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IntegrateUnitary.jl: A Julia package for symbolic integration over Haar measures
arXiv:2605.23830v2 Announce Type: replace-cross Abstract: Symbolic integration over the Haar measure of compact groups is a computational cornerstone in quantum information science and random matrix theory. We present \texttt{IntegrateUnitary.jl}, a comprehensive Julia package for computing exact expectations of polynomial functions over a wide range of compact groups ($U(d)$, $O(d)$, $Sp(d)$, and $SU(d)$ for balanced polynomials), circular and Gaussian ensembles, Ginibre ensembles,...
Wavelet as Tokenizer: Preliminary Results on a Shared Wavelet Token Schema for Natural Signals
arXiv:2606.02631v1 Announce Type: cross Abstract: This paper studies whether audio, images, and video can share a common wavelet token schema rather than relying on separate modality-specific latent grids. It introduces a preliminary continuous-token model built around a one-level Haar DWT/IDWT frontend, a shared coefficient-token layout, optional structural metadata, lightweight modality value adapters, and a shared token-wise encoder-decoder trunk. On Speech Commands, EuroSAT RGB, and...
Neural Networks Provably Learn Spectral Representations for Group Composition
arXiv:2606.02993v1 Announce Type: new Abstract: Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict $g_1 \star g_2$ for elements of a finite group $G$. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient...
FAF-CD: Frequency-Aware Fusion for Change Detection under Imperfect Multimodal Remote Sensing
arXiv:2606.03114v1 Announce Type: new Abstract: Remote sensing change detection for real-world monitoring often relies on imperfect heterogeneous observations, where pre- and post-event images may be asynchronous, cross-sensor, or affected by illumination, seasonal, and modality shifts. This setting is especially challenging for EO-SAR disaster mapping, where nuisance variation can resemble structural damage. We propose FAF-CD, a frequency-aware hybrid framework with a DINOv3-pretrained...
Coherent Swap Regret and Channel-Proof Learning
arXiv:2606.02655v1 Announce Type: cross Abstract: External regret certifies stability only against replacing one's behavior by a fixed alternative. In a quantum game, this misses a natural physical move: a player can apply a local completely positive trace-preserving (CPTP) map to the state it actually received or prepared.
Shortcomings and capacities of real-constrained neural networks in complex spaces
Announce Type: new Abstract: We find the asymptotic ratio between the storage capacities when enforcing real pre-activations in a complex hypothesis class as opposed to complex ones in the same class. Our methods depend on Gardner volume comparisons at critical capacity. Our proof relies on an application of the Harish-Chandra-Itzykson-Zuber (HCIZ) formula, nonstandard in literature.
Efficient Mean Curvature Computation on High-Dimensional Data Manifolds
Announce Type: new Abstract: Estimating local mean curvature at each point of a high-dimensional dataset is a key ingredient of geometry-aware machine learning algorithms, such as the Mean Curvature Boundary Points (MCBP) method. The naive implementation of this computation, based on a local shape operator approximated from k-nearest neighbor patches, involves an explicit construction of a matrix $H$ whose trace form yields an $O(m^4)$ cost per point, rendering the approach intractable for...
WaveDiT: Distribution-Aware Wavelet Flow Matching for Efficient 3D Brain MRI Synthesis
arXiv:2606.08670v1 Announce Type: new Abstract: Large and demographically balanced datasets are essential for reliable neuroimaging biomarkers. Full-resolution 3D brain MRI synthesis can support data augmentation in this setting, but existing approaches either incur prohibitive computational cost at volumetric scale or rely on lossy latent compression that may compromise anatomical detail. As a result, practical 3D generative augmentation often requires specialized compute infrastructure.
Stain-Aware Wavelet Regularization for Instant Adversarial Purification in Histopathology
arXiv:2606.08745v1 Announce Type: new Abstract: Deep learning has become prevalent in computational pathology pipelines that support tasks such as cancer screening and digital pathology analysis. However, the susceptibility of neural networks to adversarial perturbations raises safety concerns for reliable deployment in clinical practice. In histopathological images, this challenge is exacerbated by the difficulty of distinguishing high-frequency adversarial noise from subtle and...