Abstract

In this talk, I will argue that supervised deep learning cannot achieve the rigour of syllogistic reasoning, and, thus, will not reach the rigour of logical reasoning. I will spatialise syllogistic statements into part-whole relations between regions and define the neural criterion that is equivalent to the rigour of the symbolic level of syllogistic reasoning. By dissecting Euler Net (EN), a well-designed supervised deep learning system for syllogistic reasoning (reaching 99.8% accuracy on the benchmark dataset), I will show three methodological limitations that prevent EN from reaching the rigour of syllogistic reasoning: (1) the methodology of reasoning through a combination table — they cannot cover all valid syllogistic reasoning types. ); (2) the end-to-end mapping from the premises to the conclusions—this introduces contradictory features of object recognition (good to recognise the whole from parts) and logical reasoning (not good to inject new parts); (3) using latent feature vectors to represent geometric structures, which may not be there. As Transformer’s Key-Query-Value structure is automatically learned combination tables through end-to-end mapping, they and neural networks built upon them will not reach the rigour of syllogistic reasoning.  

https://www.youtube.com/watch?v=x38GySbuGJg