arXiv:2606. 00296v1 Announce Type: cross Abstract: Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining.
arXiv:2606. 00677v1 Announce Type: new Abstract: Fourier Neural Operators are often assumed to generalize across spatial resolutions, enabling training on a coarse grid and deployment on a finer grid.
arXiv:2404. 06294v2 Announce Type: replace-cross Abstract: Super-Resolution (SR) is a time-hallowed image processing problem that aims to improve the quality of a Low-Resolution (LR) sample up to the standard of its High-Resolution (HR) counterpart.
arXiv:2608.20812v1 Announce Type: new Abstract: We develop constructive approximation and learning guarantees for shallow neural models with infinite-dimensional inputs observed through finitely many...
arXiv:2608. 05839v1 Announce Type: cross Abstract: Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging.
arXiv:2608. 14744v1 Announce Type: new Abstract: Recovering high-resolution states from sparse, low-resolution observations is a central challenge in scientific machine learning and data assimilation.
arXiv:2606. 18538v1 Announce Type: new Abstract: One of the major difficulties in the mechanistic interpretability of neural networks is the occurrence of polysemanticity, which suggests that each neuron is typically responsible for multiple different tasks, impeding a clean interpretation of their function.
MIAR introduces a multi‑scale autoregressive framework for medical image super‑resolution, treating the task as a conditional, progressive next‑scale prediction. It incorporates a Scale‑Adaptive Structural Decoder to preserve structural fidelity and uses a hierarchical beam search during inference to reduce recursive error accumulation. Experiments show MIAR outperforms existing methods, achieving a 7.86% MUSIQ improvement and a 2.02× speedup over diffusion‑based approaches.
arXiv:2609.09556v1 Announce Type: new Abstract: Neural networks can leverage feature superposition to encode more concepts than dimensions, but cross-feature interference constrains the linear access...
The paper develops a statistical theory for minimum‑norm interpolation in high‑dimensional regression, showing how regularization geometry and signal sparsity affect generalization. It identifies regimes where sparsity‑promoting regularizers yield exact interpolation that is far more accurate than approximate fitting, and proves a zero–one generalization law for strongly overparameterized noiseless problems. The authors also characterize training and generalization errors along ρ‑regularization paths when feature dimension and sample size are proportional, demonstrating that generalization improves with more sparsity‑promoting norms and sparser targets, and that small changes in regularization strength can cause large shifts in generalization. whyItMatters":"The work provides a quantitative understanding of delayed generalization (grokking) and reveals a statistical instability in minimum‑norm interpolation, offering insights that could guide the design of regularizers for better generalization in overparameterized models."
arXiv:2609.39512v1 Announce Type: new Abstract: The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation a...
The paper develops a mathematical theory of superposition in neural networks using frame theory and compressed sensing. It shows that a sparse binary vector of active features can be encoded by an overcomplete dictionary and recovered via a ReLU operation with a suitable bias. The authors prove recovery theorems for both random-support and worst-case support settings, providing high-probability guarantees for low-coherence dictionaries and a sharp criterion for sparsity levels, with explicit results for Gaussian random matrices and equiangular tight frames.
arXiv:2609.39926v1 Announce Type: new Abstract: Achieving cross-sensor generalization and arbitrary-scale reconstruction with a single model remains challenging in hyperspectral super-resolution (HSR...