Event
Microsoft at SODA 2021
Microsoft is proud to be a sponsor of the ACM-SIAM Symposium on Discrete Algorithms (SODA 21).
Mathematics
Working on fundamental problems in mathematics and theoretical computer science, and interacting with the academic community and other researchers on challenging applied problems
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1,027 results found
Publication
Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning
We formally study how Ensemble of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using Knowledge Distillation. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the SAME architecture, trained using the SAME algorithm on the SAME data set, and they only differ by the random seeds used…
Publication
Improved Maximally Recoverable LRCs using Skew Polynomials
An (n,r,h,a,q)-LRC is a linear code over F_q of length n, whose codeword symbols are partitioned into n/r local groups each of size r. Each local group satisfies ‘a’ local parity checks to recover from ‘a’ erasures in that local group and there are further h global parity checks to provide fault tolerance from more global erasure patterns. Such an LRC is Maximally Recoverable (MR), if it can correct all erasure patterns which are information-theoretically…
Video
Different Career Paths: Academia and Industry Panel | Microsoft PhD Summit 2020
A panel of four researchers across academia and industry discuss their different career paths in research. Speakers: Gonzalo Ramos, Principal Researcher, Microsoft [Discussion Lead] Valerie Taylor, CEO and President, CMD-IT & Director, Mathematics and Computer Science Division, Argonne National Laboratory Armando Solar-Lezama, Professor in EECS and Associate Director and COO of CSAIL Kristin Lauter, Principal Researcher and Partner Research Manager, Microsoft
Publication
Learning the Linear Quadratic Regulator from Nonlinear Observations
We introduce a new problem setting for continuous control called the LQR with Rich Observations, or RichLQR. In our setting, the environment is summarized by a low-dimensional continuous latent state with linear dynamics and quadratic costs, but the agent operates on high-dimensional, nonlinear observations such as images from a camera. To enable sample-efficient learning, we assume that the learner has access to a class of decoder functions (e.g., neural networks) that is flexible enough to…
Publication
Feature Learning in Infinite-Width Neural Networks
As its width tends to infinity, a deep neural network’s behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to…
Publication
A Matrix Chernoff Bound for Markov Chains and Its Application to Co-occurrence Matrices
We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued function on its state space. Our result gives exponentially decreasing bounds on the tail distributions of the extreme eigenvalues of the sample mean matrix. Our proof is based on the matrix expander (regular undirected graph) Chernoff bound [Garg et al.…
Career Opportunity
Research Intern – Computational Social Science
The Microsoft Research Computational Social Science (CSS) group is widely recognized as a leading center of CSS research, lying at the intersection of computer science, statistics and the social sciences. Our approach is motivated by two longstanding difficulties for traditional social science: first, that simply gathering observational data on human activity is extremely difficult at scale and over time; and second, that running experiments to manipulate the conditions under which these measurements are made (e.g.,…
Career Opportunity
Research Intern – Mathematics
Microsoft Research New England has a twelve-week research intern position available in mathematics for the summer of 2021, with Henry Cohn as mentor. Eligible applicants include graduate students in mathematics or related fields, exceptionally knowledgeable and experienced undergraduates, or students starting their graduate program in the fall. Research Internships at Microsoft provide a dynamic environment for research careers with a network of world-class research labs led by globally-recognized scientists and engineers. Our researchers and engineers…
Career Opportunity
Post Doc Researcher – Machine Learning and Statistics
The machine learning and statistics group at Microsoft Research NE is actively seeking a qualified postdoctoral researcher to join us in advancing the state-of-the-art in ML and statistics. If your research background is in Machine Learning, Statistics, Artificial Intelligence, or a related field, we would like to hear from you! Microsoft Research offers an exhilarating and supportive environment for cutting-edge, multidisciplinary research, both theoretical and applied, with access to an extraordinary diversity of big and…