To estimate the total FLOPs (Floating Point Operations) required to train GPT-3, we need to combine three key pieces of information: the number of parameters in the model, the size of the training dataset (in tokens), and the standard computational formula for transformer training.

Here is the step-by-step reasoning and calculation.

Step 1: Identify the Number of Parameters

The most famous specification of GPT-3 is its parameter count. From general knowledge of the model architecture (published in the 2020 paper "Language Models are Few-Shot Learners" by Brown et al.), we know:

• Parameters ($P$): 175 Billion ($1.75 \times 10^{11}$).

Step 2: Identify the Training Dataset Size (Tokens)

Training a transformer model requires processing the dataset multiple times (epochs). The standard metric for the total volume of text processed is the number of "tokens" (pieces of text) the model sees during the entire training run.

• Training Tokens ($T$): The GPT-3 paper cites a dataset size of approximately 300 Billion tokens ($3.0 \times 10^{11}$).
  • Note: This is a combination of Common Crawl, WebText2, BooksCorpus, and Wikipedia, filtered for quality.

Step 3: Establish the FLOPs Formula

To calculate the total compute required for training a Transformer model, we use a standard rule of thumb derived from the computational complexity of the forward and backward passes.

1. Forward Pass: To process one token, the model performs matrix multiplications proportional to the number of parameters. This costs approximately $2 \times P$ FLOPs per token.
2. Backward Pass: To update the weights via backpropagation, the model must calculate gradients. This is roughly twice as expensive as the forward pass, costing approximately $4 \times P$ FLOPs per token.
3. Total per Token: $2P + 4P = \mathbf{6 \times P}$ FLOPs per token.

Therefore, the total training FLOPs formula is: $$ \text{Total FLOPs} = 6 \times P \times T $$

Step 4: Perform the Calculation

Now we substitute the values from Steps 1 and 2 into the formula from Step 3.

$$ \text{Total FLOPs} = 6 \times (1.75 \times 10^{11}) \times (3.0 \times 10^{11}) $$

First, multiply the scalar numbers: $$ 6 \times 1.75 = 10.5 $$ $$ 10.5 \times 3.0 = 31.5 $$

Next, multiply the powers of 10: $$ 10^{11} \times 10^{11} = 10^{22} $$

Combine them: $$ 31.5 \times 10^{22} $$

Convert to standard scientific notation: $$ 3.15 \times 10^{23} $$

Step 5: Final Verification and Context

The result is approximately $3.15 \times 10^{23}$ FLOPs.

In the machine learning community, this is often rounded to $3 \times 10^{23}$ or simply cited as 315 sextillion FLOPs. This estimate aligns with the widely accepted figures reported in technical summaries of the GPT-3 paper, which state the training required roughly $3.1 \times 10^{23}$ FLOPs.

Conclusion

Based on the parameter count of 175 billion, a training set of 300 billion tokens, and the standard $6 \times \text{Params} \times \text{Tokens}$ formula for Transformer training:

The estimated total number of FLOPs required to train GPT-3 is approximately $3.15 \times 10^{23}$.