The requirement of generating predictions that exactly fulfill the fundamental symmetry of the corresponding physical quantities has profoundly shaped the development of machine-learning models for physical simulations. In many cases, models are built using constrained mathematical forms that ensure that symmetries are enforced exactly. However, unconstrained models that do not obey rotational symmetries are often found to have competitive performance, and to be able to \emph{learn} to a high level of accuracy an approximate equivariant behavior with a simple data augmentation strategy. In this paper, we introduce rigorous metrics to measure the symmetry content of the learned representations in such models, and assess the accuracy by which the outputs fulfill the equivariant condition. We apply these metrics to two unconstrained, transformer-based models operating on decorated point clouds (a graph neural network for atomistic simulations and a PointNet-style architecture for particle physics) to investigate how symmetry information is processed across architectural layers and is learned during training. Based on these insights, we establish a rigorous framework for diagnosing spectral failure modes in ML models. Enabled by this analysis, we demonstrate that one can achieve superior stability and accuracy by strategically injecting the minimum required inductive biases, preserving the high expressivity and scalability of unconstrained architectures while guaranteeing physical fidelity.

Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of training efforts over clinical targets. However, even the most modern approaches fall short in two important scenarios: open-loop models with known mean flow and assumed waveform shapes, and anatomies affected by vascular lesions where segmentation influences the reachability of pressure or flow split targets. In both cases, boundary conditions cannot be tuned in isolation. We introduce a general amortized inference framework based on probabilistic flow that treats clinical targets, inflow features, and point cloud embeddings of patient-specific anatomies as either conditioning variables or quantities to be jointly estimated. We demonstrate the approach on two patient-specific models: an aorto-iliac bifurcation with varying stenosis locations and severity, and a coronary arterial tree.

We present a simple and general framework for feature learning from point cloud. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g.

Neural implicit function based on signed distance field (SDF) has achieved impressiveprogress inreconstructing 3Dmodels withhighfidelity. However,such approaches canonlyrepresent closed surfaces.

MA TLAB, as shown in Table 2. To enhance the sensing quality, we have aggregated five adjacent frames into a new frame for use. WiFi CSI data, there are some "-inf" values in some sequences. The "-inf" number comes from the To facilitate the users, we have embedded these processing codes into our dataset tool. When the user loads our WiFi CSI data, these numbers will be handled by linear interpolation. As presented in Section 4.3, we provide the temporal Each sequence is annotated by at least 5 human annotators.

However, existing solutions which mainly rely on cameras and wearable devices are either privacy intrusive or inconvenient to use.

This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces.

The FAUST test set contains 200 scans of undressed people in challenging poses andthescans themselvesarenoisy. Nonetheless we report the results as per the protocol in Table 2. For competing approaches we take the numbers from the corresponding papers. It can be clearly seen that our model trained primarily with selfsupervision performs better than the competing approaches. Our formulation allows us to jointly differentiate through the correspondences and the instance specific human model parameters. This allows us to create a self-supervised loop for registration.