Re: [Maxima-discuss] ML for symbolic math

[Soegtrop, M. <mic...@in...>]

Dear Richard,

> Has anyone else looked at this paper?.

Yes, and I came to the same conclusion that it doesn’t really tell us that much without testing the integration mechanism with common symbolic integration benchmarks.

But I am less pessimistic than you regarding the outcome of such a test. Maybe at first it might perform bad, but it should be possible to extend the random set to improve.

One should not forget that pattern recognition mechanisms outperform by orders of magnitude purely symbolic methods in games like chess or go. Also modern integration mechanisms like Rubi are pattern based. The main difference between Rubi and the method in the paper is that all the patterns in Rubi are made manually, while the neural network finds them on its own.

In the past neural network image recognition required manual creation of patterns. This was called “feature engineering”. The essence of what is called “deep learning” these days is that this previously manual feature engineering step is now also left to the machine. The performance gain (in terms of quality) by this is very substantial. I think it is not unlikely that something similar will happen in symbolic math.

But again,  I completely agree that the paper would be substantially more interesting, if it would do comparisons with known benchmarks and also with state of the art symbolic integrators like Rubi.

Best regards,

Michael
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