GPT-4.5
Let's estimate the total number of floating-point operations (FLOPs) required to train GPT-3 step by step, using reasonable assumptions and approximations:
Step 1: Identify GPT-3 Parameters and Training Setup
- GPT-3 has approximately (175 ext{ billion}) parameters.
- Typically, GPT-3 is trained using transformer architecture, which primarily consists of attention layers and feed-forward layers.
- Let's assume GPT-3 is trained with a context length (sequence length) of approximately (2048) tokens per training example.
- Assume GPT-3 was trained for approximately (300 ext{ billion tokens}) (a common estimate).
Step 2: Estimate FLOPs per Token
The transformer architecture primarily consists of two main components per layer:
- Self-attention layers: complexity (O(n^2 cdot d))
- Feed-forward layers: complexity (O(n cdot d^2))
Where:
- (n) is the sequence length (context length)
- (d) is the hidden dimension size of the model
GPT-3 (175B) typically has:
- Hidden dimension (d approx 12288) (common for GPT-3)
- Number of layers (L approx 96) (common for GPT-3)
Let's verify quickly:
- Parameters in transformer ≈ (2 imes d^2 imes L) (approximation, ignoring embedding layers and biases)
- Check: (2 imes 12288^2 imes 96 approx 2 imes 1.51 imes 10^8 imes 96 approx 2.9 imes 10^{10}) parameters. This is about 29 billion parameters. GPT-3 has 175 billion parameters, meaning the actual GPT-3 has more complexity (due to embedding layers, attention heads, biases, and output layers). Indeed, GPT-3 has multiple attention heads and embedding layers, so let's trust the known parameter count (175B) and proceed with a simplified calculation.
Step 3: Simplified FLOPs per Token Estimation
A common simplified rule-of-thumb for transformer models is that training one token requires approximately (6 imes) the number of parameters in FLOPs (forward + backward pass combined). This heuristic is widely used in practice.
Thus, for GPT-3 (175B parameters):
- FLOPs per token ≈ (6 imes 175 imes 10^9 = 1.05 imes 10^{12}) FLOPs per token.
Step 4: Total FLOPs for Training
Given GPT-3 was trained on approximately (300 ext{ billion tokens}):
[ ext{Total FLOPs} = ( ext{FLOPs per token}) imes ( ext{number of tokens}) ]
[ = (1.05 imes 10^{12}) imes (3.0 imes 10^{11}) ]
[ = 3.15 imes 10^{23} ext{ FLOPs} ]
Step 5: Final Approximation
Thus, the total number of FLOPs required to train GPT-3 is approximately:
[ oxed{3.15 imes 10^{23} ext{ FLOPs}} ]
Summary of Reasoning:
- GPT-3 parameters: (175 ext{ billion})
- FLOPs per token (heuristic): (6 imes ext{parameters})
- Total tokens trained: (300 ext{ billion})
- Total FLOPs ≈ (3.15 imes 10^{23})
This is a rough but reasonable estimate based on common heuristics and known GPT-3 parameters.