backprop
Heterogeneous, typesafe automatic backpropagation in Haskell https://github.com/mstksg/backprop
Version on this page:  0.0.3.0 
LTS Haskell 14.27:  0.2.6.3 
Stackage Nightly 20190921:  0.2.6.3 
Latest on Hackage:  0.2.6.3 
Module documentation for 0.0.3.0
[email protected]:54e62773bcc423aa829ca19d8fd2d1d852467d13496f7b955fdbbe91d5d0408f,3902
backprop
Literate Haskell Tutorial/Demo on MNIST data set (and PDF rendering)
Automatic heterogeneous backpropagation that can be used either implicitly (in the style of the ad library) or using explicit graphs built in monadic style. Implements reversemode automatic differentiation. Differs from ad by offering full heterogeneity – each intermediate step and the resulting value can have different types. Mostly intended for usage with tensor manipulation libraries to implement automatic backpropagation for gradient descent and other optimization techniques.
Currently up on hackage (with 100% documentation coverage), but more uptodate documentation is currently rendered on github pages!
At the moment this project is in prealpha (v0.0.1.0), and is published/put up on Hackage as a call for comments and thoughts. It has 100% documentation coverage at the moment. Performance was not yet a priority before this, but will be from now on. (Previously, highest priority was API/usability). See the todos section for more information on what’s missing, and how one would be able to contribute!
MNIST Digit Classifier Example
Tutorial and example on training on the MNIST data set available here as a literate haskell file, or rendered here as a PDF! Read this first!
The literate haskell file is a standalone haskell file that you
can compile (preferably with O2
) on its own with stack or some other
dependency manager. It can also be compiled with the build script in the
project directory (if stack is installed, and appropriate dependencies are
installed), using
$ ./Build.hs exe
Brief example
The quick example below describes the running of a neural network with one
hidden layer to calculate its squared error with respect to target targ
,
which is parameterized by two weight matrices and two bias vectors.
Vector/matrix types are from the hmatrix package.
logistic :: Floating a => a > a
logistic x = 1 / (1 + exp (x))
matVec
:: (KnownNat m, KnownNat n)
=> Op '[ L m n, R n ] (R m)
neuralNetImplicit
:: (KnownNat m, KnownNat n, KnownNat o)
=> R m
> BPOpI s '[ L n m, R n, L o n, R o ] (R o)
neuralNetImplicit inp = \(w1 :< b1 :< w2 :< b2 :< Ø) >
let z = logistic (liftB2 matVec w1 x + b1)
in logistic (liftB2 matVec w2 z + b2)
where
x = constRef inp
neuralNetExplicit
:: (KnownNat m, KnownNat n, KnownNat o)
=> R m
> BPOp s '[ L n m, R n, L o n, R o ] (R o)
neuralNetExplicit inp = withInps $ \(w1 :< b1 :< w2 :< b2 :< Ø) > do
y1 < matVec ~$ (w1 :< x1 :< Ø)
let x2 = logistic (y1 + b1)
y2 < matVec ~$ (w2 :< x2 :< Ø)
return $ logistic (y2 + b2)
where
x1 = constVar inp
Now neuralNetExplicit
and neuralNetImplicit
can be “run” with the input
vectors and parameters (a L n m
, R n
, L o n
, and R o
) and calculate the
output of the neural net.
runNet
:: (KnownNat m, KnownNat n, KnownNat o)
=> R m
> Tuple '[ L n m, R n, L o n, R o ]
> R o
runNet inp = evalBPOp (neuralNetExplicit inp)
But, in defining neuralNet
, we also generated a graph that backprop can
use to do backpropagation, too!
dot :: KnownNat n
=> Op '[ R n , R n ] Double
netGrad
:: forall m n o. (KnownNat m, KnownNat n, KnownNat o)
=> R m
> R o
> Tuple '[ L n m, R n, L o n, R o ]
> Tuple '[ L n m, R n, L o n, R o ]
netGrad inp targ params = gradBPOp opError params
where
 calculate squared error, in *explicit* style
opError :: BPOp s '[ L n m, R n, L o n, R o ] Double
opError = do
res < neuralNetExplicit inp
err < bindRef (res  t)
dot ~$ (err :< err :< Ø)
where
t = constRef targ
The result is the gradient of the input tuple’s components, with respect
to the Double
result of opError
(the squared error). We can then use
this gradient to do gradient descent.
For a more fleshed out example, see the MNIST tutorial (also rendered as a pdf)
Benchmarks
The current version isn’t optimized, but here are some basic benchmarks comparing the library’s automatic differentiation process to “manual” differentiation by hand. When using the MNIST tutorial as an example:
Calculating the gradient using backprop and calculating it by hand (by manual symbolic differentiation) are within an order of magnitude of eachother, timewise. Using the backprop library takes about 6.5x as long in this case.
However, a full update step (calculate the gradient and update the neural net) adds a lot of constant costs, so for a full training step, the backprop library takes only 2.7x as long as manual symbolic differentation.
This means using this library only slows down your program by a factor of about 2.5x, compared to using only hmatrix.
It’s still definitely not ideal that more than half of the computation time is overhead from the library, but this is just where we stand at the moment. Optimization is just now starting!
Note that at the moment, simply running the network is only slightly slower when using backprop.
Todo

