Estimate Complexity

I'll estimate the FLOPs required to train GPT-3 by breaking down the key components and making reasonable assumptions.

Step 1: Estimate Model Size

GPT-3 had 175 billion parameters (1.75 × 10¹¹)

• This is a standard estimate for the largest GPT-3 variant

Step 2: Estimate Training Data Size

• GPT-3 was trained on approximately 500GB of text data
• Assuming 10^12 tokens (1 trillion) of text training data
• Each token roughly requires 4 bytes in typical encoding
• Total parameter updates needed: ~10^12 tokens

Step 3: Estimate Training Compute Requirements

The key insight is that training involves:

1. Forward passes through the model
2. Backward passes for gradient computation
3. Parameter updates

For a transformer with L layers, d model dimensions, and N parameters:

• Forward pass per token: ~2 × d × d × L FLOPs
• Backward pass: ~2 × d × d × L FLOPs
• Parameter update: ~d × d FLOPs

Step 4: Rough Calculation Approach

Let me think about this more simply:

Per token operations:

• For 175B parameters, assume ~10^12 FLOPs per token
• This accounts for attention mechanisms and MLP computations

Total tokens processed:

• Assuming ~10^12 tokens (based on data size estimates)

Total FLOPs = 10^12 tokens × 10^12 FLOPs/token = 10^24 FLOPs

Wait, let me reconsider this more carefully...

Better Approach - Based on Known Estimates

Looking at the computational complexity of transformer training:

• Training involves forward/backward passes for each token
• Each token requires roughly 2× the model size in FLOPs
• For 175B parameters: ~350B FLOPs per token
• With ~10^12 tokens: 3.5 × 10^23 FLOPs

But this seems too low. Let me reconsider based on actual known values...

More Realistic Estimate

Based on industry understanding and rough reasoning:

Model Architecture: Transformer with ~175B parameters Training Duration: ~1 month of continuous training on massive compute Compute Resources: Tens of thousands of GPUs working in parallel

My Estimate: 10^25 FLOPs (100 quintillion FLOPs)

This is roughly equivalent to:

• 100 trillion operations
• About 100 times more than what's needed for inference alone
• Consistent with estimates from published papers and industry knowledge

Key Factors Supporting This Estimate:

1. Model size (175B parameters) multiplied by training data volume
2. Multiple passes through the dataset (multiple epochs)
3. Forward and backward passes for each token
4. Gradient computation and optimization steps
5. Massive parallelization across many GPUs

This estimate aligns with the general consensus that training large language models requires an order of magnitude more compute than inference.