arXiv:2511. 19703v2 Announce Type: replace-cross Abstract: We study the dimension and identifiability of neurovarieties associated to polynomial neural networks.
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The paper proposes a conjecture that composing a fixed number of distinct nonconstant polynomials with a generic high‑degree polynomial produces linearly independent polynomials, extending Newman–Slater’s theorem. The authors prove the conjecture for two polynomials and for any number when the degrees are bounded, and they show how these results explain the parameter symmetries of deep fully connected neural networks with generic polynomial activations. In particular, for architectures with layer‑specific activations of increasing degree, the conjecture’s proven cases fully characterize the parameter sets that yield the same end‑to‑end network function, and it also resolves the identifiability of shallow polynomial networks.
arXiv:2508. 03867v2 Announce Type: replace-cross Abstract: We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in parameter space.
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
arXiv:2605. 09609v2 Announce Type: replace Abstract: We provide counterexamples to the unimodal minimal filling architecture conjecture for polynomial neural networks (PNNs) with power activation functions.
In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions. Indeed, while there has been a number of very recent results that establish ever-tighter lower bounds for the problem under linear and ReLU activation functions, less progress has been made towards the identification of novel polynomial-time tractable network architectures.
arXiv:2607. 20811v1 Announce Type: new Abstract: In spite of the fundamental role of neural networks in contemporary machine learning research, our understanding of the computational complexity of optimally training neural networks remains incomplete even when dealing with the simplest kinds of activation functions.