Profiling, to gauge where the overhead comes from (compared to “manual” backpropagation) and how to bring it down.

Some simple performance and API tweaks that are probably possible now and would clearly benefit: (if you want to contribute)
a. ~~Providing optimized
Num
/Fractional
/Floating
instances forBVal
by supplying known gradients directly instead of relying on ad.~~ (Now finished, since b3898ae)
b. Switch from `ST s` to `IO`, and use `unsafePerformIO` to automatically
bind `BVal`s (like *ad* does) when using `liftB`. This might remove
some overhead during graph building, and, from an API standpoint,
remove the need for explicit binding.
c. Switch from `STRef`s/`IORef`s to `Array`. (This one I'm unclear if it
would help any)
 Benchmark against competing backpropagation libraries like ad, and autodifferentiating tensor libraries like grenade

Explore opportunities for parallelization. There are some naive ways of directly parallelizing right now, but potential overhead should be investigated.

Some open questions:
a. Is it possible to offer pattern matching on sum types/with different constructors for implicitgraph backprop? It’s possible for explicitgraph versions already, with
choicesVar
, but not yet with the implicitgraph interface. Could be similar to an “Applicative vs. Monad” issue where you can only have predetermined fixed computation paths when usingApplicative
, but I’m not sure. Still, it would be nice, because if this was possible, we could possibly do away with explicitgraph mode completely.b. Though we already have safe sum type support with explicitgraph mode, we can’t support GADTs yet safely. It’d be nice to see if this is possible, because a lot of dependently typed neural network stuff is made much simpler with GADTs.
As of v0.0.3.0, we have a way of dealing with GADTs in explicitgraph mode (using
withGADT
) that is unsafe, and requires some ugly manual plumbing by the user that could potentially be confusing. But it would still be nice to have a way that is safe and doesn’t require the manual plumbing and isn’t as easy to mess up.
Changes
Changelog
Version 0.0.3.0
https://github.com/mstksg/backprop/releases/tag/v0.0.3.0

Removed samples as registered executables in the cabal file, to reduce dependences to a bare minimum. For convenience, build script now also compiles the samples into the local directory if stack is installed.

Added experimental (unsafe) combinators for working with GADTs with existential types,
withGADT
, to Numeric.Backprop module. 
Fixed broken links in Changelog.
Version 0.0.2.0
https://github.com/mstksg/backprop/releases/tag/v0.0.2.0

Added optimized numeric
Op
s, and rewriteNum
/Fractional
/Floating
instances in terms of them. 
Removed all traces of
Summer
/Unity
from the library, eliminating a whole swath of “explicitSummer”/“explicitUnity” versions of functions. As a consequence, the library now only works withNum
instances. The API, however, is now much more simple. 
Benchmark suite added for MNIST example.
Version 0.0.1.0
https://github.com/mstksg/backprop/releases/tag/v0.0.1.0
 Initial prerelease, as a request for comments. API is in a usable form and everything is fully documented, but there are definitely some things left to be done. (See README.md)