> but the insight is probably stated immediately after it.

If the intermediate tokens represent reasoning or thought, you would expect "aha" to occur after the thoughts that led to the realisation, including the thoughts encoding the explanation: they don't have any other state. There is no reason to draw the conclusion you've drawn. Furthermore, what LLMs are doing isn't thought.

> If the intermediate tokens represent reasoning or thought, you would expect "aha" to occur after the thoughts that led to the realisation, including the thoughts encoding the explanation: they don't have any other state.

Yes they do, they have their KV caches-- it's a pure function of the input tokens, sure but that doesn't prevent it from containing latent 'insight'. LLMs can and do pre-form the tokens they're expecting to output multiple steps in the future.

I wouldn't argue that the 'aha' means anything, but the structural argument that it can't that I think you're making isn't sound.

Consider this: while the inner state of an LLM (all its activations, residuals stream that is cached in the KV cache) is fully deterministic given its input sequence, the information contained in it IS NOT identical to the information in the input sequence. The reason is obvious: the LLM itself contains an enormous amount of information in its parameters and it transfers it to its residuals stream at each forward pass.

In other words: the final state given the two input sequences (where NT stands for "null token"):

[NT]

and

[NT] [NT] [NT] [NT] [NT] [NT] [NT] [NT]

is not the same, and at each forward pass the LLM keeps working on the solution even if the input tokens provide absolutely no further information.

If this is correct, then there is no need for the model to have already verbalized the key elements that drive the "aha" moment, so no need for the "aha" to appear after a full explanation.

I don't get your argument.

Let's say that the forward pass that selected "Aha" produces activations that indicate a wrong assumption, and a plausible explanation.

It puts learned projections of the activation into the KV Cache and outputs Aha.

Both the cached projections and the current Aha token can now influence further activations in an additional Forward pass that the Aha bought the model.

At least that's how I thought it works.

A cache is just a cache. I'm not sure what significance you're ascribing to it.

What is put in the cache?

Things that the software running the model would otherwise recompute, if not for the cache. What special meaning are you assigning to it?

Beats me how it works, honestly can't wrap my head around it.

From what I understand, at position Aha in each layer it's constructing a query based on the current activation and looking at the key of each other token position for that layer, in order to decide how much attention to pay to the value.

In this way it attends to the previous values, such as perhaps the incorrect assumption and plausible explanation.

Ooh so lets just change the initial prompt to

    [old prompt asking for some complicated solution requiring insight]
    
    Aha!

and since Aha! is near the good stuff in the network it will just work =P

It really isn't useful though, unless it is a summary. At best it is a semantic trick to tell the next iteration to come up with something smart.

“Aha” as a single token records the LLM discovered it made a mistake and needs to pivot.

On the next forward pass: it rediscovers the mistake, its “aha” noting that, and then provides the first token of the new idea.

That “aha” contains information: the previous conclusion was somehow insufficient.

it's a rhetorical heuristic that a writer should know to use when directing a reader to a declarative that they want them to pay attention to, usually because it's a non-obvious or roundabout insight

when utilized by AI, it's a probabilistic output and it's variable whether or not that rhetorical trick is useful. it also pushes a non-skeptical reader to focus too much on the following text or even to believe that they, themselves, derived some insight. this is effectively a kind of persuasive sophistry which is not helpful - adding rules around it prevents people from deluding themselves with AI

Did not read the paper so apologies if this is covered but isn't it possible that there is some recognizable semantic pattern in the training data where an "aha" is often followed by a subtle semantic shift that proves closer to the original premise in some critical way, and by emitting the "aha" token the model causes itself to produce such a subtle semantic shift that pushes the subsequent reasoning closer to the desired response?

It amounts to noise overall, but it has further unwanted and potentially misleading 'properties'. I think it's rather sobering to see how much bandwidth is still being wasted.