Since its great success in computer vision[Krizhevsky et al.2012]Krizhevsky et al.2012, LeCun et al.2015]. Along with the progress of research to obtain better accuracy, DNNs are becoming deeper, i.e., having more layers, and/or wider
, i.e., having more branches and more neuron units in each layer. For example, in image recognition, AlexNet[Krizhevsky et al.2012], the winner of ILSVRC 2012, consists of only nine layers and has a sequential structure; GoogLeNet [Szegedy et al.2015]
introduces the so-called inception modules, which are a technique to widen DNNs; ResNet[He et al.2016] consists of more than 50 layers; and the more recent network, Inception-ResNet [Szegedy et al.2017], which extends ResNet with the inception modules, is even larger than ResNet and GoogLeNet.
Although expanding neural networks seems to be a key to obtain better accuracy, it comes with the high memory cost required to store weight parameters and intermediate results (e.g., activations, feature maps, etc.) in the propagation for training and inference. For example, the training of Inception-ResNet consumes 12.5 times as much memory as that of AlexNet in some configuration (see Figure 2). This gives rise to several undesirable consequences. First, for training DNNs, we can only use smaller mini-batches to avoid risk running out of memory, and hence having slow convergence. Second, inference using such large DNNs may require many machines in the deployment environment. Third, and even worse, the flexibility of the design of neural networks is constrained so that the DNNs can fit in the memory of the underlying devices. The high memory consumption is more serious in the use of GPUs and edge devices that have much smaller and less extendable memory storage than CPUs.111 Augmenting devices may mitigate the problem but it makes another issue about the communication between devices.
We study memory optimization for DNNs. Our approach is based on the observation that propagation of a network model is computed in the same way for different inputs and learnable parameters; we call such propagation hot.222This term originates from just-in-time compilation, where repeatedly executed code blocks to be optimized are called hot.
This is indeed the case in many networks including convolutional neural networks (CNNs) such as AlexNet, GoogLeNet, ResNet, and Inception-ResNet. On the basis of this observation, we can profile the memory usage in a sample run and then utilize the profile to find the allocation of memory to minimize the peak memory usage in the succeeding runs. The allocation problem is a special case of a two-dimensional rectangle packing problem that is known to be NP-hard. We develop a simple and fast heuristic to generate good approximate solutions quickly.
Even when the whole propagation is not hot, there are cases where some partHochreiter and Schmidhuber1997] takes variable-length inputs, and a part of its propagation is computed differently depending on inputs. We find that our approach can also reduce the memory consumption in such RNNs, as discussed in Section 4.3.
A byproduct of our approach is that training and inference of DNNs may be accelerated. After a sample run, our method produces an absolute memory address for each memory request and just returns it in the succeeding runs. The run-time cost of our memory allocation is thus very low in the succeeding runs, compared with that of dynamic memory allocation, a standard approach in many deep learning frameworks. We describe the dynamic method in Section 2 briefly and compare it with our approach from the perspective of the running time performance as well as the memory consumption in Section 5. In addition, the memory reduction allows use of larger mini-batch sizes, which leads to higher utilization of GPU cores and further acceleration of training.
Our contributions are summarized as follows.
We propose a profile-guided memory optimization technique for DNNs. Our approach optimizes memory usage in a hot part of a propagation and never incurs performance overhead once the memory usage is optimized, while preserving the computation of the DNNs.
We develop a simple heuristic algorithm for allocating memory to minimize the peak memory usage. We empirically show that it works well from the perspectives of both computation time and solution quality.
We implement our memory optimization on the common deep learning framework Chainer [Tokui et al.2015]; our approach can be applied to other frameworks as well. We conduct experiments on training and inference using four CNNs (AlexNet, GoogLeNet, ResNet-50, and Inception-ResNet) and one RNN (seq2seq [Sutskever et al.2014]). We find that our method not only reduces the memory consumption by up to 49.5% but also accelerates propagation by up to a factor of four thanks to the rapidity of the optimized memory allocation and the ability to use larger mini-batch sizes.
One may raise a concern that a sample run for a profile can be memory-inefficient and needs more memory than the physical capacity. We can obtain the profile even in such a case by utilizing an out-of-core technique [Rhu et al.2016, Meng et al.2017] or Unified Memory in NVIDIA CUDA, which enables us to run the model requiring memory over the capacity with additional performance overhead, and then perform the succeeding runs without the overhead by disabling those techniques.
