Voltage Stability Kernel: A Cofactor Theory of Voltage Stability in Lossy Power Systems
arXiv:2607.02843
2026
Regularization
1 ideas extracted · analyzed Aug 30, 2026
What the math gives to ML
The paper constructs a bus-wise stability certificate for a nonsymmetric Laplacian with a symmetry-induced zero eigenvalue: principal cofactors form a left-kernel vector, while their sum equals the product of all nonzero eigenvalues. This is transferable to directed attention and message-passing graphs, where a row-stochastic attention matrix induces a nonsymmetric Laplacian with an exact trivial null vector. A cofactor vector can expose token-level bottlenecks or nearly disconnected attention components, and the nonzero-eigenvalue product provides a global connectivity margin. The most practical first use is a regularizer on attention logits that discourages reducible or nearly singular token-interaction graphs.
Ideas from this paper
Unverified
2026
Treat each directed attention matrix as a graph transition matrix and form its Laplacian L = I - A. Compute the principal-cofactor vector to identify tokens with weak global access to the rest of the layer, and regularize the nonzero-eigenvalue product so attention does not become reducible or nearly singular. This targets pathological attention heads that isolate token groups and produce unstable or poorly propagated representations.
Useful5/10
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