Summary of On the Hardness Of Learning One Hidden Layer Neural Networks, by Shuchen Li et al.
On the Hardness of Learning One Hidden Layer Neural Networks
by Shuchen Li, Ilias Zadik, Manolis Zampetakis
First submitted to arxiv on: 4 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computational Complexity (cs.CC); Statistics Theory (math.ST); 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 A medium-difficulty summary: This research paper investigates the learnability of one hidden layer ReLU neural networks when fed with inputs from ^d. The authors demonstrate that learning such networks is computationally hard even under standard cryptographic assumptions, provided certain conditions are met. Specifically, the network size must be polynomial in d, the input distribution a standard Gaussian, and the noise Gaussian and polynomially small in d. The hardness result relies on the difficulty of solving the Continuous Learning with Errors (CLWE) problem, which is closely tied to the widely believed worst-case hardness of approximately solving the shortest vector problem up to a multiplicative polynomial factor. This work has implications for understanding the limitations of neural networks and developing more robust machine learning models. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A low-difficulty summary: Imagine trying to train a special kind of computer program called a ReLU neural network. Researchers have been wondering if it’s possible to make these programs learn from random noise. In this study, scientists prove that making certain types of ReLU neural networks learn is actually very hard, even when we use simple and standard inputs. The difficulty comes from the way we represent numbers in computers, which makes some problems very challenging to solve. This finding helps us understand what limits how well these neural networks can work and might lead to new ways of building more reliable computer programs. |
Keywords
» Artificial intelligence » Machine learning » Neural network » Relu
