In the final post of the series we come full circle, speeding up our single-GPU training implementation to take on a field of multi-GPU competitors.
Training to 94% test accuracy took 341s and with some minor adjustments to network and data loading we had reduced this to 297s. We’ve reached the end of the series and a few words are in order.
We then freeze the final model from run b) and recompute losses over the last several epochs from the training run just completed. Training on smaller images can also increase the batch size, which usually speeds things up due to vectorization. If batch normalization is placed after the addition, it has the effect of normalizing the output of the entire block. We start with the practical matter of some code optimisation. This gives an impressive improvement to 94.3% test accuracy (mean of 50 runs) allowing a further 3 epoch reduction in training and a 20 epoch time of 52s for 94.1% accuracy. If we SGD with mini-batches is similar to training one example at a time, with the difference being that parameter updates are delayed until the end of a batch. These results were run on the deeper 110-layer models. 15 epochs brings a test accuracy of 94.1% in 39s, closing in on the 4-GPU, test-time-augmentation assisted DAWNBench leader! First, we argued that delaying updates until the end of a mini-batch is a higher order effect and that it should be ok in the limit of small learning rates. If we choose evenly-sized groups, this is not quite the same as making a random choice for each example (which leads to irregular group sizes) but it’s close enough. The far right plot shows why this is so.
First let’s plot the leading eigenvectors of the covariance matrix of 3×3 patches of the input data. At batch size 512 we enter the regime where curvature effects dominate and the focus should shift to mitigating these. Natalia Gimelshein, Nicolas Vasilache, Jeff Johnson for code and discussions around multi-GPU optimization. This eminently sensible approach goes by the name of test-time augmentation. Quick turnaround time and continuous validation are helpful when designing the full system because overlooked details can often bite you in the end. Finally we can use the increased accuracy to reduce training to 17 epochs. This is larger than many of the effects that we are measuring. While ResNets have definitely improved over Oxford’s VGG models in terms of efficiency, GoogleNet seems to still be more efficient in terms of the accuracy / ms ratio. Our basic implementation is rather simple, taking about 35 lines of code (without any Pytorch DataLoaders.) There are 625 possible 8×8 cutout regions in a 32×32 image, so we can achieve random augmentation by shuffling the dataset and splitting into 625 groups, one for each of the possible cutout regions. We can avoid this by applying the same augmentation to groups of examples and we can preserve randomness by shuffling the data beforehand. This way, we can quickly identify the parts of the research that are the most important to focus on during further development.
We did not tune our models heavily over the validation error and so haven’t overfitted to the validation set. In the limit of low learning rates, one can argue that this delay is a higher order effect and that batching doesn’t change anything to first order, so long as gradients are summed, not averaged, over mini-batches. Recall that we are normalising, transposing and padding the dataset before training to avoid repeating the work at each epoch. through further algorithmic developments.
We can restore the previous accuracy by adding an extra epoch to training.
For the learning rate, a simple choice is to stick with the piecewise linear schedule that we’ve been using throughout, floored at a low fixed value for the last 2 epochs and we choose a momentum of 0.99 so that averaging takes place over a timescale of roughly the last epoch. For a more in-depth report of the ablation studies, read here. This automatically benchmarks each possible algorithm on your GPU and chooses the fastest one. We plot the final training and test losses at batch size 128 when we train using subsets of the training set of different sizes. We are going to pick a fixed learning rate schedule with lower learning rates appropriate for longer training and increase the amount of cutout augmentation to 12×12 patches to allow training for longer without overfitting.
By default, Torch uses a smoothing factor of 0.1 for the moving average. We need to choose a new learning rate schedule with higher learning rates towards the end of training, and a momentum for the moving average. The results are as we would hope: We can directly observe the effects of forgetfulness with the following experiment. According to our discussion above, any reasonable rule to limit this kind of approach should be based on inference time constraints and not an arbitrary feature of the implementation and so from this point-of-view, we should accept the approach. Deep feed-forward conv nets tend to suffer from optimization difficulty. Earlier batches will be effectively forgotten. I hope that the reader will find this useful in their work and believe that training times have a long way to fall yet (or accuracies improve if that’s your thing!)
“Very deep convolutional networks for large-scale image recognition.” arXiv preprint arXiv:1409.1556 (2014). We are also training a 152-layer ResNet model, but the model has not finished converging at the time of this post. The author of ResNet9 has written a series of blogsto explain, step-by-step, how the network achieved such a significant speedup. Note that our earlier submission, allowing the same TTA, would achieve a time of 60s on a 19 epoch training schedule without further changes. This also includes options for training on CIFAR-10, and we also describe how one can train Resnets on their own datasets. We roll-out a bag of standard and not-so-standard tricks to reduce training time to 34s, or 26s with test-time augmentation. Our main weapon is statistical significance. ImageNet/ResNet -50 is one of the most popular datasets and DNN models for benchmarking large-scale distributed deep learning.
