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This package contains some utilities to enhance training of Flux.jl models.

Train using Optim

Optim.jl can be used to train Flux models (if Flux is on version 0.10 or above), here's an example how

using Flux, Zygote, Optim, FluxOptTools, Statistics
m      = Chain(Dense(1,3,tanh) , Dense(3,1))
x      = LinRange(-pi,pi,100)'
y      = sin.(x)
loss() = mean(abs2, m(x) .- y)
pars   = Flux.params(m)
lossfun, gradfun, fg!, p0 = optfuns(loss, pars)
res = Optim.optimize(Optim.only_fg!(fg!), p0, Optim.Options(iterations=1000, store_trace=true))

The utility provided by this package is the function optfuns which returns three functions and p0, a vectorized version of pars. BFGS typically has better convergence properties than, e.g., the ADAM optimizer. Here's a benchmark where BFGS in red beats ADAGrad with tuned step size in blue, and a stochastic L-BFGS [1] (implemented in this repository) in green performs somewhere in between. losses

From a computational time perspective, S-LBFGS is about 2 times slower than ADAM (with additionnal memory complexity) while the traditional L-BFGS algorithm is around 3 times slower than ADAM (but similar memory burden as SL-BFGS). times

The code for this benchmark is in the runtests.jl.

Visualize loss landscape

Based on the work on loss landscape visualization [2], we define a plot recipe such that a loss landscape can be plotted with

using Plots
contourf(() -> log10(1 + loss()), pars, color=:turbo, npoints=50, lnorm=1)


The landscape is plotted by selecting two random directions and extending the current point (pars) a distance lnorm * norm(pars) (both negative and positive) along the two random directions. The number of loss evaluations will be npoints^2.

Flatten and Unflatten

What this package really does is flattening and reassembling the types Flux.Params and Zygote.Grads to and from vectors. These functions are used like so

p = zeros(pars)  # Creates a vector of length sum(length, pars)
copy!(p,pars)  # Store pars in vector p
copy!(pars,p)  # Reverse

g = zeros(grads) # Creates a vector of length sum(length, grads)
copy!(g,grads) # Store grads in vector g
copy!(grads,g) # Reverse

This is what is used under the hood in the functions returned from optfuns in order to have everything on a form that Optim understands.


[1] "Stochastic quasi-Newton with adaptive step lengths for large-scale problems", Adrian Wills, Thomas Schön, 2018

[2] "Visualizing the Loss Landscape of Neural Nets", Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, Tom Goldstein, 2018