6 pages, LaTeX, to appear in Proc. of International Conf. "Geometrization of Physics - II", Kazan, Russia, Oct 28 - Nov 2, 1995. Withdrawn
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While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…
In this paper we propose a deep neural network model with an encoder-decoder architecture that translates images of math formulas into their LaTeX markup sequences. The encoder is a convolutional neural network (CNN) that transforms images into a group of feature maps. To better capture the spatial relationships of mat…
Galactica learns from scientific literature to help researchers.
problem Information overload in scientific literature makes it hard to find useful insights.
method Trained on a large corpus of scientific papers, reference material, and knowledge bases.
result Outperforms existing models on various scientific tasks, including LaTeX equations and mathematical reasoning.
This survey of some of the more topological aspects of the placement problem for complex curves in complex surfaces was originally published in L'Enseignement Mathematique 29 (1983). The present LaTeXed redaction corrects several typographical errors without, I hope, introducing new ones; some minor emendations and ref…
Polylab is a MATLAB toolbox for multivariate polynomial modeling.
problem Efficiently modeling and manipulating multivariate polynomials across CPU and GPU.
method Unified symbolic-numeric interface, three aligned classes (MPOLY, MPOLY_GPU, MPOLY_HP), polynomial operations, differentiation, matrix computations.
result Advantages of MPOLY-HP for reduction-heavy simplification and large-scale computations, and the stochastic log-determinant variant for sparse regimes.
Because the choice and tuning of the optimizer affects the speed, and ultimately the performance of deep learning, there is significant past and recent research in this area. Yet, perhaps surprisingly, there is no generally agreed-upon protocol for the quantitative and reproducible evaluation of optimization strategies…