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Homepage: http://transcranial.github.io
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MXnet.js [1] is an emscripten port of the base C++ framework. It runs entirely in the browser and works fairly well. The actual code produced by emscripten isn't that large, but the model weights can become an issue. I've tried to get emscripten working on tensorflow, even just for forward prediction, but have been pretty much gotten nowhere. Of course this doesn't let you harness GPU power.
Lots of cool potential applications of doing deep learning over the web are just waiting to be discovered and built.
Here's an example of a paper where they simultaneously optimize high-level semantics with token-level sequence probabilities: http://arxiv.org/pdf/1606.00776v2.pdf.
Here's a interesting example from Google DeepMind learning to generate code for Magic The Gathering and Hearthstone: http://arxiv.org/pdf/1603.06744v2.pdf
[1] https://en.wikipedia.org/wiki/Lung_cancer#/media/File:Cancer...
"2. Dahl, R.: Automatic colorization. In: http://tinyclouds.org/colorize/. (2016)"
They even included it in their comparisons (Table 1; Figure 5).
For those who use Jupyter: there's a package called Hydrogen that let's you run your code directly within Atom using Jupyter kernels (not just python!). To me, that's the perfect example of the power of a hackable editor.