Estimate Complexity

Step 1: Recalling GPT-3's Key Parameters

GPT-3 is a large language model with 175 billion parameters (weights). This is the standard figure I recall from its architecture as a transformer-based model. The number of parameters directly influences the computational cost of training, as most operations (e.g., matrix multiplications) scale with this size.

Step 2: Understanding FLOPs in Transformer Training

In transformer models like GPT-3, training primarily involves forward and backward passes during backpropagation. For large models, the dominant compute is in the matrix multiplications for attention and feed-forward layers.

A widely used approximation for the total FLOPs to train a transformer model is: [ \text{Total FLOPs} \approx 6 \times N \times D ]

• (N) is the number of parameters (175 billion for GPT-3).
• (D) is the number of tokens processed during training (i.e., the total dataset size in tokens).
• The factor of 6 accounts for roughly 2 FLOPs per parameter per token in the forward pass, doubled for the backward pass (gradient computation), and an additional factor of ~1.5-2 for overhead like activations and optimizer steps—but 6 is a standard empirical estimate that captures the full training cost.

This approximation is derived from analyses of transformer compute (e.g., from papers like those on scaling laws), where each token requires processing through the entire model, and backprop adds comparable compute to the forward pass.

Step 3: Estimating the Number of Tokens (D)

GPT-3 was trained on a massive corpus, including sources like Common Crawl, books, and Wikipedia. I estimate the total training dataset size as approximately 300 billion tokens. This is based on:

• Common Crawl subsets typically yielding hundreds of billions of tokens after filtering.
• Reports of GPT-3 using a diverse web-scale dataset, with token counts in the 10^{11} to 10^{12} range.
• For context, smaller models like GPT-2 used ~40 billion tokens, and GPT-3 scaled up by orders of magnitude, so 300 billion feels like a reasonable midpoint estimate without exact recall.

This is an estimate; actual figures might vary slightly, but it aligns with the model's scale.

Step 4: Computing the Total FLOPs

Plugging in the values: [ \text{Total FLOPs} \approx 6 \times 175 \times 10^9 \times 300 \times 10^9 = 6 \times 175 \times 300 \times 10^{18} ] First, (175 \times 300 = 52,500).

Then, (6 \times 52,500 = 315,000).

So, (315,000 \times 10^{18} = 3.15 \times 10^5 \times 10^{18} = 3.15 \times 10^{23}).

Final Estimate

Based on this reasoning, the total number of FLOPs required to train GPT-3 is approximately (3 \times 10^{23}). This is a rough order-of-magnitude estimate, as exact dataset sizes and training details (e.g., batch size, epochs, or hardware efficiencies) can adjust it by 10-20%, but it captures the core scaling.