---
title: "A Parametric Linear Conic Projection for Structured Sparse Attention"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.04479v1"
permalink: "https://feed.astralor.com/items/itm_ab9cb5e0b5bfa5fc20f25641"
published: "2026-11-03T08:12:35.000Z"
score: 60
channel: "tech"
tags: ["推理效率","安全","Parametric Linear Conic","Projection","Structured Sparse Attention","Cone Alignment Index","CAI","Lorentz-cone"]
---

# A Parametric Linear Conic Projection for Structured Sparse Attention

## At a glance

In this paper, we introduce the Cone Alignment Index (CAI), a scale-invariant sparsity measure associated with a Lorentz-cone geometry. We provide a probabilistic analysis of the distribution of the CAI score, including…

## Key points

- In this paper, we introduce the Cone Alignment Index (CAI), a scale-invariant sparsity measure associated with a Lorentz-cone geometry.
- We provide a probabilistic analysis of the distribution of the CAI score, including a general theorem and explicit corollaries for Gaussian and uniform distributions.
- As a consequence, we show that, in the high-sparsity regime, the probability that the samples lie within the convex cone tends to one.

## Full text

In this paper, we introduce the Cone Alignment Index (CAI), a scale-invariant sparsity measure associated with a Lorentz-cone geometry. We provide a probabilistic analysis of the distribution of the CAI score, including a general theorem and explicit corollaries for Gaussian and uniform distributions. As a consequence, we show that, in the high-sparsity regime, the probability that the samples lie within the convex cone tends to one. Building upon this formulation, we derive two complementary projections: the \emph{Parametric Linear Conic Projection} (PLCP), an efficient closed-form approximation, and the \emph{Parametric Euclidean Conic Projection} (PECP), the exact Euclidean projection onto the cone boundary. Our analysis establishes several fundamental theoretical properties. We prove that PLCP and PECP are collinear, differ only by a positive radial scaling factor, and induce exactly the same sparsity threshold, thereby preserving an identical active support. Furthermore, we derive a support-identification theorem showing that, for any prescribed sparsity level $l<n$, the number of coefficients discarded at each iteration is theoretically controlled. Building on this theoretical foundation, we develop a bilevel PLCP framework for structured matrix sparsification. The proposed method naturally generates hardware-friendly structured sparsity patterns, including row-wise, column-wise, and diagonal masks, making it particularly well suited for accelerating Transformer attention mechanisms.

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