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We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in…
Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when…
Colloidal bodies of irregular shape rotate as they descend under gravity in solution. This rotational response provides a means of bringing a dispersion of identical bodies into a synchronized rotation with the same orientation using…
We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set $[k]$). Then, in every (synchronous) round, each agent can revise…
Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean.…
We analyze the effect of interference on the convergence rate of average consensus algorithms, which iteratively compute the measurement average by message passing among nodes. It is usually assumed that these algorithms converge faster…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
In two-time-scale stochastic approximation (SA), two iterates are updated at varying speeds using different step sizes, with each update influencing the other. Previous studies on linear two-time-scale SA have shown that the convergence…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We present an algorithm for maintaining maximal matching in a graph under addition and deletion of edges. Our data structure is randomized that takes O(log n) expected amortized time for each edge update where n is the number of vertices in…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…
We present a new approach for finding matchings in dense graphs by building on Szemer\'edi's celebrated Regularity Lemma. This allows us to obtain non-trivial albeit slight improvements over longstanding bounds for matchings in streaming…
Linear consensus iterations guarantee asymptotic convergence, thereby, limiting their applicability in applications where consensus value needs to be used in real time to perform a system level task. It also leads to wastage of power and…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown…
We study dynamic $(1-\epsilon)$-approximate rounding of fractional matchings -- a key ingredient in numerous breakthroughs in the dynamic graph algorithms literature. Our first contribution is a surprisingly simple deterministic rounding…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electron charges as a trace/diagonal of a matrix function,…