| name | variational-phasor-circuits-bci |
| description | Variational Phasor Circuits (VPC) for phase-native Brain-Computer Interface classification using continuous S1 unit circle manifold with trainable phase shifts and unitary mixing |
| authors | ["Dibakar Sigdel"] |
| arxiv_id | 2603.18078 |
| published | 2026-06-15T00:00:00.000Z |
| categories | ["cs.LG","q-bio.NC"] |
| tags | ["bci","phase-native","variational-circuits","unitary-mixing","complex-space"] |
| score | 8 |
| status | novel |
Variational Phasor Circuits for Phase-Native BCI Classification
Paper: Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification
arXiv: 2603.18078
Authors: Dibakar Sigdel
Published: 2026-06-15
Summary
Variational Phasor Circuit (VPC) is a deterministic classical learning architecture operating on the continuous S1 unit circle manifold. Inspired by variational quantum circuits, VPC replaces dense real-valued weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space.
Core Methodology
Phase-Native Architecture
-
S1 Unit Circle Manifold
- Continuous circular topology for phase-based representations
- Avoids Euclidean weight matrices
- Compact parameter space
-
Trainable Phase Shifts
- Replace dense weight matrices with phase rotations
- Local unitary mixing operations
- Structured interference in complex space
-
VPC Block Design
- Single blocks: compact phase-based decision boundaries
- Stacked compositions: deeper circuits via pull-back normalization
- Inter-block normalization for stability
Key Features
- Parameter Efficiency: Substantially fewer trainable parameters than Euclidean baselines
- Competitive Accuracy: Matches standard approaches on BCI tasks
- Phase-Native: Natural encoding of oscillatory neural signals
Applications
Brain-Computer Interface
- Mental-state classification tasks
- EEG signal decoding
- Phase-based neural signal processing
Advantages vs Euclidean Methods
| Metric | VPC | Standard Euclidean |
|---|
| Parameters | Compact | Dense matrices |
| Accuracy | Competitive | Baseline |
| Phase encoding | Native | Requires transformation |
Implementation Insights
Phase Shift Operations
