The Cost of Large Scale Training

Statements

I find it hard to imagine OpenAI could finance a training run much over $50m. There’s probably a good reason they recently raised more capital. $...$ we are looking at a model with 600B-1T parameters trained on 1.5T to 4T tokens. (r/Singularity/Realistic size of GPT-4)[https://www.reddit.com/r/singularity/comments/106sd1z/realistic_size_of_gpt4/]

GPT$3$ has a vocabulary of 50257 words (The GPT-3 Architecture, on a Napkin)[https://dugas.ch/artificial_curiosity/GPT_architecture.html#:~:text=(GPT%20has%20a%20vocabulary%20of%2050257%20words).]

Cloud TPU type	v4 cores	Chips	VMs	Total memory	Evaluation price (USD)	1-year commitment price (USD)	3-year commitment price (USD)
...	...	...	...	...	...	...	...
v4-64	64	32	8	1024 GiB	$103.04 / hour	$47,388 / month	$33,849 / month
...	...	...	...	...	...	...	...
(Cloud TPU pricing

#TPU Pod type pricing )[https://cloud.google.com/tpu/pricing]

Peak compute per chip 275 teraflops (bf16 or int8) (System Architecture # TPU v4)[https://cloud.google.com/tpu/docs/system-architecture-tpu-vm#tpu_v4]

they claim that the forward pass of decoder-only Transformers involves $\approx 2N$ add-multiply operations, where $N$ is the number of non-embedding parameters in the model. (Understanding FLOPs-per-token estimates from OpenAI’s scaling laws)[https://discuss.huggingface.co/t/understanding-flops-per-token-estimates-from-openais-scaling-laws/23133]

Assumptions

6. GPT4 cost $100m (1)

7. GPT4 trained on 4T tokens (1)

8. GPT4 uses 50k vocab size (2)

9. 64 TPUv4 cores cost $33,849 / month at best (3)

10. The TPUv4 provides 275 teraflops (4)

11. GPT4 has N parameters (5)

12. GPT4 uses 2N flops per token (5)

Implications

13. 4T tokens (7) × 50k vocab size (8) = 2e17 bits of training data compressed into GPT4 (though many are reduntant)

14. 2e17 bits (13) ÷ $100m *(6)* = 2Gb/$ training cost

15. 4T tokens (7) ÷ $100m *(6)* = 40k tokens/$ training cost

16. A TPUv4 offers 275 $teraflops / sec$ (10) × 1 month ÷ $33,849 *(9)* = 2.12e16 flops/$

17. 40k tokens/$*(15)* \div (2.12e16 flops/$) (16) = 1.89e-12 training tokens / flop

18. 1 / (1.89e-12 training tokens / flop) (17) = 5.31e13 flops / training token

19. GPT4 uses 5.31e13 operations per training token (18)

20. GPT4 has 5.31e13 operations / 2 $operations per parameter$ = 2.65e13 parameters = 26T parameters

21. GPT cost $100m / 26T parameters = 3.85e-6$/param or cost 260k params/$

Comments

I am only willing to spend 4k on a NN. Based on these assumptions and implications, I could only expect to train a 1B parameter model. However, that's assuming the same data efficiency and architecture as the decoder only transformer. I can utilize sparsity, like tok k layers, hyper recurrent architectures, and smart sampling to improve performance at smaller scales.

Update (6/29/23): George Hotz: “Sam Altman won't tell you that GPT-4 has 220B parameters and is a 16-way mixture model with 8 sets of weights?”