2 Related work
The need to manage memory has emerged as DNNs have consumed huge memory. Many deep learning frameworks—e.g., Theano[Bastien et al.2012]Abadi et al.2016], and Chainer [Tokui et al.2015]—allocate GPU memory dynamically, based on memory pools, which are sets of unused memory blocks, and garbage collection. Given a GPU memory request, they find a memory block of an adequate size from a memory pool, or allocate it from the physical memory if there is no such a block in the pool, and wrap the block with a reference count. When the memory block is reclaimed by the garbage collection, it returns to the pool. Our approach not only requires less memory but also makes propagation faster thanks to no needs to search for memory blocks dynamically, as discussed in Section 5.
DNNs usually need much memory to store outputs from hidden layers for backpropagation; we call such outputsintermediate results. MXNet [Chen et al.2015] analyzes a computational graph of a network model for memory optimization. While it optimizes memory usage of only intermediate results, our approach can optimize the usage of, for example, temporary memory used to speed up convolution, as well as memory for intermediate results. Another advantage of our approach is compatibility with dynamic memory allocation, which is discussed in Section 4.3. Chen et al. recompute and Meng et al. mem_tf reduce the memory consumption for intermediate results by recomputing them as needed by backpropagation. Although the recomputation can reduce the memory consumption to sublinear with respect to the number of layers, it needs an additional forward propagation in every backpropagation. Our approach never incurs such performance overhead once the memory allocation is optimized. Shirahata et al. shirahata reuse as many memory blocks allocated in forward propagation as possible for backpropagation and develop an in-place parameter update. Their memory reduction method works only for training, whereas our approach works effectively for both training and inference.
Another research direction for memory reduction is compression of DNNs. The work in this direction prunes connections of a network model [Han et al.2015, Han et al.2016] and/or quantizes learnable parameters [Gong et al.2014] in a way that preserves accuracy. The compression approach seems complementary to our method, but a major difference is that the compression changes the behavior of the model and so the compressed model may not work as intended by network designers. On the other hand, our approach does not change the computation involved by the model. Another issue of the compression is the need of time-consuming retraining [Han et al.2015].
Out-of-core algorithms, which offload device memory not used immediately to a slower storage and prefetch it as necessary, are another way to run large models on a device with limited memory. Rhu et al. vdnn and Meng et al. mem_tf offload intermediate results on GPUs to CPU memory. Although their work can run a very large model as long as the peak memory consumption does not exceed the GPU memory capacity, it causes performance degradation due to CPU-GPU communication for data transfer. Unified Memory in NVIDIA CUDA allows more fine-grained offloading, but it incurs significant and difficult-to-control overhead [Meng et al.2017].
Wang et al. superneuron integrate computational graph analysis, out-of-core technology, and recomputation into one system, which has pros and cons of those methods inherently. They focus on CNNs as a target, but it is not clear how well their system works on other network models, such as RNNs.
Memory allocation generally can be regarded as a two dimensional strip packing problem (2SP). It asks for a set of rectangular items to be placed in a container with a fixed width and for the variable height to be minimized. A memory block corresponds to a rectangular item with its allocation time as width and its memory size as height. In this paper, we deal with a special case where the allocation times of all memory blocks are fixed as input. The problem is also known as the Dynamic Storage Allocation problem (DSA), a typical NP-hard problem [Garey and Johnson1979]. 2SP has been extensively studied theoretically and practically. Steinberg Steinberg1997 proposed a heuristic algorithm, whose approximation ratio is 2. Arahori et al. arahori2012 proposed a branch-and-bound-based exact algorithm to 2SP, which works well for small and medium-sized instances. Burk et al. best-fit proposed the best-fit algorithm, which is a simple, constructive type of heuristics. They showed that it works well for large-sized instances even compared with metaheuristics-based algorithms.
