Estimate Complexity

Estimating the total FLOPs for training GPT-3 without searching online requires making some educated assumptions and using scaling laws and general knowledge about large language models. Here's a step-by-step reasoning process:

1. Understanding the Core Components of FLOPs Calculation in Transformer Training:

• Model Size (Number of Parameters): The number of parameters in GPT-3 is the most crucial factor. We know it's approximately 175 billion parameters. This is a widely reported figure and a good starting point. Larger models inherently require more computations.
• Dataset Size (Number of Tokens): GPT-3 was trained on a massive dataset. While the exact size isn't publicly memorized to a precise number, it's known to be in the trillions of tokens. Let's assume a dataset size in the order of 300 billion to 1 trillion words initially for estimation, which translates to roughly 400 billion to 1.3 trillion tokens (assuming approximately 1.3 tokens per word on average in English text). We'll use a mid-range estimate for now.
• Number of Training Epochs/Passes: Large language models are typically not trained for a full epoch (one complete pass through the entire dataset). They are trained for a fraction of an epoch. Let's assume GPT-3 was trained for roughly 0.5 to 1 effective epochs or passes over the dataset. "Effective epoch" means the data is sampled in a way that is roughly equivalent to passing through the dataset a fraction of a time.
• FLOPs per Parameter per Token: For a Transformer model, a simplified approximation for the FLOPs per parameter per token in a single forward and backward pass is often considered to be around 6 FLOPs. This '6' is a rough estimate that accounts for matrix multiplications and other operations in the attention and feedforward layers during both forward and backward propagation. It's a simplification, but useful for estimation.

2. Calculating FLOPs per Token:

Using the approximation of 6 FLOPs per parameter per token and the model size:

• FLOPs per token per pass ≈ 6 * (Number of Parameters)
• FLOPs per token per pass ≈ 6 * (175 * 10⁹)
• FLOPs per token per pass ≈ 1050 * 10⁹
• FLOPs per token per pass ≈ 1.05 * 10¹² FLOPs per token per pass (approximately 1 TeraFLOP per token per pass).

3. Estimating Total Tokens Processed:

Let's take a mid-range estimate for the dataset size in tokens. If we assume around 500 billion words in the training dataset, and roughly 1.3 tokens per word, we get:

• Estimated tokens ≈ 500 * 10⁹ words * 1.3 tokens/word
• Estimated tokens ≈ 650 * 10⁹ tokens
• Estimated tokens ≈ 650 billion tokens

Let's also consider a slightly larger estimate as GPT-3's dataset was massive, perhaps closer to 1 trillion tokens as an upper bound for this estimation range.

4. Estimating Total Training FLOPs:

Now we can combine the FLOPs per token, estimated tokens, and the number of passes:

• Total FLOPs ≈ (FLOPs per token per pass) * (Total Tokens) * (Number of Passes)

Let's calculate a lower and upper bound estimate based on our assumptions:

• Lower Bound Estimate (using 650 billion tokens and 0.5 passes):

  • Total FLOPs ≈ (1.05 * 10¹² FLOPs/token) * (650 * 10⁹ tokens) * (0.5 passes)
  • Total FLOPs ≈ (1.05 * 650 * 0.5) * 10⁽¹²⁺⁹⁾
  • Total FLOPs ≈ 341.25 * 10²¹
  • Total FLOPs ≈ 3.4 * 10²³ FLOPs

• Upper Bound Estimate (using 1 trillion tokens and 1 pass):

  • Total FLOPs ≈ (1.05 * 10¹² FLOPs/token) * (1 * 10¹² tokens) * (1 pass)
  • Total FLOPs ≈ 1.05 * 10^(12+12)
  • Total FLOPs ≈ 1.05 * 10²⁴ FLOPs

5. Reasoning and Interpretation:

• Model Size Dominance: The 175 billion parameters are the primary driver of the high FLOPs count. Every token processed involves computations proportional to this massive parameter count.
• Dataset Size Influence: The trillions of tokens ensure the model sees a vast amount of data, but the number of passes is less than a full epoch for efficiency and generalization. A larger dataset naturally leads to more FLOPs.
• Simplified FLOPs per Token: The '6 FLOPs per parameter per token' is a significant simplification. The actual number can vary depending on the specific Transformer architecture, optimizations, and hardware. However, it provides a reasonable order-of-magnitude estimate.
• Epochs and Data Usage: Training for less than a full epoch is common in large models. This is a trade-off between compute cost and model performance. It's likely GPT-3 was trained with sophisticated data sampling and potentially multiple passes over parts of the dataset, but less than a full epoch in terms of unique data exposure.
• Order of Magnitude Estimate: These calculations are intended to provide an estimate of the order of magnitude. The actual FLOPs can vary based on implementation details, optimizations, and hardware used. However, the range of 3 * 10²³ to 1 * 10²⁴ FLOPs is a reasonable estimate based on general principles.

Conclusion:

Based on these estimations, the total number of FLOPs required to train GPT-3 is likely in the range of 3 * 10²³ to 1 * 10²⁴ FLOPs. A reasonable single point estimate within this range would be around ~3 * 10²³ FLOPs to ~1 * 10²⁴ FLOPs.

In summary, the estimated total FLOPs for training GPT-3 is in the order of hundreds of zettaFLOPs (10²¹ FLOPs) to a few exaFLOPs (10¹⁸ FLOPs) per second for a certain duration, ultimately resulting in a total computation in the range of 10²³ to 10²⁴ FLOPs. This is a massive amount of computation, highlighting the scale of resources needed to train state-of-the-art large language models.

Important Note: This is an estimation without searching online. Actual numbers might be slightly different, but the order of magnitude should be in the ballpark. Precise details would require access to internal training logs and architecture specifics which are not publicly available.