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Deep Symbolic Regression for Recurrent Sequences

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arxiv 2201.04600 v2 pith:4XAO2MJ4 submitted 2022-01-12 cs.LG

Stéphane d'Ascoli , Pierre-Alexandre Kamienny , Guillaume Lample , François Charton This is my paper · ORCID
classification cs.LG
keywords sequencesapproxfunctionfunctionsmodelrecurrenceregressionsymbolic
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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. $\operatorname{bessel0}(x)\approx \frac{\sin(x)+\cos(x)}{\sqrt{\pi x}}$ and $1.644934\approx \pi^2/6$. An interactive demonstration of our models is provided at https://symbolicregression.metademolab.com.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Neuro-Symbolic ODE Discovery with Latent Grammar Flow

    cs.LG 2026-04 unverdicted novelty 7.0 of 10

    Latent Grammar Flow embeds grammar-based ODE representations into a discrete latent space with a behavioural loss and samples candidate equations via discrete flow to fit observed data.

  2. On Forgetting and Stability of Score-based Generative models

    stat.ML 2026-01 conditional novelty 7.0 of 10

    Reverse-time diffusion samplers contract in a weighted total variation metric, so initialization, discretization, and score errors are forgotten geometrically along the backward trajectory.

  3. Decoding-based Regression

    cs.LG 2025-01 conditional novelty 5.0 of 10

    Autoregressive decoder heads trained with cross-entropy match pointwise heads on tabular regression and can estimate smooth conditional densities.

  4. Position: The Future of Bayesian Prediction Is Prior-Fitted

    cs.LG 2025-05 conditional novelty 4.0 of 10

    PFNs, which amortize Bayesian inference by training on datasets sampled from a prior, are likely to supersede MCMC and variational inference for most prediction tasks, the authors argue.

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