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Fundamental Novel Consistency Theory: $H$-Consistency Bounds

Zhong, Yutao

arXiv.org Machine Learning

In machine learning, the loss functions optimized during training often differ from the target loss that defines task performance due to computational intractability or lack of differentiability. We present an in-depth study of the target loss estimation error relative to the surrogate loss estimation error. Our analysis leads to $H$-consistency bounds, which are guarantees accounting for the hypothesis set $H$. These bounds offer stronger guarantees than Bayes-consistency or $H$-calibration and are more informative than excess error bounds. We begin with binary classification, establishing tight distribution-dependent and -independent bounds. We provide explicit bounds for convex surrogates (including linear models and neural networks) and analyze the adversarial setting for surrogates like $ρ$-margin and sigmoid loss. Extending to multi-class classification, we present the first $H$-consistency bounds for max, sum, and constrained losses, covering both non-adversarial and adversarial scenarios. We demonstrate that in some cases, non-trivial $H$-consistency bounds are unattainable. We also investigate comp-sum losses (e.g., cross-entropy, MAE), deriving their first $H$-consistency bounds and introducing smooth adversarial variants that yield robust learning algorithms. We develop a comprehensive framework for deriving these bounds across various surrogates, introducing new characterizations for constrained and comp-sum losses. Finally, we examine the growth rates of $H$-consistency bounds, establishing a universal square-root growth rate for smooth surrogates in binary and multi-class tasks, and analyze minimizability gaps to guide surrogate selection.


Design and Control of a Coaxial Dual-rotor Reconfigurable Tailsitter UAV Based on Swashplateless Mechanism

Liang, Jinfeng, Guo, Haocheng, Lyu, Ximin

arXiv.org Artificial Intelligence

The tailsitter vertical takeoff and landing (VTOL) UAV is widely used due to its lower dead weight, which eliminates the actuators and mechanisms for tilting. However, the tailsitter UAV is susceptible to wind disturbances in multi-rotor mode, as it exposes a large frontal fuselage area. To address this issue, our tailsitter UAV features a reconfigurable wing design, allowing wings to retract in multi-rotor mode and extend in fixed- wing mode. Considering power efficiency, we design a coaxial heterogeneous dual-rotor configuration, which significantly re- duces the total power consumption. To reduce structural weight and simplify structural complexity, we employ a swashplateless mechanism with an improved design to control pitch and roll in multi-rotor mode. We optimize the structure of the swashplateless mechanism by adding flapping hinges, which reduces vibration during cyclic acceleration and deceleration. Finally, we perform comprehensive transition flight tests to validate stable flight performance across the entire flight envelope of the tailsitter UAV.


Toggling stiffness via multistability

Oliveira, Hugo de Souza, Curatolo, Michele, Sachse, Renate, Milana, Edoardo

arXiv.org Artificial Intelligence

Mechanical metamaterials enable unconventional and programmable mechanical responses through structural design rather than material composition. In this work, we introduce a multistable mechanical metamaterial that exhibits a toggleable stiffness effect, where the effective shear stiffness switches discretely between stable configurations. The mechanical analysis of surrogate beam models of the unit cell reveal that this behavior originates from the rotation transmitted by the support beams to the curved beam, which governs the balance between bending and axial deformation. The stiffness ratio between the two states of the unit cell can be tuned by varying the slenderness of the support beams or by incorporating localized hinges that modulate rotational transfer. Experiments on 3D-printed prototypes validate the numerical predictions, confirming consistent stiffness toggling across different geometries. Finally, we demonstrate a monolithic soft clutch that leverages this effect to achieve programmable, stepwise stiffness modulation. This work establishes a design strategy for toggleable stiffness using multistable metamaterials, paving the way for adaptive, lightweight, and autonomous systems in soft robotics and smart structures.