Estimate Complexity

Below is a back-of-the-envelope estimate of the total FLOPs needed to train GPT-3 “175 B” (the largest 96-layer, 12288-d model with 175 billion parameters) from scratch on the full 300 B-token corpus, assuming the standard transformer training setup used by OpenAI.

Step 1 – FLOPs per forward+backward pass
A single transformer block has

• 2 matrix-multiply operations per attention layer (QKᵀ and OV)
• 2 matrix-multiply operations per MLP (Wi and Wo)
• 1 extra attention output projection (optional, but small)
• 1 residual add per block

For 96 layers and 12288 hidden units, each matrix multiply is roughly
(12288²) ≈ 1.5 × 10⁸ FLOPs.
So per block: 2 attention + 2 MLP ≈ 8 × 1.5 × 10⁸ ≈ 1.2 × 10⁹ FLOPs.
Add residual adds and layer norms (~10 % overhead) ⇒ ≈ 1.3 × 10⁹ FLOPs per block.

With 96 blocks, forward+backward per token ≈ 1.25 × 10¹¹ FLOPs ≈ 125 GFLOPs.

Step 2 – Tokens processed per forward+backward step
The batch size is 3,200 sequences × 2,048 tokens = 6.55 million tokens.
Thus each SGD step consumes ≈ 6.6 × 10⁶ tokens.

Step 3 – Total SGD steps
300 billion tokens / 6.6 million tokens per step ≈ 45,500 steps.

Step 4 – Total FLOPs
45,500 steps × 125 GFLOPs/step ≈ 5.7 × 10¹² FLOPs ≈ 5.7 petaflop-days.

Step 5 – Overhead for data loading, optimizer states, and communication

• Adam: 8 extra copies of the parameter matrix (2 × 4 bytes per float32) → +50 %
• Gradient communication and padding → +20 %
• Data loading and tokenization → +10 %

Overall multiply by 1.8 ⇒ ≈ 1.0 × 10¹³ FLOPs ≈ 10 petaflop-days.

Step 6 – Round to one significant figure
≈ 10¹³ FLOPs, i.e. ten petaflop-days.

So a rough estimate is on the order of 10¹³ total floating-point operations to train GPT-3 175 B from scratch on 300 B tokens with the standard transformer architecture and training setup.