3 Profile-guided memory allocation
From a profile of memory usage during hot propagation, we gather the information of the memory blocks requested. Such information allows us to better determine where to allocate the memory blocks in the physical memory. We formulate the memory allocation problem as a special case of the two-dimensional rectangle packing problems that is known as the Dynamic Storage Allocation (DSA). We show the mixed integer programming (MIP) formulation of DSA, that can be solved optimally for small instances, and then introduce a heuristic algorithm for solving larger instances.
We first introduce parameters of DSA. We suppose that the number of requested memory blocks, times when memory blocks are requested and released, and sizes of memory blocks are given by the profile. We also take the available maximum memory size as a parameter. Formally:
: number of memory blocks.
: a set of IDs of memory blocks.
: the available maximum memory size.
: size of memory block .
: time when is requested.
: time when is released.
We assume that these parameters do not change during the entire run (training and inference) of a neural network. This assumption is satisfied if the propagation involved by the neural network is hot. Many commonly used models satisfy this condition. We give workarounds for network models where only a part of the propagation is hot in Section 4.3. A memory block is allocated during a time period ; we call the time period lifetime of memory block .
We next introduce the following decision variables of DSA.
: the peak memory usage.
: memory offset (or, starting address) of memory block within the entire allocated memory.
: means that memory block is located lower than block (i.e., ) and means that it is not (i.e., ).
We call the interval of memory address of memory block address space of memory block .
We assign memory offsets to memory blocks so that no two memory blocks occupy the same address space at any given time. We do not need to check for all pairs of memory blocks: it suffices to check those with overlapping lifetimes. To this end, we introduce a notion of possible colliding pairs:
which is a set of memory block pairs that have overlapping lifetimes. Note that any two memory blocks not in do not share the same address space at the same time because their lifetimes do not overlap.
The objective of DSA is to minimize the peak memory usage. We formulate DSA in the form of a MIP as follows:
Equations (1) and (2) represent the minimization of the peak memory usage. Equations (3) and (4) denote the non-overlapping constraints of possible colliding pairs. We can exactly solve the above MIP with CPLEX for small instances.
3.2 Best-fit heuristic
We design our heuristic to DSA on the basis of the best-fit heuristic [Burke et al.2004] to 2SP. In Figure 1, the -axis and -axis denote times and memory offsets, respectively. Note that the objective is to place all memory blocks in the rectangle so that the top block is placed as low as possible. The heuristic repeats two operations until all memory blocks are placed: (1) choosing an offset and (2) searching for a memory block that can be placed at the chosen offset without colliding with memory blocks placed already. We illustrate how our heuristic works via an example shown in Figure 1. In the beginning of the heuristic (Figure 0(a)), since no memory blocks are placed, we choose zero as the memory offset. When searching for a memory block, we always choose a block with the longest lifetime among blocks that can be placed at the considered offset. In the case of Figure 1, we choose the memory block that has the longest lifetime and place it (Figure 0(b)). After the placement, there are three candidates of a memory offset (the bold lines in Figure 1; we call them offset lines). When there are multiple offsets, we always choose the lowest one (if there are multiple lowest offsets, the leftmost one is chosen). Next, we search for a memory block for the chosen offset and place it (Figure 0(c)). If there are no blocks that can be placed at the chosen offset, we “lift up” the line for the offset by merging it with the lowest adjacent offset line as in Figure 0(d) (if offsets of adjacent lines are the same, it is merged with both) and again choose an offset and search for a memory block. The computational time complexity of our heuristic is quadratic in the number of memory blocks.
We incorporate the best-fit heuristic in Chainer to optimize the GPU memory usage. This section describes the details including how to apply our approach to any network models.
4.1 Memory profiling
Since Chainer allocates memory blocks at run time, we profile GPU memory usage by monitoring memory allocation and free operations in a sample run. To obtain memory request time and release time , we use a global integer variable , which represents the current time and is increased after each allocation and free. We also have a global integer variable that denotes the ID of the next requested memory block.
Given a sample input, we initialize the global variables with one and run the model with the input. When receiving a request with memory size , we extend (the set of memory block IDs) with , set and to and , respectively, and finally increase and . When memory block is released, is set to and then increased.
4.2 Memory allocation
After obtaining the parameters from the sample run, we calculate the peak memory usage and memory offsets for memory blocks by solving DSA and then allocate GPU memory of size ; we write for the address of the memory. In the rest of the running of the model, we return memory address for a request of memory block . We identify memory blocks by maintaining the global variable , which is initialized with one before starting each forward propagation. When a memory block is requested, we return address and increase . This is sound since the propagation should be computed in the same way as in the sample run, where is always increased after each allocation.
