The supplementary material is organized as follows. We give details of the definitions and notation in Section B.1 . Then, we provide the technical details of the lower bound (Lemma 3.3). In Section D.4 we provide insights into auto-labeling using This suggests, in these settings auto-labeling using active learning followed by selective classification is expected to work well. This idea is captured by the Chow's excess risk [ Nevertheless, it would be interesting future work to explore the connections between auto-labeling and active learning with abstention.

The supplementary material is organized as follows. We give details of the definitions and notation in Section B.1 . Then, we provide the technical details of the lower bound (Lemma 3.3). In Section D.4 we provide insights into auto-labeling using This suggests, in these settings auto-labeling using active learning followed by selective classification is expected to work well. This idea is captured by the Chow's excess risk [ Nevertheless, it would be interesting future work to explore the connections between auto-labeling and active learning with abstention.

The classifier for density ratio estimation is based on deep neural networks. Our algorithm and baselines are based on the identical outcome prediction network architecture. The results are reported in Table 4. A.5 Results of synthetic experiments under misspecification of the dimension of latent space The dimension of latent factors is hardly known in many scenarios.

A Method Details A.1 The attention network The attention network is implemented as a feedforward neural network with one hidden layer: Input layer: 12 units Hidden layer: N units coupled with a dropout layer p = 0 . From these three policies, we tried to extract all possible information. The information should be cheap to extract and dependent on the current data, so we prefer features extracted from the outputs of these policies (value, entropy, distance, return, etc.). Intuitively, the most important features should be the empirical returns, values associated with each policy and the distances, which gives a good hint of which virtual policy will yield high performance (e.g., a virtual policy that is closer to the policy that obtained high return and low value loss). A.2 The advantage function In this paper, we use GAE [18] as the advantage function for all models and experiments ˆ A Note that Algo. 1 illustrates the procedure for 1 actor. A.3 The objective function Following [19], our objective function also includes value loss and entropy terms.

The widespread use of Magnetic Resonance Imaging (MRI) in combination with deep learning shows promise for many high-impact automated diagnostic and prognostic tools. However, training new models requires large amounts of labeled data, a challenge due to high cost of precise annotations and data privacy. To address this issue, we introduce the MRI-CORE, a vision foundation model trained using more than 6 million slices from over 110 thousand MRI volumes across 18 body locations. Our experiments show notable improvements in performance over state-of-the-art methods in 13 data-restricted segmentation tasks, as well as in image classification, and zero-shot segmentation, showing the strong potential of MRI-CORE to enable data-efficient development of artificial intelligence models. We also present data on which strategies yield most useful foundation models and a novel analysis relating similarity between pre-training and downstream task data with transfer learning performance. Our model is publicly available with a permissive license. Magnetic Resonance Imaging (MRI) is one of the most widely used imaging modalities in medical diagnostics, with around 100-150 million scans performed annually worldwide (Papanicolas et al. 2018). MRI supports a wide range of clinical tasks, including lesion detection, tissue classification, and disease monitoring. Among these tasks, segmentation plays a particularly important role, as it enables precise delineation of anatomical structures and pathological regions, directly impacting diagnosis, treatment planning, and longitudinal studies (Mazurowski et al. 2023; Ma et al. 2024; Azad et al. 2024; Xu et al. 2024). Recent advances in deep learning have significantly improved the automation and accuracy of MRI-based analyses across a variety of tasks. However, deep learning-based methods typically require large amounts of manually annotated data and lack task transferability, making them difficult to scale across new tasks, anatomies, or patient populations.