Abstract:Large language models (LLMs) exhibit two striking and ostensibly unrelated behaviours: in-context learning (ICL) and repetitive generation. In both, the model behaves as though it had summarised the context into a population-level statistic and discarded token-level detail. We ask whether this ``summarisation and forgetting'' can be derived from the attention mechanism itself, and answer in the affirmative. Under stationary, ergodic and elliptical inputs, the softmax attention output converges almost surely to $\Theta_V\Sigma\Theta_K^{\top}\Theta_Q x_t$, where $\Sigma$ is the input covariance; the long-context limit is therefore a linear readout of the input's second-order statistics. Two consequences follow. (i) For in-context linear regression, a single softmax head can implement one step of population gradient descent. Stacking such heads with residual connections iterates this update and implements multiple gradient descent steps. (ii) Propagated across an $L$-layer transformer, this readout drives the terminal hidden state at the parametric $1/t$ rate to a deterministic function of the current token alone, so that autoregressive generation collapses asymptotically to a first-order Markov chain whose attracting orbits furnish a structural account of repetition and mode collapse. The two phenomena thus emerge as facets of a single covariance-readout principle.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.10466 [cs.LG] |
| (or arXiv:2605.10466v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.10466 arXiv-issued DOI via DataCite (pending registration) |
From: Haoren Xu [view email]
[v1]
Mon, 11 May 2026 12:33:15 UTC (369 KB)
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