Related papers: Overlap Gap and Computational Thresholds in the Sq…
The symmetric binary perceptron ($\texttt{SBP}$) exhibits a dramatic statistical-to-computational gap: the densities at which known efficient algorithms find solutions are far below the threshold for the existence of solutions. Furthermore,…
In [97,99,100], an fl-RDT framework is introduced to characterize \emph{statistical computational gaps} (SCGs). Studying \emph{symmetric binary perceptrons} (SBPs), [100] obtained an \emph{algorithmic} threshold estimate $\alpha_a\approx…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
Quantitative descriptions of network structure in big data can provide fundamental insights into the function of interconnected complex systems. Small-world structure, commonly diagnosed by high local clustering yet short average path…
For many computational problems involving randomness, intricate geometric features of the solution space have been used to rigorously rule out powerful classes of algorithms. This is often accomplished through the lens of the multi Overlap…
Deep learning has transformed seismic phase picking, but a systematic failure mode persists: for some S-wave arrivals that appear unambiguous to human analysts, the model produces only a distorted peak trapped below the detection threshold,…
When neural networks are trained to classify a dataset, one finds a set of weights from which the network produces a label for each data point. We study the algorithmic complexity of finding a collision in a single-layer neural net, where a…
Tremendous progress has been made experimentally in the hadron spectrum containing heavy quarks in the last two decades. It is surprising that many resonant structures are around thresholds of a pair of heavy hadrons. There should be a…
The paper combines two topics belonging to the general theme of the spontaneous symmetry breaking (SSB) in systems including two basic competing ingredients: the self-focusing cubic nonlinearity and a double-well-potential (DWP) structure.…
Learning in Deep Neural Networks (DNN) takes place by minimizing a non-convex high-dimensional loss function, typically by a stochastic gradient descent (SGD) strategy. The learning process is observed to be able to find good minimizers…
We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher--student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples…
The evidence for the spin density wave (SDW) nature of the pseudogap in HTSC cuprates is presented from resistive and direct gap measurements (ARPES, tunneling experiments, etc.). Its d-wave symmetry mimics the symmetry of the order…
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to…
We develop a theory of percolation with plasticity systems (PWPs) rendering properties of interest for neuromorphic computing. Unlike the standard percolation between two large electrodes, they have multiple ($N\gg 1$) interfaces and…
Recently, it has been observed that when training a deep neural net with SGD, the majority of the loss landscape's curvature quickly concentrates in a tiny *top* eigenspace of the loss Hessian, which remains largely stable thereafter.…
We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width $\epsilon$. Motivated by applications to surface wave propagation phenomena, we study…
Cortical slow oscillations are an emergent property of the cortical network, a hallmark of low complexity brain states like sleep, and represent a default activity pattern. Here, we present a methodological approach for quantifying the…
We consider the algorithmic problem of finding a near-optimal solution for the number partitioning problem (NPP). The NPP appears in many applications, including the design of randomized controlled trials, multiprocessor scheduling, and…
Distributed stochastic gradient descent (SGD) is essential for scaling the machine learning algorithms to a large number of computing nodes. However, the infrastructures variability such as high communication delay or random node slowdown…
Wireless time-sensitive networking (WTSN) is essential for Industrial Internet of Things. We address the problem of minimizing time slots needed for WTSN transmissions while ensuring reliability subject to interference constraints -- an…