogeneous neural networks (PHNNs), which include matrix factorization, single-layer multi-head attention mechanisms, and tensor factorization. We link the non-convex empirical risk minimization (ERM) problem to a convex optimization problem over prediction functions, providing a global lower-bound for ERM. This framework allows us to analyze generalization in the convex space while controlling the discrepancy between convex and non-convex models. We demonstrate our approach’s effectiveness by achieving sample complexity bounds that scale almost linearly with network width across various PHNNs, including low-rank matrix sensing, structured matrix sensing, two-layer linear networks, two-layer ReLU networks, and single-layer multi-head attention mechanisms. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary We created a new way to understand how well neural networks generalize, or make accurate predictions on new data. Our method works for a special type of network called parallel positively homogeneous neural networks (PHNNs), which are used in tasks like image recognition and natural language processing. We compared the non-convex problem of training these networks with a related convex problem, allowing us to analyze how well they generalize while controlling any differences between the two approaches. Our method was successful across many different types of PHNNs, providing insights into how we can design better neural networks that make accurate predictions. |
Keywords
* Artificial intelligence * Generalization * Multi head attention * Natural language processing * Optimization * Relu
