Efficient Multi-Modal Fusion via Preconditioned and Asynchronously Parallel ADMM for On-Device Personalization and Security

The convergence of multi-modal sensing and constrained computing on personal devices demands efficient algorithmic frameworks for fusing heterogeneous data streams—visual, depth, inertial, and biometric—under stringent latency, memory, and power constraints. This paper presents a unified mathematical framework for on-device multi-modal fusion, grounded in constrained convex optimization and operator splitting theory. We formulate the fusion problem as minimization of a composite objective function, coupling modality-specific loss terms through linear consensus constraints, regularized by structured sparsity and low-rank priors. The central contribution is a Preconditioned Asynchronously Parallel Alternating Direction Method of Multipliers (PAP-ADMM), tailored for architectures with heterogeneous computational loads across modalities. We derive closed-form solutions for proximal operators associated with logistic regression, group lasso, and nuclear norm regularization, which are ubiquitous in personalization and security tasks. Convergence analysis establishes a non-asymptotic rate of O(1/k) under bounded delay conditions. Extensive experiments on synthetic benchmarks and a concrete application—fusing RGB and depth features for contactless palm-print authentication—validate the framework's efficacy. The proposed solver achieves up to 3.5x speedup over synchronous ADMM and reduces memory footprint by 45% on embedded hardware, while maintaining or improving accuracy. This work provides both theoretical foundations and practical tools for developing efficient, private, and robust on-device intelligent systems.