用相位干扰实现高效脑机接口分类,参数少且跨被试稳定性高。
Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification
- 基于单位圆相位扰动与酉混合,替代传统全连接层
- 在10名被试上达60%平均解码准确率,优于所有基准模型
- 适合低资源脑电信号分类,可作为量子混合系统前端
我们提出变分相量电路(VPC),一种定义在连续S¹单位圆流形上的确定性经典学习架构。受变分量子电路启发,VPC以可训练的相位偏移、局部酉混合和环境复空间中的结构化干涉取代密集权重矩阵,统一处理空间分布信号的二分类与多分类任务。我们在PhysioNet运动想象数据库(10名被试,共空间模式特征,被试间交叉验证)上评估VPC,其平均解码准确率达0.60,为标准脑机接口基线(线性判别分析、逻辑回归、RBF-SVM及多层感知机)中最高,且参数量少一个数量级,跨被试方差最低。我们还如实刻画了其容量:仅使用相位偏移与酉混合时,VPC在固定余弦/正弦特征提升下实现线性决策函数,契合脑电信号频带功率结构的强可分性,但无法表示奇偶性等复杂函数,深度也无法突破此上限。这些结果表明,单位圆相位干涉是信号分类中参数高效的密集神经计算替代方案,并推动VPC作为独立分类器或混合相量-量子系统的前段应用。
原文摘要 · Abstract (English)
We present the Variational Phasor Circuit (VPC), a deterministic classical learning architecture on the continuous $S^1$ unit-circle manifold. Inspired by variational quantum circuits, VPC replaces dense weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space, giving a unified method for binary and multi-class classification of spatially distributed signals. We evaluate VPC on real motor-imagery electroencephalography (EEG) from the PhysioNet Motor Movement/Imagery database (10 subjects, Common Spatial Pattern features, subject-wise cross-validation), where it attains a mean decoding accuracy of $0.60$ -- the highest among standard brain--computer-interface baselines (linear discriminant analysis, logistic regression, RBF-SVM, and a multilayer perceptron) -- using an order of magnitude fewer parameters and the lowest cross-subject variance. We also characterize capacity honestly: with phase-only shifts and unitary mixing, VPC realizes a linear decision function in a fixed cosine/sine feature lifting, well matched to the largely separable band-power structure of EEG but unable to represent parity-type functions, a ceiling that depth does not raise. These results position unit-circle phase interference as a parameter-efficient alternative to dense neural computation for signal classification, and motivate VPC both as a standalone classifier and a front-end for hybrid phasor-quantum systems.
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