To estimate the total number of FLOPs (floating-point operations) required to train GPT-3 without searching online, we rely on known architectural details and standard computational models for transformer training. Here's the step-by-step reasoning:

Step 1: Key Parameters of GPT-3

• Number of parameters (P): GPT-3 has 175 billion parameters (175 × 10⁹).
• Training dataset size (D): The model was trained on approximately 300 billion tokens (300 × 10⁹ tokens). This is a standard figure associated with GPT-3.

Step 2: FLOPs per Token Calculation

Training a transformer model involves two main operations per token:

1. Forward pass: Computes the model's output.
2. Backward pass: Computes gradients for backpropagation.

For transformer architectures, the combined FLOPs for forward and backward passes per token is empirically estimated as 6 × P. This is derived from:

• Forward pass: Requires ~2 × P FLOPs per token (matrix multiplications dominate, with each parameter used in multiply-add operations).
• Backward pass: Typically requires ~2× the FLOPs of the forward pass due to gradient calculations (~4 × P FLOPs per token).
• Total per token: 2P (forward) + 4P (backward) = 6P FLOPs per token.

Step 3: Total FLOPs for the Entire Dataset

The total FLOPs scales linearly with the dataset size:

• Total FLOPs = FLOPs per token × Number of tokens.
• Substituting the values:
  Total FLOPs = (6 × P) × D = 6 × (175 × 10⁹) × (300 × 10⁹).

Step 4: Calculation

• Compute the product:
  6 × 175 × 300 × 10⁹ × 10⁹ = 6 × 52,500 × 10¹⁸.
• Simplify:
  6 × 52,500 = 315,000.
  Total FLOPs = 315,000 × 10¹⁸ = 3.15 × 10²³ FLOPs.

Step 5: Validation with Known Compute

• GPT-3 training reportedly used ~3,640 petaflop-days of compute.
• Convert petaflop-days to FLOPs:
  1 petaflop-day = 10¹⁵ FLOPs × 86,400 seconds/day = 8.64 × 10¹⁹ FLOPs.
  3,640 petaflop-days = 3,640 × 8.64 × 10¹⁹ ≈ 3.14 × 10²³ FLOPs.
• This closely matches our estimate of 3.15 × 10²³ FLOPs, confirming the calculation.

Step 6: Batch Size and Steps Consideration

• Batch size: GPT-3 used a batch size of 3.2 million tokens per step (80 batches × 4096 tokens/batch).
• Number of training steps:
  Steps = Total tokens / Batch size = 300 × 10⁹ / 3.2 × 10⁶ = 93,750 steps.
• FLOPs per step:
  Per step FLOPs = 6 × P × Batch size = 6 × 175 × 10⁹ × 3.2 × 10⁶ = 3.36 × 10¹⁸ FLOPs/step.
• Total FLOPs:
  93,750 steps × 3.36 × 10¹⁸ FLOPs/step ≈ 3.15 × 10²³ FLOPs.
  This consistency reinforces the estimate.

Step 7: Negligible Factors

• Parameter updates: Optimizer steps (e.g., Adam) add O(P) FLOPs per step. For 93,750 steps:
  Update FLOPs ≈ 93,750 × 175 × 10⁹ ≈ 1.64 × 10¹⁶ FLOPs (negligible vs. 3.15 × 10²³).
• Embedding/softmax layers: Included in the 6P per-token estimate.
• Attention mechanisms: Captured by the 6P heuristic (validated for transformers).

Final Estimate

The total FLOPs required to train GPT-3 is 3.15 × 10²³ FLOPs. This is derived from:

• Standard transformer FLOPs per token (6P).
• GPT-3 parameters (175B) and dataset size (300B tokens).
• Cross-validation with reported compute usage (3,640 petaflop-days).

Of course. Here is an estimate of the total number of FLOPs required to train GPT-3, based on my internal kn owledge and first principles, without searching online.

