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Parallel-elastic joints can improve the efficiency and strength of robots by assisting the actuators with additional torques. For these benefits to be realized, a spring needs to be carefully designed. However, designing robots is an…
Alignment is crucial for text-to-image (T2I) models to ensure that generated images faithfully capture user intent while maintaining safety and fairness. Direct Preference Optimization (DPO), prominent in large language models (LLMs), is…
Claims that humanoid robots achieve ``human-level'' actuation are common but rarely quantified. Peak torque or speed specifications tell us little about whether a joint can deliver the right combination of torque, power, and endurance at…
The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…
Generalization is important for peg-in-hole assembly, a fundamental industrial operation, to adapt to dynamic industrial scenarios and enhance manufacturing efficiency. While prior work has enhanced generalization ability for pose…
We use deep learning to model interactions across two or more sets of objects, such as user-movie ratings, protein-drug bindings, or ternary user-item-tag interactions. The canonical representation of such interactions is a matrix (or a…
Given a rational polytope $P \subset \mathbb R^d$, the numerical function counting lattice points in the integral dilations of $P$ is known to become a quasi-polynomial, called the Ehrhart quasi-polynomial $\mathrm{ehr}_P$ of $P$. In this…
In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approximant. The analytical continuation is then carried out through…
Existing methods for constructing splines and Bezier curves on a Lie group G involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local…
This paper explores innovations to parameter estimation in generalized linear and nonlinear models, which may be used in item response modeling to account for guessing/pretending or slipping/dissimulation and for the effect of covariates.…
Robots operating in complex and unknown environments frequently require geometric-semantic representations of the environment to safely perform their tasks. While inferring the environment, they must account for many possible scenarios when…
Given a demonstration, a robot should be able to generalize a skill to any object it encounters-but existing approaches to skill transfer often fail to adapt to objects with unfamiliar shapes. Motivated by examples of improved transfer from…
The Euler-Poincar\'e (EP) equations describe the geodesic motion on the diffeomorphism group. For template matching (template deformation), the Euler-Lagrangian equation, arising from minimizing an energy function, falls into the…
Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…
In this paper, we introduce and study the quadratic-phase Dunkl transform, a novel integral transform on the real line parameterized by five real numbers $(a, b, c, d, e)$ and a multiplicity parameter $\mu\geq -1/2$. We define the transform…
The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…
The numerical solution of high dimensional partial differential equations (PDEs) is severely constrained by the curse of dimensionality (CoD), rendering classical grid--based methods impractical beyond a few dimensions. In recent years,…
A d-dimensional rational polytope P is a polytope whose vertices are located at the nodes of d-dimensional Z-lattice. Consider a number of points inside the inflated polytope (with coefficient of inflation k, k=1,2, 3...). The Ehrhart…
Due to the lack of diversity of datasets, the generalization ability of the pose estimator is poor. To solve this problem, we propose a pose augmentation solution via DH forward kinematics model, which we call DH-AUG. We observe that the…
Structural identifiability concerns the question of which unknown parameters of a model can be recovered from (perfect) input-output data. If all of the parameters of a model can be recovered from data, the model is said to be identifiable.…