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.
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.
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.
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.
In other words: the final state given the two input sequences (where NT stands for "null token"):
<problem-prompt> [NT]
and
<problem-prompt> [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.