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.
Constraining the outputs of ReLU neural 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.
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arXiv Machine Learning
Jul 7
A Complete Symmetry Classification of Shallow ReLU Networks
arXiv:2604. 14037v2 Announce Type: replace Abstract: Parameter space is not function space for neural network architectures.
arXiv Machine Learning
Jun 9
Characterizing the Discrete Geometry of ReLU Networks
arXiv:2606. 07728v1 Announce Type: new Abstract: It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space.
arXiv AI
Jul 9
On the Principles of Deep Feedforward ReLU Networks
arXiv:2607. 07035v1 Announce Type: cross Abstract: The architecture of deep feedforward neural networks is ubiquitous in deep learning, either as a whole system or as a subnetwork of other architectures, and thus its mechanism is a key ingredient of the black box of neural networks.
arXiv Machine Learning
Jul 24
New Complexity-Theoretic Frontiers of Tractability for Neural Network Training
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.
Hugging Face Trending Papers
Jul 23
New Complexity-Theoretic Frontiers of Tractability for Neural Network Training
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 Machine Learning
Jun 4
Path-conditioned training: a principled way to rescale ReLU neural networks
arXiv:2602. 19799v2 Announce Type: replace-cross Abstract: Despite recent algorithmic advances, we still lack principled ways to leverage the well-documented rescaling symmetries in ReLU neural network parameters.
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 30
Singular Learning and Occam's Razor in Deep Monomial Networks
arXiv:2606. 28464v1 Announce Type: new Abstract: In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture.
arXiv AI
Jul 9
Understanding Two-Layer Neural Networks with Smooth Activation Functions
arXiv:2507. 14177v2 Announce Type: replace-cross Abstract: This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid type most commonly used before the advent of ReLUs.
arXiv Machine Learning
Jul 14
Tropical Circuits with Scalar Multiplication Gates
arXiv:2607. 11540v1 Announce Type: cross Abstract: We study tropical circuits with scalar multiplication gates, that is, algebraic circuits whose gates implement $\max$, $+$, or multiplication with a positive constant.
arXiv Machine Learning
Jun 5
Decomposition Polyhedra of Piecewise Linear Functions
arXiv:2410. 04907v2 Announce Type: replace-cross Abstract: In this paper we contribute to the frequently studied question of how to decompose a continuous piecewise linear (CPWL) function into a difference of two convex CPWL functions.