5,644 research outputs found
Laplacian flow for closed G_2 structures: Shi-type estimates, uniqueness and compactness
We develop foundational theory for the Laplacian flow for closed G_2
structures which will be essential for future study. (1). We prove Shi-type
derivative estimates for the Riemann curvature tensor Rm and torsion tensor T
along the flow, i.e. that a bound on will imply bounds on all
covariant derivatives of Rm and T. (2). We show that will blow
up at a finite-time singularity, so the flow will exist as long as
remains bounded. (3). We give a new proof of forward uniqueness
and prove backward uniqueness of the flow, and give some applications. (4). We
prove a compactness theorem for the flow and use it to strengthen our long time
existence result from (2). (5). Finally, we study compact soliton solutions of
the Laplacian flow.Comment: 59 pages, v2: minor corrections and additions, accepted version for
GAF
What Are People Asking About COVID-19? A Question Classification Dataset
We present COVID-Q, a set of 1,690 questions about COVID-19 from 13 sources,
which we annotate into 15 question categories and 207 question clusters. The
most common questions in our dataset asked about transmission, prevention, and
societal effects of COVID, and we found that many questions that appeared in
multiple sources were not answered by any FAQ websites of reputable
organizations such as the CDC and FDA. We post our dataset publicly at
https://github.com/JerryWei03/COVID-Q. For classifying questions into 15
categories, a BERT baseline scored 58.1% accuracy when trained on 20 examples
per category, and for a question clustering task, a BERT + triplet loss
baseline achieved 49.5% accuracy. We hope COVID-Q can help either for direct
use in developing applied systems or as a domain-specific resource for model
evaluation.Comment: Published in Proceedings of the 1st Workshop on NLP for COVID-19 at
ACL 202
Label Noise Reduction Without Assumptions
We propose an algorithm for training neural networks in noisy label scenarios that up-weighs per-example gradients that are more similar to other gradients in the same minibatch. Our approach makes no assumptions about the amount or type of label noise, does not use a held-out validation set of clean examples, makes relatively few computations, and only modifies the minibatch gradient aggregation module in a typical neural network training workflow. For CIFAR-10 classification with varying levels of label noise, our method successfully up-weighs clean examples and de-prioritizes noisy examples, showing consistent improvement over a vanilla training baseline. Our results open the door to potential future work involving per-example gradient comparisons
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