This paper proposes a novel geometric method for analytically determining the base inertial parameters of robotic systems. The rigid body dynamics is reformulated using projective geometric algebra, leading to a new identification model named ``tetrahedral-point (TP)" model. Based on the rigid body TP model, coefficients in the regresoor matrix of the identification model are derived in closed-form, exhibiting clear geometric interpretations. Building directly from the dynamic model, three foundational principles for base parameter analysis are proposed: the shared points principle, fixed points principle, and planar rotations principle. With these principles, algorithms are developed to automatically determine all the base parameters. The core algorithm, referred to as Dynamics Regressor Nullspace Generator (DRNG), achieves $O(1)$-complexity theoretically following an $O(N)$-complexity preprocessing stage, where $N$ is the number of rigid bodies. The proposed method and algorithms are validated across four robots: Puma560, Unitree Go2, a 2RRU-1RRS parallel kinematics mechanism (PKM), and a 2PRS-1PSR PKM. In all cases, the algorithms successfully identify the complete set of base parameters. Notably, the approach demonstrates high robustness and computational efficiency, particularly in the cases of PKMs. Through the comprehensive demonstrations, the method is shown to be general, robust, and efficient.

Large models support great zero-shot and few-shot capabilities. However, updating these models on new tasks can break performance on previous seen tasks and their zero/few-shot unseen tasks. Our work explores how to update zero/fewshot learners such that they can maintain performance on seen/unseen tasks of previous tasks as well as new tasks. By manipulating the parameter updates of a gradient-based meta learner as the projected task-specific subnetworks, we show improvements for large models to retain seen and zero/few shot task performance in online settings. The adaptation of deep neural networks have practical importance. It enables models to adapt to varying test-time distributions, attributed to shifts in time, person, environment, etc. The more difficult adaptation cases arise when there may be no clear task boundaries, when the task was not seen during training, and only few/zero samples are available to update a model. To tackle adaptation broadly, given a base learner optimizing its inner objective with respect to its assigned task, a meta learner computes the update to the base learner such that it optimizes its outer objective across a distribution of tasks (Hospedales et al., 2021).