We investigate the optimal model size and number of tokens for training a transformer language model under a given compute budget. We find that current large language models are significantly undertrained, a consequence of the recent focus on scaling language models whilst keeping the amount of training data constant. By training over 400 language models ranging from 70 million to over 16 billion parameters on 5 to 500 billion tokens, we find that for compute-optimal training, the model size and the number of training tokens should be scaled equally: for every doubling of model size the number of training tokens should also be doubled. We test this hypothesis by training a predicted compute-optimal model, Chinchilla, that uses the same compute budget as Gopher but with 70B parameters and 4$\times$ more more data. Chinchilla uniformly and significantly outperforms Gopher (280B), GPT-3 (175B), Jurassic-1 (178B), and Megatron-Turing NLG (530B) on a large range of downstream evaluation tasks. This also means that Chinchilla uses substantially less compute for fine-tuning and inference, greatly facilitating downstream usage. As a highlight, Chinchilla reaches a state-of-the-art average accuracy of 67.5% on the MMLU benchmark, greater than a 7% improvement over Gopher.

Natural language communication is core to intelligence, as it allows ideas to be efficiently shared between humans or artificially intelligent systems. The generality of language allows us to express many intelligence tasks as taking in natural language input and producing natural language output. Autoregressive language modelling -- predicting the future of a text sequence from its past -- provides a simple yet powerful objective that admits formulation of numerous cognitive tasks. At the same time, it opens the door to plentiful training data: the internet, books, articles, code, and other writing. However this training objective is only an approximation to any specific goal or application, since we predict everything in the sequence rather than only the aspects we care about. Yet if we treat the resulting models with appropriate caution, we believe they will be a powerful tool to capture some of the richness of human intelligence. Using language models as an ingredient towards intelligence contrasts with their original application: transferring text over a limited-bandwidth communication channel. Shannon's Mathematical Theory of Communication (Shannon, 1948) linked the statistical modelling of natural language with compression, showing that measuring the cross entropy of a language model is equivalent to measuring its compression rate.

Sparse neural networks are becoming increasingly important as the field seeks to improve the performance of existing models by scaling them up, while simultaneously trying to reduce power consumption and computational footprint. Unfortunately, most existing methods for inducing performant sparse models still entail the instantiation of dense parameters, or dense gradients in the backward-pass, during training. For very large models this requirement can be prohibitive. In this work we propose Top-KAST, a method that preserves constant sparsity throughout training (in both the forward and backward-passes). We demonstrate the efficacy of our approach by showing that it performs comparably to or better than previous works when training models on the established ImageNet benchmark, whilst fully maintaining sparsity. In addition to our ImageNet results, we also demonstrate our approach in the domain of language modeling where the current best performing architectures tend to have tens of billions of parameters and scaling up does not yet seem to have saturated performance. Sparse versions of these architectures can be run with significantly fewer resources, making them more widely accessible and applicable. Furthermore, in addition to being effective, our approach is straightforward and can easily be implemented in a wide range of existing machine learning frameworks with only a few additional lines of code. We therefore hope that our contribution will help enable the broader community to explore the potential held by massive models, without incurring massive computational cost.

Abstract--Scientific workloads have traditionally exploited high levels of sparsity to accelerate computation and reduce memory requirements. While deep neural networks can be made sparse, achieving practical speedups on GPUs is difficult because these applications have relatively moderate levels of sparsity that are not sufficient for existing sparse kernels to outperform their dense counterparts. In this work, we study sparse matrices from deep learning applications and identify favorable properties that can be exploited to accelerate computation. Based on these insights, we develop high-performance GPU kernels for two sparse matrix operations widely applicable in neural networks: sparse matrix-dense matrix multiplication and sampled dense-dense matrix multiplication. Using our kernels, we demonstrate sparse Transformer and MobileNet models that achieve 1.2-2.1 speedups and up to 12.8 memory savings without sacrificing accuracy. This work enables speedups for all problems in the highlighted region. Existing GPU kernels for sparse linear algebra are procedure, a sparsification algorithm is applied to produce a primarily optimized for scientific applications, where matrices neural network where a high fraction of the weights are zerovalued are extremely (99%) sparse. The weight matrices can then be stored in levels of sparsity found in deep neural networks, these kernels a compressed format, and sparse linear algebra kernels can be are not able to outperform their dense counterparts. In the context of generative To address this issue, structure can be enforced on the models, sparsity has been applied to reduce the computational topology of nonzeros such that nonzero values are grouped requirements of self-attention in Transformer architectures [6], into blocks [12]-[14]. While this approach is able to recover [10], [11].

It has long been argued that minibatch stochastic gradient descent can generalize better than large batch gradient descent in deep neural networks. However recent papers have questioned this claim, arguing that this effect is simply a consequence of suboptimal hyperparameter tuning or insufficient compute budgets when the batch size is large. In this paper, we perform carefully designed experiments and rigorous hyperparameter sweeps on a range of popular models, which verify that small or moderately large batch sizes can substantially outperform very large batches on the test set. This occurs even when both models are trained for the same number of iterations and large batches achieve smaller training losses. Our results confirm that the noise in stochastic gradients can enhance generalization. We study how the optimal learning rate schedule changes as the epoch budget grows, and we provide a theoretical account of our observations based on the stochastic differential equation perspective of SGD dynamics.

