Presents an active-sampling method that approximates the weight subspace from Hessian finite differences, recovers the rank-1 tensors by robust nonlinear programming, and attributes layers with gradient descent, yielding stable recovery under a-posteriori verifiable conditions.
Orthogonal Decomposition of Symmetric Tensors
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abstract
A real symmetric tensor is orthogonally decomposable (or odeco) if it can be written as a linear combination of symmetric powers of $n$ vectors which form an orthonormal basis of $\mathbb R^n$. Motivated by the spectral theorem for real symmetric matrices, we study the properties of odeco tensors. We give a formula for all of the eigenvectors of an odeco tensor. Moreover, we formulate a set of polynomial equations that vanish on the odeco variety and we conjecture that these polynomials generate its prime ideal. We prove this conjecture in some cases and give strong evidence for its overall correctness.
fields
cs.LG 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Robust and Resource Efficient Identification of Two Hidden Layer Neural Networks
Presents an active-sampling method that approximates the weight subspace from Hessian finite differences, recovers the rank-1 tensors by robust nonlinear programming, and attributes layers with gradient descent, yielding stable recovery under a-posteriori verifiable conditions.