#deeplearning #symbolic #research

This video includes an interview with first author Stéphane d'Ascoli (https://sdascoli.github.io/).

Deep neural networks are typically excellent at numeric regression, but using them for symbolic computation has largely been ignored so far. This paper uses transformers to do symbolic regression on integer and floating point number sequences, which means that given the start of a sequence of numbers, the model has to not only predict the correct continuation, but also predict the data generating formula behind the sequence. Through clever encoding of the input space and a well constructed training data generation process, this paper's model can learn and represent many of the sequences in the OEIS, the online encyclopedia of integer sequences and it also features an interactive demo if you want to try it by yourself. 

OUTLINE:

0:00 - Introduction

2:20 - Summary of the Paper

16:10 - Start of Interview

17:15 - Why this research direction?

20:45 - Overview of the method

30:10 - Embedding space of input tokens

33:00 - Data generation process

42:40 - Why are transformers useful here?

46:40 - Beyond number sequences, where is this useful?

48:45 - Success cases and failure cases

58:10 - Experimental Results

1:06:30 - How did you overcome difficulties?

1:09:25 - Interactive demo

Paper: https://arxiv.org/abs/2201.04600

Interactive demo: http://recur-env.eba-rm3fchmn.us-east...

Abstract:

Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers or floats, a typical task in human IQ tests which has hardly been tackled in the machine learning literature. We evaluate our integer model on a subset of OEIS sequences, and show that it outperforms built-in Mathematica functions for recurrence prediction. We also demonstrate that our float model is able to yield informative approximations of out-of-vocabulary functions and constants, e.g. bessel0(x)≈sin(x)+cos(x)πx√ and 1.644934≈π2/6. An interactive demonstration of our models is provided at this https URL.

Authors: Stéphane d'Ascoli, Pierre-Alexandre Kamienny, Guillaume Lample, François Charton

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