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Linear algebra with transformers

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arxiv 2112.01898 v2 pith:GTZIRURJ submitted 2021-12-03 cs.LG cs.CL

Linear algebra with transformers

classification cs.LG cs.CL
keywords matricestransformersalgebraeigenvaluesgeneralizelinearmodelsproblems
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Transformers can learn to perform numerical computations from examples only. I study nine problems of linear algebra, from basic matrix operations to eigenvalue decomposition and inversion, and introduce and discuss four encoding schemes to represent real numbers. On all problems, transformers trained on sets of random matrices achieve high accuracies (over 90%). The models are robust to noise, and can generalize out of their training distribution. In particular, models trained to predict Laplace-distributed eigenvalues generalize to different classes of matrices: Wigner matrices or matrices with positive eigenvalues. The reverse is not true.

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Cited by 6 Pith papers

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