Positional encoding is essential for supplementing transformer with positional information of tokens. Existing positional encoding methods demand predefined token/feature order, rendering them unsuitable for real-world data with non-sequential yet causally-related features. To address this limitation, we propose CAPE, a novel method that identifies underlying causal structure over non-sequential features as a weighted directed acyclic graph (DAG) using generalized structural equation modeling. The DAG is then embedded in hyperbolic space where its geometric structure is well-preserved using a hyperboloid model-based approach that effectively captures two important causal graph properties (causal strength & causal specificity). This step yields causality-aware positional encodings for the features, which are converted into their rotary form for integrating with transformer's self-attention mechanism. Theoretical analysis reveals that CAPE-generated rotary positional encodings possess three valuable properties for enhanced self-attention, including causal distance-induced attenuation, causal generality-induced attenuation, and robustness to positional disturbances. We evaluate CAPE over both synthetic and real-word datasets, empirically demonstrating its theoretical properties and effectiveness in enhancing transformer for data with non-sequential features. Our code is available at https://github.com/Catchxu/CAPE.

Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard practice is to threshold the calibrated score at a confidence cutoff and treat the hard label as the truth. Building on a recent identification result for the underlying moment equation, we develop a calibration-aware diagnostic apparatus for pseudo-labelling pipelines. We derive a closed-form expression for the attenuation bias that confidence thresholding induces in the downstream regression coefficient, and show that the bias can be predicted, before any inference is run, from the residual score variance $V^{*}=\mathbb{E}[\operatorname{Var}(p\mid X)]$ on the unlabelled set after partialling out the downstream controls $X$. We further obtain a sharp sensitivity bound under bounded calibration drift, and identify the boundary $V^{*}=0$, which holds iff $p$ is a deterministic function of $X$; this motivates a structural separation between classifier features $W$ and downstream controls $X\subsetneq W$. Five controlled simulations and a UCI Adult illustration trace the predictions. The contribution is operational: a $(V^{*}, κ)$ decision rule that practitioners can compute from any classifier output to decide whether confidence thresholding is safe.

Underwater visual localization remains challenging due to wavelength-dependent attenuation, poor texture, and non-Gaussian sensor noise. We introduce MARVO, a physics-aware, learning-integrated odometry framework that fuses underwater image formation modeling, differentiable matching, and reinforcement-learning optimization. At the front-end, we extend transformer-based feature matcher with a Physics Aware Radiance Adapter that compensates for color channel attenuation and contrast loss, yielding geometrically consistent feature correspondences under turbidity. These semi dense matches are combined with inertial and pressure measurements inside a factor-graph backend, where we formulate a keyframe-based visual-inertial-barometric estimator using GTSAM library. Each keyframe introduces (i) Pre-integrated IMU motion factors, (ii) MARVO-derived visual pose factors, and (iii) barometric depth priors, giving a full-state MAP estimate in real time. Lastly, we introduce a Reinforcement-Learningbased Pose-Graph Optimizer that refines global trajectories beyond local minima of classical least-squares solvers by learning optimal retraction actions on SE(2).

-- A robust and compact magneto - optical rotary encoder for the characterisation of robotic rotary joints is demonstrated. The system employs magnetic field - induced optical attenuation in a double - pass configuration using rotating nonuniform magnets around an optical circulator operating in reflection . The encoder tracks continuous 360 rotation with rotation sweep rates from ν = 135 /s to ν = 3 70 /s, and an angular resolution of Δ θ = 0. 3 . I NTRODUCTION OTARY encoders convert rotation into electromagnetic signals, most commonly electrical. Examples include precision monitoring and control of steering wheels [1], [2], motors of autopilot vehicles [2], [3], robot ics [4], [5], and prosthetic arms [6] . In robotics, the encoder is a crucial part of the positional feedback needed to perform precision movements.

There are two major types of uncertainty one can model.

Low-dose computed tomography (LDCT) is the current standard for lung cancer screening, yet its adoption and accessibility remain limited. Many regions lack LDCT infrastructure, and even among those screened, early-stage cancer detection often yield false positives, as shown in the National Lung Screening Trial (NLST) with a sensitivity of 93.8 percent and a false-positive rate of 26.6 percent. We aim to investigate whether X-ray dark-field imaging (DFI) radiograph, a technique sensitive to small-angle scatter from alveolar microstructure and less susceptible to organ shadowing, can significantly improve early-stage lung tumor detection when coupled with deep-learning segmentation. Using paired attenuation (ATTN) and DFI radiograph images of euthanized mouse lungs, we generated realistic synthetic tumors with irregular boundaries and intensity profiles consistent with physical lung contrast. A U-Net segmentation network was trained on small patches using either ATTN, DFI, or a combination of ATTN and DFI channels. Results show that the DFI-only model achieved a true-positive detection rate of 83.7 percent, compared with 51 percent for ATTN-only, while maintaining comparable specificity (90.5 versus 92.9 percent). The combined ATTN and DFI input achieved 79.6 percent sensitivity and 97.6 percent specificity. In conclusion, DFI substantially improves early-tumor detectability in comparison to standard attenuation radiography and shows potential as an accessible, low-cost, low-dose alternative for pre-clinical or limited-resource screening where LDCT is unavailable.

Digitally reconstructed radiographs (DRRs) are simulated 2D X-ray images generated from 3D CT volumes, widely used in preoperative settings but limited in intraoperative applications due to computational bottlenecks, especially for accurate but heavy physics-based Monte Carlo methods.

How to achieve such spatial adaptation in a principled manner has been an open problem in both traditional model-based and modern learning-based approaches toward SISR. In this paper, we propose a new adaptive weighted loss for SISR to train deep networks focusing on challenging situations such as textured and edge pixels with high uncertainty.