[Matryoshka-devel] Paper Draft - A Formal Proof of the Expressiveness of Deep Learning

Anders Schlichtkrull andschl at dtu.dk
Sat Apr 8 12:28:42 CEST 2017


Dear Alex

I looked very briefly at your paper and I think it is a really cool formalization!

The only other feedback I have is these two small suggestions:

On page 4:
"We focus on an arbitrary entry yi of the ouput vector y."
I think "ouput" should be "output".

On page 5:
"On the other hand, our analysis is build upon inequalities, which only provide an upper bound."
I think "build" should be "built".

Best regards,
Anders

On 6 Apr 2017, at 10.45, Alexander Bentkamp <a.bentkamp at vu.nl<mailto:a.bentkamp at vu.nl>> wrote:


Dear colleagues,

I would like to share with you the draft of a paper about my master thesis project that we will submit to ITP.

A Formal Proof of the Expressiveness of Deep Learning
Alexander Bentkamp, Jasmin Christian Blanchette, and Dietrich Klakow
http://matryoshka.gforge.inria.fr/pubs/deep_learning_paper.pdf

The paper presents a formalization in Isabelle/HOL of a mathematical result explaining the superiority of deep learning over shallow learning. We simplified and restructured the original proof to facilitate the formalization. The project led to the development and extension of reusable libraries of tensors, matrices, multivariate polynomials, and the Borel measure.

Comments are welcome, before or after the deadline (10 April).

Best regards,
Alex

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