24 citations · 27 across the 17 of their papers we have counts for
20 papers
Fourier entropy of threshold functions and their compositions
Yitzchak Shmalo
We prove the Fourier entropy--influence inequality for every linear threshold function, with a constant below and no restrictions on its weights or threshold. The argument…
Finite-state counterexamples to Ross's second queueing conjecture
Yitzchak Shmalo
We construct finite-state Markov arrival-rate processes for which faster modulation increases the mean stationary workload of a stable single-server queue, disproving the universal…
Entropy and singularity of spectral and pivotal sets in planar percolation
Yitzchak Shmalo
The spectral sample and pivotal set of a percolation crossing have the same one- and two-coordinate inclusion probabilities under the uniform product measure. We prove that both Sh…
Neural means and kernel corrections for operator learning
Yitzchak Shmalo
We combine neural network means with exact Matérn kernel regressions of their residuals and of their learned features, and evaluate the pairing on two public emulation problems wit…
Mesoscopic Rectangular Spikes under Subspace Local Laws: Outlier Values and Singular Subspaces
Yitzchak Shmalo
A rectangular data matrix is often modelled as noise plus a signal of low rank. When that rank is fixed the picture is classical: a signal direction must exceed a critical strength…
Extreme least singular values of random row submatrices with bounded-density subgaussian entries
Xiufan Yang, Shu Wen, Yitzchak Shmalo
Let be a centered real subgaussian random variable with positive variance and a bounded Lebesgue density, and let have independent entries dist…
Randomly initialized autoencoders: fixed points and edge-of-chaos
Leonid Berlyand, Roman Sarapin, Yitzchak Shmalo +2
In this paper we study autoencoders, a special class of deep neural nets (DNNs) whose performance can be characterized via their fixed points. This perspective naturally raises que…
The storage capacity of the Ising perceptron: verification of the outstanding numerical conditions
Yitzchak Shmalo
Krauth and Mézard predicted in 1989 that the storage capacity of the Ising perceptron at zero margin is an explicit constant . Let be the largest num…
A law of robustness for two-layer neural networks with arbitrary weights
Yitzchak Shmalo
Bubeck, Li and Nagaraj conjectured that, for generic data, any two-layer neural network with neurons that fits noisy labels must have Lipschitz constant at least of order $…
Extreme least singular values of Gaussian row submatrices and a phase retrieval stability problem
Yitzchak Shmalo
Let and . If has independent standard Gaussian entries and $N_m/m\toγ…
Pruning Deep Neural Networks via the Marchenko--Pastur Distribution
Leonid Berlyand, Theo Bourdais, Houman Owhadi +1
We study a Marchenko--Pastur (MP) random-matrix approach to pruning deep neural networks with very small post-pruning fine-tuning budgets. The main practical contribution is accura…
Pruning Deep Neural Networks via a Combination of the Marchenko-Pastur Distribution and Regularization
Leonid Berlyand, Theo Bourdais, Houman Owhadi +1
Deep neural networks (DNNs) have brought significant advancements in various applications in recent years, such as image recognition, speech recognition, and natural language proce…
Enhancing Accuracy in Deep Learning Using Random Matrix Theory
Leonid Berlyand, Etienne Sandier, Yitzchak Shmalo +1
We explore the applications of random matrix theory (RMT) in the training of deep neural networks (DNNs), focusing on layer pruning that is reducing the number of DNN parameters (w…
Deep Learning Weight Pruning with RMT-SVD: Increasing Accuracy and Reducing Overfitting
Yitzchak Shmalo, Jonathan Jenkins, Oleksii Krupchytskyi
In this work, we present some applications of random matrix theory for the training of deep neural networks. Recently, random matrix theory (RMT) has been applied to the overfittin…
Stability of Accuracy for the Training of DNNs Via the Uniform Doubling Condition
Yitzchak Shmalo
We study the stability of accuracy during the training of deep neural networks (DNNs). In this context, the training of a DNN is performed via the minimization of a cross-entropy l…
Algorithm for computing Representations of the Braid Group and Temperley-Lieb algebra
Yitzchak Shmalo
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of m…
Combinatorial Proof of Kakutani's Fixed Point Theorem
Yitzchak Shmalo
Kakutani's fixed point theorem is a generalization of Brouwer's fixed point theorem to upper semicontinuous multivalued maps and is used extensively in game theory and other areas…
The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
Emil Prodan, Yitzchak Shmalo
Starting from a dynamical system , with a generic topological group, we devise algorithms that generate families of patterns in the Euclidean space, which densely embed…
A Proof of Atanassov's Conjecture and Other Generalizations of Sperner's Lemma
Yitzchak Shmalo
A simple proof of Atanassov's Conjecture is presented. Atanassov's Conjecture is a generalization of Sperner's Lemma, a lemma which has been used to prove Brouwer's Fixed Point The…
Combinatorial approach to detection of fixed points, periodic orbits, and symbolic dynamics
Marian Gidea, Yitzchak Shmalo
We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find…