Training Compute-Optimal Large Language Models

Introduction

Recently a series of Large Language Models (LLMs) have been introduced (Brown et al., 2020; Lieber et al., 2021; Rae et al., 2021; Smith et al., 2022; Thoppilan et al., 2022), with the largest dense language models now having over 500 billion parameters. These large autoregressive transformers (Vaswani et al., 2017) have demonstrated impressive performance on many tasks using a variety of evaluation protocols such as zero-shot, few-shot, and fine-tuning.

The compute and energy cost for training large language models is substantial (Rae et al., 2021; Thoppilan et al., 2022) and rises with increasing model size. In practice, the allocated training compute budget is often known in advance: how many accelerators are available and for how long we want to use them. Since it is typically only feasible to train these large models once, accurately estimating the best model hyperparameters for a given compute budget is critical (Tay et al., 2021).

Kaplan et al. (2020) showed that there is a power law relationship between the number of parameters in an autoregressive language model (LM) and its performance. As a result, the field has been training larger and larger models, expecting performance improvements. One notable conclusion in Kaplan et al. (2020) is that large models should not be trained to their lowest possible loss to be compute optimal. Whilst we reach the same conclusion, we estimate that large models should be trained for many more training tokens than recommended by the authors. Specifically, given a $10\times$ increase computational budget, they suggests that the size of the model should increase $5.5\times$ while the number of training tokens should only increase 1.8$\times$. Instead, we find that model size and the number of training tokens should be scaled in equal proportions.

Following Kaplan et al. (2020) and the training setup of GPT-3 (Brown et al., 2020), many of the recently trained large models have been trained for approximately 300 billion tokens (Table 1), in line with the approach of predominantly increasing model size when increasing compute.

In this work, we revisit the question: Given a fixed FLOPs budget,111For example, knowing the number of accelerators and a target training duration. how should one trade-off model size and the number of training tokens? To answer this question, we model the final pre-training loss222 For simplicity, we perform our analysis on the smoothed training loss which is an unbiased estimate of the test loss, as we are in the infinite data regime (the number of training tokens is less than the number of tokens in the entire corpus). $L(N,D)$ as a function of the number of model parameters $N$, and the number of training tokens, $D$. Since the computational budget $C$ is a deterministic function $\text{FLOPs}(N,D)$ of the number of seen training tokens and model parameters, we are interested in minimizing $L$ under the constraint $\text{FLOPs}(N,D)=C$:

The functions $N_{opt}(C)$, and $D_{opt}(C)$ describe the optimal allocation of a computational budget $C$. We empirically estimate these functions based on the losses of over 400 models, ranging from under $70$M to over $16$B parameters, and trained on $5$B to over $400$B tokens – with each model configuration trained for several different training horizons. Our approach leads to considerably different results than that of Kaplan et al. (2020). We highlight our results in Figure 1 and how our approaches differ in Section 2.

Based on our estimated compute-optimal frontier, we predict that for the compute budget used to train Gopher, an optimal model should be 4 times smaller, while being training on 4 times more tokens. We verify this by training a more compute-optimal 70B model, called Chinchilla, on 1.4 trillion tokens. Not only does Chinchilla outperform its much larger counterpart, Gopher, but its reduced model size reduces inference cost considerably and greatly facilitates downstream uses on smaller hardware. The energy cost of a large language model is amortized through its usage for inference an fine-tuning. The benefits of a more optimally trained smaller model, therefore, extend beyond the immediate benefits of its improved performance.

Related Work

A variety of large language models have been introduced in the last few years. These include both dense transformer models (Brown et al., 2020; Lieber et al., 2021; Smith et al., 2022; Rae et al., 2021; Thoppilan et al., 2022) and mixture-of-expert (MoE) models (Du et al., 2021; Fedus et al., 2021; Zoph et al., 2022). The largest dense transformers have passed 500 billion parameters (Smith et al., 2022). The drive to train larger and larger models is clear—so far increasing the size of language models has been responsible for improving the state-of-the-art in many language modelling tasks. Nonetheless, large language models face several challenges, including their overwhelming computational requirements (the cost of training and inference increase with model size) (Rae et al., 2021; Thoppilan et al., 2022) and the need for acquiring more high-quality training data. In fact, in this work we find that larger, high quality datasets will play a key role in any further scaling of language models.

Understanding the scaling behaviour of language models and their transfer properties has been important in the development of recent large models (Kaplan et al., 2020; Hernandez et al., 2021). Kaplan et al. (2020) first showed a predictable relationship between model size and loss over many orders of magnitude. The authors investigate the question of choosing the optimal model size to train for a given compute budget. Similar to us, they address this question by training various models. Our work differs from Kaplan et al. (2020) in several important ways. First, the authors use a fixed number of training tokens and learning rate schedule for all models; this prevents them from modelling the impact of these hyperparameters on the loss. In contrast, we find that setting the learning rate schedule to approximately match the number of training tokens results in the best final loss regardless of model size—see Figure A1. For a fixed learning rate cosine schedule to 130B tokens, the intermediate loss estimates (for $D^{\prime}<<130$B) are therefore overestimates of the loss of a model trained with a schedule length matching $D^{\prime}$. Using these intermediate losses results in underestimating the effectiveness of training models on less data than 130B tokens, and eventually contributes to the conclusion that model size should increase faster than training data size as compute budget increases. In contrast, our analysis predicts that both quantities should scale at roughly the same rate. Secondly, we include models with up to 16B parameters, as we observe that there is slight curvature in the FLOP-loss frontier (see Appendix E)—in fact, the majority of the models used in our analysis have more than 500 million parameters, in contrast the majority of runs in Kaplan et al. (2020) are significantly smaller—many being less than 100M parameters.

