Hinge Regression Tree: A Newton Method for Oblique Regression Tree Splitting

Oblique decision trees combine the transparency of trees with the power of multivariate decision boundaries, but learning high-quality oblique splits is NP-hard, and practical methods still rely on slow search or theory-free heuristics. We present the Hinge Regression Tree (HRT), which reframes each split as a non-linear least-squares problem over two linear predictors whose max/min envelope induces ReLU-like expressive power. The resulting alternating fitting procedure is exactly equivalent to a damped Newton (Gauss-Newton) method within fixed partitions. We analyze this node-level optimization and, for a backtracking line-search variant, prove that the local objective decreases monotonically and converges; in practice, both fixed and adaptive damping yield fast, stable convergence and can be combined with optional ridge regularization. We further prove that HRT's model class is a universal approximator with an explicit $O(δ^2)$ approximation rate, and show on synthetic and real-world benchmarks that it matches or outperforms single-tree baselines with more compact structures.

Variable Search Stepsize for Randomized Local Search in Multi-Objective Combinatorial Optimization

Over the past two decades, research in evolutionary multi-objective optimization has predominantly focused on continuous domains, with comparatively limited attention given to multi-objective combinatorial optimization problems (MOCOPs). Combinatorial problems differ significantly from continuous ones in terms of problem structure and landscape. Recent studies have shown that on MOCOPs multi-objective evolutionary algorithms (MOEAs) can even be outperformed by simple randomised local search. Starting with a randomly sampled solution in search space, randomised local search iteratively draws a random solution (from an archive) to perform local variation within its neighbourhood. However, in most existing methods, the local variation relies on a fixed neighbourhood, which limits exploration and makes the search easy to get trapped in local optima. In this paper, we present a simple yet effective local search method, called variable stepsize randomized local search (VS-RLS), which adjusts the stepsize during the search. VS-RLS transitions gradually from a broad, exploratory search in the early phases to a more focused, fine-grained search as the search progresses. We demonstrate the effectiveness and generalizability of VS-RLS through extensive evaluations against local search and MOEAs methods on diverse MOCOPs.

LSA: Localized Semantic Alignment for Enhancing Temporal Consistency in Traffic Video Generation

Controllable video generation has emerged as a versatile tool for autonomous driving, enabling realistic synthesis of traffic scenarios. However, existing methods depend on control signals at inference time to guide the generative model towards temporally consistent generation of dynamic objects, limiting their utility as scalable and generalizable data engines. In this work, we propose Localized Semantic Alignment (LSA), a simple yet effective framework for fine-tuning pre-trained video generation models. LSA enhances temporal consistency by aligning semantic features between ground-truth and generated video clips. Specifically, we compare the output of an off-the-shelf feature extraction model between the ground-truth and generated video clips localized around dynamic objects inducing a semantic feature consistency loss. We fine-tune the base model by combining this loss with the standard diffusion loss. The model fine-tuned for a single epoch with our novel loss outperforms the baselines in common video generation evaluation metrics. To further test the temporal consistency in generated videos we adapt two additional metrics from object detection task, namely mAP and mIoU. Extensive experiments on nuScenes and KITTI datasets show the effectiveness of our approach in enhancing temporal consistency in video generation without the need for external control signals during inference and any computational overheads.

Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting

Low-rank matrix sensing is a fundamental yet challenging nonconvex problem whose optimization landscape typically contains numerous spurious local minima, making it difficult for gradient-based optimizers to converge to the global optimum. Recent work has shown that over-parameterization via tensor lifting can convert such local minima into strict saddle points, an insight that also partially explains why massive scaling can improve generalization and performance in modern machine learning. Motivated by this observation, we propose a Simulated Oracle Direction (SOD) escape mechanism that simulates the landscape and escape direction of the over-parametrized space, without resorting to actually lifting the problem, since that would be computationally intractable. In essence, we designed a mathematical framework to project over-parametrized escape directions onto the original parameter space to guarantee a strict decrease of objective value from existing local minima. To the best of the our knowledge, this represents the first deterministic framework that could escape spurious local minima with guarantee, especially without using random perturbations or heuristic estimates. Numerical experiments demonstrate that our framework reliably escapes local minima and facilitates convergence to global optima, while incurring minimal computational cost when compared to explicit tensor over-parameterization. We believe this framework has non-trivial implications for nonconvex optimization beyond matrix sensing, by showcasing how simulated over-parameterization can be leveraged to tame challenging optimization landscapes.

TrajVG: 3D Trajectory-Coupled Visual Geometry Learning

Feed-forward multi-frame 3D reconstruction models often degrade on videos with object motion. Global-reference becomes ambiguous under multiple motions, while the local pointmap relies heavily on estimated relative poses and can drift, causing cross-frame misalignment and duplicated structures. We propose TrajVG, a reconstruction framework that makes cross-frame 3D correspondence an explicit prediction by estimating camera-coordinate 3D trajectories. We couple sparse trajectories, per-frame local point maps, and relative camera poses with geometric consistency objectives: (i) bidirectional trajectory-pointmap consistency with controlled gradient flow, and (ii) a pose consistency objective driven by static track anchors that suppresses gradients from dynamic regions. To scale training to in-the-wild videos where 3D trajectory labels are scarce, we reformulate the same coupling constraints into self-supervised objectives using only pseudo 2D tracks, enabling unified training with mixed supervision. Extensive experiments across 3D tracking, pose estimation, pointmap reconstruction, and video depth show that TrajVG surpasses the current feedforward performance baseline.

