Summary of Function Gradient Approximation with Random Shallow Relu Networks with Control Applications, by Andrew Lamperski and Siddharth Salapaka
Function Gradient Approximation with Random Shallow ReLU Networks with Control Applications
by Andrew Lamperski, Siddharth Salapaka
First submitted to arxiv on: 7 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Systems and Control (eess.SY); Optimization and Control (math.OC); Statistics Theory (math.ST)
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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 closes a long-standing gap in neural network theory for control problems by demonstrating that randomly generated input parameters can be combined with trained output parameters to achieve accurate function approximation and gradient estimation. The researchers build upon their prior work, which showed that shallow networks can approximate smooth functions with high probability, but only considered the unknown function itself, not its gradient. In this paper, they extend these results to show that the network can also estimate the gradient of the unknown function with an error of O((log(m)/m)^(1/2)), where m is the number of neurons. The authors also provide a practical application of their result to policy evaluation problems. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research paper helps us understand how neural networks can be used in control systems, like self-driving cars or robots. It shows that by using random input parameters and training the output parameters, we can get very accurate results. This is important because sometimes we need not only to know what’s happening now, but also what will happen next (like knowing where a car will go if it turns left). The researchers found out how to make this work with errors that are really small, which is great for making sure our control systems work well. |
Keywords
» Artificial intelligence » Neural network » Probability