Recently, Clark et al. (2022) specifically looked in to the scaling properties of Mixture of Expert language models, showing that the scaling with number of experts diminishes as the model size increases—their approach models the loss as a function of two variables: the model size and the number of experts. However, the analysis is done with a fixed number of training tokens, as in Kaplan et al. (2020), potentially underestimating the improvements of branching.

The model size and the number of training tokens are not the only two parameters to chose when selecting a language model and a procedure to train it. Other important factors include learning rate, learning rate schedule, batch size, optimiser, and width-to-depth ratio. In this work, we focus on model size and the number of training steps, and we rely on existing work and provided experimental heuristics to determine the other necessary hyperparameters. Yang et al. (2021) investigates how to choose a variety of these parameters for training an autoregressive transformer, including the learning rate and batch size. McCandlish et al. (2018) finds only a weak dependence between optimal batch size and model size. Shallue et al. (2018); Zhang et al. (2019) suggest that using larger batch-sizes than those we use is possible. Levine et al. (2020) investigates the optimal depth-to-width ratio for a variety of standard model sizes. We use slightly less deep models than proposed as this translates to better wall-clock performance on our hardware.

Recently, various promising alternatives to traditional dense transformers have been proposed. For example, through the use of conditional computation large MoE models like the 1.7 trillion parameter Switch transformer (Fedus et al., 2021), the 1.2 Trillion parameter GLaM model (Du et al., 2021), and others (Artetxe et al., 2021; Zoph et al., 2022) are able to provide a large effective model size despite using relatively fewer training and inference FLOPs. However, for very large models the computational benefits of routed models seems to diminish (Clark et al., 2022). An orthogonal approach to improving language models is to augment transformers with explicit retrieval mechanisms, as done by Borgeaud et al. (2021); Guu et al. (2020); Lewis et al. (2020). This approach effectively increases the number of data tokens seen during training (by a factor of $\sim 10$ in Borgeaud et al. (2021)). This suggests that the performance of language models may be more dependant on the size of the training data than previously thought.

Estimating the optimal parameter/training tokens allocation

We present three different approaches to answer the question driving our research: Given a fixed FLOPs budget, how should one trade-off model size and the number of training tokens? In all three cases we start by training a range of models varying both model size and the number of training tokens and use the resulting training curves to fit an empirical estimator of how they should scale. We assume a power-law relationship between compute and model size as done in Clark et al. (2022); Kaplan et al. (2020), though future work may want to include potential curvature in this relationship for large model sizes. The resulting predictions are similar for all three methods and suggest that parameter count and number of training tokens should be increased equally with more compute333We compute FLOPs as described in Appendix F.—with proportions reported in Table 2. This is in clear contrast to previous work on this topic and warrants further investigation.

In our first approach we vary the number of training steps for a fixed family of models (ranging from 70M to over 10B parameters), training each model for 4 different number of training sequences. From these runs, we are able to directly extract an estimate of the minimum loss achieved for a given number of training FLOPs. Training details for this approach can be found in Appendix D.

For each parameter count $N$ we train 4 different models, decaying the learning rate by a factor of 10$\times$ over a horizon (measured in number of training tokens) that ranges by a factor of $16\times$. Then, for each run, we smooth and then interpolate the training loss curve. From this, we obtain a continuous mapping from FLOP count to training loss for each run. Then, for each FLOP count, we determine which run achieves the lowest loss. Using these interpolants, we obtain a mapping from any FLOP count $C$, to the most efficient choice of model size $N$ and number of training tokens $D$ such that $\text{FLOPs}(N,D)=C$.444Note that all selected points are within the last 15% of training. This suggests that when training a model over $D$ tokens, we should pick a cosine cycle length that decays $10\times$ over approximately $D$ tokens—see further details in Appendix B. At 1500 logarithmically spaced FLOP values, we find which model size achieves the lowest loss of all models along with the required number of training tokens. Finally, we fit power laws to estimate the optimal model size and number of training tokens for any given amount of compute (see the center and right panels of Figure 2), obtaining a relationship $N_{opt}\propto C^{a}$ and $D_{opt}\propto C^{b}$. We find that $a=0.50$ and $b=0.50$—as summarized in Table 2. In Section D.4, we show a head-to-head comparison at $10^{21}$ FLOPs, using the model size recommended by our analysis and by the analysis of Kaplan et al. (2020)—using the model size we predict has a clear advantage.

2 Approach 2: IsoFLOP profiles

In our second approach we vary the model size555In approach 2, model size varies up to 16B as opposed to approach 1 where we only used models up to 10B. for a fixed set of 9 different training FLOP counts666The number of training tokens is determined by the model size and training FLOPs. (ranging from $6\times 10^{18}$ to $3\times 10^{21}$ FLOPs), and consider the final training loss for each point777We set the cosine schedule length to match the number of tokens, which is optimal according to the analysis presented in Appendix B.. in contrast with Approach 1 that considered points $(N,D,L)$ along the entire training runs. This allows us to directly answer the question: For a given FLOP budget, what is the optimal parameter count?

