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I work as as a researcher and am kind of new to neural networks. I have an RNN (1e4 x 1e4 network) that I would like to train in either MATLAB or Julia.

One option I considered is writing my own code for Hessian-free optimization, but the implementational details are really, really hard to figure out.

I am aware there is a Theano or TF implementation of HFO but I I am primarily interested in having the code in MATLAB/Julia.

Also, are there better/alternative techniques than Hessian-free optimization for training RNN's ?
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Hessian-free second order will not likely work. There are reasons why everyone using gradient descent. The only working second order method seems K-FAC (disclaimer - I have no first hand experience) but as you will use Julia you will have to implement it from scratch, and it's highly non-trivial (as you can expect from method which work where other failed)
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I know you said you are interested in MATLAB or Julia, but I'm interested in why not a python library? I mean a simple Google search would show lots of pytorch HFO solutions.
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Matlab has a deep learning Toolbox that makes it easy and efficient to train any type of model. Including RNNs.
Although, there is a good argument (and a famous paper) that anything you can do with RNN you can do better with CNN.
Julia has deep learning libraries, but don't expect nearly the level of support and ease of use as Matlab.
Matlab's DL is underrated.
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