Impact of diversity on bounded archives for multi-objective local search

This work tackles two critical challenges related to the development of metaheuristics for Multi-Objective Optimization Problems (MOOPs): the exponential growth of non-dominated solutions and the tendency of metaheuristics to disproportionately concentrate their search on a subset of the Pareto Front. To counteract the first, bounded archives are employed as a strategic mechanism for effectively managing the increasing number of non-dominated solutions. Addressing the second challenge involves an in-depth exploration of solution diversity algorithms found in existing literature. Upon recognizing that current approaches predominantly center on diversity within the objective space, this research introduces innovative methods specifically designed to enhance diversity in the solution space. Results demonstrate the efficacy of the Hamming Distance Archiving Algorithm, one of the newly proposed algorithms for multi-objective local search, surpassing the performance of the Adaptive Grid Archiving and the Hypervolume Archiving, both drawn from the literature. This outcome suggests a promising avenue for enhancing the overall efficiency of metaheuristics employed for solving MOOPs.

PIRATR: Parametric Object Inference for Robotic Applications with Transformers in 3D Point Clouds

We present PIRATR, an end-to-end 3D object detection framework for robotic use cases in point clouds. Extending PI3DETR, our method streamlines parametric 3D object detection by jointly estimating multi-class 6-DoF poses and class-specific parametric attributes directly from occlusion-affected point cloud data. This formulation enables not only geometric localization but also the estimation of task-relevant properties for parametric objects, such as a gripper's opening, where the 3D model is adjusted according to simple, predefined rules. The architecture employs modular, class-specific heads, making it straightforward to extend to novel object types without re-designing the pipeline. We validate PIRATR on an automated forklift platform, focusing on three structurally and functionally diverse categories: crane grippers, loading platforms, and pallets. Trained entirely in a synthetic environment, PIRATR generalizes effectively to real outdoor LiDAR scans, achieving a detection mAP of 0.919 without additional fine-tuning. PIRATR establishes a new paradigm of pose-aware, parameterized perception. This bridges the gap between low-level geometric reasoning and actionable world models, paving the way for scalable, simulation-trained perception systems that can be deployed in dynamic robotic environments. Code available at https://github.com/swingaxe/piratr.

A Mixed Reality System for Robust Manikin Localization in Childbirth Training

Opportunities for medical students to gain practical experience in vaginal births are increasingly constrained by shortened clinical rotations, patient reluctance, and the unpredictable nature of labour. To alleviate clinicians' instructional burden and enhance trainees' learning efficiency, we introduce a mixed reality (MR) system for childbirth training that combines virtual guidance with tactile manikin interaction, thereby preserving authentic haptic feedback while enabling independent practice without continuous on-site expert supervision. The system extends the passthrough capability of commercial head-mounted displays (HMDs) by spatially calibrating an external RGB-D camera, allowing real-time visual integration of physical training objects. Building on this capability, we implement a coarse-to-fine localization pipeline that first aligns the maternal manikin with fiducial markers to define a delivery region and then registers the pre-scanned neonatal head within this area. This process enables spatially accurate overlay of virtual guiding hands near the manikin, allowing trainees to follow expert trajectories reinforced by haptic interaction. Experimental evaluations demonstrate that the system achieves accurate and stable manikin localization on a standalone headset, ensuring practical deployment without external computing resources. A large-scale user study involving 83 fourth-year medical students was subsequently conducted to compare MR-based and virtual reality (VR)-based childbirth training. Four senior obstetricians independently assessed performance using standardized criteria. Results showed that MR training achieved significantly higher scores in delivery, post-delivery, and overall task performance, and was consistently preferred by trainees over VR training.

Self-Supervised Learning with a Multi-Task Latent Space Objective

Self-supervised learning (SSL) methods based on Siamese networks learn visual representations by aligning different views of the same image. The multi-crop strategy, which incorporates small local crops to global ones, enhances many SSL frameworks but causes instability in predictor-based architectures such as BYOL, SimSiam, and MoCo v3. We trace this failure to the shared predictor used across all views and demonstrate that assigning a separate predictor to each view type stabilizes multi-crop training, resulting in significant performance gains. Extending this idea, we treat each spatial transformation as a distinct alignment task and add cutout views, where part of the image is masked before encoding. This yields a simple multi-task formulation of asymmetric Siamese SSL that combines global, local, and masked views into a single framework. The approach is stable, generally applicable across backbones, and consistently improves the performance of ResNet and ViT models on ImageNet.

PLATO Hand: Shaping Contact Behavior with Fingernails for Precise Manipulation

We present the PLATO Hand, a dexterous robotic hand with a hybrid fingertip that embeds a rigid fingernail within a compliant pulp. This design shapes contact behavior to enable diverse interaction modes across a range of object geometries. We develop a strain-energy-based bending-indentation model to guide the fingertip design and to explain how guided contact preserves local indentation while suppressing global bending. Experimental results show that the proposed robotic hand design demonstrates improved pinching stability, enhanced force observability, and successful execution of edge-sensitive manipulation tasks, including paper singulation, card picking, and orange peeling. Together, these results show that coupling structured contact geometry with a force-motion transparent mechanism provides a principled, physically embodied approach to precise manipulation.