4.3 Generalization for non-hot propagation
The memory allocation in Section 4.2 is unsound for models which, for different inputs, (1) perform non-hot propagation (that is, it is computed differently) and (2) request memory of different sizes. This section gives workarounds to avoid them.
A workaround for the first issue is very simple: we do not optimize the usage of memory requested in the non-hot part of the propagation. To this end, we provide two operations, interrupt and resume, which interrupt and resume the monitoring of memory operations, respectively. When entering a non-hot part, we call interrupt; and, when leaving that part, we call resume. Since our method optimizes only the profiled part of memory usage, the memory requested between calls to interrupt and resume is out of the scope of the optimization.
The second issue is resolved by reoptimization. In this approach, we continue the monitoring of memory operations after optimizing the memory usage and, when detecting a request for larger memory than expected, we reoptimize the memory allocation by using the new observed parameters—note that we do not need reoptimization for requests of smaller memory. This workaround may incur an additional performance cost, but it is very low as shown in Section 5.3.
We compare the GPU device memory consumption (Figure 2) and the running times to process one mini-batch in training and inference (Figure 3) in Chainer (version 3 RC 1.0), which is a baseline and denoted by orig in figures for shorthand, and our optimized version, denoted by opt
, on four CNNs (AlexNet, GoogLeNet, ResNet-50, and Inception-ResNet), and one RNN (seq2seq). Training of the CNNs is performed with 32, 64, and 128 mini-batch sizes, and that of seq2seq is with 32, 64, 128, and 256 ones. Inference performs only forward propagation for one input data. We use ImageNet[Russakovsky et al.2015] and the English-French corpus from WMT15333http://www.statmt.org/wmt15/ as datasets for the CNNs and seq2seq, respectively. We use the first 1000 training mini-batches for the warm-up and next 2000 mini-batches for the evaluation. We turn on Unified Memory of NVIDIA CUDA, which allows us to run models requiring more memory than the physical capacity, in the experiments for memory consumption but turn it off in the measurement of running times since it may incur performance overhead.
We also evaluate the best-fit heuristic implemented in Python in two experiments. We first compare the solutions by the heuristic with the optimal solutions found by CPLEX version 12.8 within one hour. We also compare the computation time of the heuristic for different configurations (Figure 4).
All experiments are run on an IBM POWER8 machine with two 4GHz 10-core POWER8 processors, 512 GB RAM, and NVIDIA Tesla P100 GPUs equipped with 16 GB device memory. Options except mini-batch sizes follow the scripts provided by Chainer.
Finally, we make a few remarks. The first is on the GPU memory management system of our baseline. The original Chainer uses memory pools for memory reuse, as described in Section 2, and reduces the memory consumption somewhat compared with naive, network-wise memory allocation, which always allocates a memory block from the physical device memory for each request. For example, we observed that, in the training of AlexNet with 32 mini-batch size, the network-wise memory allocation consumes 1.50 GB device memory whereas the pool-based memory allocation does only 1.21 GB memory. In this section, we show that our approach achieves reduction of more memory than the pool-based method. The second remark is on convolution algorithms. There are many algorithms for computing convolution. The most memory-efficient algorithm needs memory only for inputs and outputs, but we can calculate the convolution much faster by allocating additional temporary memory, called workspace. Although the optimized version could be accelerated by allocating larger workspace than the original Chainer, the experiments use workspace of the same size (8 MB by default) in both versions for comparing only the effect of the memory optimization.
The total memory consumption during the training of CNNs is shown in Figure 1(a), where the amount of memory retained in the entire training (e.g., memory for learnable parameters and gradients) is indicated by doted red bars and the amount of memory released until the end of each propagation is indicated by solid blue bars; our method optimizes usage of only the latter. Figure 1(a) shows that our optimization works well in all models and is the most effective for Inception-ResNet. Specifically, in 64 mini-batch size, the memory consumption in the optimized version fits within the physical memory capacity (16 GB), whereas the required memory in the original Chainer exceeds the capacity considerably.