Moving the whole dataset (in uint8 format) to the GPU takes a negligible 40ms whilst completing the preprocessing steps on the GPU is even faster, completing in about 15ms. We are otherwise happy with ReLU so we’re going to pick a simple smoothed-out alternative.
By the end of the post our single-GPU implementation surpasses the top multi-GPU times comfortably, reclaiming the coveted DAWNBench crown with a time of 34s and achieving a 10× improvement over the single-GPU state-of-the-art at the start of the series!
Our results come fairly close to those in the paper: accuracy correlates well with model size, but levels off after 40 layers or so.
This dropout-training viewpoint makes it clear that any attempt to introduce a rule disallowing TTA from a benchmark is going to be fraught with difficulties. Our training thus far uses a batch size of 128. Now speedups are great, but this result is surprising to me. Finishing 90-epoch ImageNet-1k training with ResNet-50 on a NVIDIA M40 GPU takes 14 days. The optimal learning rate factor (measured by test set loss) is close to one for the full training dataset which is expected since this has been hand optimised. The classic way to remove input correlations is to perform global PCA (or ZCA) whitening. This is the sort of thing a friendly compiler might do for you, but for now let’s switch the order by hand. The results above suggest that if one wishes to train a neural network at high learning rates then there are two regimes to consider. To fix this, we introduced a multi-threaded mode for DataParallelTable that uses a thread per GPU to launch kernels concurrently. These arguments are not only relevant to artificial benchmarks but also to end use-cases. When running a hyperparameter search, it can often pay off to try fancier optimization strategies than vanilla SGD with momentum. Let’s see what improvement TTA brings. Batch norm does a good job at controlling distributions of individual channels but doesn’t tackle covariance between channels and pixels. Multi-threaded kernel launching : The FFT-based convolutions require multiple smaller kernels that are launched rapidly in succession. In our case, the tasks in question are different parts of the same training set and forgetfulness can occur within a single epoch at high enough learning rates.
The main goal of today’s post is to provide a well-tuned baseline on which to test novel techniques, allowing one to complete a statistically significant number of training runs within minutes on a single GPU. This is probably a good approach for training benchmarks too. The bulk of the time is spent transferring the preprocessed dataset back to the CPU which takes nearly half-a-second. Here are two random augmentations of the same 4 images to show it in action: More importantly it’s fast, taking under 400ms to iterate through 24 epochs of training data and apply random cropping, horizontal flipping and cutout data augmentation, shuffling and batching.
We shall discuss the validity of this approach towards the end of the post (our conclusion is that any reasonable restriction should be based on total inference cost and that the form of mild TTA used here, along with a lightweight network, passes on that front.) An example residual block is shown in the figure below. First we should explain what we mean. The noisier validation results during training at batch size 512 are expected because of batch norm effects, but more on this in a later post. If we rerun the network and training from our DAWNBench submission with the new GPU data processing, training time drops just under 70s, moving us up two places on the leaderboard!
Each bypass gives rise to a residual block in which the convolution layers predict a residual that is added to the block’s input tensor. The reasons presumably have to do with noise in the batch statistics and specifically a balance between a beneficial regularising effect at intermediate batch sizes and an excess of noise at small batches. In the case at hand, the Kakao Brain team has applied the simple form of TTA described here – presenting an image and its left-right mirror at inference time, thus doubling the computational load. Kaiming He for discussing ambiguous and missing details in the original paper and helping us reproduce the results. We are also applying weight decay after each batch and this should be increased by a factor of batch size to compensate for the reduction in the number of batches processed. However, this also forces every skip connection to perturb the output. The logs from our earlier DAWNBench submission show three seconds wasted on data preprocessing, which counts towards training time. With DataParallelTable, all the kernels for the first GPU are enqueued before kernels any are enqueued on the second, third, and fourth GPUs. It isn’t supported directly in PyTorch but we can roll our own easily enough. So how can it be that we are simultaneously at the speed limit of training and able to increase batch size without sustaining instability from curvature effects? GPU memory usage when using the baseline, network-wide allocation policy (left axis). In the context of convex optimisation (or just gradient descent on a quadratic), one achieves maximum training speed by setting learning rates at the point where second order effects start to balance first order ones and any benefits from increased first order steps are offset by curvature effects. For example, consider applying 8×8 cutout augmentation to CIFAR10 images. and achieve a TTA test accuracy of 94.1% in 26s! We finally compare ResNets to GoogleNet and VGG networks.
The residual network architecture solves this by adding shortcut connections that are summed with the output of the convolution layers. Batch norm standardises the mean and variance of each channel but is followed by a learnable scale and bias. This may also help generalisation since smoothed functions lead to a less expressive function class – in the large smoothing limit we recover a linear network.
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