Estimate Complexity

Estimating the total number of FLOPs (floating point operations) required to train a model like GPT-3 involves considering several key factors: model architecture, number of parameters, amount of training data, and number of training iterations. Here's a step-by-step approach to derive an estimate:

1. Model Architecture Understanding:

   • GPT-3 is a transformer-based model. The transformer architecture primarily involves self-attention mechanisms and feed-forward neural networks.
   • Each transformer layer consists of multi-head self-attention and position-wise feed-forward networks.

2. Number of Parameters:

   • GPT-3 has 175 billion parameters.

3. Training Data:

   • The model was trained on roughly 300 billion tokens (words or subwords).

4. Number of Training Iterations:

   • To estimate the number of training iterations, we need to make some assumptions. Let's assume the model was trained for around 3 epochs over the entire dataset.

5. FLOPs per Token per Layer:

   • Calculating FLOPs for transformers is complex, but we can approximate.
   • For self-attention: The complexity is approximately ( O(n^2 \cdot d) ) per layer for sequence length ( n ) and model dimension ( d ).
   • For feed-forward layers: The complexity is approximately ( O(n \cdot d^2) ).

   Given that GPT-3 uses a context window (sequence length) of around 1024 (n = 1024) and a model dimension (d) of approximately 12,288 (derived from 175B parameters and architecture details), we can estimate the FLOPs.

   Let's simplify by combining these complexities. An estimate often used in literature is that each token processed through one transformer layer requires about ( 2 \cdot 10^4 ) FLOPs.

6. Total FLOPs Calculation:

   • Number of layers in GPT-3: Let's assume 96 layers (common for large transformers).
   • Number of tokens processed: ( 300 , \text{billion tokens} \times 3 , \text{epochs} = 900 , \text{billion tokens} ).

   So, approximately: [ \text{FLOPs per token per layer} = 2 \times 10^4 ]

   [ \text{FLOPs per token for the whole model} = 2 \times 10^4 \times 96 = 1.92 \times 10^6 , \text{FLOPs} ]

   [ \text{Total FLOPs} = 1.92 \times 10^6 , \text{FLOPs/token} \times 900 \times 10^9 , \text{tokens} = 1.728 \times 10^{18} , \text{FLOPs} ]

   Thus, the estimated total number of FLOPs required to train GPT-3 is on the order of ( 1.7 \times 10^{18} ) FLOPs, or 1.7 exaFLOPs.

This is a rough estimation and the actual number can vary based on implementation details and optimizations. However, it provides a reasonable approximation based on known architectural details and typical scaling laws for transformer models.