arXiv Machine Learning
Jul 24
Compiling to recurrent neurons
arXiv:2511. 14953v2 Announce Type: replace-cross Abstract: Discrete structures are currently second-class in differentiable programming.
Recurrent neural networks approximate continuous functions
arXiv:2606. 20325v1 Announce Type: new Abstract: Classical approximation theorems ask for a new neural network whenever the target accuracy is improved.
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arXiv AI
Jun 9
MinMax Recurrent Neural Cascades
arXiv:2605. 06384v3 Announce Type: replace-cross Abstract: We introduce MinMax Recurrent Neural Cascades (MinMax RNCs), a class of recurrent neural networks built from a novel form of recurrence over the MinMax algebra.
arXiv Machine Learning
Jun 2
An Algebraic View of the Expressivity of Recurrent Language Models
arXiv:2606. 01765v1 Announce Type: cross Abstract: What formal languages can a recurrent neural language model recognize?
arXiv Machine Learning
Sep 22
Approximating Smooth Functionals with ReLU Networks
arXiv:2609.15355v2 Announce Type: replace-cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by ReLU neural netw...
arXiv Machine Learning
Jun 11
Time-multiplexed layer reuse for physical neural networks
arXiv:2511. 00044v3 Announce Type: replace Abstract: Physical neural networks (PNNs) are promising candidates for next-generation computing, but existing demonstrations remain several orders of magnitude smaller than modern digital neural networks, whose recent advances have been driven by rapid growth in trainable parameters.
arXiv AI
Jul 16
Uniform Approximation of Functions with Asymmetric Growth and Decay by Deep Weighted Polynomials
arXiv:2506. 21306v2 Announce Type: replace-cross Abstract: Functions that grow without bound on one side of the real line and decay to zero on the other cannot be approximated uniformly by ordinary polynomials on unbounded domains.
arXiv Machine Learning
Jun 3
R2DN: Scalable Parameterization of Contracting and Lipschitz Recurrent Deep Networks
arXiv:2504. 01250v2 Announce Type: replace Abstract: This paper presents the Robust Recurrent Deep Network (R2DN), a scalable parameterization of robust recurrent neural networks for machine learning and data-driven control.
arXiv AI
Aug 25
Which Algorithms Can Graph Neural Networks Learn?
arXiv:2602.13106v2 Announce Type: replace-cross Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...
arXiv AI
Jun 26
Algorithmic Foundations of Deep Learning: Complexity-Theoretic Rates and a Characterization of Universal Approximation
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
arXiv Machine Learning
Jun 4
Certified Neural Approximations of Nonlinear Dynamics
arXiv:2505. 15497v3 Announce Type: replace Abstract: Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems.
arXiv Machine Learning
Jun 25
Frequency Domain Reservoir Computing
arXiv:2606. 24969v1 Announce Type: new Abstract: While the quadratic sequence-length bottleneck of transformers has fueled a resurgence in recurrent models, effectively capturing complex dynamics requires architectures that balance efficient training with highly expressive latent states.
arXiv Machine Learning
Sep 23
Neural Approximation by Function Composition: Rigidity and Doubly Exponential Convergence
arXiv:2609.25874v1 Announce Type: new Abstract: Deep neural networks approximate functions by composing affine maps with nonlinear activations, but how composition itself creates approximation power...