arXiv Machine Learning
Minimal Filling Architectures for Polynomial Neural Networks
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arXiv Machine Learning
Jun 19
Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects
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.
arXiv Machine Learning
Jun 15
On the Geometry and Optimization of Polynomial Convolutional Networks
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
arXiv Machine Learning
Oct 15
Trainable at Depth, Solvable at Small Size: What the Loss Surface of a Polynomial Activation Dictates for Designing, Initializing and Training Networks
arXiv:2610. 20069v1 Announce Type: new Abstract: What makes a deep network train, and what shape is its loss surface?
arXiv Machine Learning
Aug 28
Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks
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 Machine Learning
Jul 10
Tubular Neighbourhoods of Pfaffian Sets and Applications to Neural Networks
arXiv:2607. 08370v1 Announce Type: cross Abstract: We derive bounds for the volume of tubular neighbourhoods of smooth Pfaffian hypersurfaces, generalising known results for algebraic varieties.
arXiv AI
Sep 2
The Alexander-Hirschowitz theorem for neurovarieties
arXiv:2511. 19703v2 Announce Type: replace-cross Abstract: We study the dimension and identifiability of neurovarieties associated to polynomial neural networks.