For each FLOP budget, we plot the final loss (after smoothing) against the parameter count in Figure 3 (left). In all cases, we ensure that we have trained a diverse enough set of model sizes to see a clear minimum in the loss. We fit a parabola to each IsoFLOPs curve to directly estimate at what model size the minimum loss is achieved (Figure 3 (left)). As with the previous approach, we then fit a power law between FLOPs and loss-optimal model size and number of training tokens, shown in Figure 3 (center, right). Again, we fit exponents of the form $N_{opt}\propto C^{a}$ and $D_{opt}\propto C^{b}$ and we find that $a=0.49$ and $b=0.51$—as summarized in Table 2.

3 Approach 3: Fitting a parametric loss function

Lastly, we model all final losses from experiments in Approach 1 & 2 as a parametric function of model parameter count and the number of seen tokens. Following a classical risk decomposition (see Section D.2), we propose the following functional form

𝐸𝐴superscript𝑁𝛼𝐵superscript𝐷𝛽\hat{L}(N,D)\triangleq E+\frac{A}{N^{\alpha}}+\frac{B}{D^{\beta}}. (2) The first term captures the loss for an ideal generative process on the data distribution, and should correspond to the entropy of natural text. The second term captures the fact that a perfectly trained transformer with $N$ parameters underperforms the ideal generative process. The final term captures the fact that the transformer is not trained to convergence, as we only make a finite number of optimisation steps, on a sample of the dataset distribution.

To estimate $(A,B,E,\alpha,\beta)$, we minimize the Huber loss (Huber, 1964) between the predicted and observed log loss using the L-BFGS algorithm (Nocedal, 1980):

We account for possible local minima by selecting the best fit from a grid of initialisations. The Huber loss ($\delta=10^{-3}$) is robust to outliers, which we find important for good predictive performance over held-out data points. Section D.2 details the fitting procedure and the loss decomposition.

We can approximate the functions $N_{opt}$ and $D_{opt}$ by minimizing the parametric loss $\hat{L}$ under the constraint $\text{FLOPs}(N,D)\approx 6ND$ (Kaplan et al., 2020). The resulting $N_{opt}$ and $D_{opt}$ balance the two terms in Equation (3) that depend on model size and data. By construction, they have a power-law form:

𝛼𝛽formulae-sequence𝑎𝛽𝛼𝛽 and 𝑏𝛼𝛼𝛽N_{opt}(C)=G{\left(\frac{C}{6}\right)}^{a},\quad D_{opt}(C)=G^{-1}{\left(\frac{C}{6}\right)}^{b},\quad\text{ where }\quad G={\left(\frac{\alpha A}{\beta B}\right)}^{\frac{1}{\alpha+\beta}},\quad a=\frac{\beta}{\alpha+\beta},\text{ and }b=\frac{\alpha}{\alpha+\beta}. (4) We show contours of the fitted function $\hat{L}$ in Figure 4 (left), and the closed-form efficient computational frontier in blue. From this approach, we find that $a=0.46$ and $b=0.54$—as summarized in Table 2.

4 Optimal model scaling

We find that the three approaches, despite using different fitting methodologies and different trained models, yield comparable predictions for the optimal scaling in parameters and tokens with FLOPs (shown in Table 2).

All three approaches suggest that as compute budget increases, model size and the amount of training data should be increased in approximately equal proportions. The first and second approaches yield very similar predictions for optimal model sizes, as shown in Figure 1 and Figure A3. The third approach predicts even smaller models being optimal at larger compute budgets. We note that the observed points $(L,N,D)$ for low training FLOPs ($C\leqslant 1e21$) have larger residuals ${\|L-\hat{L}(N,D)\|}_{2}^{2}$ than points with higher computational budgets. The fitted model places increased weight on the points with more FLOPs—automatically considering the low-computational budget points as outliers due to the Huber loss. As a consequence of the empirically observed negative curvature in the frontier $C\to N_{opt}$ (see Appendix E), this results in predicting a lower $N_{opt}$ than the two other approaches.

. Parameters FLOPs FLOPs (in Gopher unit) Tokens 400 Million 1.92e+19 $1/29,968$ 8.0 Billion 1 Billion 1.21e+20 $1/4,761$ 20.2 Billion 10 Billion 1.23e+22 $1/46$ 205.1 Billion 67 Billion 5.76e+23 $1$ 1.5 Trillion 175 Billion 3.85e+24 $6.7$ 3.7 Trillion 280 Billion 9.90e+24 $17.2$ 5.9 Trillion 520 Billion 3.43e+25 $59.5$ 11.0 Trillion 1 Trillion 1.27e+26 $221.3$ 21.2 Trillion 10 Trillion 1.30e+28 $22515.9$ 216.2 Trillion

In Table 3 we show the estimated number of FLOPs and tokens that would ensure that a model of a given size lies on the compute-optimal frontier. Our findings suggests that the current generation of large language models are considerably over-sized, given their respective compute budgets, as shown in Figure 1. For example, we find that a 175 billion parameter model should be trained with a compute budget of $4.41\times 10^{24}$ FLOPs and on over 4.2 trillion tokens. A 280 billion Gopher-like model is the optimal model to train given a compute budget of approximately $10^{25}$ FLOPs and should be trained on 6.8 trillion tokens. Unless one has a compute budget of $10^{26}$ FLOPs (over 250$\times$ the compute used to train Gopher), a 1 trillion parameter model is unlikely to be the optimal model to train. Furthermore, the amount of training data that is projected to be needed is far beyond what is currently used to train large models, and underscores the importance of dataset collection in addition to engineering improvements that allow for model scale. While there is significant uncertainty extrapolating out many orders of magnitude, our analysis clearly suggests that given the training compute budget for many current LLMs, smaller models should have been trained on more tokens to achieve the most performant model.

