Estimate Complexity

Estimating the total number of Floating Point Operations (FLOPs) required to train GPT-3 involves understanding the model's architecture, training process, and computational requirements. Here's a step-by-step breakdown of the reasoning:

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1. Understand GPT-3's Architecture

GPT-3 is a transformer-based language model with the following key parameters:

• Number of parameters: 175 billion (175 × 10⁹).
• Number of layers: 96.
• Hidden size: 12,288.
• Attention heads: 96.

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2. Compute FLOPs per Forward Pass

In a transformer model, the FLOPs per forward pass can be approximated using the formula: [ \text{FLOPs} \approx 2 \times \text{Parameters} \times \text{Sequence Length} ]

• Sequence length: GPT-3 uses a sequence length of 2048 tokens.
• Parameters: 175 × 10⁹.

So, the FLOPs per forward pass are: [ \text{FLOPs}_{\text{forward}} \approx 2 \times 175 \times 10^9 \times 2048 = 7.168 \times 10^{14} ]

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3. Compute FLOPs per Backward Pass

Backpropagation typically requires about twice the FLOPs of a forward pass. Therefore: [ \text{FLOPs}{\text{backward}} \approx 2 \times \text{FLOPs}{\text{forward}} = 2 \times 7.168 \times 10^{14} = 1.4336 \times 10^{15} ]

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4. Total FLOPs per Training Step

Each training step consists of one forward pass and one backward pass. Thus: [ \text{FLOPs}{\text{step}} = \text{FLOPs}{\text{forward}} + \text{FLOPs}_{\text{backward}} = 7.168 \times 10^{14} + 1.4336 \times 10^{15} = 2.1504 \times 10^{15} ]

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5. Total Training Steps

GPT-3 was trained on 300 billion tokens. With a batch size of 3.2 million tokens per step, the total number of training steps is: [ \text{Steps} = \frac{\text{Total Tokens}}{\text{Batch Size}} = \frac{300 \times 10^9}{3.2 \times 10^6} = 93,750 ]

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6. Total FLOPs for Training

Multiply the FLOPs per step by the total number of steps: [ \text{Total FLOPs} = \text{FLOPs}_{\text{step}} \times \text{Steps} = 2.1504 \times 10^{15} \times 93,750 \approx 2.016 \times 10^{20} ]

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Final Estimate

The total number of FLOPs required to train GPT-3 is approximately: [ \boxed{2 \times 10^{20} \text{ FLOPs}} ]

This estimate aligns with publicly reported figures and provides a reasonable approximation based on the model's architecture and training process.