The average training times per mini-batch are reported in Figure 2(a), where “N/A” means that we could not train the model due to insufficient memory. The results indicate that our approach accelerates the training of some models (GoogLeNet, ResNet-50, and Inception-ResNet) even using the same mini-batch size. This is because the optimized version allocates memory quite quickly. The original Chainer, given a memory request, searches for an available, sufficiently sized memory block from a memory pool, and the running cost of this memory search increase as the number of memory blocks in the pool increases. In contrast, the optimized version just returns a memory address calculated before the training. This is significant especially in Inception-ResNet, for which the training in the optimized version is 2.19 times as fast as in the original. This advantage however may be hidden behind GPU computation in a large mini-batch size, as in GoogLeNet and ResNet-50 with 128 mini-batch size. Figure 2(a) also shows that our method allows use of a larger mini-batch size, which may enable us to utilize GPUs more fully. For example, the training of Inception-ResNet in the optimized version (64 mini-batch size) utilizes more GPU cores than that in the original (32 mini-batch size), and the number of images processed per second by the former is 3.95 times as large as that by the latter.
The memory consumption in inference is shown in Figure 1(b). Since the inference does not need to retain memory for intermediate results, most memory blocks can be reused even in the pool-based memory management of Chainer. Nevertheless, we successfully reduce the total memory amounts in GoogLeNet and ResNet-50 by 12.6% and 10.0%, respectively. As for running time performance, inference is accelerated in all models, as shown in Figure 2(b), because the GPU computation for inference is lightweight and the cost of search for memory blocks is more dominant.
CPLEX could obtain the optimal solutions only in two configurations (inference using AlexNet and GoogLeNet), and the objective function values by the heuristic and CPLEX match (10169344 and 12202496, respectively). Our heuristic thus works very well at least in small instances. The execution times of the heuristic are shown in Figure 3(a), which indicates that the heuristic works quickly enough for practical use.
5.3.1 Training and inference
Figure 1(c) shows the memory consumption immediately after processing 10 mini-batches in the training of seq2seq and demonstrates that our approach significantly reduces the memory consumption. In the original Chainer, since the training of seq2seq requires differently sized memory for different inputs, memory blocks allocated in a training loop may not be used in the succeeding loops, and the whole of such unused blocks finally reaches the device memory capacity. In contrast, we recompute how to allocate memory when necessary, which allows us to keep the memory consumption as low as possible.
The growth of unused memory blocks causes degradation of the running time performance. Figure 2(c), which gives the running times of training seq2seq, shows that the optimized version is faster in 32 mini-batch size and the original Chainer catches up in 64 mini-batch size for the same reason as in CNNs. In 128 and 256 mini-batch sizes, however, the training in the optimized version becomes faster than that in the original. We guess that this is due to the waste of GPU memory by the pool-based memory management system. When requested memory cannot be allocated due to insufficient free memory, the pool-based memory management system frees all unused memory blocks and allocates subsequent requested memory from the physical GPU memory, which has higher run-time cost than reusing memory blocks in a pool. Our memory allocation does not use memory pools except a small part enclosed by interrupt and resume, so we rarely need to free memory. While our approach instead must recompute memory addresses when the requested memory is larger than expected (Section 4.3), the recomputation cost in the training is low, as shown in Figure 3(b), and the recomputation becomes less frequent as the training proceeds.
As shown in Figure 3(b), the heuristic algorithm takes much longer in the inference, whereas it terminates quickly for the training formulas. This is due to the Chainer script that we use for the evaluation: the script always generates 100 words for inference, whereas it cuts sentences used for the training into up to 50 words. Thus, the inference requests many more memory blocks than the training, and the heuristic takes long in the inference. Fortunately, this should not be problematic in practice, because we can solve DSA with idle CPUs after responding to an inference request. We note that the running time performance of the heuristic can be improved by using faster languages, such as C and C++. CPLEX could not obtain the optimal solutions within the 1-hour time limit.
We propose a profile-guided memory optimization for DNNs. We develop a simple heuristic algorithm to DSA to obtain efficient and fast memory allocation, and incorporate the heuristic in Chainer. We experimentally confirmed that our method reduces the memory consumption and accelerates propagation in both training and inference using CNNs and seq2seq.
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