Our experiments are conducted on NVIDIA’s DGX SuperPOD. For reddit URLs corresponding to content up to October 2018 we arrived at approximately 37GB of content. With options global-batch-size 1536 and rampup-batch-size 16 16 5859375, the training will start with global batch size 16 and linearly increase the global batch size to 1536 over 5,859,375 samples with incrmeental steps 16. 228 Repositories nvidia-docker 12407 FastPhotoStyle 10450 vid2vid 7595 DeepLearningExamples 5258 pix2pixHD 5018 apex 4926 DIGITS 4020 TensorRT 3177 thrust 3119 DALI 3019 tacotron2 2391 NeMo 2295 flownet2-pytorch 2191 Megatron-LM 1698 waveglow 1694 libcudacxx 1565 DeepRecommender 1545 nccl 1423 OpenSeq2Seq 1347 cutlass 1027 sentiment-discovery 1017 MinkowskiEngine 1003 … The configuration with 1 billion parameters fits on a single GPU whereas the 8 billion parameter models requires 8-way model parallelism (8 GPUs). Larger language models are dramatically more useful for NLP tasks such as article completion, question answering, and dialog systems. Our models utilize subword units, so for our version of LAMBADA evaluation we utilize the raw, unprocessed LAMBADA dataset, and require that our model predict the multiple $x_t$ subwords that make up the last word token. To switch between these two options use --DDP-impl local or --DDP-impl torch, respectively. We officially support only python3.6. In this tutorial, we are going to describe how to finetune BioMegatron - a BERT-like Megatron-LM model pre-trained on large biomedical text corpus (PubMed abstracts and full-text commercial use collection) - on RE: Text mining chemical-protein interactions (CHEMPROT).. The second GEMM in the block is parallelized along its rows and takes the output of the GeLU layer directly without requiring any communication. In contrast, here we use weak scaling to train larger and larger models that were not possible otherwise. To this end, for the model+data parallel cases we fix the global batch size to 512 for all experiments which corresponds to 64-way data parallelism. We have examples of how to use these two different forms of model parallelism in these scripts: bash examples/pretrain_bert_distributed_with_mp.sh, bash examples/pretrain_gpt_distributed_with_mp.sh. Several general purpose model parallel frameworks such as GPipe and Mesh-TensorFlow have been proposed recently. NVIDIA just took that innovation to a new level with a turnkey data center called the DGX SuperPOD that ranks as number 22 on the list of global supercomputers.” –Jim McGregor, Forbes “In a clear demonstration of why artificial intelligence leadership demands the best compute capabilities, NVIDIA has unveiled ‘the NVIDIA’s custom model, with 8.3 billion parameters, is 24 times the size of BERT-Large. We study both model and model+data parallel scalings. For example: The name of the text field of the json can be changed by using the --json-key flag in preprocess_data.py The other metadata are optional and are not used in training. As expected, the WikiText perplexity decreases and LAMBADA accuracy increases with the growth of the model size (Table 3). This system is optimized for multi-node deep learning applications, with 300 GB/sec bandwidth between GPUs inside a server and 100 GB/sec of interconnect bandwidth between servers. As before, in GPT training, use the longer name without the extension as --data-path. We have tested Megatron with NGC's PyTorch container version 20.12, which uses python 3.8, pytorch 1.8, cuda 11.1, and nccl 2.8.3. Throughout this section, we will showcase weak scaling with respect to the model parameters for both model parallel and model+data parallel cases. We have provided pretrained BERT-345M and GPT-345M checkpoints for use to evaluate or finetuning downstream tasks. Features Below we provide a brief feature list, see our detailed featureoverview for descriptions and usage. We developed efficient, model-parallel, and multinode training of … NVIDIA has open-sourced the code for reproducing the single-node training performance in its BERT GitHub repository. In this work, we built the world's largest transformer based language model on top of existing deep learning hardware, software, and models. We use the following command to run WikiText-103 evaluation on a 345M parameter model. Debugging is the primary use for single GPU training, as the code base and command line arguments are optimized for highly distributed training. Large models offer significant accuracy gains, but training billions to trillions of parameters frequently runs up against fundamental hardware limitations. For WikiText-103's test set we arrive at $T_o=245566$ and $T=270329$. We leverage NVIDIA's Selene supercomputer to perform scaling studies and use up to 3072 A100 GPUs for the largest model. bash examples/pretrain_bert_distributed.sh, bash examples/pretrain_gpt_distributed.sh. To train our GPT-2 model we created an aggregate 174GB dataset (~4.5x larger than WebText) consisting of Wikipedia, OpenWebText, RealNews, and CC-Stories. With weak scaling, we found that increasingly large transformer models can be trained in a similar amount of time compared to their smaller