Delay Pipelining/Queues in Accelerate

[Andrew Gozzard]

Hi all,

Sorry if this is the wrong place to ask about this, or if the question is particularly naive. I have just started looking into Accelerate and am hoping to use it for a personal research project of mine.

Long story short, I am hoping to implement a fast-wavenet style wavenet evaluator (https://github.com/tomlepaine/fast-wavenet). The fast-wavenet evaluation method runs in O(N) time as opposed to O(2^N), so I am sure you can see the benefits of this method. The imperative implementation of this uses queues as a sort of delay pipeline in order to reuse a generated intermediate result at a later step of the evaluation, rather than having to recompute it.

I see no logical reason this should not be possible with Accelerate. Implementing a general queue may not be feasible, as every implementation I can think of either requires exposed mutable memory or uses asymptotic tricks that require significant amount of work in branches and so would likely cause significant divergence on GPU. However, the specific purpose of delay pipelining I think would be of benefit to Accelerate. Also, using array permutations or similar mutations would require (to my understanding, correct me if I am wrong) copying the array every time, thereby achieving no speedup over the naive wavenet implementation.

I would appreciate any advice you might have on how to implement this functionality. As I say, I see no logical reason it should be impossible, but I am by no means and expert, so please correct me if this is not feasible.

Regards,

Andrew

[Trevor McDonell]

Hi Andrew,

On Tue, 4 Apr 2017 at 21:51 Andrew Gozzard <gozz...@gmail.com> wrote:

Hi all,

Sorry if this is the wrong place to ask about this, or if the question is particularly naive. I have just started looking into Accelerate and am hoping to use it for a personal research project of mine.

Perfectly fine place to ask questions. Welcome (:

 

Long story short, I am hoping to implement a fast-wavenet style wavenet evaluator (https://github.com/tomlepaine/fast-wavenet). The fast-wavenet evaluation method runs in O(N) time as opposed to O(2^N), so I am sure you can see the benefits of this method. The imperative implementation of this uses queues as a sort of delay pipeline in order to reuse a generated intermediate result at a later step of the evaluation, rather than having to recompute it.

I see no logical reason this should not be possible with Accelerate. Implementing a general queue may not be feasible, as every implementation I can think of either requires exposed mutable memory or uses asymptotic tricks that require significant amount of work in branches and so would likely cause significant divergence on GPU. However, the specific purpose of delay pipelining I think would be of benefit to Accelerate. Also, using array permutations or similar mutations would require (to my understanding, correct me if I am wrong) copying the array every time, thereby achieving no speedup over the naive wavenet implementation.

I am not familiar with the algorithm, but at a glance I guess it should be possible in the way you describe. You are correct though in that permute will copy the array each time, so that might not be what you want after all (it tries to avoid the copy, but you might not want to hinge your algorithm on this occurring).

 

If the queue is dynamic, it could be better to do the queuing logic in regular Haskell, and use Accelerate only for the computations between nodes. Accelerate will only copy results back from the GPU when you demand the actual values (or `deepseq` the array), not after each `run`, so splitting the computation in that way shouldn't impose extra overhead compared to feeding it a single large computation. It might make it easier to use `run1` as well, for each of the individual computations, which can be important.

If the queue is more static, just given by that dilation parameter which you set up front rather than being derived from intermediate results, then maybe you can just use Haskell as your meta-programming language to generate the Accelerate program of the correct shape (`Acc` is really just a data structure, so you can manipulate it much like any other; only when you call `run` does it turn that data structure into code and execute it).

I hope that makes sense?

Cheers,

-Trev

I would appreciate any advice you might have on how to implement this functionality. As I say, I see no logical reason it should be impossible, but I am by no means and expert, so please correct me if this is not feasible.

Regards,

Andrew

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[Andrew Gozzard]

Hi Trevor,

Thanks for the quick reply, and sorry for my delay in responding.

The queues are absolutely static in size, determined by the dilation value, as you realized. If I was writing this in an imperative language I would write a simple cyclic implementation of a queue.

I am not sure I entirely follow what you are saying about using Haskell as a meta-programming language. I take it you mean to automatically generate the structure, including the queues, but I don't see how to do that without having to perform the full linear rotation on the array I am using as a queue. I can't imagine Accelerate is able to optimize that out, but having said that I have been amazed by what you have been able to achieve in other areas.

