A preprocessing step is proposed that rescales the input Jacobian tensor, removing both the bias towards larger magnitude outputs and the ill-conditioning of certain factor updates caused by such a mismatch.
Abstract
Tensor decoupling algorithms recover compact representations of multivariate functions by combining linear factor matrices with univariate internal nonlinearities. We identify two limitations of recent methods. First, their performance is not invariant to mismatched output or gradient magnitudes, and second, their spline internals require manual tuning of their degrees of freedom. We propose two lightweight fixes. The first is a preprocessing step that rescales the input Jacobian tensor, removing both the bias towards larger magnitude outputs and the ill-conditioning of certain factor updates caused by such a mismatch. The second replaces B-spline internals by penalized splines coupled with generalized cross-validation, making the method less dependent on the user selecting the right number of control points. Finally, we release an efficient open-source JAX implementation of our algorithm.
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