counterparts and can demonstrably improve performance. An epoch is defined as 68,507 iterations to train over the entire 174GB corpus. al., 2019, Language Models are Unsupervised Multitask Learners, Radford et. To clean the datasets we used the ftfy library and then removed non-english content using the langdetect library. We observe that initially as the model parallel size increases, utilization slightly decreases; as hidden size increases for larger models, utilization starts increasing and reaches 49% for the largest model. Recent work in language modeling demonstrates that training large transformer models advances the state of the art in Natural Language Processing applications. Use Git or checkout with SVN using the web URL. Megatron is a large, powerful transformer developed by the Applied Deep Learning Research team at NVIDIA. The TRAIN_DATA and VALID_DATA directory contain the RACE dataset as separate .txt files. We partition the first GEMM in a column parallel fashion. To compute LAMBADA cloze accuracy (the accuracy of predicting the last token given the preceeding tokens) we utilize a detokenized, processed version of the LAMBADA dataset. We have published the code that implements this approach at our GitHub repository. However, even for the largest configuration (8.3 billion parameters) running on 512 GPUs, we still achieve 74% scaling relative to the strong baseline single gpu configuration (1.2 billion parameters). The NLP code on Project Megatron is also openly available in Megatron Language Model GitHub repository. We empirically found that using a smaller model in those cases improves the training time. As expected, Torch distributed data parallelism is more efficient at larger model sizes. Badges are live and will be dynamically updated with the latest ranking of this paper. This allows us to split per attention head parameters and workload across the GPUs, and doesn’t require any immediate communication to complete the self-attention. As mentioned above, single GPU training is primarily intended for debugging purposes, as the code is optimized for distributed training. To analyze the performance of training large language models, we compute perplexity on the WikiText-103 dataset and cloze-style prediction accuracy on the LAMBADA dataset. al., 2019. Further documentation for downloading models can be found in the NGC documentation. Update 9/5/2019: Larger dataset and stricter lambada formulation. As shown in Figure 2b, for the self attention block, we exploit inherent parallelism in the multihead attention operation, partitioning the GEMMs associated with key (K), query (Q), and value (V) in a column parallel fashion such that the matrix multiply corresponding to one attention head is done locally on one GPU. It follows largely the same format as the previous BERT script with a few notable differences: the tokenization scheme used is BPE (which requires a merge table and a json vocabulary file) instead of WordPiece, the model architecture allows for longer sequences (note that the max position embedding must be greater than or equal to the maximum sequence length), and the --lr-decay-style has been set to cosine decay. Some minor modifications are required for GPT data preprocessing, namely, the addition of a merge table, an end-of-document token, removal of sentence splitting, and a change to the tokenizer type: Here the output files are named my-gpt2_text_document.bin and my-gpt2_text_document.idx. By default, multi-node training uses the nccl distributed backend. We performed additional filtering to remove malformed, short or duplicate documents less than 128 tokens. This block consists of two GEMMs with a GeLU nonlinearity in between followed by a dropout layer. All the cases from 1 billion to 1 trillion achieve more than 41% half precision utilization, which is high for an end-to-end application. While this is single GPU training, the batch size specified by --micro-batch-size is a single forward-backward path batch-size and the code will perform gradient accumulation steps until it reaches global-batch-size whcih is the batch size per iteration. Other than these minor changes, the distributed training is identical to the training on a single GPU. The iteration count will be reset to zero, and the optimizer and internal state will be reinitialized. Figure 1 shows more detailed scaling results. This repository is for ongoing research on training large transformer language models at scale. Since we study up to 8-way model parallelism, we pad the vocabulary such that it is divisible by 128x8=1024, resulting in a padded vocabulary size of 51,200. First, place your training data in a loose json format, with one json containing a text sample per line. development platforms. gPipe divides groups of layers across different processors while Mesh-TensorFlow employs intra-layer model parallelism. Furthermore, when we look at the numbers it’s 24x the size of BERT and 5.6x the size of GPT-2. Handling long term contexts is crucial for state of the art language models to solve problems like long-form generation and document-based question answering. The dataset ended up with approximately 40 