Emergent Structure in the Marginal Attention Space of Language Models

arXiv:2610.03109v1 Announce Type: new Abstract: While representation similarity across independently trained language models is well-documented, how internal mechanics such as attention behave across models remains far less characterized. Inspired by this gap, we examine the structure of post-softmax attention weights by marginalizing over query positions, mapping them into a joint token-head "marginal attention space". Evaluating across 60+ diverse LLMs, we find that different properties emerge when reducing this space along its token and head axes. When reduced token-wise, marginal attention yields a text-intrinsic signal robustly conserved across models. To explain this property, we empirically connect marginal attention to the input-output Jacobian of the network, and prove theoretically that under a smoothness assumption, models with similar next-token distributions are guaranteed to have similar input-output Jacobian statistics. When reduced head-wise, it forms a model-private signature conserved across documents. Practically, this provides a natural way to estimate a per-head budget for key-value (KV) cache eviction, effectively decoupling model-specific budget allocation from text-intrinsic token scoring. On standard eviction benchmarks, a per-head budget precomputed offline on pretraining text, combined with a training-free token score, shows competitive performance with methods that recompute the budget on every document or train it per target. Code available at https://github.com/Flegyas/marginal-attention

Abstract:While representation similarity across independently trained language models is well-documented, how internal mechanics such as attention behave across models remains far less characterized. Inspired by this gap, we examine the structure of post-softmax attention weights by marginalizing over query positions, mapping them into a joint token-head "marginal attention space". Evaluating across 60+ diverse LLMs, we find that different properties emerge when reducing this space along its token and head axes. When reduced token-wise, marginal attention yields a text-intrinsic signal robustly conserved across models. To explain this property, we empirically connect marginal attention to the input-output Jacobian of the network, and prove theoretically that under a smoothness assumption, models with similar next-token distributions are guaranteed to have similar input-output Jacobian statistics. When reduced head-wise, it forms a model-private signature conserved across documents. Practically, this provides a natural way to estimate a per-head budget for key-value (KV) cache eviction, effectively decoupling model-specific budget allocation from text-intrinsic token scoring. On standard eviction benchmarks, a per-head budget precomputed offline on pretraining text, combined with a training-free token score, shows competitive performance with methods that recompute the budget on every document or train it per target. Code available at this https URL

Computation and Language (cs.CL)

arXiv:2610.03109 [cs.CL]

(or arXiv:2610.03109v1 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2610.03109 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Emergent Structure in the Marginal Attention Space of Language Models

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