Symbolic Mathematics Finally Yields to Neural Networks

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    • #319568
      • Total Posts: 5,563

      However, neural networks have always lagged in one conspicuous area: solving difficult symbolic math problems. These include the hallmarks of calculus courses, like integrals or ordinary differential equations. The hurdles arise from the nature of mathematics itself, which demands precise solutions. Neural nets instead tend to excel at probability. They learn to recognize patterns — which Spanish translation sounds best, or what your face looks like — and can generate new ones.

      The situation changed late last year when Guillaume Lample and François Charton, a pair of computer scientists working in Facebook’s AI research group in Paris, unveiled a successful first approach to solving symbolic math problems with neural networks. Their method didn’t involve number crunching or numerical approximations. Instead, they played to the strengths of neural nets, reframing the math problems in terms of a problem that’s practically solved: language translation.

      “We both majored in math and statistics,” said Charton, who studies applications of AI to mathematics. “Math was our original language.”

      As a result, Lample and Charton’s program could produce precise solutions to complicated integrals and differential equations — including some that stumped popular math software packages with explicit problem-solving rules built in.
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    • #319576
      • Total Posts: 858

      When Colossus (the super-computer of the movie “Colossus: The Forbin Project”) discovers the Russian super-computer Guardian, and finds a way into its communications. Soon both computers have developed their own language based on math and what looks like calculus on the computer screens.

      I was never any good at calculus or foreign languages. It makes a lot of sense for these two mathematicians to use language translation to solve that problem.

      Thanks for sharing 🙂

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