Due to the fact that objects in the world may be of different size and at different distances from the camera, there may in general be substantial (a priori unknown) scaling variabilities in the image data generated from a natural environment. When analysing aerial images, satellite images or medical images there may in addition by a priori unknown rotations relative to any reference view in the training data. Traditional deep networks are by default, however, not robust to such scaling or orientation variabilities. To address this problem, we will in this project develop jointly scale- and rotation-covariant deep networks, which obey provable covariance properties under these transformations. Specifically, we will study extensions a previously proposed notion of scale-covariant and scale-invariant Gaussian derivative networks, to enable classification at scales and image orientations that are not spanned by the training data. The research that we will perform will comprise extensions of the scale-covariant network architecture, (Lindeberg 2022, Perzanowski and Lindeberg 2025, 2026), including extensive experimental work on comparing different scale- and rotation-covariant network architectures on both single-scale and single-orientation image classification tasks and jointly scale and orientation generalisation tasks. The reason why we need good GPUs is to explore large networks, that have more parameters and thereby a much better ability to learn the image structures needed to handle more complex datasets, which we believe could substantially improve the joint scale and rotation generalisation properties. The extension of scale covariance to joint scale and rotation covariance does additionally increase both the computation and memory requirements. In the work performed with the computing resources provided by our 12-month grant 2025/5-378, we have developed new scale-covariant and scale-invariant deep network architectures (Perzanowski and Lindeberg 2026) and shown that these architectures lead to both significantly better accuracy and better scale generalisation compared to our previous work in (Lindeberg 2022, Perzanowski and Lindeberg 2025). We have also performed extensive ablation studies. In this proposal, we will extend those advances to joint scale- and rotation-covariant networks on three orientation extensions of our previous datasets, consider defining possible new fourth dataset and also perform a set of additional ablation studies, which requires access to high-performance GPU:s to be able to handle the substantially larger deep networks. When that goal has been completed, we will use any possibly remaining GPU resources for initiating our next planned subproject within the project on ”Covariant and invariant deep networks” supported by Vetenskapsrådet that finances this research. References: Lindeberg (2022) "Scale-covariant and scale-invariant Gaussian derivative networks", Journal of Mathematical Imaging and Vision, 64(3): 223-242. Perzanowski and Lindeberg (2025) "Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations”, Journal of Mathematical Imaging and Vision, 67(29): 1-39. Perzanowski and Lindeberg (2026) “Scale-invariant Gaussian derivative residual networks”, arXiv preprint arXiv:2603.02843.