Abstract

This talk was recorded https://www.youtube.com/watch?v=9hnM9C4xHeM

In my last talk (https://talks.cam.ac.uk/talk/index/228790), I show four methodological limitations that prevent machine learning systems from reaching the rigour of syllogistic reasoning. They cannot achieve the rigour, not because of insufficient amount of training data, instead, to achieve the rigour, they shall not use training data. What kind of neural networks can be? Neural networks use vector embedding, which is a sphere embedding with zero radius. In this talk, I will show the four limitations can be completely avoided by promoting vector embedding into sphere embedding with non-zero radius and the criterion of achieving deterministic neural reasoning, namely, for any satisfiable reasoning, there is a constant number of M that the neural network shall correctly construct a model within M epochs. I will introduce a novel neural network, Sphere Neural Network (SphNN), which explicitly represents geometric objects, here spheres, and introduces the method of syllogistic reasoning by constructing Euler diagrams in the vector space. Instead of using training data, SphNN uses a neighbourhood transition map to transform the current sphere configuration into the target. SphNN is the first neural network that achieves deterministic human-like syllogistic reasoning in one epoch (M=1).