We start with the practical matter of some code optimisation. It should be more efficient to apply pooling first. It has been tremendous fun working on this project, exploring dynamics of neural network training and extending the work of others to bring training times to a level where rapid experimentation becomes possible. Can we remove overhead this by doing data augmentation on the GPU? Alternate optimizers. Fancier optimizers that make nuanced assumptions may improve training times, but they may instead have more difficulty training these very deep models. 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. In Part 3 we speed up batch norms, add some regularisation and overtake another benchmark. In Torch, an easy way to achieve this is to modify modules of the same type to share their underlying storages. If we 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. We compare training runs on two different datasets: a) 50% of the full training set with no data augmentation and b) the full dataset with our standard augmentation. It appears that 96% accuracy is reached in about 70 epochs and 3 minutes of total training time, answering a question that I’ve been asked several times by people who (perhaps rightly) believe that the 94% threshold of DAWNBench is too low. If gradients are being averaged over mini-batches, then learning rates should be scaled to undo the effect and weight decay left alone since our weight decay update incorporates a factor of the learning rate. We investigate the effects of mini-batch size on training and use larger batches to reduce training time to 256s.
We used the scale and aspect ratio augmentation described in “Going Deeper with Convolutions” instead of the scale augmentation described in the ResNet paper. #####################################################################################################################. This post gives some data points for one trying to understand residual nets in more detail from an optimization perspective. 17 epoch test accuracy jumps to 94.4% allowing a further 2 epoch reduction in training time. 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. With DataParallelTable, all the kernels for the first GPU are enqueued before kernels any are enqueued on the second, third, and fourth GPUs. Training to 94% test accuracy took 341s and with some minor adjustments to network and data loading we had reduced this to 297s. 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. Here are the results: Despite the lack of tuning of the various extra hyperparameters of the final training setup for longer runs, it appears to maintain a healthy lead over the baseline even out to 100 epochs of training and approximate convergence.
In this case, we could claim to have changed the network by splitting into two identical branches, one of which sees the flipped image, and then merging at the end. To fix this, we introduced a multi-threaded mode for DataParallelTable that uses a thread per GPU to launch kernels concurrently. 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. These improvements are based on a collection of standard and not-so-standard tricks. 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! As you see, our ResNet-101 model gets a higher accuracy than MSR-A’s ResNet-152 model. The 27 input channels to this layer are a transformed version of the original 3×3×3 input patches whose covariance matrix is approximately the identity, which should make optimisation easier.
At training time, we still present the network with a single version of each image – potentially subject to random flipping as a data augmentation so that different versions are presented on different training epochs. We are hoping that this will help accelerate research in the community. This eminently sensible approach goes by the name of test-time augmentation.
We have already seen a first piece of evidence for our claim: increasing batch sizes does not immediately lead to training instability as it should if curvature was the issue, but not if the issue is forgetfulness which should be mostly unaffected by batch size. The classic way to remove input correlations is to perform global PCA (or ZCA) whitening. Multi-GPU training. © Myrtle.ai | Company No: 4978210 | VAT Reg No: 831979590 | Privacy Policy. Torch uses an exponential moving average to compute the estimates of mean and variance used in the batch normalization layers for inference.
