Temporal sequences, even after stationarization, often exhibit leptokurtic distributions with fat tails and persistent distribution shifts. These properties destabilize feature dynamics, amplify model variance, and hinder model convergence in time series forecasting. To address this, we propose Morphing-Flow (MoF), a framework that combines a spline-based transform layer (Flow) and a test-time-trained method (Morph), which adaptively normalizes non-stationary, fat-tailed distributions while preserving critical extreme features. MoF ensures that inputs remain within a network’s effective activation space—a structured, normal-like distribution—even under distributional drift. Experiments across eight datasets show that MoF achieves state-of-the-art performance: With a simple linear backbone architecture, it matches the performance of state-of-the-art models on datasets such as Electricity and ETTh2. When paired with a patch-based Mamba architecture, MoF outperforms its closest competitor by 6.3% on average and reduces forecasting errors in fat-tailed datasets such as Exchange by 21.7%. Moreover, MoF acts as a plug-and-play module, boosting performance in existing models without architectural changes.

Soft robots, compared to regular rigid robots, as their multiple segments with soft materials bring flexibility and compliance, have the advantages of safe interaction and dexterous operation in the environment. However, due to its characteristics of high dimensional, nonlinearity, time-varying nature, and infinite degree of freedom, it has been challenges in achieving precise and dynamic control such as trajectory tracking and position reaching. To address these challenges, we propose a framework of Deep Koopman-based Model Predictive Control (DK-MPC) for handling multi-segment soft robots. We first employ a deep learning approach with sampling data to approximate the Koopman operator, which therefore linearizes the high-dimensional nonlinear dynamics of the soft robots into a finite-dimensional linear representation. Secondly, this linearized model is utilized within a model predictive control framework to compute optimal control inputs that minimize the tracking error between the desired and actual state trajectories. The real-world experiments on the soft robot “Chordata” demonstrate that DK-MPC could achieve highprecision control, showing the potential of DK-MPC for future applications to soft robots. More visualization results can be found at https://pinkmoon-io.github.io/DKMPC/.

Unsupervised non-rigid point cloud shape correspondence underpins a multitude of 3D vision tasks, yet itself is non-trivial given the exponential complexity stemming from inter-point degree-of-freedom, i.e., pose transformations. Based on the assumption of local rigidity, one solution for reducing complexity is to decompose the overall shape into independent local regions using Local Reference Frames (LRFs) that are equivariant to SE(3) transformations. However, the focus solely on local structure neglects global geometric contexts, resulting in less distinctive LRFs that lack crucial semantic information necessary for effective matching. Furthermore, such complexity introduces out-of-distribution geometric contexts during inference, thus complicating generalization. To this end, we introduce 1) EquiShape, a novel structure tailored to learn pair-wise LRFs with global structural cues for both spatial and semantic consistency, and 2) LRF-Refine, an optimization strategy generally applicable to LRF-based methods, aimed at addressing the generalization challenges. Specifically, for EquiShape, we employ cross-talk within separate equivariant graph neural networks (Cross-GVP) to build long-range dependencies to compensate for the lack of semantic information in local structure modeling, deducing pair-wise independent SE(3)-equivariant LRF vectors for each point. For LRF-Refine, the optimization adjusts LRFs within specific contexts and knowledge, enhancing the geometric and semantic generalizability of point features. Our overall framework surpasses the state-of-the-art methods by a large margin on three benchmarks. Codes are available at https://github.com/2019EPWL/EquiShape.

Cardiovascular image registration is an essential approach to combine the advantages of preoperative 3D computed tomography angiograph (CTA) images and intraoperative 2D X-ray/digital subtraction angiography (DSA) images together in minimally invasive vascular interventional surgery (MIVI). Recent studies have shown that convolutional neural network (CNN) regression model can be used to register these two modality vascular images with fast speed and satisfactory accuracy. However, CNN regression model trained by tens of thousands of images of one patient is often unable to be applied to another patient due to the large difference and deformation of vascular structure in different patients. To overcome this challenge, we evaluate the ability of transfer learning (TL) for the registration of 2D/3D deformable cardiovascular images. Frozen weights in the convolutional layers were optimized to find the best common feature extractors for TL. After TL, the training data set size was reduced to 200 for a randomly selected patient to get accurate registration results. We compared the effectiveness of our proposed nonrigid registration model after TL with not only that without TL but also some traditional intensity-based methods to evaluate that our nonrigid model after TL performs better on deformable cardiovascular image registration.