Vector Symbolic Architecture (VSA) is emerging in machine learning due to its efficiency, but they are hindered by issues of hyperdimensionality and accuracy. As a promising mitigation, the Low-Dimensional Computing (LDC) method significantly reduces the vector dimension by ~100 times while maintaining accuracy, by employing a gradient-based optimization. Despite its potential, LDC optimization for VSA is still underexplored. Our investigation into vector updates underscores the importance of stable, adaptive dynamics in LDC training. We also reveal the overlooked yet critical roles of batch normalization (BN) and knowledge distillation (KD) in standard approaches. Besides the accuracy boost, BN does not add computational overhead during inference, and KD significantly enhances inference confidence. Through extensive experiments and ablation studies across multiple benchmarks, we provide a thorough evaluation of our approach and extend the interpretability of binary neural network optimization similar to LDC, previously unaddressed in BNN literature.

Many features have been proposed in on-line signature verification. Generally, these features rely on the position of the on-line signature samples and their dynamic properties, as recorded by a tablet. This paper proposes a novel feature space to describe efficiently on-line signatures. Since producing a signature requires a skeletal arm system and its associated muscles, the new feature space is based on characterizing the movement of the shoulder, the elbow and the wrist joints when signing. As this motion is not directly obtained from a digital tablet, the new features are calculated by means of a virtual skeletal arm (VSA) model, which simulates the architecture of a real arm and forearm. Specifically, the VSA motion is described by its 3D joint position and its joint angles. These anthropomorphic features are worked out from both pen position and orientation through the VSA forward and direct kinematic model. The anthropomorphic features' robustness is proved by achieving state-of-the-art performance with several verifiers and multiple benchmarks on third party signature databases, which were collected with different devices and in different languages and scripts.