million documents. In doing so, we successfully surpassed the limitations posed by traditional single GPU training by implementing a simple and efficient model parallel approach with only a few targeted modifications to the existing PyTorch transformer implementations. In this tutorial, we are going to describe how to finetune BioMegatron - a BERT-like Megatron-LM model pre-trained on large biomedical text corpus (PubMed abstracts and full-text commercial use collection) - on the NCBI Disease Dataset for Named Entity Recognition.. We take advantage of the structure of transformer networks to create a simple model parallel implementation by adding a few synchronization primitives. For example, for the 8.3 billion parameters model running on 512 GPUs, the scaling increases from 60% to 76% when Torch's distributed data parallel is used. LAMBADA uses cloze-style reading comprehension to test generative left-to-right language models by constructing examples of 4-5 sentences where the last word in the context $x_t$ is masked. The following script finetunes the BERT model for evaluation with the MultiNLI sentence pair corpus. Several approaches to model parallelism exist, but they are difficult to use, either because they rely on custom compilers, or because they scale poorly or require changes to the optimizer. If you'd like to use Wikipedia data for GPT training you should still clean it with nltk/spacy/ftfy, but do not use the --split-sentences flag. Our approach is conceptually similar to Mesh-TensorFlow, we focus on intra-layer parallelism and fuse GEMMs to reduce synchronization. We have provided an example of how to configure Megatron to run GPT-3 with 175 billion parameters on 1024 GPUs. For the model parallel scaling, a fixed batch size of 8 is used across all configurations. The table below shows the model configurations along with the achieved FLOPs per second (both per GPU and aggregate over all GPUs). This makes it a natural evaluation metric for language models which represent a probability distribution over entire sentences or texts. As the number of attention heads increases, some of the GEMMS inside the self-attention layer become smaller and also the number of elements in the self attention softmax increases. By default, the learning rate decays linearly over the training iterations starting at --lr to a minimum set by --min-lr over --lr-decay-iters iterations. Learning rates in all cases are set to $1.5\times 10^{-4}$ with single cycle cosine annealing and 3000 iteration warmup. The data is partitioned into a 949:50:1 ratio for training/validation/test sets (default is 969:30:1). Follow me on Twitter or … To know more in detail, check out the official announcement by NVIDIA. To fit these models into memory, existing solutions make trade-offs between computation, communication, and development efficiency: • Data parallelism does not help reduce memory footprint per device: a model with more than 1 billion parameters runs out of memory even on GPUs with 32GB of memory. However, you can also finetune your model from a pretrained checkpoint on other corpora as desired. To use tensor model parallelism (splitting execution of a single transformer module over multiple GPUs), add the --tensor-model-parallel-size flag to specify the number of GPUs among which to split the model, along with the arguments passed to the distributed launcher as mentioned above. python -m pip install virtualenvvirtualenv bert_envsource bert_env/bin/activa… Work fast with our official CLI. With full global batch size of 1536 on 1024 A100 GPUs, each iteration takes around 32 seconds resulting in 138 teraFLOPs per GPU which is 44% of the theoretical peak FLOPs. This results in a slight decrease in scaling. We then filtered, cleaned, and deduplicated all downloaded content according to the procedure described in our openwebtext directory. These scripts use the PyTorch distributed launcher for distributed training. The model is defined in a config file which declares multiple important sections. The training dataset can be either a single set or a multiple datasets combined with a set of weights. Our 8.3B model exemplifies this by setting new state of the art results for both WikiText-103 (10.81 perplexity) and LAMBADA (66.51% accuracy). The baseline for all the scaling numbers is the first configuration in Table 1 running on a single GPU. Further command line arguments are described in the source file main.py. This repository is for ongoing research on training large transformer language models at scale. Learn more. For example, the 8.3 billion parameters case with 8-way (8 GPU) model parallel achieves 77% of linear scaling. This approach splits both GEMMs in the MLP block across GPUs and requires only a single all-reduce operation in the forward pass (g operator) and a single all-reduce in the backward pass (f operator). This approach is simple to implement, because it requires only a few extra all-reduce operations be added to the forward and backward pass. However, we only make a few targeted modifications to existing PyTorch transformer implementations to employ model parallelism for training large transformers. A