Neural networks have historically been built layerwise from the set of functions in ${f: \mathbb{R}^n \to \mathbb{R}^m }$, i.e. with activations and weights/parameters represented by real numbers, $\mathbb{R}$. Our work considers a richer set of objects for activations and weights, and undertakes a comprehensive study of alternative algebras as number representations by studying their performance on two challenging problems: large-scale image classification using the ImageNet dataset and language modeling using the enwiki8 and WikiText-103 datasets. We denote this broader class of models as AlgebraNets. Our findings indicate that the conclusions of prior work, which explored neural networks constructed from $\mathbb{C}$ (complex numbers) and $\mathbb{H}$ (quaternions) on smaller datasets, do not always transfer to these challenging settings. However, our results demonstrate that there are alternative algebras which deliver better parameter and computational efficiency compared with $\mathbb{R}$. We consider $\mathbb{C}$, $\mathbb{H}$, $M_{2}(\mathbb{R})$ (the set of $2\times2$ real-valued matrices), $M_{2}(\mathbb{C})$, $M_{3}(\mathbb{R})$ and $M_{4}(\mathbb{R})$. Additionally, we note that multiplication in these algebras has higher compute density than real multiplication, a useful property in situations with inherently limited parameter reuse such as auto-regressive inference and sparse neural networks. We therefore investigate how to induce sparsity within AlgebraNets. We hope that our strong results on large-scale, practical benchmarks will spur further exploration of these unconventional architectures which challenge the default choice of using real numbers for neural network weights and activations.

Current methods for training recurrent neural networks are based on backpropagation through time, which requires storing a complete history of network states, and prohibits updating the weights `online' (after every timestep). Real Time Recurrent Learning (RTRL) eliminates the need for history storage and allows for online weight updates, but does so at the expense of computational costs that are quartic in the state size. This renders RTRL training intractable for all but the smallest networks, even ones that are made highly sparse. We introduce the Sparse n-step Approximation (SnAp) to the RTRL influence matrix, which only keeps entries that are nonzero within n steps of the recurrent core. SnAp with n=1 is no more expensive than backpropagation, and we find that it substantially outperforms other RTRL approximations with comparable costs such as Unbiased Online Recurrent Optimization. For highly sparse networks, SnAp with n=2 remains tractable and can outperform backpropagation through time in terms of learning speed when updates are done online. SnAp becomes equivalent to RTRL when n is large.

We investigate the difficulties of training sparse neural networks and make new observations about optimization dynamics and the energy landscape within the sparse regime. Recent work of \citep{Gale2019, Liu2018} has shown that sparse ResNet-50 architectures trained on ImageNet-2012 dataset converge to solutions that are significantly worse than those found by pruning. We show that, despite the failure of optimizers, there is a linear path with a monotonically decreasing objective from the initialization to the "good" solution. Additionally, our attempts to find a decreasing objective path from "bad" solutions to the "good" ones in the sparse subspace fail. However, if we allow the path to traverse the dense subspace, then we consistently find a path between two solutions. These findings suggest traversing extra dimensions may be needed to escape stationary points found in the sparse subspace.

In this work we show that Evolution Strategies (ES) are a viable method for learning non-differentiable parameters of large supervised models. ES are black-box optimization algorithms that estimate distributions of model parameters; however they have only been used for relatively small problems so far. We show that it is possible to scale ES to more complex tasks and models with millions of parameters. While using ES for differentiable parameters is computationally impractical (although possible), we show that a hybrid approach is practically feasible in the case where the model has both differentiable and non-differentiable parameters. In this approach we use standard gradient-based methods for learning differentiable weights, while using ES for learning non-differentiable parameters - in our case sparsity masks of the weights. This proposed method is surprisingly competitive, and when parallelized over multiple devices has only negligible training time overhead compared to training with gradient descent. Additionally, this method allows to train sparse models from the first training step, so they can be much larger than when using methods that require training dense models first.

We rigorously evaluate three state-of-the-art techniques for inducing sparsity in deep neural networks on two large-scale learning tasks: Transformer trained on WMT 2014 English-to-German, and ResNet-50 trained on ImageNet. Across thousands of experiments, we demonstrate that complex techniques (Molchanov et al., 2017; Louizos et al., 2017b) shown to yield high compression rates on smaller datasets perform inconsistently, and that simple magnitude pruning approaches achieve comparable or better results. Additionally, we replicate the experiments performed by (Frankle & Carbin, 2018) and (Liu et al., 2018) at scale and show that unstructured sparse architectures learned through pruning cannot be trained from scratch to the same test set performance as a model trained with joint sparsification and optimization. Together, these results highlight the need for large-scale benchmarks in the field of model compression. We open-source our code, top performing model checkpoints, and results of all hyperparameter configurations to establish rigorous baselines for future work on compression and sparsification.