Perhaps I lack imagination, but I am struggling to think of any way to make an Accelerate structure do this.

I feel I am somewhat out of my depth here. Thanks for all the help.

Cheers,

Andrew

[Trevor McDonell]

Hey Andrew,

Sorry for the delay in replying, this got buried.

The metaprogramming approach is a slightly tricky thing. The key is that since the Accelerate program is compiled and executed at program runtime, then you can have a Haskell program which generates the Accelerate program, that you then compile and execute.

For example, I use this here when defining an MD5 hash routine. Note that the step function takes a regular Haskell i :: Int, together with the current state of the expression (a0, b0 …) which are of type Exp Word32, and generates a new quadruple of expressions of type Exp Word32 representing the next step of the hash routine. The overall effect being that we are using Prelude.foldl to generate an unrolled loop. A corollary of this is that we can just use regular Haskell data structures to store the intermediate program, like a, b in a tuple, and the constants k and r in a list, and these bits do not have to be fast at all — since these happen at program construction time, not within the core loop during execution (which is why just using slow list indexing for the constants is fine).

You might be able to do a similar thing with your program. If the queues are used as a method to keep track of the intermediate computations, and determine what should be combined with what next, then maybe you can move the queue structure to the Haskell part and do an analagous thing to loop unrolling. If you can do that, then what you’ll have is a Haskell program which generates a completely unfolded computation; no queues in the Accelerate part at all, since they are just used to describe how the computation should proceed (which nodes connect to which), in the same way that Prelude.foldl in the MD5 program specifies that the loop should go from [0..64], but the list is not present in the final program at all.

Another example here, which generates a divide-and-conquer style computation.

Just to be clear though, make sure you know which phase a particular computation is happening in, because you can’t mix the two. For example, if you need to push to the front of the queue or to the back depending on the value of the computation, you probably won’t be able to use this method, because those happen at different phases. It’s very easy to trip up on this (one of the strengths and weaknesses of embedded languages).

It is probably worthwhile to try, for a given diliation parameter, would it be possible to draw what the program execution graph would look like, only using the queue to decide which nodes/computations to connect to which others.

Hope that clarifies some things.

Feel free to ping me directly if I’m not being responsive.

-Trev

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[Andrew Gozzard]

Hi Trev,

Thanks for the response. That sounds like it should do the trick.

The queues are simply to add a delay to the use of a value. Whenever an intermediate value is computed, it is put into the queue for later use as well as being used immediately. This is because the binary tree structure of the WaveNet has symmetry between left and right branches, and so as the signal is fed in and shuffles towards the left, eventually the left subtree will be exactly duplicating a computation made by the right subtree earlier. By reusing this value (hence the queue, as they are consumed by the left and produced by the right at exactly the same rate) we can save having to evaluate any left subtree, thereby taking the time complexity of evaluating a step of this algorithm down to O(N) rather than O(2^N) where N is the number of layers.

I will have a look at the examples you linked when time permits, but I feel this seems quite promising.

Thank you for all your help and input.

Cheers,

Andrew

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[Andrew Gozzard]

Hi Trev,

I have been quite busy, and have only just had a chance to take a crack at this, and I quite frankly just can't see how to get this to work. If it is not too much to ask, I was hoping I might be able to ask you for how you might implement a simple example that should be transferable to my problem.

In rough C++, I want to implement logic something like this:

vector<float> input(...); // Some sequential input signal
queue<float> q1, q2; // The delay lines, storing previous values until they are required again
for (int i = 0; i < 4; ++i) q1.push(0); // Set delay line "lengths"
for (int i = 0; i < 8; ++i) q2.push(0); // One queue per "layer"
vector<float> output();
for (float s : input) {
    float result1 = q1.front() + s; // Evaluate layer 1, reusing an old input
    q1.pop(); // Discard the old input, as we wont need it again
    q1.push(s); // Push the new input to the delay line
    float result2 = q2.front() + result1; // Evaluate layer 2, input from layer 1
    q2.pop();
    q2.push(result1);
    output.push_back(result2); // The output from the last layer is the result of the whole system
}

Obviously this is a tremendously simplified example, my real application evaluates the output of an entire layer of neurons rather than just adding two numbers together, but this is an example of the sort of structure I am struggling with. My hope is that I can use accelerate to be able to run multiple pipelines (with different weights, but the same shape) over multiple input signals, all in parallel, on GPU.

