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Physics-Informed Neural Networks with hard constraints (HC-PINNs) are increasingly favored for their ability to strictly enforce boundary conditions via a trial function ansatz $\tilde{u} = A + B \cdot N$, yet the theoretical mechanisms…
We develop the spectral edge analysis: phase transitions in neural network training -- grokking, capability gains, loss plateaus -- are controlled by the spectral gap of the rolling-window Gram matrix of parameter updates. In the extreme…
Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…
Sound field reconstruction refers to the problem of estimating the acoustic pressure field over an arbitrary region of space, using only a limited set of measurements. Physics-informed neural networks have been adopted to solve the problem…
Linear probes are widely used to interpret and evaluate neural representations, yet their reliability remains unclear, as probes may appear accurate in some regimes but collapse unpredictably in others. We uncover a spectral mechanism…
Angular differential imaging is a high-contrast imaging technique that reduces quasi-static speckle noise and facilitates the detection of nearby companions. A sequence of images is acquired with an altitude/azimuth telescope while the…
Functional Spectral Imaging (FSI) models image formation as the recovery of tissue surrogates such as density and stiffness from spectral perturbations of a self-adjoint elliptic operator. Rather than relying on reflectivity or relaxation…
This paper develops convolutional neural network (CNN) methods for simultaneous approximation and elliptic boundary value problems on compact Riemannian manifolds. We establish simultaneous Sobolev approximation results for single- and…
Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of…
Multi-index models provide a popular framework to investigate the learnability of functions with low-dimensional structure and, also due to their connections with neural networks, they have been object of recent intensive study. In this…
Accurate monocular depth estimation is critical in colonoscopy for lesion localization and navigation. Foundation models trained on natural images fail to generalize directly to colonoscopy. We identify the core issue not as a semantic gap,…
Ground-penetrating radar (GPR) combines depth resolution, non-destructive operation, and broad material sensitivity, yet it has seen limited use in diagnosing building envelopes. The compact geometry of wall assemblies, where reflections…
Many current neural networks for medical imaging generalise poorly to data unseen during training. Such behaviour can be caused by networks overfitting easy-to-learn, or statistically dominant, features while disregarding other potentially…
Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary layers are responsible for the stiffness of solutions, which…
Recent applications of deep learning in the seismic domain have shown great potential in different areas such as inversion and interpretation. Deep learning algorithms, in general, require tremendous amounts of labeled data to train…
Radio spectrum monitoring in contested environments motivates the need for reliable automatic signal classification technology. Prior work highlights deep learning as a promising approach, but existing models depend on brute-force Doppler…
This paper presents the first application of spiking neural networks (SNNs) for the classification of chronic lower back pain (CLBP) using the EmoPain dataset. Our work has two main contributions. We introduce Spike Threshold Adaptive…
Speckle based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown,…
Physics-informed neural networks (PINNs) train a single neural approximation by minimizing multiple physics- and data-derived losses, but the gradients of these losses often interfere and can stall optimization. Existing remedies typically…
We conduct an investigation on various hyper-parameters regarding neural networks used to generate spectral envelopes for singing synthesis. Two perceptive tests, where the first compares two models directly and the other ranks models with…