AI Innovation Institute

Abstract: Machine learning (ML) systems fueled by neural networks have entered our daily lives and led to scientific breakthroughs, but many open questions remain. After a nod toward the question of rigor with ML and recent progress, I'll turn to the theory of neural networks. I will argue that understanding neural networks inevitably leads to ideas from field theory (FT), which was already realized in the simplest case in the 1990s, and I will review some essential FT-for-NN results. I will then propose that the connection might be more general, an NN-FT correspondence of sorts, with neural networks providing a way to define a field theory. I'll end with comments on known results including the origin of interactions and various symmetries, but I will also list some open questions. The apparent non-sequitur in the title will be used as a rhetorical device to explore where we are and where we'd like to go.

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