1 citations · 2 across the 12 of their papers we have counts for
15 papers
Convex Equilibrium Potentials for Monge--Ampère: Curvature Bounds and A Posteriori Evaluation
Edison Vázquez, Yingdong Lu, Tomasz Nowicki
Equilibrium neural networks define their hidden state as the fixed point of a contraction, so their effective depth is set at evaluation time rather than by the architecture. Using…
Counting Triangles of Graphs via Randomized Trace Estimation with Incomplete Matrix-Vector Products
Soumyadip Ghosh, Lior Horesh, Vasileios Kalantzis +3
Counting triangles in graphs is a fundamental operation in network analysis, underpinning metrics such as clustering coefficients and serving as a signal for community detection, l…
Analysis of Power Iteration Algorithm with Partially Observed Matrix-vector Products
Soumyadip Ghosh, Lior Horesh, Vassilis Kalantzis +3
We consider the problem of computing the dominant eigenvector of a symmetric matrix via the power iteration algorithm subject to constraints in the computation of matrix-vector pr…
Optimality and NP-Hardness of Transformers in Learning Markovian Dynamical Functions
Yanna Ding, Songtao Lu, Yingdong Lu +2
Transformer architectures can solve unseen tasks based on input-output pairs in a given prompt due to in-context learning (ICL). Existing theoretical studies on ICL have mainly foc…
Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion
Anton Lebedev, Won Kyung Lee, Soumyadip Ghosh +7
Large, sparse linear systems are pervasive in modern science and engineering, and Krylov subspace solvers are an established means of solving them. Yet convergence can be slow for…
Dynamical Behaviors of the Gradient Flows for In-Context Learning
Songtao Lu, Yingdong Lu, Tomasz Nowicki
We derive the system of differential equations for the gradient flow characterizing the training process of linear in-context learning in full generality. Next, we explore the geom…
On The Variance of Schatten -Norm Estimation with Gaussian Sketching Matrices
Lior Horesh, Vasileios Kalantzis, Yingdong Lu +1
Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations…
On the iterations of some random functions with Lipschitz number one
Yingdong Lu, Tomasz Nowicki
For the iterations of random functions with Lipschitz number one, we represent the dynamics as a Markov chain and prove its convergence under mild conditions. We a…
Regenerative Ulam-von Neumann Algorithm: An Innovative Markov chain Monte Carlo Method for Matrix Inversion
Soumyadip Ghosh, Lior Horesh, Vassilis Kalantzis +2
This paper presents a regenerative variant of the classical Ulam-von Neumann Markov chain Monte Carlo algorithm for the approximation of the matrix inverse. The algorithm presented…
On Convergence of the Alternating Directions SGHMC Algorithm
Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki
We study convergence rates of Hamiltonian Monte Carlo (HMC) algorithms with leapfrog integration under mild conditions on stochastic gradient oracle for the target distribution (SG…
Multi-Function Multi-Way Analog Technology for Sustainable Machine Intelligence Computation
Vassilis Kalantzis, Mark S. Squillante, Shashanka Ubaru +12
Numerical computation is essential to many areas of artificial intelligence (AI), whose computing demands continue to grow dramatically, yet their continued scaling is jeopardized…
On Representations of Mean-Field Variational Inference
Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki +1
The mean field variational inference (MFVI) formulation restricts the general Bayesian inference problem to the subspace of product measures. We present a framework to analyze MFVI…
Polynomial convergence of iterations of certain random operators in Hilbert space
Soumyadip Ghosh, Yingdong Lu, Tomasz J. Nowicki
We study the convergence of a random iterative sequence of a family of operators on infinite dimensional Hilbert spaces, inspired by the Stochastic Gradient Descent (SGD) algorithm…
Neural Network Training with Asymmetric Crosspoint Elements
Murat Onen, Tayfun Gokmen, Teodor K. Todorov +5
Analog crossbar arrays comprising programmable nonvolatile resistors are under intense investigation for acceleration of deep neural network training. However, the ubiquitous asymm…
Hamiltonian Monte Carlo with Asymmetrical Momentum Distributions
Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki
Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. W…