Rheumatoid arthritis (RA) is a common autoimmune disease that has been the focus of research in computer-aided diagnosis (CAD) and disease monitoring. In clinical settings, conventional radiography (CR) is widely used for the screening and evaluation of RA due to its low cost and accessibility. The wrist is a critical region for the diagnosis of RA. However, CAD research in this area remains limited, primarily due to the challenges in acquiring high-quality instance-level annotations.

Enforcing nonlinear inequality constraints in neural networks remains challenging, especially when the output is subject to many coupled constraints. Existing hard constraint methods often impose structural restrictions on the constraint set or introduce substantial computational overhead for large-scale nonlinear problems. Here, we propose DiffSlack, a differentiable projection layer for nonlinear inequality-constrained neural prediction. DiffSlack reformulates inequalities as equalities with learnable slack variables, which are predicted as part of the augmented network output and provide a data-driven warm start for damped Gauss-Newton projection. The projection layer maps raw predictions onto the augmented feasible manifold while preserving end-to-end differentiability. A two-stage curriculum further stabilizes training and improves constraint satisfaction. We evaluate DiffSlack on vehicle path planning with 200 nonlinear inequality constraints from collision avoidance, curvature limits, and waypoint spacing. Compared with existing learning-based baselines, DiffSlack achieves a higher planning success rate and stronger geometric constraint satisfaction under a comparable inference budget. Ablation studies further show that the hard projection layer reduces sensitivity to supervision quality. Closed-loop tracking in CARLA and real-world vehicle experiments confirms the executability of the generated trajectories. These results demonstrate that DiffSlack provides a practical and scalable approach to embedding hard inequality constraints into neural networks for engineering applications.

AAbout Equation (1) As we discussed in Section 3, label smoothing and focal loss are equivalent to the standard CE loss with an additional maximum-entropy regularizer (see in Equation (1) and (2) in the main text). The proof of Equation (2) can be found in the corresponding paper [4]. SVHN is an image dataset which consists of 32 32 colored images of 0 9 digits. CIFAR-10 and CIFAR-100 consist of 32 32 colored natural images arranged in 10 and 100 classes, respectively. For 20Newsgroups, we use the GloVe word embedding [7] for text representation before the 1D-CNN model and set the embedding dimension as 100.

To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived the optimization problem for this model from a maximum likelihood perspective. Additionally, we presented specific implementation details for the iterative process, including the regularized optimization algorithm and the geometric search cross-validation tuning algorithm. Three distinct penalty methods, Lasso, Ridge, and Elastic-net regularization, were meticulously considered. Meanwhile, the proposed Theta-regularized Kriging models were tested on nine common numerical functions and two practical engineering examples. The results demonstrate that, compared with other penalized Kriging models, the proposed model performs better in terms of accuracy and stability.

Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, while the smoothing technique used to mitigate this issue introduces conditional variance, potentially masking anomalies. We propose a continuous inference relaxation that resolves this dilemma by decoupling local adaptation from tail resolution via continuous weighted kernel density estimation. While relaxing finite-sample exactness to asymptotic validity, our method eliminates Monte Carlo variability and recovers the statistical power lost to discretization. Empirical evaluations confirm that our approach not only restores detection capabilities where discrete baselines yield zero discoveries, but outperforms standard methods in statistical power while maintaining valid marginal error control in practice.

Our motivation is grounded in a fundamental observation: aligning the gradient and the Hessian of the SDF provides a more efficient mechanism to govern gradient directions.

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As reviewers noticed, detailed description of the experiments is provided in the3 supplement. Wealso6 switched to a finer discretization of 1 minute on Physionet dataset, instead of 6 minutes. Modeling state-interactions via26 an ODE allows better generalization outside the training interval compared to directly modeling a function of time.27 Using an ODE-RNN as a decoder is a possible extension.