In Appendix C, we reproduce the IsoFLOP analysis on two additional datasets: C4 (Raffel et al., 2020a) and GitHub code (Rae et al., 2021). In both cases we reach the similar conclusion that model size and number of training tokens should be scaled in equal proportions.

Chinchilla

Based on our analysis in Section 3, the optimal model size for the Gopher compute budget is somewhere between 40 and 70 billion parameters. We test this hypothesis by training a model on the larger end of this range—70B parameters—for 1.4T tokens, due to both dataset and computational efficiency considerations. In this section we compare this model, which we call Chinchilla, to Gopher and other LLMs. Both Chinchilla and Gopher have been trained for the same number of FLOPs but differ in the size of the model and the number of training tokens.

While pre-training a large language model has a considerable compute cost, downstream fine-tuning and inference also make up substantial compute usage (Rae et al., 2021). Due to being $4\times$ smaller than Gopher, both the memory footprint and inference cost of Chinchilla are also smaller.

The full set of hyperparameters used to train Chinchilla are given in Table 4. Chinchilla uses the same model architecture and training setup as Gopher with the exception of the differences listed below.

We train Chinchilla on MassiveText (the same dataset as Gopher) but use a slightly different subset distribution (shown in Table A1) to account for the increased number of training tokens.

We use AdamW (Loshchilov and Hutter, 2019) for Chinchilla rather than Adam (Kingma and Ba, 2014) as this improves the language modelling loss and the downstream task performance after finetuning.888Interestingly, a model trained with AdamW only passes the training performance of a model trained with Adam around 80% of the way through the cosine cycle, though the ending performance is notably better– see Figure A7

We train Chinchilla with a slightly modified SentencePiece (Kudo and Richardson, 2018) tokenizer that does not apply NFKC normalisation. The vocabulary is very similar– 94.15% of tokens are the same as those used for training Gopher. We find that this particularly helps with the representation of mathematics and chemistry, for example.

Whilst the forward and backward pass are computed in bfloat16, we store a float32 copy of the weights in the distributed optimiser state (Rajbhandari et al., 2020). See Lessons Learned from Rae et al. (2021) for additional details.

In Appendix G we show the impact of the various optimiser related changes between Chinchilla and Gopher. All models in this analysis have been trained on TPUv3/TPUv4 (Jouppi et al., 2017) with JAX (Bradbury et al., 2018) and Haiku (Hennigan et al., 2020). We include a Chinchilla model card (Mitchell et al., 2019) in LABEL:tab:chinchilla-model-card.

2 Results

We perform an extensive evaluation of Chinchilla, comparing against various large language models. We evaluate on a large subset of the tasks presented in Rae et al. (2021), shown in Table 5. As the focus of this work is on optimal model scaling, we included a large representative subset, and introduce a few new evaluations to allow for better comparison to other existing large models. The evaluation details for all tasks are the same as described in Rae et al. (2021).

Chinchilla significantly outperforms Gopher on all evaluation subsets of The Pile (Gao et al., 2020), as shown in Figure 5. Compared to Jurassic-1 (178B) Lieber et al. (2021), Chinchilla is more performant on all but two subsets– dm_mathematics and ubuntu_irc– see Table A5 for a raw bits-per-byte comparison. On Wikitext103 (Merity et al., 2017), Chinchilla achieves a perplexity of 7.16 compared to 7.75 for Gopher. Some caution is needed when comparing Chinchilla with Gopher on these language modelling benchmarks as Chinchilla is trained on 4$\times$ more data than Gopher and thus train/test set leakage may artificially enhance the results. We thus place more emphasis on other tasks for which leakage is less of a concern, such as MMLU (Hendrycks et al., 2020) and BIG-bench (BIG-bench collaboration, 2021) along with various closed-book question answering and common sense analyses.

2.2 MMLU

The Massive Multitask Language Understanding (MMLU) benchmark (Hendrycks et al., 2020) consists of a range of exam-like questions on academic subjects. In Table 6, we report Chinchilla’s average 5-shot performance on MMLU (the full breakdown of results is shown in Table A6). On this benchmark, Chinchilla significantly outperforms Gopher despite being much smaller, with an average accuracy of 67.6% (improving upon Gopher by 7.6%). Remarkably, Chinchilla even outperforms the expert forecast for June 2023 of 63.4% accuracy (see Table 6) (Steinhardt, 2021). Furthermore, Chinchilla achieves greater than 90% accuracy on 4 different individual tasks– high_school_gov_and_politics, international_law, sociology, and us_foreign_policy. To our knowledge, no other model has achieved greater than 90% accuracy on a subset.

In Figure 6, we show a comparison to Gopher broken down by task. Overall, we find that Chinchilla improves performance on the vast majority of tasks. On four tasks (college_mathematics, econometrics, moral_scenarios, and formal_logic) Chinchilla underperforms Gopher, and there is no change in performance on two tasks.

2.3 Reading comprehension

On the final word prediction dataset LAMBADA (Paperno et al., 2016), Chinchilla achieves 77.4% accuracy, compared to 74.5% accuracy from Gopher and 76.6% from MT-NLG 530B (see Table 7). On RACE-h and RACE-m (Lai et al., 2017), Chinchilla greatly outperforms Gopher, improving accuracy by more than 10% in both cases—see Table 7.

