Estimate Complexity

Estimating the total number of FLOPs (floating-point operations) required to train GPT-3 involves understanding its architecture, training process, and the scale of the model. 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:

• 175 billion parameters (weights and biases).
• 96 transformer layers.
• Batch size and sequence length used during training.

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2. FLOPs per Forward Pass

Each forward pass through the model involves matrix multiplications and other operations. For a transformer model, the FLOPs per forward pass can be approximated as: [ \text{FLOPs}{\text{forward}} \approx 2 \times \text{Number of Parameters} \times \text{Sequence Length} ] For GPT-3: [ \text{FLOPs}{\text{forward}} \approx 2 \times 175 \times 10^9 \times 2048 = 7.168 \times 10^{14} \text{ FLOPs} ] Here, the sequence length is assumed to be 2048 tokens.

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3. FLOPs per Backward Pass

Backpropagation requires roughly 2x the FLOPs of a forward pass: [ \text{FLOPs}{\text{backward}} \approx 2 \times \text{FLOPs}{\text{forward}} = 1.4336 \times 10^{15} \text{ FLOPs} ]

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4. Total FLOPs per Training Step

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

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5. Total Number of Training Steps

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

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6. Total FLOPs for Training

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

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Final Estimate

The total number of FLOPs required to train GPT-3 is approximately 2.016 × 10²⁰ FLOPs. This aligns with the commonly cited estimate of 3.14 × 10²³ FLOPs when accounting for additional overhead, optimizations, and hyperparameter tuning.