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Differentiating Through Linear Solvers
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Computer programs containing calls to linear solvers are a known challenge for automatic differentiation. Previous publications advise against differentiating through the low-level solver implementation, and instead advocate for high-level approaches that express the derivative in terms of a modified linear system that can be solved with a separate solver call. Despite this ubiquitous advice, we are not aware of prior work comparing the accuracy of both approaches. With this article we thus empirically study a simple question: What happens if we ignore common wisdom, and differentiate through linear solvers?
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Matrix-free Neural Preconditioner for the Dirac Operator in Lattice Gauge Theory
A matrix-free neural preconditioner learns to map gauge configurations to modified configurations whose Dirac operators approximate the inverse, halving CG iterations and transferring across lattice sizes.
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