Related papers: Spectral Superposition: A Theory of Feature Geomet…
In this paper, we apply the Feature Space Decomposition (FSD) method developed in [LS24, GLS25, LSSW26, ALSS26] to obtain, under fairly general conditions, matching upper and lower bounds for the population excess risk of spectral methods…
Accurate upsampling of Head-Related Transfer Functions (HRTFs) from sparse measurements is crucial for personalized spatial audio rendering. Traditional interpolation methods, such as kernel-based weighting or basis function expansions,…
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork,…
Spectral-spatial processing has been increasingly explored in remote sensing hyperspectral image classification. While extensive studies have focused on developing methods to improve the classification accuracy, experimental setting and…
We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N=2 theories coupled to…
Characterizing the structural properties of neural networks is crucial yet poorly understood, and there are no well-established similarity measures between networks. In this work, we observe that neural networks can be represented as…
Speckle patterns are ubiquitous in optics and have multiple applications for which the control of their spatial correlations is essential. Here, we report on a method to engineer speckle correlations behind a scattering medium through the…
Texture is one of the most-studied visual attribute for image characterization since the 1960s. However, most hand-crafted descriptors are monochromatic, focusing on the gray scale images and discarding the color information. In this…
Measuring similarity of neural networks to understand and improve their behavior has become an issue of great importance and research interest. In this survey, we provide a comprehensive overview of two complementary perspectives of…
A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…
One of the distinguishing characteristics of modern deep learning systems is that they typically employ neural network architectures that utilize enormous numbers of parameters, often in the millions and sometimes even in the billions.…
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…
In sufficiently complex tasks, it is expected that as a side effect of learning to solve a problem, a neural network will learn relevant abstractions of the representation of that problem. This has been confirmed in particular in machine…
Weight space learning is an emerging paradigm in the deep learning community. The primary goal of weight space learning is to extract informative features from a set of parameters using specially designed neural networks, often referred to…
Here we introduce a new model of natural textures based on the feature spaces of convolutional neural networks optimised for object recognition. Samples from the model are of high perceptual quality demonstrating the generative power of…
Mass spectrometry, especially so-called tandem mass spectrometry, is commonly used to assess the chemical diversity of samples. The resulting mass fragmentation spectra are representations of molecules of which the structure may have not…
In this paper, we propose a spectral-spatial feature extraction and classification framework based on artificial neuron network (ANN) in the context of hyperspectral imagery. With limited labeled samples, only spectral information is…
Superposition or Neuron Polysemanticity are important concepts in the field of interpretability and one might say they are these most intricately beautiful blockers in our path of decoding the Machine Learning black-box. The idea behind…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or…