Symbolic Mathematics Finally Yields to Neural Networks

Abstraction: Facebook AI neural network solves symbolic integrals and ODEs via sequence translation

Key points:

• Guillaume Lample and François Charton (Facebook AI, Paris) reframed symbolic math as a language translation problem; mathematical expressions are encoded as trees (operators = junctions, variables/numbers = leaves)
• Trained on ~200 million tree-shaped equations; the neural net solved nearly 100% of 5,000 integration test problems in under 1 second, outperforming Mathematica and Matlab on some problems
• Training data only covered single-variable equations from elementary functions — a "thin slice" of possible expressions; Bessel and error functions not tested
• The system doesn't understand math; it develops pattern-recognition instinct ("math was our original language") — but its implicit rules handle exceptions that stumped rule-based CAS tools
• Proposed future uses: automated theorem generation, mathematician's assistant for conjecture identification, and using math problems to reverse-engineer how neural networks reason internally

Connections: Facebook AI · Wolfram · Symbolic Mathematics · Neural Networks · Sequence To Sequence

Source: https://www.quantamagazine.org/symbolic-mathematics-finally-yields-to-neural-networks-20200520/