A.1 Datasets We use two standardized few-shot image classification datasets. We also use the test splits of the following four datasets, as defined by Triantafillou et al. [57]. CUB-200: CUB-200 was collected by Welinder et al. The test split contains 30 classes. A.2 Network architectures We train two of the most popular network architectures in few-shot learning literature. Episode difficulty is approximately normally distributed - density plots.

Then, we repeat the branching and bounding steps on subproblems that still have a negative lower bound. We terminate when all unstable neurons are split or all subproblems are verified.

Convolutions (Convs) and multi-head self-attentions (MHSAs) are typically considered alternatives to each other for building vision backbones. Although some works try to integrate both, they apply the two operators simultaneously at the finest pixel granularity. With Convs responsible for per-pixel feature extraction already, the question is whether we still need to include the heavy MHSAs at such a fine-grained level. In fact, this is the root cause of the scalability issue w.r.t. the input resolution for vision transformers. To address this important problem, we propose in this work to use MSHAs and Convs in parallel \textbf{at different granularity levels} instead. Specifically, in each layer, we use two different ways to represent an image: a fine-grained regular grid and a coarse-grained set of semantic slots.

Recent progress in vision Transformers exhibits great success in various tasks driven by the new spatial modeling mechanism based on dot-product self-attention. In this paper, we show that the key ingredients behind the vision Transformers, namely input-adaptive, long-range and high-order spatial interactions, can also be efficiently implemented with a convolution-based framework. We present the Recursive Gated Convolution ($\textit{g}^\textit{n}$Conv) that performs high-order spatial interactions with gated convolutions and recursive designs. The new operation is highly flexible and customizable, which is compatible with various variants of convolution and extends the two-order interactions in self-attention to arbitrary orders without introducing significant extra computation.

Learning models over factorized joins avoids redundant computations by identifying and pre-computing shared cofactors. Previous work has investigated the performance gain when computing cofactors on traditional disk-based database systems. Due to the absence of published code, the experiments could not be reproduced on in-memory database systems. This work describes the implementation when using cofactors for in-database factorized learning. We benchmark our open-source implementation for learning linear regression on factorized joins with PostgreSQL -- as a disk-based database system -- and HyPer -- as an in-memory engine. The evaluation shows a performance gain of factorized learning on in-memory database systems by 70\% to non-factorized learning and by a factor of 100 compared to disk-based database systems. Thus, modern database engines can contribute to the machine learning pipeline by pre-computing aggregates prior to data extraction to accelerate training.

Estimating the Remaining Useful Life (RUL) of mechanical systems is pivotal in Prognostics and Health Management (PHM). Rolling-element bearings are among the most frequent causes of machinery failure, highlighting the need for robust RUL estimation methods. Existing approaches often suffer from poor generalization, lack of robustness, high data demands, and limited interpretability. This paper proposes a novel multimodal-RUL framework that jointly leverages image representations (ImR) and time-frequency representations (TFR) of multichannel, nonstationary vibration signals. The architecture comprises three branches: (1) an ImR branch and (2) a TFR branch, both employing multiple dilated convolutional blocks with residual connections to extract spatial degradation features; and (3) a fusion branch that concatenates these features and feeds them into an LSTM to model temporal degradation patterns. A multi-head attention mechanism subsequently emphasizes salient features, followed by linear layers for final RUL regression. To enable effective multimodal learning, vibration signals are converted into ImR via the Bresenham line algorithm and into TFR using Continuous Wavelet Transform. We also introduce multimodal Layer-wise Relevance Propagation (multimodal-LRP), a tailored explainability technique that significantly enhances model transparency. The approach is validated on the XJTU-SY and PRONOSTIA benchmark datasets. Results show that our method matches or surpasses state-of-the-art baselines under both seen and unseen operating conditions, while requiring ~28 % less training data on XJTU-SY and ~48 % less on PRONOSTIA. The model exhibits strong noise resilience, and multimodal-LRP visualizations confirm the interpretability and trustworthiness of predictions, making the framework highly suitable for real-world industrial deployment.

Previously, image interpretation in radiology relied heavily on manual methods. However, manual classification of brain tumor medical images is time-consuming and labor-intensive. Even with shallow convolutional neural network models, the accuracy is not ideal. To improve the efficiency and accuracy of brain tumor image classification, this paper proposes a brain tumor classification model based on an improved ResNet34 network. This model uses the ResNet34 residual network as the backbone network and incorporates multi-scale feature extraction. It uses a multi-scale input module as the first layer of the ResNet34 network and an Inception v2 module as the residual downsampling layer. Furthermore, a channel attention mechanism module assigns different weights to different channels of the image from a channel domain perspective, obtaining more important feature information. The results after a five-fold crossover experiment show that the average classification accuracy of the improved network model is approximately 98.8%, which is not only 1% higher than ResNet34, but also only 80% of the number of parameters of the original model. Therefore, the improved network model not only improves accuracy but also reduces clutter, achieving a classification effect with fewer parameters and higher accuracy.

Active imitation learning (AIL) combats covariate shift by querying an expert during training. However, expert action labeling often dominates the cost, especially in GPU-intensive simulators, human-in-the-loop settings, and robot fleets that revisit near-duplicate states. We present Conformalized Rejection Sampling for Active Imitation Learning (CRSAIL), a querying rule that requests an expert action only when the visited state is under-represented in the expert-labeled dataset. CRSAIL scores state novelty by the distance to the $K$-th nearest expert state and sets a single global threshold via conformal prediction. This threshold is the empirical $(1-α)$ quantile of on-policy calibration scores, providing a distribution-free calibration rule that links $α$ to the expected query rate and makes $α$ a task-agnostic tuning knob. This state-space querying strategy is robust to outliers and, unlike safety-gate-based AIL, can be run without real-time expert takeovers: we roll out full trajectories (episodes) with the learner and only afterward query the expert on a subset of visited states. Evaluated on MuJoCo robotics tasks, CRSAIL matches or exceeds expert-level reward while reducing total expert queries by up to 96% vs. DAgger and up to 65% vs. prior AIL methods, with empirical robustness to $α$ and $K$, easing deployment on novel systems with unknown dynamics.