2.4 BIG-bench

We analysed Chinchilla on the same set of BIG-bench tasks (BIG-bench collaboration, 2021) reported in Rae et al. (2021). Similar to what we observed in MMLU, Chinchilla outperforms Gopher on the vast majority of tasks (see Figure 7). We find that Chinchilla improves the average performance by 10.7%, reaching an accuracy of 65.1% versus 54.4% for Gopher. Of the 62 tasks we consider, Chinchilla performs worse than Gopher on only four—crash_blossom, dark_humor_detection, mathematical_induction and logical_args. Full accuracy results for Chinchilla can be found in Table A7.

2.5 Common sense

We evaluate Chinchilla on various common sense benchmarks: PIQA (Bisk et al., 2020), SIQA (Sap et al., 2019), Winogrande (Sakaguchi et al., 2020), HellaSwag (Zellers et al., 2019), and BoolQ (Clark et al., 2019). We find that Chinchilla outperforms both Gopher and GPT-3 on all tasks and outperforms MT-NLG 530B on all but one task—see Table 8.

On TruthfulQA (Lin et al., 2021), Chinchilla reaches 43.6%, 58.5%, and 66.7% accuracy with 0-shot, 5-shot, and 10-shot respectively. In comparison, Gopher achieved only 29.5% 0-shot and 43.7% 10-shot accuracy. In stark contrast with the findings of Lin et al. (2021), the large improvements (14.1% in 0-shot accuracy) achieved by Chinchilla suggest that better modelling of the pre-training data alone can lead to substantial improvements on this benchmark.

2.6 Closed-book question answering

Results on closed-book question answering benchmarks are reported in Table 9. On the Natural Questions dataset (Kwiatkowski et al., 2019), Chinchilla achieves new closed-book SOTA accuracies: 31.5% 5-shot and 35.5% 64-shot, compared to 21% and 28% respectively, for Gopher. On TriviaQA (Joshi et al., 2017) we show results for both the filtered (previously used in retrieval and open-book work) and unfiltered set (previously used in large language model evaluations). In both cases, Chinchilla substantially out performs Gopher. On the filtered version, Chinchilla lags behind the open book SOTA (Izacard and Grave, 2020) by only 7.9%. On the unfiltered set, Chinchilla outperforms GPT-3—see Table 9.

2.7 Gender bias and toxicity

Large Language Models carry potential risks such as outputting offensive language, propagating social biases, and leaking private information (Weidinger et al., 2021; Bender et al., 2021). We expect Chinchilla to carry risks similar to Gopher because Chinchilla is trained on the same data, albeit with slightly different relative weights, and because it has a similar architecture. Here, we examine gender bias (particularly gender and occupation bias) and generation of toxic language. We select a few common evaluations to highlight potential issues, but stress that our evaluations are not comprehensive and much work remains to understand, evaluate, and mitigate risks in LLMs.

As discussed in Rae et al. (2021), large language models reflect contemporary and historical discourse about different groups (such as gender groups) from their training dataset, and we expect the same to be true for Chinchilla. Here, we test if potential gender and occupation biases manifest in unfair outcomes on coreference resolutions, using the Winogender dataset (Rudinger et al., 2018) in a zero-shot setting. Winogender tests whether a model can correctly determine if a pronoun refers to different occupation words. An unbiased model would correctly predict which word the pronoun refers to regardless of pronoun gender. We follow the same setup as in Rae et al. (2021) (described further in Section H.3).

As shown in Table 10, Chinchilla correctly resolves pronouns more frequently than Gopher across all groups. Interestingly, the performance increase is considerably smaller for male pronouns (increase of 3.2%) than for female or neutral pronouns (increases of 8.3% and 9.2% respectively). We also consider gotcha examples, in which the correct pronoun resolution contradicts gender stereotypes (determined by labor statistics). Again, we see that Chinchilla resolves pronouns more accurately than Gopher. When breaking up examples by male/female gender and gotcha/not gotcha, the largest improvement is on female gotcha examples (improvement of 10%). Thus, though Chinchilla uniformly overcomes gender stereotypes for more coreference examples than Gopher, the rate of improvement is higher for some pronouns than others, suggesting that the improvements conferred by using a more compute-optimal model can be uneven.

Language models are capable of generating toxic language—including insults, hate speech, profanities and threats (Gehman et al., 2020; Rae et al., 2021). While toxicity is an umbrella term, and its evaluation in LMs comes with challenges (Xu et al., 2021; Welbl et al., 2021), automatic classifier scores can provide an indication for the levels of harmful text that a LM generates. Rae et al. (2021) found that improving language modelling loss by increasing the number of model parameters has only a negligible effect on toxic text generation (unprompted); here we analyze whether the same holds true for a lower LM loss achieved via more compute-optimal training. Similar to the protocol of Rae et al. (2021), we generate 25,000 unprompted samples from Chinchilla, and compare their PerspectiveAPI toxicity score distribution to that of Gopher-generated samples. Several summary statistics indicate an absence of major differences: the mean (median) toxicity score for Gopher is 0.081 (0.064), compared to 0.087 (0.066) for Chinchilla, and the $95^{\textrm{th}}$ percentile scores are 0.230 for Gopher, compared to 0.238 for Chinchilla. That is, the large majority of generated samples are classified as non-toxic, and the difference between the models is negligible. In line with prior findings (Rae et al., 2021), this suggests that toxicity levels in unconditional text generation are largely independent of the model quality (measured in language modelling loss), i.e. that better models of the training dataset are not necessarily more toxic.

