Search Results for author:
Found 58 papers, 20 papers with code
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.
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
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 $\{(x_i, y_i)\}_{1 \leq i \leq m}$.
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.
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.
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.
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 Oracle of DLphi
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Expressivity of Deep Neural Networks
In this review paper, we give a comprehensive overview of the large variety of approximation results for neural networks.
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.
The Modern Mathematics of Deep Learning
We describe the new field of mathematical analysis of deep learning.
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 devices and satellites is low.
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.
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.
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.
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.
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.
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.
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.
Limitations of Deep Learning for Inverse Problems on Digital Hardware
Deep neural networks have seen tremendous success over the last years.
The Mathematics of Artificial Intelligence
We currently witness the spectacular success of artificial intelligence in both science and public life.
Inverse Problems Are Solvable on Real Number Signal Processing Hardware
For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements.
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.
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.
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.
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.
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.
Computability of Optimizers
Optimization problems are a staple of today's scientific and technical landscape.
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.
A Fractional Graph Laplacian Approach to Oversmoothing
In this paper, we generalize the concept of oversmoothing from undirected to directed graphs.
On the Interplay of Subset Selection and Informed Graph Neural Networks
However, learning on large datasets is strongly limited by the availability of computational resources and can be infeasible in some scenarios.
Reliable AI: Does the Next Generation Require Quantum Computing?
The cause of these computability problems is rooted in the fact that digital hardware is based on the computing model of the Turing machine, which is inherently discrete.
Sumformer: Universal Approximation for Efficient Transformers
Natural language processing (NLP) made an impressive jump with the introduction of Transformers.
Neural Poisson Surface Reconstruction: Resolution-Agnostic Shape Reconstruction from Point Clouds
Overall, the neural Poisson surface reconstruction not only improves upon the limitations of classical deep neural networks in shape reconstruction but also achieves superior results in terms of reconstruction quality, running time, and resolution agnosticism.
Expressivity of Spiking Neural Networks
The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications.
ParFam -- Symbolic Regression Based on Continuous Global Optimization
In this paper, we present our new method ParFam that utilizes parametric families of suitable symbolic functions to translate the discrete symbolic regression problem into a continuous one, resulting in a more straightforward setup compared to current state-of-the-art methods.
The First Pathloss Radio Map Prediction Challenge
To foster research and facilitate fair comparisons among recently proposed pathloss radio map prediction methods, we have launched the ICASSP 2023 First Pathloss Radio Map Prediction Challenge.
SuperHF: Supervised Iterative Learning from Human Feedback
Here, we focus on two prevalent methods used to align these models, Supervised Fine-Tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF).
Learning-based adaption of robotic friction models
Subsequently, to adapt to more complex asymmetric settings, we train a second network on a small dataset, focusing on predicting the residual of the initial network's output.
Learning Interpretable Queries for Explainable Image Classification with Information Pursuit
To solve the optimization problem, we propose a new query dictionary learning algorithm inspired by classical sparse dictionary learning.
Mathematical Algorithm Design for Deep Learning under Societal and Judicial Constraints: The Algorithmic Transparency Requirement
Motivated by the observation that the current evolution of deep learning models necessitates a change in computing technology, we derive a mathematical framework which enables us to analyze whether a transparent implementation in a computing model is feasible.
Error Estimation for Physics-informed Neural Networks Approximating Semilinear Wave Equations
This paper provides rigorous error bounds for physics-informed neural networks approximating the semilinear wave equation.
Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning
We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell{}$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell{}$MPNN, that can count cycles up to length $r + 2$.
Generalization Bounds for Message Passing Networks on Mixture of Graphons
In this more realistic and challenging scenario, we provide a generalization bound that decreases as the average number of nodes in the graphs increases.
