To compute the discrepancy term dst, we add a per-location domain classifier h tw ˆ . It W consti semantic tutes map corresponds to the either source or target domain. On the other hand, hˆ predicts the Bird-Eye View binary segmentation map. In figure 9.1 we show the Lift-Splat Adapt diagram. Our training strategy requires little modification to the original architecture, e.g.

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.

Detecting 3D keypoints with semantic consistency is widely used in many scenarios such as pose estimation, shape registration and robotics. Currently, most unsupervised 3D keypoint detection methods focus on the rigid-body objects. However, when faced with deformable objects, the keypoints they identify do not preserve semantic consistency well. In this paper, we introduce an innovative unsupervised keypoint detector Key-Grid for both the rigid-body and deformable objects, which is an autoencoder framework. The encoder predicts keypoints and the decoder utilizes the generated keypoints to reconstruct the objects. Unlike previous work, we leverage the identified keypoint in formation to form a 3D grid feature heatmap called grid heatmap, which is used in the decoder section.

The current methods follow the paradigm of adapting the visual task outputs to language-oriented formats.

Similarly to previous methods, our approach is fully unsupervised in a sense that it does not require or make any use of annotated landmarks for the target object category.

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