Discussion & Conclusion

The trend so far in large language model training has been to increase the model size, often without increasing the number of training tokens. The largest dense transformer, MT-NLG 530B, is now over $3\times$ larger than GPT-3’s 170 billion parameters from just two years ago. However, this model, as well as the majority of existing large models, have all been trained for a comparable number of tokens—around 300 billion. While the desire to train these mega-models has led to substantial engineering innovation, we hypothesize that the race to train larger and larger models is resulting in models that are substantially underperforming compared to what could be achieved with the same compute budget.

We propose three predictive approaches towards optimally setting model size and training duration, based on the outcome of over 400 training runs. All three approaches predict that Gopher is substantially over-sized and estimate that for the same compute budget a smaller model trained on more data will perform better. We directly test this hypothesis by training Chinchilla, a 70B parameter model, and show that it outperforms Gopher and even larger models on nearly every measured evaluation task.

Whilst our method allows us to make predictions on how to scale large models when given additional compute, there are several limitations. Due to the cost of training large models, we only have two comparable training runs at large scale (Chinchilla and Gopher), and we do not have additional tests at intermediate scales. Furthermore, we assume that the efficient computational frontier can be described by a power-law relationship between the compute budget, model size, and number of training tokens. However, we observe some concavity in $\log\left(N_{opt}\right)$ at high compute budgets (see Appendix E). This suggests that we may still be overestimating the optimal size of large models. Finally, the training runs for our analysis have all been trained on less than an epoch of data; future work may consider the multiple epoch regime. Despite these limitations, the comparison of Chinchilla to Gopher validates our performance predictions, that have thus enabled training a better (and more lightweight) model at the same compute budget.

Though there has been significant recent work allowing larger and larger models to be trained, our analysis suggests an increased focus on dataset scaling is needed. Speculatively, we expect that scaling to larger and larger datasets is only beneficial when the data is high-quality. This calls for responsibly collecting larger datasets with a high focus on dataset quality. Larger datasets will require extra care to ensure train-test set overlap is properly accounted for, both in the language modelling loss but also with downstream tasks. Finally, training for trillions of tokens introduces many ethical and privacy concerns. Large datasets scraped from the web will contain toxic language, biases, and private information. With even larger datasets being used, the quantity (if not the frequency) of such information increases, which makes dataset introspection all the more important. Chinchilla does suffer from bias and toxicity but interestingly it seems less affected than Gopher. Better understanding how performance of large language models and toxicity interact is an important future research question.

While we have applied our methodology towards the training of auto-regressive language models, we expect that there is a similar trade-off between model size and the amount of data in other modalities. As training large models is very expensive, choosing the optimal model size and training steps beforehand is essential. The methods we propose are easy to reproduce in new settings.

Acknowledgements

We’d like to thank Jean-baptiste Alayrac, Kareem Ayoub, Chris Dyer, Nando de Freitas, Demis Hassabis, Geoffrey Irving, Koray Kavukcuoglu, Nate Kushman and Angeliki Lazaridou for useful comments on the manuscript. We’d like to thank Andy Brock, Irina Higgins, Michela Paganini, Francis Song, and other colleagues at DeepMind for helpful discussions. We are also very grateful to the JAX and XLA team for their support and assistance.

References

Appendix

Appendix A Training dataset

In Table A1 we show the training dataset makeup used for Chinchilla and all scaling runs. Note that both the MassiveWeb and Wikipedia subsets are both used for more than one epoch.

Appendix B Optimal cosine cycle length

One key assumption is made on the cosine cycle length and the corresponding learning rate drop (we use a 10$\times$ learning rate decay in line with Rae et al. (2021)).999We find the difference between decaying by $10\times$ and decaying to 0.0 (over the same number of steps) to be small, though decaying by a factor of $10\times$ to be slightly more performant. Decaying by less ($5\times$) is clearly worse. We find that setting the cosine cycle length too much longer than the target number of training steps results in sub-optimally trained models, as shown in Figure A1. As a result, we assume that an optimally trained model will have the cosine cycle length correctly calibrated to the maximum number of steps, given the FLOP budget; we follow this rule in our main analysis.

Appendix C Consistency of scaling results across datasets

We show scaling results from an IsoFLOP (Approach 2) analysis after training on two different datasets: C4 (Raffel et al., 2020b) and GitHub code (we show results with data from Rae et al. (2021)), results are shown in Table A2. For both set of experiments using subsets of MassiveText, we use the same tokenizer as the MassiveText experiments.

We find that the scaling behaviour on these datasets is very similar to what we found on MassiveText, as shown in Figure A2 and Table A2. This suggests that our results are independent of the dataset as long as one does not train for more than one epoch.

Appendix D Details on the scaling analyses

We use a maximum learning rate of $2\times 10^{-4}$ for the smallest models and $1.25\times 10^{-4}$ for the largest models. In all cases, the learning rate drops by a factor of $10\times$ during training, using a cosine schedule. We make the assumption that the cosine cycle length should be approximately matched to the number of training steps. We find that when the cosine cycle overshoots the number of training steps by more than 25%, performance is noticeably degraded—see Figure A1.101010This further emphasises the point of not only determining model size, but also training length before training begins. We use Gaussian smoothing with a window length of 10 steps to smooth the training curve.

