We reduce the warmup period – during which learning rates increase linearly – in proportion to the overall number of epochs. This way, we can quickly identify the parts of the research that are the most important to focus on during further development.
We use the original learning rate schedule rescaled by a range of factors between 1/8 and 16.
We released optimized training code, as well as pre-trained models, in the hope that this benefits the community.
Interestingly, had we not increased the learning rate of the batch norm biases, we would have achieved a substantially lower accuracy. Focussing on the first three plots, corresponding to a high learning rate, we can observe that the test loss is almost the same when the model is trained on 50% of the dataset with no augmentation or the full dataset with augmentation. 13 epoch training reaches a test accuracy of 94.1%, achieving a training time below 34s and a 10× improvement over the single-GPU state-of-the-art at the outset of the series!
We can avoid this by applying the same augmentation to groups of examples and we can preserve randomness by shuffling the data beforehand. Our training thus far uses a batch size of 128.
On the other hand, if we don’t limit the amount of work that we are prepared to do at test time then there are some obvious degenerate solutions in which training takes as little time as is required to store the dataset!
The larger the learning rates, the more parameters move about during a single training epoch and at some point this must impair the model’s ability to absorb information from the whole dataset.
and achieve a TTA test accuracy of 94.1% in 26s! There is much scope for improvement on that front as well. This training requires 1018 single precision operations in total. More extensive forms of TTA are of course possible for other symmetries (such as translational symmetry, variations in brightness/colour etc.) 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.
The paper achieved state-of-the-art results in image classification and detection, winning the ImageNet and COCO competitions. However, the effect is fairly minor. “Very deep convolutional networks for large-scale image recognition.” arXiv preprint arXiv:1409.1556 (2014). Multi-threaded kernel launching : The FFT-based convolutions require multiple smaller kernels that are launched rapidly in succession. I am training the Inception-ResNet-v2 network with the DeepLab v3+ architecture. places on the DAWNBench leaderboard: The top six entries all use 9-layer ResNets which are cousins – or twins – of the network we developed earlier in the series. Larger batches should allow for more efficient computation so let’s see what happens if we increase batch size to 512. Deep Residual Learning for Image Recognition, For a more in-depth report of the ablation studies, read here, includes instructions for fine-tuning on your own datasets.
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. These improvements are based on a collection of standard and not-so-standard tricks. We trained variants of the 18, 34, 50, and 101-layer ResNet models on the ImageNet classification dataset. Batch norm does a good job at controlling distributions of individual channels but doesn’t tackle covariance between channels and pixels. 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! We are otherwise happy with ReLU so we’re going to pick a simple smoothed-out alternative. What’s notable is that we achieved error rates that were better than the published results by using a different data augmentation method.
ReLU layers also perturb data that flows through identity connections, but unlike batch normalization, ReLU’s idempotence means that it doesn’t matter if data passes through one ReLU or thirty ReLUs. GPU memory usage when using the baseline, network-wide allocation policy (left axis). After learning about each other’s efforts, we decided to collectively write a single post combining our experiences. The 5s gain from a more efficient network more than compensates the 2.5s loss from the extra training epoch. An example residual block is shown in the figure below. For these experiments, we replicated Section 4.2 of the residual networks paper using the CIFAR-10 dataset. NCCL Collectives : We also used the NVIDIA NCCL multi-GPU communication primitives, which sped up training by an additional 4%.
Kaiming He for discussing ambiguous and missing details in the original paper and helping us reproduce the results.
The results above suggest that if one wishes to train a neural network at high learning rates then there are two regimes to consider. Many of them appear to converge faster initially (see the training curve below), but ultimately, SGD+momentum has 0.7% lower test error than the second-best strategy. Actually we can fix the batch norm scales to 1 instead if we rescale the $\alpha$ parameter of CELU by a compensating factor of 4 and the learning rate and weight decay for the batch norm biases by $4^2$ and $1/4^2$ respectively. So without further ado, let’s train with batch size 512. Thus, second order differences between small and large batch training could accumulate over time and lead to substantially different training trajectories.
These experiments help verify the model’s correctness and uncover some interesting directions for future work.
We set batch size=128 and train with a learning rate schedule which increases linearly for the first 5 epochs and then remains constant at a fixed maximal rate for a further 25 epochs so that the training and test losses stabilise at the given learning rate. More exploration is needed. When I set the 'ExecutionEnvironment' option to multi-gpu the processing time for each iteration is higher than using only gpu, that is a single GPU. Let’s try freezing these at a constant value of 1/4 – roughly their average at the midpoint of training. This suggests that the learnable biases are indeed doing something useful – either learning appropriate levels of sparsity or perhaps just adding regularisation noise.
One possibility, that we’ve been using till now, is to present the network with a large amount of data, possibly augmented by label preserving left-right flips, and hope that the network will eventually learn the invariance through extensive training. Here is a typical conv-pool block before: Switching the order leads to a further 3s reduction in 24 epoch training time with no change at all to the function that the network is computing!
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.
The net effect brings our time to 64s, up to third place on the leaderboard. Although CUDA kernel launches are asynchronous, they still take some time on the CPU to enqueue.
Instead, it’s often helpful to run ablation studies on a smaller dataset to independently measure the impact of each aspect of the model. An alternative, would be to use the same procedure at training time as at test time and present each image along with its mirror.
The table below shows a comparison of single-crop top-1 validation error rates between the original residual networks paper and our released models.
The most recently seen training batches have a significantly lower loss than older ones, but the loss reverts to the level of the test set of unseen examples within half a training epoch.
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