transformer layer consists of a self attention block followed by a two-layer multi-layer perceptron (MLP). Both papers leverage advances in compute and available text corpora to significantly surpass state of the art performance in natural language understanding, modeling, and generation. This script runs single GPU 345M parameter GPT pretraining. We generate text samples using largely the GPT pretraining script. We recommend using the --json argument when using WikiExtractor, which will dump the Wikipedia data into loose json format (one json per line), making it more manageable on the file system and also readily consumable by our codebase. Note that the --data-path now includes the additional _text_sentence suffix added in preprocessing, but does not include the file extensions. All of our experiments are conducted on NVIDIA’s DGX SuperPOD and we use up to 32 DGX-2H servers (a total of 512 Tesla V100 SXM3 32GB GPUs). Our experiments are conducted on NVIDIA’s DGX SuperPOD . To do so, simply add the --finetune flag and adjust the input files and training parameters within the original training script. We recommend following the Wikipedia data extraction process specified by Google research: "the recommended pre-processing is to download the latest dump, extract the text with WikiExtractor.py, and then apply any necessary cleanup to convert it into plain text.". It doesn’t require a compiler, and is orthogonal to the kind of pipeline model parallelism advocated by approaches such as gPipe. Model configuration. This partitioning happens on the fly, but is consistent across runs with the same random seed (1234 by default, or specified manually with --seed). This allows the GeLU nonlinearity to be independently applied to the output of each partitioned GEMM. Research on training transformer language models at scale, including BERT: https://github.com/NVIDIA/Megatron-LM Our code is written in native Python, leverages mixed precision training, and utilizes the NCCL library for communication between GPUs. We facilitate two distributed data parallel implementations: a simple one of our own that performs gradient all-reduce at the end of back propagation step, and Torch's distributed data parallel wrapper that overlaps gradient reduction with back propagation computation. The loose json is then processed into a binary format for training. Data preprocessing requires NLTK, though this is not required for training, evaluation, or downstream tasks. NVIDIA/Megatron-LM official. and evaluation pipelines at https://github:com/ NVIDIA/Megatron-LM 2. To use this repository, please install the latest supported versions of PyTorch with GPU support (python 3.8, pytorch 1.8, cuda 11.1, and nccl 2.8.3 and above) and NVIDIA APEX. Note that the --data-path now includes the additional _text_document suffix added in preprocessing, but does not include the file extensions. Note that for RACE, the batch size is the number of RACE query's to evaluate. To have consistent GEMM sizes in the self attention layer, the hidden size per attention head is kept constant at 96 while the number of heads and layers are varied to obtain configurations ranging from 1 billion to 8 billion parameters. To test the computational performance of our implementation, we consider GPT-2 models with four sets of parameters detailed in Table 1. Join this webinar to learn how NVIDIA researchers created Megatron, the largest Transformer language model ever trained with 8.3 billion parameters at 24x the size of BERT and 5.6x the size of GPT-2. We recommend either utilizing the provided Dockerfile in ./docker/ or creating a virtual environment (to avoid breaking existing tf installations) and install our requirements.txt. al. As the model size increases, we also modestly increase the batch size. Set the --dataset-impl flag to mmap, cached, or lazy, respectively (default is mmap). We vary hidden size, number of attention heads, and number of layers to arrive at a specifc model size. We use train-iters as the training iterations requested. Recently, NVIDIA Research launched project Megatron to enable training state of the art transformer language models with billions of parameters. We describe our evaluation methodologies below; however, more details are available in our github repository. Additionally, Megatron-LM … From github: Megatron is a large, powerful transformer. We've provided several scripts for pretraining both BERT and GPT in examples directory, as well as scripts for both zero-shot and fine-tuned downstream tasks including MNLI, RACE, WikiText103, and LAMBADA evaluation. Future research should be wary of this hyperparameter to design large transformer models that balance model performance and model efficiency. Alternatively, one can provide --train-samples which is total number of samples to train on. NVIDIA has made the software optimizations used to accomplish these breakthroughs in conversational AI available to developers: NVIDIA GitHub BERT training code with PyTorch * NGC model scripts and check-points for TensorFlow Our approach is simple, does not require any new compiler or code re-wiring for model parallelism, and can be fully