D.2 Approach 3: Parametric fitting of the loss

In this section, we first show how Equation (2) can be derived. We repeat the equation below for clarity,

𝐸𝐴superscript𝑁𝛼𝐵superscript𝐷𝛽\hat{L}(N,D)\triangleq E+\frac{A}{N^{\alpha}}+\frac{B}{D^{\beta}}, (5) based on a decomposition of the expected risk between a function approximation term and an optimisation suboptimality term. We then give details on the optimisation procedure for fitting the parameters.

Formally, we consider the task of predicting the next token $y\in\mathcal{Y}$ based on the previous tokens in a sequence $x\in\mathcal{Y}^{s}$, with $s$ varying from to $s_{\max}$—the maximum sequence length. We consider a distribution $P\in\mathcal{D}(\mathcal{X}\times\mathcal{Y})$ of tokens in $\mathcal{Y}$ and their past in $\mathcal{X}$. A predictor $f:\mathcal{X}\to\mathcal{D}(\mathcal{Y})$ computes the probability of each token given the past sequence. The Bayes classifier, $f^{\star}$, minimizes the cross-entropy of $f(x)$ with the observed tokens $y$, with expectation taken on the whole data distribution. We let $L$ be the expected risk

The set of all transformers of size $N$, that we denote $\mathcal{H}_{N}$, forms a subset of all functions that map sequences to distributions of tokens $\mathcal{X}\to\mathcal{D}(\mathcal{Y})$. Fitting a transformer of size $N$ on the expected risk $L(f)$ amounts to minimizing such risk on a restricted functional space

When we observe a dataset ${(x_{i},y_{i})_{i}}_{i\in[1,D]}$ of size $D$, we do not have access to $\mathbb{E}_{P}$, but instead to the empirical expectation $\hat{\mathbb{E}}_{D}$ over the empirical distribution $\hat{P}_{D}$. What happens when we are given $D$ datapoints that we can only see once, and when we constrain the size of the hypothesis space to be $N$-dimensional ? We are making steps toward minimizing the empirical risk within a finite-dimensional functional space $\mathcal{H}_{N}$:

We are never able to obtain $\hat{f}_{N,D}$ as we typically perform a single epoch over the dataset of size $D$. Instead, be obtain $\bar{f}_{N,D}$, which is the result of applying a certain number of gradient steps based on the $D$ datapoints—the number of steps to perform depends on the gradient batch size, for which we use well-tested heuristics.

Using the Bayes-classifier $f^{\star}$, the expected-risk minimizer $f_{N}$ and the “single-epoch empirical-risk minimizer” $\bar{f}_{N,D}$, we can finally decompose the loss $L(N,D)$ into

𝐿superscript𝑓⋆𝐿subscript𝑓𝑁𝐿superscript𝑓⋆𝐿subscript¯𝑓𝑁𝐷𝐿subscript𝑓𝑁L(N,D)\triangleq L(\bar{f}_{N,D})=L(f^{\star})+\left(L(f_{N})-L(f^{\star})\right)+\left(L(\bar{f}_{N,D})-L(f_{N})\right). (9) The loss comprises three terms: the Bayes risk, i.e. the minimal loss achievable for next-token prediction on the full distribution $P$, a.k.a the “entropy of natural text.”; a functional approximation term that depends on the size of the hypothesis space; finally, a stochastic approximation term that captures the suboptimality of minimizing $\hat{L}_{D}$ instead of $L$, and of making a single epoch on the provided dataset.

In the decomposition (9), the second term depends entirely on the number of parameters $N$ that defines the size of the functional approximation space. On the set of two-layer neural networks, it is expected to be proportional to $\frac{1}{N^{1/2}}$ (Siegel and Xu, 2020). Finally, given that it corresponds to early stopping in stochastic first order methods, the third term should scale as the convergence rate of these methods, which is lower-bounded by $\frac{1}{D^{1/2}}$ (Robbins and Monro, 1951) (and may attain the bound). This convergence rate is expected to be dimension free (see e.g. Bubeck, 2015, for a review) and depends only on the loss smoothness; hence we assume that the second term only depends on $D$ in (2). Empirically, we find after fitting (2) that

𝐸𝐴superscript𝑁0.34𝐵superscript𝐷0.28L(N,D)=E+\frac{A}{N^{0.34}}+\frac{B}{D^{0.28}}, (10) with $E=1.69$, $A=406.4$, $B=410.7$. We note that the parameter/data coefficients are both lower than $\frac{1}{2}$; this is expected for the data-efficiency coefficient (but far from the known lower-bound). Future models and training approaches should endeavor to increase these coefficients.

We effectively minimize the following problem

where $LSE$ is the log-sum-exp operator. We then set $A,B,E=\exp(a),\exp(b),\exp(e)$.

We use the LBFGS algorithm to find local minima of the objective above, started on a grid of initialisation given by: $\alpha\in\{0.,0.5,\dots,2.\}$, $\beta\in\{0.,0.5,\dots,2.\}$, $e\in\{-1.,-.5,\dots,1.\}$, $a\in\{0,5,\dots,25\}$, and $b\in\{0,5,\dots,25\}$. We find that the optimal initialisation is not on the boundary of our initialisation sweep.

We use $\delta=10^{-3}$ for the Huber loss. We find that using larger values of $\delta$ pushes the model to overfit the small compute regime and poorly predict held-out data from larger runs. We find that using a $\delta$ smaller than $10^{-3}$ does not impact the resulting predictions.

D.3 Predicted compute optimal frontier for all three methods

For Approaches 2 and 3, we show the estimated model size and number of training tokens for a variety of compute budgets in Table A3. We plot the predicted number of tokens and parameters for a variety of FLOP budgets for the three methods in Figure A3.

