DeepSeek V3.2 Speciale
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:
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.
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} ]
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} ]
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} ]
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 ]
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} ]
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.