The Logic and Formula

To estimate the computational cost of training a large language model like GPT-3, we can use a well-establis hed formula. The total number of Floating Point Operations (FLOPs) is approximately:

Total FLOPs ≈ 6 × P × D

Let's break down what each part of this formula means:

• P: The number of parameters in the model. This is the total count of all the weights and biases that the model learns during training.
• D: The total number of tokens in the training dataset. This represents the volume of data the mo del processes.
• 6: This is a constant factor that provides a good approximation for transformer-based models. It com es from:
  • Forward Pass (1 × P × D): For each token processed, the number of operations is roughly proporti onal to the number of parameters. A common rule of thumb is 2 * P FLOPs per token for a forward pass (one multiplication and one addition for each parameter). So the total for one pass over the data is 2 * P * D.
  • Backward Pass (2 × Forward Pass): The backward pass (backpropagation), where the model calculate s gradients to update its parameters, is computationally more intensive. It's typically estimated to require about twice the operations of the forward pass. So, 2 * (2 * P * D) = 4 * P * D.
  • Total: Adding the forward and backward pass gives us 2PD + 4PD = 6PD.

Now, let's estimate the values for P and D for GPT-3.

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Step-by-Step Estimation

Step 1: Estimate the Number of Parameters (P)

My internal knowledge base indicates that the largest version of GPT-3, which is the one most people refer t o, has a specific number of parameters.

• P ≈ 175 billion parameters
• In scientific notation, this is 175 x 10⁹

Step 2: Estimate the Training Dataset Size (D)

GPT-3 was trained on a massive corpus of text data scraped from the internet (like the Common Crawl dataset) , books, and Wikipedia. The key is not the raw size of the dataset, but the number of tokens actually used f or training. My recollection is that the model was trained for a single epoch on a curated dataset.

• D ≈ 300 billion tokens
• In scientific notation, this is 300 x 10⁹

Step 3: Perform the Calculation

Now we can plug these estimated values into our formula:

Total FLOPs ≈ 6 × P × D

1. Substitute the values for P and D: Total FLOPs ≈ 6 × (175 × 10⁹) × (300 × 10⁹)

2. Multiply the constants first: 6 × 175 = 1050 1050 × 300 = 315,000

3. Multiply the powers of 10: 10⁹ × 10⁹ = 10¹⁸

4. Combine the results: Total FLOPs ≈ 315,000 × 10¹⁸

5. Express this in standard scientific notation: Total FLOPs ≈ 3.15 × 10⁵ × 10¹⁸ = 3.15 × 10²³

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Final Estimate and Conclusion

Based on my reasoning and the standard formula for calculating training costs, the estimated number of FLOPs required to train the 175B parameter GPT-3 model is approximately:

3.15 x 10²³ FLOPs

To put this astronomical number into perspective:

• A petaFLOP is 10¹⁵ FLOPs. Our estimate is 315,000,000 petaFLOPs.
• If you had a supercomputer that could perform one petaFLOP per second (10¹⁵ FLOPs/sec), it would take ** 3.15 x 10⁸ seconds** to complete the training.
• There are about 31.5 million seconds in a year, so this is equivalent to roughly 10 years of continu ous computation on that machine.

This calculation demonstrates why training foundational models like GPT-3 requires massive-scale data center s with thousands of GPUs running in parallel for months and is an undertaking that costs millions of dollars . The actual paper from OpenAI stated the training took approximately 3.6 x 10²³ FLOPs, so my estimate i s very close to the reported figure.

Here are 5 generated jokes:

1. Why don't scientists trust atoms? Because they make up everything!
2. I told my wife she was drawing her eyebrows too high. She looked surprised.
3. Why did the scarecrow win an award? Because he was outstanding in his field!
4. Why don't scientists trust atoms? Because they make up everything!
5. I used to play piano by ear, but now I use my hands.

How many are unique?

Jokes 1 and 4 are identical (both are the atom joke). The other jokes (2, 3, and 5) are distinct. Thus, there are 4 unique jokes in total.

Breakdown:

• Unique jokes: Jokes 1, 2, 3, and 5 (4 jokes).
• Duplicate: Joke 4 repeats Joke 1.

Answer: 4 unique jokes.

Here are 5 jokes:

1. Why did the scarecrow win an award? Because he was outstanding in his field.

2. I have a joke about construction... But I'm still working on it.

3. What do you call a fake noodle? An Impasta.

4. I told my wife she was drawing her eyebrows too high. She looked surprised.

5. Why don't scientists trust atoms? Because they make up everything.

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How many are unique?

Zero. The real joke is asking an AI for original content.