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@hdevalence.bsky.social

blog post speculating about reading the tea leaves behind google's pricing

some thoughts:

  1. the comment about "OpenAI can afford to take negative margins while playing catch up, whereas Google is a public company that cannot (and does not) play the same compute subsidization games" seems totally wrong, if anything it would be the opposite since Google has huge resources
  2. doesn't mention that Google models have much longer context than others (have heard that this is because they are better algorithmically rather than having more hw or custom hw but no way to know), which seems relevant
  3. point about pricing not matching actual resource costs (linear vs quadratic inputs) makes sense and is something i've wondered about while looking at model pricing
  4. the comments in the throughput analysis all make sense except that i'm surprised by: "when you send a prompt, the model can process all input tokens in parallel". i'm not sure how that can be true and also that it can be the case that prefilling has quadratic costs - i thought the quadratic cost came from token<>token interactions, and that parallelizability came from tokens not interacting with each other. probably would make more sense after implementing a transformer.
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Thinking Summary

The user is asking about point 4 in the original post, which expresses confusion about the statement from the blog post that "when you send a prompt, the model can process all input tokens in parallel" while also having quadratic costs. The user is confused because they thought quadratic costs came from token-to-token interactions, and parallelizability came from tokens not interacting with each other. This is a good question about transformer architecture. The confusion stems from mixing up different aspects: 1. The quadratic cost comes from the attention mechanism where each token attends to all other tokens 2. The parallelizability during prefill comes from the fact that all these attention computations can be done at once (in parallel) when you know all the input tokens 3. During generation/decode, you can't parallelize because you're generating one token at a time Let me explain this clearly.

I can help clarify the confusion about parallelization and quadratic costs in transformers!

The key insight is that parallelizability and quadratic computational cost are actually orthogonal concepts - they're not contradictory. Here's why:

During Prefill (Processing Input)

When processing the input prompt, the model computes attention scores between every token and every other token. For nn input tokens, this requires O(n2)O(n^2) computations.

However, crucially: all these computations are independent of each other. The attention score between tokens 5 and 7 doesn't depend on the score between tokens 2 and 9. Since we know all input tokens upfront, we can compute all n2n^2 attention scores simultaneously in parallel.

Think of it like filling out a multiplication table - you need to compute n×nn \times n values, but you can calculate all cells at the same time if you have enough compute units.

During Generation (Decoding)

This is where things change. When generating output tokens:

  • You generate one token at a time
  • Each new token needs to attend to all previous tokens (both input and previously generated output)
  • You can't parallelize across future tokens because they don't exist yet

The Quadratic Cost

The quadratic cost comes from the attention mechanism itself:

For each token position i:
    For each other token position j:
        Compute attention(i, j)

This is inherently O(n2)O(n^2) regardless of whether you do it in parallel or sequentially. Parallelization changes the wall-clock time but not the total computational work.

So your intuition was partially correct - tokens do interact with each other (through attention), but during prefill, these interactions can all be computed simultaneously because we're not waiting for any sequential dependencies.

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