Summary of Neural Networks Generalize on Low Complexity Data, by Sourav Chatterjee et al.
Neural Networks Generalize on Low Complexity Data
by Sourav Chatterjee, Timothy Sudijono
First submitted to arxiv on: 19 Sep 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); 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 This paper demonstrates that feedforward neural networks with ReLU activation can generalize well on low-complexity data, as defined by the authors. Specifically, they show that a minimum description length (MDL) feedforward neural network, trained to interpolate simple programming language-generated data, generalizes with high probability. The authors define this simple programming language and provide examples of basic computational tasks, such as primality testing. For primality testing, their theorem proves that an MDL network fitted to i.i.d. samples can accurately determine whether a newly drawn number is prime or not, with test error bounded by O(N^(-δ)). This breakthrough does not require designing the network for specific tasks; instead, minimum description learning discovers a network that can accomplish this feat. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper shows that special kinds of artificial neural networks are really good at guessing things on simple data. They use a unique way to define what “simple” means and show examples of basic math problems, like checking if a number is prime or not. Their main result says that these networks can solve this problem very accurately, even when they’re given new numbers to check. The amazing thing is that the network doesn’t need to be specifically designed for primality testing; it just works because of how the data is defined. |
Keywords
» Artificial intelligence » Neural network » Probability » Relu