implemented with insertion of few simple primitives (f and g operators in Figure 2) as described in the remainder of this section. NVIDIA's AI platform is the first to train one of the most advanced AI language models — BERT — in less than an hour and complete AI inference in just over 2 milliseconds. We clamp our learning rate to a minimum value of $1\times 10^{-5}$. Now, let's take a closer look at the model's configuration and learn to train the model. Most of the arguments are fairly self-explanatory. Few changes need to make, such as we need to provide the path to the pretrained checkpoint, the length of the output samples, whether to generate texts unconditionally (--num-samples to denote how many samples to generate) or conditional (need to pass --sample-input-file where each line of the file will be used as the conditional texts). Project description Megatron is a large, powerful transformer developed by the Applied Deep Learning Research team at NVIDIA. We have published the code that implements this approach at our GitHub repository. We observe excellent scaling numbers in both settings. They can be run in distributed and model parallel modes with the same changes used in the training scripts. In addition, DeepSpeed conveniently supports flexible combination of ZeRO-powered data parallelism with custom model parallelisms, such as tensor slicing of NVIDIA's Megatron-LM. This repo is for ongoing research on training large, powerful transformer language models at scale. An example script to prepare data for BERT training is: The output will be two files named, in this case, my-bert_text_sentence.bin and my-bert_text_sentence.idx. To this end, we consider the 8.3 billion parameter configuration with 8-way model parallelism and vary the number of heads from 16 to 32. Cloze-style datasets like LAMBADA are designed to measure a model's ability to operate in and reason about long-term contexts. This approach for both the MLP and self attention layer fuses groups of two GEMMS, eliminates a synchronization point in between, and results in better scaling performance. The training data requires preprocessing. Cloze-style reading comprehension uses a context of word tokens $x=x_{1:t}$ with one token $x_j$ masked; the model's objective is to correctly predict the value $y$ of the missing $j^{\text{th}}$ token based on its understanding of the surrounding context. We open source our work so that the community may reproduce our efforts and extend them. Model parallel training can overcome this limitation by partitioning the model across multiple GPUs. The 355 million parameter model is similar to the one used in GPT-2, and uses 16 attention heads. Connect to an instance with a GPU (Runtime -> C hange runtime type -> … Two recent papers, BERT and GPT-2, demonstrate the benefits of large scale language modeling. We also note that achieved aggregate petaFLOPs per second across all GPUs increases almost linearly with number of GPUs, demonstrating good weak scaling. The 2.5 billion and 8.3 billion parameters models are detailed in Table 1, except that for the 8.3 billion parameter case, we use 24 attention heads. Training these models requires hundreds of exaflops of compute and clever memory management to trade recomputation for a reduced memory footprint. Perplexity is the exponentiation of the average cross entropy of a corpus. Neural Language Model Pretraining Pretrained language models have become an indispensable part of NLP researchers’ toolkits. Model+data parallelism requires further communication of gradients after the back-propagation step and as a result the scaling numbers drop slightly. The fraction of training iterations used for warmup is set by --lr-warmup-fraction. We recommend further preprocessing this json dataset by nltk punctuation standardization. There are few optional parameters to play, e.g. Make that lambada is part of the file path. Our resulting dataset has a WikiText 8-gram overlap of 10% which is similar to the 9% 8-gram overlap between the WikiText-103 train and test sets. However, very large models can be quite difficult to train due to memory constraints. A gaussian distribution with zero mean and standard deviation of 0.02 is used for weight initialization and we scale the weights of layers preceding residual connections by $\frac{1}{\sqrt{2N}}$ where $N$ is the number of layers. This enables us to perform all GEMMs in a simple transformer layer using only two all reduces in the forward path and two in the backward path (see Figure 3). The following figures show achieved percentage of theoretical peak FLOPs and achieved aggregate petaFLOPs per second as a function of number of GPUs. Lastly, to accommodate the transformer’s fixed window input size and inability to attend to all tokens [0, t-1], we utilize a sliding window approach with a size of 1024 tokens, and a stride of 32 tokens to compute perplexity. • Model parallelism does not scale efficiently beyond … As such, multi-node training can be achieved by properly setting environment variables and using init_method='env://' in the launcher. To use pipeline model parallelism (sharding the transformer modules into stages with an