To estimate the total number of FLOPs required to train GPT-3 without searching online, we can make several assumptions and perform calculations based on the information available about GPT-3's architecture and training process. Here's a step-by-step explanation of the reasoning:
Step 1: Determine the number of parameters in GPT-3

GPT-3 is a massive language model with 175 billion parameters. Each parameter represents a trainable weight in the neural network, and updating these weights during training requires floating-point operations (FLOPs).

Step 2: Estimate the number of training iterations

The number of training iterations refers to how many times the entire training dataset is passed through the neural network during the training process. Although the exact number may vary, let's assume that GPT-3 was trained for 100 epochs.

Step 3: Calculate the FLOPs per iteration

During each training iteration, the neural network performs forward and backward passes. The forward pass involves computing the output of the network given the input, while the backward pass involves calculating the gradients of the loss function with respect to the network's weights.
For simplicity, we can assume that the forward and backward passes have roughly the same number of FLOPs. Therefore, the total FLOPs per iteration can be estimated by multiplying the number of parameters by 2 (forward and backward passes).

Total FLOPs per iteration = (Number of parameters) x 2

(175 billion parameters) x 2 = 350 billion FLOPs per iteration

Step 4: Calculate the total FLOPs for training

Multiplying the FLOPs per iteration by the number of training iterations gives us the total FLOPs required to train GPT-3.

Total FLOPs for training = (FLOPs per iteration) x (Number of iterations)

(350 billion FLOPs per iteration) x (100 iterations) = 35 trillion FLOPs for training

Therefore, based on these assumptions, we estimate that training GPT-3 without searching online would require approximately 35 trillion FLOPs.

Here’s a back‑of‑the‑envelope estimate using standard LM training-compute heuristics.

1. Assumptions

• Model size (N): GPT-3 has about 175 billion parameters (N ≈ 1.75 × 10^11).
• Training tokens (T): GPT-3 was trained on roughly 300 billion tokens (T ≈ 3.0 × 10^11).
• FLOPs per token per parameter: A common rule of thumb for transformer LM training is FLOPs ≈ 6 × N × T The factor ~6 comes from counting forward and backward passes for the parameter-heavy matmuls (roughly 2N for forward + 4N for backward). It ignores small terms from layernorms, softmax, embeddings, and optimizer updates (which we’ll account for with a small overhead factor later).

2. Core calculation

• 6 × N × T = 6 × (1.75 × 10^11) × (3.0 × 10^11)
• First multiply N × T: 1.75 × 3.0 = 5.25; powers: 10^11 × 10^11 = 10^22 So N × T = 5.25 × 10^22
• Now multiply by 6: 6 × 5.25 × 10^22 = 31.5 × 10^22 = 3.15 × 10^23 FLOPs

3. Overheads and uncertainty

• Non-matmul ops (attention softmax, masking, residuals, layernorms), embeddings, and optimizer update steps add some overhead. A 10–20% uplift is a reasonable allowance.
• Applying +10–20%: 3.15 × 10^23 × (1.1 to 1.2) ≈ (3.5 ± 0.3) × 10^23 FLOPs.

Answer

• Point estimate: ~3.15 × 10^23 FLOPs
• With a modest overhead allowance: roughly (3.3–3.8) × 10^23 FLOPs

This is a coarse estimate; the exact number depends on details like sequence length, activation checkpointing, implementation efficiency, and the precise token count.

Sally has 2 sisters.

1

Reason: If each of the 3 brothers has 2 sisters, there are exactly 2 girls in the family. One is Sally, so she has 1 sister.

9.11 is less than 9.9.

No. 9.11 is less than 9.9. Think of 9.9 as 9.90; comparing 9.11 to 9.90 shows 11 hundredths < 90 hundredths.

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