Estimate Complexity

Okay, let's estimate the FLOPs required to train GPT-3. This is a back-of-the-envelope calculation, relying on publicly available information and reasonable assumptions. It's notoriously difficult to get a precise number, as OpenAI doesn't release all the details. We'll break it down step-by-step.

1. GPT-3 Model Size (Parameters)

• GPT-3 has 175 billion parameters. This is the foundation of our calculation. Each parameter is a weight in the neural network that needs to be updated during training.

2. Training Dataset Size

• GPT-3 was trained on a huge dataset. OpenAI stated approximately 300 billion tokens. A token can be roughly considered a word or part of a word. Let's use 300 billion tokens as our base.
• The dataset comprised sources like Common Crawl, WebText2, Books1, and Books2. The exact breakdown and filtering are proprietary, but we have the overall size.

3. FLOPs per Token

This is the trickiest part. The number of FLOPs (Floating Point Operations) per token processed depends heavily on the model architecture (Transformer in this case) and implementation details. We'll use a common approximation based on research into large language models.

• Transformer Architecture: Transformers have a complexity that scales roughly with the sequence length (number of tokens in a sequence) squared, and also with the model size (number of parameters). The core operations are matrix multiplications.
• FLOPs per Parameter per Token: A reasonable estimate for FLOPs per parameter per token for a model like GPT-3 during the forward and backward pass (which are both needed for training) is around 3. This comes from analyses of similar models (e.g., Chinchilla, PaLM). This includes the attention mechanism, matrix multiplications in the feedforward layers, and gradient calculations.
• Total FLOPs per Token: Therefore, FLOPs per token ≈ (Number of Parameters) * (FLOPs per Parameter per Token)
  • FLOPs per token ≈ 175 billion parameters * 3 FLOPs/parameter/token = 525 billion FLOPs/token = 5.25 x 10¹¹ FLOPs/token

4. Total FLOPs for Training

• Total FLOPs = (FLOPs per token) * (Number of tokens)
• Total FLOPs ≈ (5.25 x 10¹¹ FLOPs/token) * (300 x 10⁹ tokens)
• Total FLOPs ≈ 1.575 x 10²³ FLOPs

5. Expressing FLOPs in more familiar units

• 1 FLOP = 10^-15 petaFLOPs (PFLOPs)
• 1 PFLOP = 10¹⁵ FLOPs
• Therefore, 1.575 x 10²³ FLOPs = 1.575 x 10⁸ PFLOPs = 157.5 ExaFLOPs (EFLOPs)
  • 1 ExaFLOP = 10¹⁸ FLOPs

Therefore, our estimate for the total FLOPs required to train GPT-3 is approximately 157.5 ExaFLOPs.

Important Considerations and Caveats:

• Sparsity: Modern models often use techniques like sparsity (zeroing out some parameters) to reduce computational cost. If GPT-3 used significant sparsity, the actual FLOPs might be lower.
• Mixed Precision Training: GPT-3 likely used mixed-precision training (e.g., using 16-bit floating-point numbers for some operations instead of 32-bit). This reduces memory usage and can speed up computations, but it doesn't drastically change the total FLOP count (it changes the type of FLOPs, but not necessarily the number).
• Data Parallelism and Model Parallelism: GPT-3 training was distributed across many GPUs. This doesn't change the total compute required, but it affects the time to train.
• Optimization Techniques: Advanced optimizers (like Adam) have their own computational cost. Our estimate doesn't explicitly account for the FLOPs involved in the optimizer itself, but these are generally a smaller fraction of the total.
• Activation Functions: The FLOPs for activation functions have been implicitly included in the FLOPs per token calculation.
• Hyperparameter Tuning: This calculation only estimates the FLOPs for the main training run. It doesn’t include the FLOPs spent on hyperparameter tuning, which can be significant.
• The '3 FLOPs/parameter/token' is a rough estimate. Different implementations and architectures will have different values. Research continues to refine these estimates.

Comparison to other estimates:

This estimate (around 157.5 EFLOPs) falls within the range of other publicly available estimates, which vary from around 3.14EFLOPs to over 300 EFLOPs. The variation is due to the different assumptions used in each calculation. The lower estimates often assume less efficient implementations or fewer training tokens.

In conclusion, training GPT-3 was a massively expensive undertaking in terms of computational resources. This estimation provides a reasonable order-of-magnitude understanding of the scale involved.