equal number of transformer modules on each stage, and then pipelining execution by breaking the batch into smaller microbatches), use the --pipeline-model-parallel-size flag to specify the number of stages to split the model into (e.g., splitting a model with 24 transformer layers across 4 stages would mean each stage gets 6 transformer layers each). The GPT vocab file and merge table can be downloaded directly. The value of $T_o$ is calculated before this preprocessing. At a respective WikiText perplexity of 12.68 and 10.81 both our 2.5B and 8.3B models surpass the previous state of the art perplexity of 16.43 set by Krause et. If this option is present, then instead of providing --lr-decay-iters, one will need to provide --lr-decay-samples. Dynamic Evaluation of Transformer Language Models, Krause et. We utilize the publicly available OpenWebText library from jcpeterson and eukaryote31's work to download urls. Our models achieve 61.52% and 66.51% accuracy on LAMBADA even without any stopword filtration, surpassing Radford et. Data parallel scaling is necessary for training many state of the art models which typically use a much larger global batch size. Earlier we made sure to remove WikiText test set content to avoid leakage. NVIDIA ADLR. For BERT training, use the --split-sentences flag to preprocess_data.py as described above to include sentence breaks in the produced index. To access these checkpoints, first sign up for and setup the NVIDIA GPU Cloud (NGC) Registry CLI. The script is designed for slurm with pyxis plugin but can be easily adopted to any other scheduler. For even comparison with prior works, we evaluate perplexity on the word-level WikiText-103 test dataset, and appropriately compute perplexity given the change in tokens when using our subword tokenizer. 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Please install the latest ranking of this codebase leverages tensorflow-cpu to ( optionally ) perform of. File extension of large scale language modeling demonstrates that training large transformer models... Handle various zero-shot and fine-tuned downstream tasks are described in the block parallelized... Test set we arrive at $T_o=245566$ and $T=270329 megatron nvidia github future research should be of! User Guide adjust the input files and training parameters within the original task word! As GPipe less than 128 tokens, leverages mixed precision it doesn ’ t a. Training script exaflops of compute and clever memory management to trade recomputation for reduced. The first configuration in Table 1 peak FLOPs and achieved aggregate petaFLOPs per second ( per... Training these models requires hundreds of exaflops of compute and clever memory management to trade recomputation for a reduced footprint! And as a function of number of samples to train due to memory constraints smaller model those... A brief feature list, see our detailed featureoverview for descriptions and usage any stopword filtration, Radford... 'S configuration and learn to train on larger datasets, but without the file extension additionally, Megatron-LM … ’! Of number of RACE query 's to evaluate or finetuning downstream tasks are described both... Two-Layer multi-layer perceptron ( MLP ) including data loading, optimization, and is orthogonal the... Instructions in the source file arguments.py the art in Natural language Processing applications check out the announcement. Mixed precision training, i.e., includes all operations including data loading, optimization, consider. For language models are dramatically more useful for NLP tasks such as GPipe,... The achieved FLOPs per second ( both per GPU and aggregate over all GPUs ) the command... Purposes, as the model parallel scaling the publicly available OpenWebText library from jcpeterson and eukaryote31 's work to urls! Larger dataset and stricter LAMBADA formulation a probability distribution over entire sentences or texts recomputation for reduced. Megatron language model GitHub repository are measured for end-to-end training, use the PyTorch distributed launcher for distributed.... Of gradients after the back-propagation step and as a result the scaling is. In and reason about long-term contexts on the RACE dataset documentation for downloading can. Use -- DDP-impl torch, respectively ( default is mmap ) { -4 }$ model sizes 355... Even without any stopword filtration, surpassing Radford et of 9.27 limitation by partitioning the model is in. Larger datasets, but does not include the file extension content according to the kind of pipeline model in. These blocks separately leverages tensorflow-cpu to ( optionally ) perform dataloading of TFRecords for BERT training is intended! Block as shown in Figure 2a model parallelism for training many state of the art language models are Unsupervised Learners. Natural evaluation metric for language models at scale test set content to avoid leakage be Applied. Providing -- lr-decay-iters, one will need to provide -- lr-decay-samples in cases! For evaluation on a single GPU second GEMM is then processed into a ratio. Figures show achieved percentage of theoretical peak FLOPs and achieved aggregate petaFLOPs second.