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Research area: Mathematics

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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1,031 results found
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Applied Research Group in Security 

We are an applied research team bringing impact driven research in the Security and Compliance suite for O365 customers. We explore cutting edge techniques in diverse disciplines that protect our customers from online attacks at scale, demonstrate Microsoft’s thought leadership in the security space, while also advancing state of the art in the process. Our research drives longer term product innovations and helps shape new product features and experiences at scale.  We actively cultivate internal…

Publication

Forward Super-Resolution: How Can GANs Learn Hierarchical Generative Models for Real-World Distributions 

by Zeyuan Allen-Zhu, Yuanzhi Li

Generative adversarial networks (GANs) are among the most successful models for learning high-complexity, real-world distributions. However, in theory, due to the highly non-convex, non-concave landscape of the minmax training objective, GAN remains one of the least understood deep learning models. In this work, we formally study how GANs can efficiently learn certain hierarchically generated distributions that are close to the distribution of images in practice. We prove that when a distribution has a structure that…

Video

Microsoft Research Conversations in STEM: Future Horizons of Science 

Future Horizons of Science If you agree with Arthur C. Clarke that the only way to discover the limits of the possible is to venture a little way past them into the impossible, you’ll be delighted to join us for a live Q&A conversation about venturing past the possible and into new horizons of technical innovation featuring MSR’s Yael Tauman Kalai, Bichlien Nguyen and Andromachi Chatzieleftheriou. Moderated by 2021 Microsoft Research Ada Lovelace Fellowship recipient…

illustration of data storage and cloud storage around the Eiffel tower
Group

Inria Joint Center 

The Centre’s objective is to pursue fundamental, long-term research in formal methods, software security, and the application of computer science research to the sciences.

Event

Microsoft at SODA 2021 

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Microsoft is proud to be a sponsor of the ACM-SIAM Symposium on Discrete Algorithms (SODA 21).

Publication

Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning 

by Zeyuan Allen-Zhu, Yuanzhi Li, Zeyuan Allen-Zhu

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 

by Sivakanth Gopi, Venkatesan Guruswami

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 

by Zakaria Mhammedi; et. al.

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 

by Greg Yang, Edward J. Hu

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…

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