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An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
An assumption that researchers have often used to model interference in a wireless network is the unit disk graph model. While many theoretical results and performance guarantees have been obtained under this model, an open research…
In this paper we demonstrate that two common problems in Machine Learning---imbalanced and overlapping data distributions---do not have independent effects on the performance of SVM classifiers. This result is notable since it shows that a…
Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…
Due to common architecture designs, symmetries exist extensively in contemporary neural networks. In this work, we unveil the importance of the loss function symmetries in affecting, if not deciding, the learning behavior of machine…
For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…
Introducing controlled overlap among a few repetition blocks yields a fourfold asymptotic rate improvement while preserving an average stabilizer weight of \(4\). Substituting the overlapped outer layer with an LDPC code further produces a…
A pair density wave (PDW) is a superconducting (SC) state with spatially modulated order parameter. Although much is known about the properties of the PDW state, its realization in microscopic models with divergent susceptibility has been…
Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…
A lot of theoretical and empirical evidence shows that the flatter local minima tend to improve generalization. Adversarial Weight Perturbation (AWP) is an emerging technique to efficiently and effectively find such minima. In AWP we…
A single McCulloch-Pitts neuron, that is, the simple perceptron is studied, with focus on the region beyond storage capacity. It is shown that Parisi's hierarchical ansatz for the overlap matrix of the synaptic couplings with so called…
Prolate spheroidal wave functions (PSWFs) play an important role in various areas, from physics (e.g. wave phenomena, fluid dynamics) to engineering (e.g. signal processing, filter design). One of the principal reasons for the importance of…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…
Averaging neural network weights sampled by a backbone stochastic gradient descent (SGD) is a simple yet effective approach to assist the backbone SGD in finding better optima, in terms of generalization. From a statistical perspective,…
The log-density method is a powerful algorithmic framework which in recent years has given rise to the best-known approximations for a variety of problems, including Densest-$k$-Subgraph and Bipartite Small Set Vertex Expansion. These…
Weak spectral responses in hyperspectral images are often obscured by dominant endmembers and sensor noise, resulting in inaccurate abundance estimation. This paper introduces WS-Net, a deep unmixing framework specifically designed to…
We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination…
Let $\Gamma\subset \mathbb{R}^2$ be a simple closed curve which is smooth except at the origin, at which it has a power cusp and coincides with the curve $|x_2|=x_1^p$ for some $p>1$. We study the eigenvalues of the Schr\"odinger operator…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…