As I say, I just can't fathom how to achieve this in accelerate. You suggested unrolling the recurrence over the length of the signal and then letting accelerate evaluate the whole pipeline, but when I try to do exactly that I just get stumped part way through. I think I just don't understand accelerate well enough, and this seems like a very rare use case, so it is hard to learn how to handle it.

Any help you can offer is much appreciated. I will say again just how impressed I am with accelerate, and that I wish I understood it better.

Cheers,

Andrew

[Trevor McDonell]

Hey Andrew,

I think you might have simplified your example too much here. Specifically, I’m no longer sure what should be a single float, and what is actually an array. I guess everything in your real program is actually a matrix though? You should probably correct me on that though, since that is kinda important…

Assuming that your queues are actually matrices, here is a pretty literal translation of what you wrote above:

import Data.Sequence                                                ( Seq, ViewL(..) )
import qualified Data.Sequence                                      as Seq
import qualified Data.Foldable                                      as Seq

import Data.Array.Accelerate                                        as A

foo :: Exp DIM2                         -- shape of every input
    -> [ Acc (Matrix Float) ]           -- list of inputs
    -> [ Acc (Matrix Float) ]           -- what to do at the end of the loop??
foo sh input =
  let zeros = A.fill sh 0
      q1    = Seq.replicate 4 zeros
      q2    = Seq.replicate 8 zeros
      --
      go _  _  output []     = output
      go q1 q2 output (s:ss) =
        let
            q1head :< q1tail = Seq.viewl q1
            q2head :< q2tail = Seq.viewl q2

            result1 = q1head `f` s
            result2 = q2head `f` result1
        in
        go (q1tail Seq.|> s) (q2tail Seq.|> result1) (output Seq.|> result2) ss
  in
  Seq.toList $ go q1 q2 Seq.empty input

f :: Acc (Matrix Float) -> Acc (Matrix Float) -> Acc (Matrix Float)
f = undefined

I don’t know what you need to do with that output, but at some point you’ll need to turn it into an Acc a so that you can run it; the above is just generating the program, which is why the queues contain Acc things, rather than “real” matrices. (If all the actual work happens in f, then you might get away with doing the run1 at that point.)

As I mentioned above, if I have made some incorrect assumption about your types here let me know, since that might change the structure / approach quite a bit, but we’ll try and figure out something which will actually work for you. The important distinction is going to be what is a scalar Exp e vs. some Acc a array.

My hope is that I can use accelerate to be able to run multiple pipelines (with different weights, but the same shape) over multiple input signals, all in parallel,

I think there is a lot of detail here (e.g. the types of everything involved; scalar values vs. arrays/matrices) which I don’t understand yet, so it is difficult for me to provide concrete pointers…

By the way, I have started writing some BLAS bindings for Accelerate, which you may be interested in; code, haddocks.

Cheers,
-Trev

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[Andrew Gozzard]

Hi Trev,

Thanks for the reply. It is very informative. You are right to assume that I am doing matrix arithmetic rather than individual floats. instead of simply adding two numbers together, each number is actually a column-vector, which is multiplied by a weighting matrix and then added element-wise.

Regardless, your post has made things a lot clearer for me. I don't know what I was doing before to make it seem so confusing, but this looks perfect.

Sorry to oversimplify as much as I did. As I say I am in fact using matrix types everywhere.

Regarding my running multiple networks over multiple signals, as far as I understand that should be a straightforward expansion from this, as simple as passing the function a set of weights and a set of signals and having it map these operations over all pairs.

Adding BLAS bindings seems like a great idea.

Thanks for all your help, and if I manage to get anything noteworthy out of this I will be sure to let you know.

Cheers,

Andrew

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[Trevor McDonell]

Hey Andrew,

Glad to hear that it helped (:

Good luck. I'm interested to hear how it turns out (even if it doesn't work for some reason).

Cheers,

-Trev

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