THALis: A Topology-Preserving BCI for Dexterous Non-Invasive EEG-Driven Hand Control

Overview

Over 80 million people face loss of upper-limb function. However, modern non-invasive electroencephalogram (EEG) prosthetic hand interfaces are limited to cumbersome, binary movements due to severe signal noise– often 90% greater than invasive counterparts. Current deep convolutional methods still struggle in this noisy, data‑scarce environment, leaving a substantial gap in our current capabilities. To address this, I developed THALis, the first non-invasive system that proportionally decodes multi-finger motion from scalp EEG alone. My core innovation is transforming decoding into a reconstruction problem: THALis acts as a state-observer that replicates the brain’s underlying dynamics, bypassing noise as a structural bottleneck. The project’s theoretical foundation proceeds in two phases. First, I prove via center manifold theory and Takens embeddings that latent cortical mappings for finger control are reconstructable from EEG-scale observations while preserving homotopy type under noise. Second, I exploit this capability to design an echo-state reservoir with a bifurcating mechanism that produces attractors topologically conjugate to cortical limit cycles, certified via persistent homology. By engineering a phase-locked-loop decoding scheme, proportional finger position decodes linearly from the reservoir state, transforming a nonlinear problem into a tractable linear one. In industry-standard tests with consumer grade EEG, THALis tracks proportional finger kinematics at r=0.68– a 54.5% improvement over state-of-the-art CNNs while achieving 81.78% online four-primitive classification accuracy. Furthermore, THALis preserves distinct representations for each movement (Cohen’s d=1.19) alongside 10-minute calibration. By decoupling decoder integrity from signal quality, THALis opens a novel, non-surgical route to naturalistic prosthetic control. My approach extends naturally to motor disease monitoring and multi-modal neuroanalysis, warranting further investigation as a generalizable foundation for non-invasive BCI.

Competition history

• CSEF 2026 Computational Science (Senior Division) · Entry S-07-30

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