High-Resolution Range Profile Classifiers Require Aspect-Angle Awareness

Circular data, representing angles or directions, are frequently encountered in computer vision, biology, geology, and meteorology. Traditional regression targets the conditional mean, which is often geometrically misleading for circular responses under multimodal, skewed, or asymmetric data structures. To address these limitations, a lightweight deep generative framework, namely ANGLE, is introduced for non-parametric distributional regression on the circle. The full conditional distribution of an angular response, given Euclidean and circular covariates, is learned through a generative map optimized via a generalized circular energy score (GCES) loss. Desirable theoretical properties, including the strict propriety of the loss and the rotational equivariance of the estimators, are established. Furthermore, both pre- and post-additive noise models are accommodated. A unified toolbox is provided for advancing previously underexplored challenges in circular statistics: extrapolation, sufficient dimension reduction, and conditional distribution equality testing. The framework's efficacy is demonstrated through extensive simulations and real-world applications. Specifically, the proposal is utilized for object pose estimation from imagery and wind direction prediction, which are integral to surveillance, autonomous vehicles, and energy systems, respectively. Superior predictive performance and robust uncertainty quantification of the proposed method in these tasks are revealed.

In many real-world systems, including articulated robots and biomechanical models, rotations are defined in joint space and naturally parameterized by Euler angles with bounded ranges. Yet regressing Euler angles remains challenging, as their discontinuities and singularities often destabilize training. In this work, we revisit Euler-angle regression and show that its effectiveness depends critically on the interaction between rotation representation, regression architecture, and domain constraints. We introduce a new framework that combines range-aware Euler modeling with Kolmogorov-Arnold Networks (KAN), which replace fixed node-wise activations with learnable univariate functions on edges. We further provide theoretical analysis indicating that bounded Euler ranges motivate a near-additive structure in the regression function, which favors the additive functional form of KAN, and we confirm this trend empirically. Extensive experiments on controlled rotation regression, object pose estimation, and robotic and human inverse kinematics demonstrate consistent improvements in accuracy, convergence, and efficiency. The code will be publicly available.

We study the fundamental problem of calibrating a linear binary classifier of the form $σ(\hat{w}^\top x)$, where the feature vector $x$ is Gaussian, $σ$ is a link function, and $\hat{w}$ is an estimator of the true linear weight $w^\star$. By interpolating with a noninformative $\textit{chance classifier}$, we construct a well-calibrated predictor whose interpolation weight depends on the angle $\angle(\hat{w}, w_\star)$ between the estimator $\hat{w}$ and the true linear weight $w_\star$. We establish that this angular calibration approach is provably well-calibrated in a high-dimensional regime where the number of samples and features both diverge, at a comparable rate. The angle $\angle(\hat{w}, w_\star)$ can be consistently estimated. Furthermore, the resulting predictor is uniquely $\textit{Bregman-optimal}$, minimizing the Bregman divergence to the true label distribution within a suitable class of calibrated predictors. Our work is the first to provide a calibration strategy that satisfies both calibration and optimality properties provably in high dimensions. Additionally, we identify conditions under which a classical Platt-scaling predictor converges to our Bregman-optimal calibrated solution. Thus, Platt-scaling also inherits these desirable properties provably in high dimensions.