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. Quick turnaround time and continuous validation are helpful when designing the full system because overlooked details can often bite you in the end. (Minsoo Rhu et al. The second row shows for contrast what happens with a low learning rate. For a larger dataset such as ImageNet-1K, which consists of about 20× as many training examples as CIFAR10, the effects of forgetfulness are likely to be much more severe. 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 new test accuracy is 94.1% and most importantly we’ve overtaken the 8 GPUs of BaiduNet9P with a time of 43s, placing us second on the leaderboard! This is a big improvement over our previous 3s but also seems a little wasteful, since the data will need to cross to the GPU again after batching and augmentation, incurring a further delay at each training step. For example, consider applying 8×8 cutout augmentation to CIFAR10 images. By default, Torch uses a smoothing factor of 0.1 for the moving average. It is straightforward to implement proper mixed precision training but this adds about a second to overall training time and we found it to have no effect on final accuracy, so we continue to do without it below. We are otherwise happy with ReLU so we’re going to pick a simple smoothed-out alternative. 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. Let’s try freezing these at a constant value of 1/4 – roughly their average at the midpoint of training. We used a few tricks to fit the larger ResNet-101 and ResNet-152 models on 4 GPUs, each with 12 GB of memory, while still using batch size 256 (batch-size 128 for ResNet-152). The 5s gain from a more efficient network more than compensates the 2.5s loss from the extra training epoch. On the other hand, the world’s current fastest supercomputer can finish 2 1017 single precision operations per second. 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. We confirm, at the end of the post, that improvements in training speed translate into improvements in final accuracy if training is allowed to proceed towards convergence. This has a harmful effect: we found that putting batch normalization after the addition significantly hurts test error on CIFAR, which is in line with the original paper’s recommendations. In this setting, a small residual network with 20 layers takes about 8 hours to converge for 200 epochs on an Amazon EC2 g2.2xlarge instance. We also experimented with moving the stride-two downsampling in bottleneck architectures (ResNet-50 and ResNet-101) from the first 1x1 convolution to the 3x3 convolution. For example: Is it better to put batch normalization after the addition or before the addition at the end of each residual block? NCCL Collectives : We also used the NVIDIA NCCL multi-GPU communication primitives, which sped up training by an additional 4%. For larger datasets, the optimal point can be significantly lower because of the forgetfulness effect. 4% might sound insignificant, but for example, when training Resnet-101 this amounts to a saving of 13 hours. With our current network and 13 epoch training setup, the test accuracy with TTA rises to 94.6%, making this the largest individual effect we’ve studied today. First, training and test losses both become suddenly unstable at a similar learning rate (about 8 times the original learning rate) independent of training set size. Label smoothing is a well-established trick for improving the training speed and generalization of neural nets in classification problems. We roll-out a bag of standard and not-so-standard tricks to reduce training time to 34s, or 26s with test-time augmentation. © Myrtle.ai | Company No: 4978210 | VAT Reg No: 831979590 | Privacy Policy. It also investigates the contributions of certain design decisions on the effectiveness of the resulting networks. It is not at all clear that this limit applies. Our results come fairly close to those in the paper: accuracy correlates well with model size, but levels off after 40 layers or so. The table below shows a comparison of single-crop top-1 validation error rates between the original residual networks paper and our released models. Larger batches should allow for more efficient computation so let’s see what happens if we increase batch size to 512. As a further optimisation, if the number of groups for an augmentation becomes too large, we can consider capping it at a reasonable limit – say 200 randomly selected groups per epoch. We can trade this for training time by reducing the number of epochs. We also expect the optimal values of learning rate factors and losses to be similar to what they were at batch size 128, since speed of forgetting is unaffected by batch size and curvature effects are not yet dominant at the optimum. “Very deep convolutional networks for large-scale image recognition.” arXiv preprint arXiv:1409.1556 (2014). At the end of last year, Microsoft Research Asia released a paper titled “Deep Residual Learning for Image Recognition”, authored by Kaiming He, Xiangyu Zhang, Shaoqing Ren and Jian Sun. This is clear evidence that the model is forgetting what it has seen earlier in the same training epoch and this is limiting the amount of information which it can absorb at this learning rate. 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. 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. So without further ado, let’s train with batch size 512. If we increase the maximum learning rate by a further ~50% and reduce the amount of cutout augmentation, from 8×8 to 5×5 patches, to compensate for the extra regularisation that the higher learning rate brings, we can remove a further epoch and reach 94.1% test accuracy in 36s, moving us narrowly into top spot on the leaderboard!! In a backwards pass, the gradInput buffers can be reused once the module’s gradWeight has been computed.
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