Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead

2023-03-01: Math approaches can help with interpretation

Let’s take the set of all cat images and the set of all images that aren’t cats. We’re going to view them as topological shapes, or manifolds. One is the manifold of cats and the other is the manifold of non-cats. These are going to be intertwined in some complicated way. Why? Because there are certain things that look very much like cats that are not a cat. Mountain lions sometimes get mistaken for cats. Replicas. The big thing is, 2 manifolds are intertwined in some very complex manner.
I measure the shape of the manifold as it passes through the layers of a neural network. Ultimately, I can show that it reduces to the simplest possible form. You can view a neural network as a device for simplifying the topology of the manifolds under study.

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