Model Releases
Attention Manifolds: Steering or Blocking Language Models by Editing Learned B-Spline Surfaces
arXiv:2610.00257v1 Announce Type: new Abstract: In standard transformer attention, a source token sends the same value vector to every receiver. The query determines how much to attend but not what to
arXiv:2610.00257v1 Announce Type: new Abstract: In standard transformer attention, a source token sends the same value vector to every receiver. The query determines how much to attend but not what to extract. This work introduces extbf{attention manifolds}: learned 2D B-spline surfaces S_d(q_d, k_d) that modulate each value dimension based on the query-key interaction. Each surface is a tensor-product cubic B-spline initialized to zero, preserving pretrained behavior. Applied to LLaMA 3.2-1B-Instruct and 3B-Instruct, attention manifolds reduce WikiText-2 validation perplexity by 2--2.5 points with 0.3% parameter overhead. Across 112 diverse prompts, surfaces change greedy-decoded output for 69% (1B) to 83% (3B) of cases, with the strongest effects on ambiguous and polysemous inputs (94--100% change rate). The surfaces improve output quality: correcting factual errors (the CAP theorem has three main components'' o it is impossible to guarantee all three''), increasing precision (impossible to know certain properties'' o impossible to know both position and momentum''), and adding specificity (a generic quote o an attributed Saint Augustine citation, consistently at both scales). The learned surfaces are also mechanically editable: inverting a layer's coefficients changes greedy output for 9/10 prompts (KL~0.010), providing a geometric mechanism for model steering. Setting surface coefficients to -1 creates ``attention walls'' that block value flow through specific dimensions. In a preliminary experiment, a layer-wide wall redirects an explosive-device prompt from specific instructions to general educational content, suggesting a path toward safety-oriented manifold shaping.
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Source: arXiv cs.LG | 2026-10-02