arXiv:2607. 18930v1 Announce Type: cross Abstract: The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error.
The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error. However, the uniqueness of such neural network representations is not guaranteed, raising questions about practical identifiability.
arXiv:2609.38998v1 Announce Type: new Abstract: A foundational principle of connectionism is that perception, action, and cognition emerge from parallel computations among simple, interconnected unit...
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:2609.15355v1 Announce Type: cross Abstract: We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by deep ReLU neural network...
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2602. 12390v2 Announce Type: replace Abstract: We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU, ReLU, SELU, CELU, Sigmoid, SiLU, Mish, Softplus, Tanh, Softmin, Softmax, and LogSoftmax.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
The paper presents a near-complete, nonasymptotic generalization theory for multilayer neural networks using path regularization, applicable to broad Lipschitz loss functions without requiring bounded loss or extreme network hyperparameters. It provides an explicit upper bound that addresses approximation rates in generalized Barron spaces and demonstrates the double descent phenomenon for ReLU networks. The authors claim near-minimax optimality for regression problems and plan to establish matching lower bounds in future work.
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
arXiv:2606. 18676v1 Announce Type: new Abstract: Training-free neural architecture search promises efficient discovery of high-performance networks without costly training.
arXiv:2610.00420v1 Announce Type: new Abstract: A weight space network (or metanetwork) takes the weights of another neural network as input and predicts properties of it. Most prior work trains such...