https://www.youtube.com/watch?v=4kTD5KkCMQw
Make_stone_look_smooth.meme
Make_stone_look_smooth.meme
YouTube
Mollifiers
In this video I talk about mollifiers, which is a super neat way of turning any function into a smooth one. This is used in image processing, as well as PDEs. Using this, I also show that harmonic functions must be infinitely differentiable, which is a nice…
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Deep Learning for Symbolic Mathematics
Abstract:
Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.
https://arxiv.org/abs/1912.01412
#abstract
Abstract:
Neural networks have a reputation for being better at solving statistical or approximate problems than at performing calculations or working with symbolic data. In this paper, we show that they can be surprisingly good at more elaborated tasks in mathematics, such as symbolic integration and solving differential equations. We propose a syntax for representing mathematical problems, and methods for generating large datasets that can be used to train sequence-to-sequence models. We achieve results that outperform commercial Computer Algebra Systems such as Matlab or Mathematica.
https://arxiv.org/abs/1912.01412
#abstract