This applies to common objects such as chairs, but also to novel objects that wehaveneverseenbefore.

Convolutional neural networks are increasingly used outside the domain of image analysis, in particular in various areas of the natural sciences concerned with spatial data. Such networks often work out-of-the box, and in some cases entire model architectures from image analysis can be carried over to other problem domains almost unaltered. Unfortunately, this convenience does not trivially extend to data in non-euclidean spaces, such as spherical data. In this paper, we introduce two strategies for conducting convolutions on the sphere, using either a spherical-polar grid or a grid based on the cubed-sphere representation. We investigate the challenges that arise in this setting, and extend our discussion to include scenarios of spherical volumes, with several strategies for parameterizing the radial dimension. As a proof of concept, we conclude with an assessment of the performance of spherical convolutions in the context of molecular modelling, by considering structural environments within proteins. We show that the models are capable of learning non-trivial functions in these molecular environments, and that our spherical convolutions generally outperform standard 3D convolutions in this setting. In particular, despite the lack of any domain specific feature-engineering, we demonstrate performance comparable to state-of-the-art methods in the field, which build on decades of domain-specific knowledge.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

H = {( γ,t )|γ [0 , 2π ), t R }. R is the quotient space SE (3)/( SO (2) R ) up to isomorphism. SO (3) is a semidirect product group as stated in [18].

--Early and accurate assessment of brain microstruc-ture using diffusion Magnetic Resonance Imaging (dMRI) is crucial for identifying neurodevelopmental disorders in neonates, but remains challenging due to low signal-to-noise ratio (SNR), motion artifacts, and ongoing myelination. In this study, we propose a rotationally equivariant Spherical Convolutional Neural Network (sCNN) framework tailored for neonatal dMRI. We predict the Fiber Orientation Distribution (FOD) from multi-shell dMRI signals acquired with a reduced set of gradient directions (30% of the full protocol), enabling faster and more cost-effective acquisitions. We train and evaluate the performance of our sCNN using real data from 43 neonatal dMRI datasets provided by the Developing Human Connectome Project (dHCP). Our results demonstrate that the sCNN achieves significantly lower mean squared error (MSE) and higher angular correlation coefficient (ACC) compared to a Multi-Layer Perceptron (MLP) baseline, indicating improved accuracy in FOD estimation. Furthermore, tractography results based on the sCNN-predicted FODs show improved anatomical plausibility, coverage, and coherence compared to those from the MLP . These findings highlight that sCNNs, with their inherent rotational equivariance, offer a promising approach for accurate and clinically efficient dMRI analysis, paving the way for improved diagnostic capabilities and characterization of early brain development. Medical diagnostics is undergoing a transformative shift, fueled by the rapid advancements in artificial intelligence (AI) and deep learning.

Meanwhile, we make the kernel locally supported without breaking the equivariance.

Photoacoustic computed tomography (PACT) combines optical contrast with ultrasonic resolution, achieving deep-tissue imaging beyond the optical diffusion limit. While three-dimensional PACT systems enable high-resolution volumetric imaging for applications spanning transcranial to breast imaging, current implementations require dense transducer arrays and prolonged acquisition times, limiting clinical translation. We introduce Pano (PACT imaging neural operator), an end-to-end physics-aware model that directly learns the inverse acoustic mapping from sensor measurements to volumetric reconstructions. Unlike existing approaches (e.g. universal back-projection algorithm), Pano learns both physics and data priors while also being agnostic to the input data resolution. Pano employs spherical discrete-continuous convolutions to preserve hemispherical sensor geometry, incorporates Helmholtz equation constraints to ensure physical consistency and operates resolutionindependently across varying sensor configurations. We demonstrate the robustness and efficiency of Pano in reconstructing high-quality images from both simulated and real experimental data, achieving consistent performance even with significantly reduced transducer counts and limited-angle acquisition configurations. The framework maintains reconstruction fidelity across diverse sparse sampling patterns while enabling real-time volumetric imaging capabilities. This advancement establishes a practical pathway for making 3D PACT more accessible and feasible for both preclinical research and clinical applications, substantially reducing hardware requirements without compromising image reconstruction quality.