You're correct that it needs to run the full model to "verify" a token, but LLM inference benefits from batching - it's much faster to run twice in parallel than sequentially. So the draft model runs ~2-5 tokens ahead, and the full model then runs ~3-6 batches in parallel using those tokens, and can skip ahead by however many results match.

If you have some other source of parallel data (lots of users, many separate tasks) then speculative decoding might not provide any benefit.

> Naively, I would assume it must perform its normal auto regressive decoding to know what the “correct” token is in order to have something to compare the candidate token with.

Yes, but you can do it in parallel.

Suppose you predicted the tokens "D E F" in the sequence "A B C D E F". To "generate" the last token (F), it must know all preceding tokens (A B C D E). To "generate" the next-to-last token (E), it must know all preceding tokens (A B C D). And so on.

Assuming the prediction is correct, it can then run the "generation" for tokens D, E, and F at the same time. At the end, after all these tokens were "generated", it compares each token with the prediction; if the "generation" result was "D H F" it knows it has to discard the last two predicted tokens (and output "D H"), if the "generation" was "D E H" it knows it has to discard the last predicted token (and output "D E H"), etc.

And the most important part is that you can do it in parallel for each layer of the model. That is, you run "A B C D E F" through the first layer, then through the second layer, and so on; you only have to load the model weights from memory once for each layer. Instead of reading the full weights for all layers once for D, then once for E, then once for F, you only read them once for "D E F", and if the prediction was correct, you output three tokens by the (memory read) price of one (you still had to do the same amount of compute, but AFAIK LLMs tend to be more memory-bound than compute-bound).

The target model is the original LLM that is large and expensive. It can verify candidate tokens in a single forward pass. It means you give all the context + candidate tokens that passes in parallel in the backbone, then you pass the language head (a matmul transformation to produce the token distribution) on all the candidate tokens and you can keep or drop tokens based on how many "quality" you want.

> it must perform it's normal autoregressive decoding to know what is the correct token in order to have something to compare with

Correct except for the word "autoregressive". When you have to verify a sequence of tokens (which were autoregressively generated by the cheap model), you can do each token in parallel. This amortizes the cost of loading the weights from vram to the processors (the primary cost in LLM serving) across those tokens. Cost here is wall clock time, as well as power.

The autoregressive decoding that generates this batch of tokens is delegated to the cheaper model where the cost of loading the weights is lower and so not amortizing it is fine.

Verification means, how close is each token in this sequence to the one I would have output. You keep the longest prefix that is close enough for your liking.