The Use of Deep Learning for Symbolic Integration: A Review of (Lample and Charton, 2019)

By Ernest Davis. 2019

26 citations recorded by the source corpus.

Lample and Charton (2019) describe a system that uses deep learning technology to compute symbolic, indefinite integrals, and to find symbolic solutions to first- and second-order ordinary differential equations, when the solutions are elementary functions. They found that, over a particular test set, the system could find solutions more successfully than sophisticated packages for symbolic mathematics such as Mathematica run with a long time-out. This is an impressive accomplishment, as far as it goes. However, the system can handle only a quite limited subset of the problems that Mathematica deals with, and the test set has significant built-in biases. Therefore the claim that this outperforms Mathematica on symbolic integration needs to be very much qualified.

Subfields: Computational Theory and Mathematics, Statistics and Probability, Natural Language Processing, Code Generation & Program Synthesis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. David Raposo
2. Gary F. Marcus
3. Timothy P. Lillicrap
4. Sergey Levine
5. Pieter Abbeel
6. Lei Tai
7. Shixiang Shane Gu
8. Shimon Whiteson

In Statistics and Probability

1. Gary F. Marcus
2. Timothy P. Lillicrap
3. Andrew Kyle Lampinen
4. Adam Santoro

In Natural Language Processing

1. David Raposo
2. Gary F. Marcus
3. Kory Wallace Mathewson
4. Timothy P. Lillicrap
5. Andrew Kyle Lampinen
6. Adam Santoro
7. D. Gunning

In Code Generation & Program Synthesis

1. Gary F. Marcus

Citations in the corpus

• The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence (2020, methodology): “The current paradigm—long on data, but short on knowledge, reasoning and cognitive models—simply isn’t getting us to AI we can trust (Marcus & Davis, 2019).”
• Symbolic Behaviour in Artificial Intelligence (2021, background): “Lample and Charton [5] even show that transformers in some cases outperform classical symbol systems like Mathematica that were specifically designed for these tasks, though there are certainly caveats to that particular comparison [82].”
• Neurosymbolic AI: the 3rd wave (2020, unknown): “Section 6 contains more information about the neurosymbolic AI systems in each of the above categories as part of a note which seeks to clarify the terminology being used in AI, ML and DL.”