Matrix Zonotopic Attention: A Context-Adaptive Value Projection for Set Transformers

• URL: http://arxiv.org/abs/2608.05472v1
• Date: Wed, 05 Aug 2026 23:43:45 GMT
• Title: Matrix Zonotopic Attention: A Context-Adaptive Value Projection for Set Transformers
• Abstract summary: Multi-head attention combines an input-dependent softmax routing with an input-independent linear value projection.<n>We study the consequences of this asymmetry for permutation-in set targets.<n>We propose Matrix Zonotopic Attention (MZAttn), which replaces the fixed value projection with a context-adaptive matrix-zonotope family.
• Score: 3.6503889532208045
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multi-head attention combines an input-dependent softmax routing with an input-independent linear value projection, so the per-sample operator mapping aggregated values to outputs is the same for every input set. We study the consequences of this asymmetry for permutation-invariant set targets. We introduce the Transformation Degrees of Freedom (TDOF) of a target operator, a complexity measure counting the input-dependent directions an exact representation requires, and present a depth-separation analysis showing that context-rigid attention needs depth proportional to the target's TDOF, whereas a single layer with a context-adaptive value family can represent the same target. Building on this analysis, we propose Matrix Zonotopic Attention (MZAttn), which replaces the fixed value projection with a context-adaptive matrix-zonotope family: a centre matrix plus a sum of generator matrices weighted by input-dependent gates. The construction reduces to standard multi-head attention at initialisation, preserves permutation equivariance, and admits a data-driven reachability interpretation. Experiments on a range of set-prediction tasks are consistent with the TDOF prediction that the architectural advantage is selective: it appears on targets that depend on the input set in a high-rank, sparsely combinatorial way, and is small on aggregate-statistic targets where parameter-matched standard attention is already competitive.

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