CAGE-NAS introduces a method for deciding when to grow a neural network by evaluating an admissibility criterion on approximations of the functional gradient. If the current architecture allows a certified Functional Gradient Descent step, it remains unchanged; otherwise, a function-preserving expansion is performed and re-evaluated. Using a tangent-space-based instance with regularized projection, the approach achieves architectures that rank above the 99.8th percentile in held‑out RMSE among all admissible alternatives within the same parameter budget, without enumerating them during growth.
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:2606. 16926v1 Announce Type: cross Abstract: Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis.
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:2608. 14472v1 Announce Type: cross Abstract: Neural Architecture Search (NAS) aims to automate neural network architecture design, reducing reliance on human expertise.
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.
arXiv:2605. 15435v2 Announce Type: replace Abstract: Standard deep-learning pipelines usually choose the network architecture before training and keep it fixed throughout optimization.
arXiv:2608. 14443v1 Announce Type: cross Abstract: Neural Architecture Search (NAS) is naturally formulated as a bilevel optimization problem, where the upper-level optimizes the architecture using validation performance and the lower-level trains network parameters using training loss.
The paper introduces the "lift" technique for training input‑convex neural networks, replacing the traditional non‑negative weight constraint enforced by projected gradient descent or a softplus map. By adding a learnable slack variable and an unconstrained network that processes a permutation‑invariant batch summary, the lift couples batch‑dependent latent weights to the gradient, increasing update variance and enabling faster escape from the softplus shoulder. Experiments show that when the softplus method stalls at the shoulder, the lift achieves tighter fits and reconstructs targets roughly three times faster, while both methods agree when the shoulder is rarely reached.
arXiv:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.
arXiv:2607. 16568v1 Announce Type: new Abstract: Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program.
arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.