Summary of Depth Separations in Neural Networks: Separating the Dimension From the Accuracy, by Itay Safran et al.
Depth Separations in Neural Networks: Separating the Dimension from the Accuracy
by Itay Safran, Daniel Reichman, Paul Valiant
First submitted to arxiv on: 11 Feb 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: 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 investigates the limitations of neural networks with two layers (depth 2) compared to those with three layers (depth 3). Specifically, it shows that there is an exponential difference between these two architectures when approximating a target function with Lipschitz constant O(1) to a certain accuracy level. This result resolves an open problem in the field and demonstrates that the curse of dimensionality affects depth 2 networks even if the target function can be efficiently represented using a depth 3 network. The authors achieve this by introducing a novel application of random self-reducibility, which allows them to leverage existing lower bounds for threshold circuits with two layers. This result holds regardless of the activation function used and has implications for understanding the capabilities and limitations of neural networks in various domains. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores how deep neural networks can or can’t do certain things. It shows that if you have a simple target function, it’s much harder to get close to it using just two layers (like in a basic AI program) compared to having three layers (like in more advanced AI). This is important because it helps us understand what kinds of problems AI can and can’t solve. The researchers used a new way of thinking about how random things work together to prove this. They also showed that their result works no matter what “building block” you use inside the neural network, which makes it useful for many different types of problems. |
Keywords
* Artificial intelligence * Neural network
