Related papers: A Sampling Technique of Proving Lower Bounds for N…
This essay explores strong data-processing inequalities (SPDI's) as they appear in the work of Evans and Schulman \cite{ES} and von Neumann \cite{vN} on computing with noisy circuits. We first develop the framework in \cite{ES}, which leads…
This paper presents an analysis of the concept of capacity for noisy com- putations, i.e. functions implemented by unreliable or random devices. An information theoretic model of noisy computation of a perfect function f (measurable…
$ \newcommand{\cclass}[1]{{\normalfont\textsf{##1}}} $We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer $d > 1$, there…
Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting,…
A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical mechanics techniques. We utilize tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer…
Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a…
Let $\mathsf{TH}_k$ denote the $k$-out-of-$n$ threshold function: given $n$ input Boolean variables, the output is $1$ if and only if at least $k$ of the inputs are $1$. We consider the problem of computing the $\mathsf{TH}_k$ function…
Deep neural networks have been successfully applied to a broad range of problems where overparametrization yields weight matrices which are partially random. A comparison of weight matrix singular vectors to the Porter-Thomas distribution…
Noise is the defining feature of the NISQ era, but it remains unclear if noisy quantum devices are capable of quantum speedups. Quantum supremacy experiments have been a major step forward, but gaps remain between the theory behind these…
We show that the deterministic decision tree complexity of a (partial) function or relation $f$ lifts to the deterministic parity decision tree (PDT) size complexity of the composed function/relation $f \circ g$ as long as the gadget $g$…
Distributed computing models typically assume reliable communication between processors. While such assumptions often hold for engineered networks, e.g., due to underlying error correction protocols, their relevance to biological systems,…
In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by…
Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
Subset selection is a fundamental problem in combinatorial optimization, which has a wide range of applications such as influence maximization and sparse regression. The goal is to select a subset of limited size from a ground set in order…
Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions…
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…
The use of parity-check gates in information theory has proved to be very efficient. In particular, error correcting codes based on parity checks over low-density graphs show excellent performances. Another basic issue of information…
It is known that evolution strategies in continuous domains might not converge in the presence of noise. It is also known that, under mild assumptions, and using an increasing number of resamplings, one can mitigate the effect of additive…