Extremely doubtful that it boils down to quadratic scaling of attention. That whole issue is a leftover from the days of small bert models with very few parameters.
The output distribution is deterministic, the output token is sampled from the output distribution, and is therefore not deterministic.
Temperature modulates the output distribution, but sitting it to 0 (i.e. argmax sampling) is not the norm.
This paper is doing exactly that though, handwaving with a couple of floats. The paper is just a collection of observations about what their implementation of shapley value analysis gives for a few variations of a prompt.
Cosine Similarity is very much about similarity, but it's quite fickle and indirect.
Given a function f(l, r) that measures, say, the logprobability of observing both l and r, and that the function takes the form f(l, r) = <L(l), R(r)>, i.e. the dot product between embeddings of l and r, then cosine similarity of x and y, i.e. normalized dot product of L(x) and L(y) is very closely related to the correlation of f(x, Z) and f(y, Z) when we let Z vary.
For large models, compute is very rarely dominated by attention. Take, for example, this FLOPs calculation from https://www.adamcasson.com/posts/transformer-flops
Compute per token = 2(P + L × W × D)
P: total parameters L: Number of Layers W: context size D: Embedding dimension
For Llama 8b, the window size starts dominating compute cost per token only at 61k tokens.