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arXiv:1912.01412cs.SC

Deep Learning for Symbolic Mathematics

Guillaume Lample, François Charton

Abstract

Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.

arXiv comments
Journal reference
DOI
Subjects
cs.SCSymbolic Computation cs.LGMachine Learning

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Linked by 6 identifiable commenters in 7 comments across 6 threads, from Jan 2020 to Mar 2023. Found in 4 HN submissions from Dec 2019 to Jan 2020. Open submission discussions.

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Discussed in comments6 threads

  1. The Age of AI has begun 1 comment

    • I'm not sure anyone is claiming that ChatGPT is going to steal their job. I think most people are just extrapolating the ridiculously steep rate of progression and pondering what the future holds. Sure, maybe we're about to hit a wall. But I'm not seeing any evidence of that as…

      MrScruffView on HNParent context

  2. Learning to think critically about machine learning 1 comment

    • It's a model mismatch, not an inherent impossibility. A calculator needs to have an adaptive number of intermediate steps. Usually our models have fixed depth, but in auto-regressive modelling the tape can become longer as needed by the stepwise algorithm. Recent models show LMs…

      visargaView on HNParent context

  3. Natural language benchmarks don’t measure AI models’ general knowledge well 1 comment

    • It does lead to intelligence and knowledge of the world. It leads to somewhat similar understanding of the world as our understanding of 4D, quantum mechanics or environment close to a black hole. Pretty bad one, mostly based on repeating whatever we have read about in popular…

      IsinlorView on HNParent context

  4. Symbolic mathematics finally yields to neural networks 2 comments

    • To me, the article somewhat misses the point of what's interesting here. Using ASTs to represent equations, or even whole programs has plenty of precedents in ML/AI. I'd have liked to know how exactly they translate these trees to a representation suitable for an ANN.…

      _0ffhView on HNParent context

    • They don't actually use trees in the paper though. https://arxiv.org/abs/1912.01412 They express everything in reverse polish notation, exactly so the transformer network can work on streams and not care about the nesting levels. It's a bit odd that this article doesn't talk…

      thomasahleView on HNParent context

  5. Differential Equations with Transformers: Deep Learning for Symbolic Math 1 comment

    • Post by the researchers (Facebook AI): https://ai.facebook.com/blog/using-neural-networks-to-solve-... Arxiv paper: https://arxiv.org/pdf/1912.01412.pdf

      thomasahleView on HNParent context

  6. Using neural networks to solve advanced mathematics equations 1 comment

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