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Found 43 papers, 13 papers with code
Graph Scattering beyond Wavelet Shackles
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters.
Computability of Optimizers
Optimization problems are a staple of today's scientific and technical landscape.
Explaining Image Classifiers with Multiscale Directional Image Representation
However, the smoothness of a mask limits its ability to separate fine-detail patterns, that are relevant for the classifier, from nearby nuisance patterns, that do not affect the classifier.
Dataset of Pathloss and ToA Radio Maps With Localization Application
In this article, we present a collection of radio map datasets in dense urban setting, which we generated and made publicly available.
Well-definedness of Physical Law Learning: The Uniqueness Problem
Finally, we provide extensive numerical experiments showing that our algorithms in combination with common approaches for learning physical laws indeed allow to guarantee that a unique governing differential equation is learnt, without assuming any knowledge about the function, thereby ensuring reliability.
Unveiling the Sampling Density in Non-Uniform Geometric Graphs
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.
Memorization-Dilation: Modeling Neural Collapse Under Label Noise
The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems.
OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphs
This work provides the first theoretical study on the ability of graph Message Passing Neural Networks (gMPNNs) -- such as Graph Neural Networks (GNNs) -- to perform inductive out-of-distribution (OOD) link prediction tasks, where deployment (test) graph sizes are larger than training graphs.
Inverse Problems Are Solvable on Real Number Signal Processing Hardware
In this work, we show that real number computing in the framework of BSS machines does enable the algorithmic solvability of finite dimensional inverse problems.
The Mathematics of Artificial Intelligence
We currently witness the spectacular success of artificial intelligence in both science and public life.
Limitations of Deep Learning for Inverse Problems on Digital Hardware
In fact, our result even holds for Borel-Turing computability., i. e., there does not exist an algorithm which performs the training of a neural network on digital hardware for any given accuracy.
LocUNet: Fast Urban Positioning Using Radio Maps and Deep Learning
We present LocUNet: A deep learning method for localization, based merely on Received Signal Strength (RSS) from Base Stations (BSs), which does not require any increase in computation complexity at the user devices with respect to the device standard operations, unlike methods that rely on time of arrival or angle of arrival information.
Neural Tangent Kernel Beyond the Infinite-Width Limit: Effects of Depth and Initialization
We derive exact expressions for the NTK dispersion in the infinite-depth-and-width limit in all three phases and conclude that the NTK variability grows exponentially with depth at the EOC and in the chaotic phase but not in the ordered phase.
Generalization Analysis of Message Passing Neural Networks on Large Random Graphs
Message passing neural networks (MPNN) have seen a steep rise in popularity since their introduction as generalizations of convolutional neural networks to graph-structured data, and are now considered state-of-the-art tools for solving a large variety of graph-focused problems.
A Rate-Distortion Framework for Explaining Black-box Model Decisions
We present the Rate-Distortion Explanation (RDE) framework, a mathematically well-founded method for explaining black-box model decisions.
Cartoon Explanations of Image Classifiers
We present CartoonX (Cartoon Explanation), a novel model-agnostic explanation method tailored towards image classifiers and based on the rate-distortion explanation (RDE) framework.
Transferability of Graph Neural Networks: an Extended Graphon Approach
Our main contributions can be summarized as follows: 1) we prove that any fixed GCNN with continuous filters is transferable under graphs that approximate the same graphon, 2) we prove transferability for graphs that approximate unbounded graphon shift operators, which are defined in this paper, and, 3) we obtain non-asymptotic approximation results, proving linear stability of GCNNs.
Deep Microlocal Reconstruction for Limited-Angle Tomography
We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging.
Real-time Outdoor Localization Using Radio Maps: A Deep Learning Approach
Global Navigation Satellite Systems typically perform poorly in urban environments, where the likelihood of line-of-sight conditions between the devices and the satellites is low, and thus alternative localization methods are required for good accuracy.
The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning.
Analyzing Finite Neural Networks: Can We Trust Neural Tangent Kernel Theory?
We find out that whether a network is in the NTK regime depends on the hyperparameters of random initialization and the network's depth.
Expressivity of Deep Neural Networks
In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks.
The Restricted Isometry of ReLU Networks: Generalization through Norm Concentration
In case of the NeuRIP event, we then provide bounds on the expected risk, which hold for networks in any sublevel set of the empirical risk.
In-Distribution Interpretability for Challenging Modalities
It is widely recognized that the predictions of deep neural networks are difficult to parse relative to simpler approaches.
Real-time Localization Using Radio Maps
Using the approximations of the pathloss functions of all base stations and the reported signal strengths, we are able to extract a very accurate approximation of the location of the user.
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks
Here, approximation theory predicts that the performance of the model should depend only very mildly on the dimension of the parameter space and is determined by the intrinsic dimension of the solution manifold of the parametric partial differential equation.
Interval Neural Networks: Uncertainty Scores
We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) using a data-driven interval propagating network.
Shearlets as Feature Extractor for Semantic Edge Detection: The Model-Based and Data-Driven Realm
This is based on the fact that edges in images contain most of the semantic information.
RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks
In this paper we propose a highly efficient and very accurate deep learning method for estimating the propagation pathloss from a point $x$ (transmitter location) to any point $y$ on a planar domain.
Transferability of Spectral Graph Convolutional Neural Networks
Transferability, which is a certain type of generalization capability, can be loosely defined as follows: if two graphs describe the same phenomenon, then a single filter or ConvNet should have similar repercussions on both graphs.
A Rate-Distortion Framework for Explaining Neural Network Decisions
We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework.
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations.
Error bounds for approximations with deep ReLU neural networks in $W^{s,p}$ norms
We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms.
On the Transferability of Spectral Graph Filters
For filters in this space, the perturbation in the filter is bounded by a constant times the perturbation in the graph, and filters in the Cayley smoothness space are thus termed linearly stable.
The Oracle of DLphi
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results.
Extraction of digital wavefront sets using applied harmonic analysis and deep neural networks
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences.
The Mismatch Principle: The Generalized Lasso Under Large Model Uncertainties
We study the estimation capacity of the generalized Lasso, i. e., least squares minimization combined with a (convex) structural constraint.
Optimal Approximation with Sparsely Connected Deep Neural Networks
Specifically, all function classes that are optimally approximated by a general class of representation systems---so-called \emph{affine systems}---can be approximated by deep neural networks with minimal connectivity and memory requirements.
Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting
High-resolution three-dimensional (3D) cardiovascular magnetic resonance (CMR) is a valuable medical imaging technique, but its widespread application in clinical practice is hampered by long acquisition times.
A Mathematical Framework for Feature Selection from Real-World Data with Non-Linear Observations
In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$.
A Haar Wavelet-Based Perceptual Similarity Index for Image Quality Assessment
In most practical situations, the compression or transmission of images and videos creates distortions that will eventually be perceived by a human observer.
Ranked #12 on
Video Quality Assessment
on MSU FR VQA Database
Sparse Proteomics Analysis - A compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data
Results: We present a new algorithm, Sparse Proteomics Analysis (SPA), based on the theory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets.
