In the following sections, we provide additional details about the network architecture, training, and experiments. The source code and WBC-SPH data set are published at https://github.com/ A.1 Implementation Details We implement our neural network with Tensorflow (https://www.tensorflow.org), They also serve as the basis for the implementation of our antisymmetric CConv (ASCC) layer. Axis for Mirroring As mentioned in the main text, the mirror axis for ASCC layers can be chosen freely while fulfilling the requirements from theory. This provides a degree of freedom for implementation. We decided to use a fixed axis, which in our case corresponds to the spatial y-axis. While the mirroring could potentially be coupled to the spatial content of features, we found that a single, fixed axis for mirroring simplifies the implementation of the ASCCs, and hence is preferable in practice. Additional Modifications In addition to the properties of our algorithm as discussed in Section 2.3 and the ablation study in Section 3, we normalize the input data depending on the given gravitational direction in the model.

Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to have two key properties: It should be valid (guaranteeing coverage) and discriminative (more uncertain when the expected risk is high). Moreover, when combined with deep learning (DL) methods, it should be scalable and affect the DL model performance minimally. Most existing Bayesian methods lack frequentist coverage guarantees and usually affect model performance. The few available frequentist methods are rarely discriminative and/or violate coverage guarantees due to unrealistic assumptions. Moreover, many methods are expensive or require substantial modifications to the base neural network. Building upon recent advances in conformal prediction [13, 33] and leveraging the classical idea of kernel regression, we propose Locally Valid and Discriminative prediction intervals (LVD), a simple, efficient and lightweight method to construct discriminative prediction intervals (PIs) for almost any DL model. With no assumptions on the data distribution, such PIs also offer finite-sample local coverage guarantees (contrasted to the simpler marginal coverage). We empirically verify, using diverse datasets, that besides being the only locally valid method for DL, LVD also exceeds or matches the performance (including coverage rate and prediction accuracy) of existing uncertainty quantification methods, while offering additional benefits in scalability and flexibility.

The problem of reducing processing time of large deep learning models is a fundamental challenge in many real-world applications. Early exit methods strive towards this goal by attaching additional Internal Classifiers (ICs) to intermediate layers of a neural network. ICs can quickly return predictions for easy examples and, as a result, reduce the average inference time of the whole model. However, if a particular IC does not decide to return an answer early, its predictions are discarded, with its computations effectively being wasted. To solve this issue, we introduce Zero Time Waste (ZTW), a novel approach in which each IC reuses predictions returned by its predecessors by (1) adding direct connections between ICs and (2) combining previous outputs in an ensemble-like manner. We conduct extensive experiments across various datasets and architectures to demonstrate that ZTW achieves a significantly better accuracy vs. inference time trade-off than other recently proposed early exit methods.

Single image-level annotations only correctly describe an often small subset of an image's content, particularly when complex real-world scenes are depicted. While this might be acceptable in many classification scenarios, it poses a significant challenge for applications where the set of classes differs significantly between training and test time. In this paper, we take a closer look at the implications in the context of few-shot learning. Splitting the input samples into patches and encoding these via the help of Vision Transformers allows us to establish semantic correspondences between local regions across images and independent of their respective class. The most informative patch embeddings for the task at hand are then determined as a function of the support set via online optimization at inference time, additionally providing visual interpretability of'what matters most' in the image. We build on recent advances in unsupervised training of networks via masked image modelling to overcome the lack of fine-grained labels and learn the more general statistical structure of the data while avoiding negative image-level annotation influence, aka supervision collapse. Experimental results show the competitiveness of our approach, achieving new state-of-the-art results on four popular few-shot classification benchmarks for 5-shot and 1-shot scenarios.

To keep experiments uniform, for all datasets (STL-10, CIFAR-10, and CIFAR-100) we used a train/val/test partitioning. In our experiments we compared FED with four baselines. For all baselines we tried different learning rates [0.1, 0.01, 0.001] and batch sizes [32, 64, 100]. For EnDD and EnDD + AUX, we used the same temperature, temperature annealing, and optimizer that was used in the original paper. For AMT, we tried different alphas [1e1, 1e3, 1e5] and kept the rest as the original paper.