Synthetic Gradients - what's the practical benefit?

Question

I can see two motives to use Synthetic Gradients in RNN:

1. To speed up training, by imediately correcting each layer with predicted gradient
2. To be able to learn longer sequences

I see problems with both of them. Please note, I really like Synthetic Gradients and would like to implement them. But I need to understand where my trail of thought is incorrect.

I will now show why Point 1 and Point 2 don't seem to be beneficial, and I need you to correct me, if they are actually beneficial:

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Point 1:

Synthetic Gradients tell us we can rely on another "mini-helper-network" (called DNI) to advise our current layer about what gradients will arrive from above, even during fwd prop.

However, such gradients will only come several operations later. Same amount of Backprop will have to be done as without DNI, except that now we also need to train our DNI.

Adding this Asyncronisity shouldn't not make layers train faster than during the traditional "locked" full fwdprop -> full back prop sequence, because same number of computations must be done by the device. It's just that the computations will be slid in time

This makes me think Point 1) will not work. Simply adding SG between each layer shouldn't improve training speed.

Point 2:

Ok, how about adding SG only on the last layer to predict "gradient from future" and only if it's the final timestep during forward prop.

This way, even though our LSTM has to stop predicting and must backpropagate, it can still predict the future-gradient it would have received (with the help of DNI sitting on the last timestep).

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Consider several training sessions (session A, session B):

fwdprop timestep_1A ---> fwdprop timestep_2A ---> fwdprop timestep_3A ----> stop and bkprop!

fwdprop timestep_1B ---> fwdprop timestep_2B ---> fwdprop timestep_3B ----> stop and bkprop!

We've just forced our network to "parse" 6 timesteps in two halves: 3 timesteps, then 3 remaining timesteps again.

Notice, we have our DNI sitting at the very end of "Session A" and predicting "what gradient I would get flowing from the beginning of Session B (from future)". Because of that, timestep_3A will be equipped with gradient "that would have come from timestep_1B", so indeed, corrections done during A will be more reliable.

But, hey! These predicted "synthetic gradients" will be very small (negligible) anyway - after all, that's why we start a new backprop session B. Weren't they too small, we would just parse all 6 timesteps in a single long bkprop "session A".

Therefore I think Point 2) shouldn't give benefit either. Adding SG on the last timestep of fwdprop allows to effectively train longer sequences, but vanishing gradients didn't go anywhere.

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Ok. Maybe we can get the benefit of training "session A", "session B" etc on separate machines? But then how is this different to simply training with the usual minibatches in parallel? Keep in mind, was mentioned in point 2: things are worsened by sessionA predicting gradients which are vanishing anyway.

Question: Please help me understand the benefit of Synthetic Gradient, because the 2 points above don't seem to be beneficial

Answer 1

But, hey! These predicted "synthetic gradients" will be very small (negligible) anyway - after all, that's why we start a new backprop session B. Weren't they too small, we would just parse all 6 timesteps in a single long bkprop "session A".

-That's not necessarily correct. We typically truncate and start a new backprop because of hardware constraints, such as memory or computational speed. Vanishing-gradient can be improved by other means, such as Gradient Normalization - scaling-up the gradient vector if it gets too small beyond certain layers, or scaling-down if it's about to explode. Or even using Batch Normalization

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It's important to understand how to update any DNI module. To clear things up, consider an example of network with several layers and 3 DNI modules:

 input
   |
   V
Layer_0 & DNI_0
Layer_1
Layer_2
Layer_3 & DNI_3
Layer_4
Layer_5 & DNI_5
Layer_6
Layer_7
   | 
   V
output

The DNI_0 is always trained with a synthetic gradient arriving from DNI_3 (flowing through Layer_2, and Layer_1 of course), siting several layers further.

Likewise, the DNI_3 is always trained with a synthetic gradient arriving from DNI_5

DNI_0 or DNI_3 will never get to see the true gradient, because true grad is only delivered to DNI_5, and not earlier.

For anyone still struggling to understand them, read this awesome blogpost, part 3

Earlier layers will have to be content with synthetic gradients, because they or their DNI will never witness the "true gradient".

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Regarding training in parallel with minibatches instead of Parallelizing via Synthetic Grads:

Longer sequences are more precise than minibatches, however minibatches add a regulization effect. But, given some technique to prevent gradient from exploding or vanishing, training longer sequences can provide a lot better insight into context of the problem. That's because network infers output after considering a longer sequence of input, so the outcome is more rational.

For the comparison of benefits granted by SG refer to the diagrams page 6 of the Paper, mainly being able to solve longer sequences, which I feel is most beneficial (we can already parallelize via Minibatches anyway, and thus SG shouldn't speed up the process when performed on the same machine - even if we indeed only propagate up to the next DNI).

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However, the more DNI modules we have, the noisier the signal should be. So it might be worth-while to train the layers and DNI all by the legacy backprop, and only after some epochs have elapsed we start using the DNI-bootstrapping discussed above.

That way, the earliest DNI will acquire at least some sense of what to expect at the start of the training. That's because the following DNIs are themselves unsure of what the true gradient actually looks like, when the training begins, so initially, they will be advising "garbage" gradient to anyone sitting earlier than them.

Don't forget that authors also experimented with predicting the actual inputs for every layer.

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If your layers have expensive backprop (perhaps you have Batch-Normalization or some fancy activation functions), correcting with DNI might be a lot cheaper, once it's sufficiently well-trained. Just remember that DNI is not free - it requires matrix multiplication and probably won't provide much speed-up on a simple dense layer.

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Minibatches gives us speedup (via parallelization) and also give us the regularization. Synthetic Gradients allow us to infer better by working with longer sequences and (potentially) less-expensive gradient. All together this is a very powerful system.

Answer 2

Synthetic gradients make training faster, not by reducing the number of epochs needed or by speeding up the convergence of gradient descent, but rather by making each epoch faster to compute. The synthetic gradient is faster to compute than the real gradient (computing the synthetic gradient is faster than the backpropagation), so each iteration of gradient descent can be computed more rapidly.