Summary of Implicit Hypersurface Approximation Capacity in Deep Relu Networks, by Jonatan Vallin et al.
Implicit Hypersurface Approximation Capacity in Deep ReLU Networks
by Jonatan Vallin, Karl Larsson, Mats G. Larson
First submitted to arxiv on: 4 Jul 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: None
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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 develops a geometric approximation theory for deep feed-forward neural networks with ReLU activations. The authors show that a deep fully-connected ReLU network can implicitly construct an approximation as its zero contour, with a precision bound depending on the number of layers. This result is directly applicable to binary classification settings where the sign of the network is trained as a classifier. The proof relies on the geometrical structure of ReLU layers and defines a new equivalent network architecture that is easier to interpret geometrically. By repeatedly adding polyhedral cone projections, the authors construct a network that approximates the graph over a ball of radius R, with accuracy controlled by a discretization parameter δ. The required number of layers scales as (d-1)R(3/2)δ(1/2), where d is the dimensionality of the hypersurface. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how neural networks can learn to make decisions based on data. It shows that a special kind of neural network, called a deep fully-connected ReLU network, can be used to find the boundary between two groups of things. The authors use geometry and math to prove that this type of network can get better and better at making decisions as it’s trained. They also come up with a new way to think about how these networks work, which makes it easier to understand what they’re doing. |
Keywords
* Artificial intelligence * Classification * Neural network * Precision * Relu
