Summary of Proportional Infinite-width Infinite-depth Limit For Deep Linear Neural Networks, by Federico Bassetti and Lucia Ladelli and Pietro Rotondo
Proportional infinite-width infinite-depth limit for deep linear neural networks
by Federico Bassetti, Lucia Ladelli, Pietro Rotondo
First submitted to arxiv on: 22 Nov 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Probability (math.PR)
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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 This paper investigates the properties of linear neural networks with random parameters in scenarios where both depth and width grow indefinitely while maintaining a constant ratio. The authors draw on previous research showing that infinite-width neural networks converge to a Gaussian process, but this limit has limitations, such as lacking the ability to learn dependent features or produce output correlations reflecting observed labels. To address these shortcomings, the study explores the joint proportional limit where both depth and width diverge, yielding a non-Gaussian distribution retaining output correlations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research looks at how really complex neural networks work when we make them grow in two ways: getting deeper and having more neurons per layer. Other studies have shown that if we make the number of neurons grow really big while keeping the number of layers the same, these networks start to behave like a special kind of random process. However, this limit has some drawbacks, like not being able to learn important patterns in the data or reflect how well the model is doing on its test cases. To overcome these limitations, scientists are studying what happens when both depth and width grow really big but stay proportional to each other. This leads to a new kind of distribution that keeps track of relationships between different outputs. |