D.4 Small-scale comparison to Kaplan et al. (2020)

For $10^{21}$ FLOPs, we perform a head-to-head comparison of a model predicted by Approach 1 and that predicted by Kaplan et al. (2020). For both models, we use a batch size of 0.5M tokens and a maximum learning rate of $1.5\times 10^{-4}$ that decays by $10\times$. From Kaplan et al. (2020), we find that the optimal model size should be 4.68 billion parameters. From our approach 1, we estimate a 2.86 billion parameter model should be optimal. We train a 4.74 billion parameter and a 2.80 billion parameter transformer to test this hypothesis, using the same depth-to-width ratio to avoid as many confounding factors as possible. We find that our predicted model outperforms the model predicted by Kaplan et al. (2020) as shown in Figure A4.

Appendix E Curvature of the FLOP-loss frontier

We observe that as models increase there is a curvature in the FLOP-minimal loss frontier. This means that projections from very small models lead to different predictions than those from larger models. In Figure A5 we show linear fits using the first, middle, and final third of frontier-points. In this work, we do not take this in to account and we leave this as interesting future work as it suggests that even smaller models may be optimal for large FLOP budgets.

Appendix F FLOPs computation

We include all training FLOPs, including those contributed to by the embedding matrices, in our analysis. Note that we also count embeddings matrices in the total parameter count. For large models the FLOP and parameter contribution of embedding matrices is small. We use a factor of 2 to describe the multiply accumulate cost. For the forward pass, we consider contributions from:

$2\times\text{seq\_len}\times\text{vocab\_size}\times\text{d\_model}$

Key, query and value projections: $2\times 3\times\text{seq\_len}\times\text{d\_model}\times(\text{key\_size}\times\text{num\_heads})$

Key @ Query logits: $2\times\text{seq\_len}\times\text{seq\_len}\times(\text{key\_size}\times\text{num\_heads})$

Softmax: $3\times\text{num\_heads}\times\text{seq\_len}\times\text{seq\_len}$

Softmax @ query reductions: $2\times\text{seq\_len}\times\text{seq\_len}\times(\text{key\_size}\times\text{num\_heads})$

Final Linear: $2\times\text{seq\_len}\times(\text{key\_size}\times\text{num\_heads})\times\text{d\_model}$

$2\times\text{seq\_len}\times(\text{d\_model}\times\text{ffw\_size}+\text{d\_model}\times\text{ffw\_size})$

$2\times\text{seq\_len}\times\text{d\_model}\times\text{vocab\_size}$

Total forward pass FLOPs: $\text{embeddings}+\text{num\_layers}\times(\text{total\_attention}+\text{dense\_block})$ + logits

As in Kaplan et al. (2020) we assume that the backward pass has twice the FLOPs of the forward pass. We show a comparison between our calculation and that using the common approximation $C=6DN$ (Kaplan et al., 2020) where $C$ is FLOPs, $D$ is the number of training tokens, and $N$ is the number of parameters in Table A4. We find the differences in FLOP calculation to be very small and they do not impact our analysis.

Compared to the results presented in Rae et al. (2021), we use a slightly more accurate calculation giving a slightly different value ($6.3\times 10^{23}$ compared to $5.76\times 10^{23}$).

Appendix G Other differences between Chinchilla and Gopher

Beyond differences in model size and number of training tokens, there are some additional minor differences between Chinchilla and Gopher. Specifically, Gopher was trained with Adam (Kingma and Ba, 2014) whereas Chinchilla was trained with AdamW (Loshchilov and Hutter, 2019). Furthermore, as discussed in Lessons Learned in Rae et al. (2021), Chinchilla stored a higher-precision copy of the weights in the sharded optimiser state.

We show comparisons of models trained with Adam and AdamW in Figure A6 and Figure A7. We find that, independent of the learning rate schedule, AdamW trained models outperform models trained with Adam.

In Figure A6 we show a comparison of an 680 million parameter model trained with and without the higher precision copy of the weights and with Adam/AdamW for comparison.

Appendix H Results

In Table A5 we show the bits-per-byte (bpb) on The Pile (Gao et al., 2020) of Chinchilla, Gopher, and Jurassic-1. Chinchilla outperforms Gopher on all subsets. Jurassic-1 outperforms Chinchilla on 2 subsets— dm_mathematics and ubuntu_irc.

H.2 MMLU

In Table A6 we show the performance of Chinchilla and Gopher on each subset of MMLU.

H.3 Winogender Setup

We follow the same setup as in Rae et al. (2021). To test coreference resolution in Chinchilla, we input a sentence which includes a pronoun reference (e.g., “The librarian helped the child pick out a book because {pronoun} liked to encourage reading.”), then measure the probability of the model completing the sentence “‘{Pronoun}’ refers to the” with different sentence roles (“librarian” and “child” in this example). Each example is annotated with the correct pronoun resolution (the pronoun corresponds to the librarian in this example). Each sentence is tested with a female, male, and gender-neutral pronoun. An unbiased model would correctly predict which word the pronoun refers to regardless of pronoun gender.

H.4 BIG-bench

In Table A7 we show Chinchilla and Gopher performance on each subset of BIG-bench that we consider.

Appendix I Model Card

We present the Chinchilla model card in LABEL:tab:chinchilla-model-card, following the framework presented by Mitchell et al. (2019).

Appendix J List of trained models

In LABEL:tab:all_models we list the model size and configuration of all models used in this study. Many models have been trained multiple times, for a different number of training steps.