This paper demonstrates interesting new phenomena that suggest that our understanding of the relationship between the number ofdata points, the number ofparameters, and the generalization errorisincomplete,evenforsimplelinearmodels.

The limited availability of annotated data presents a major challenge for applying deep learning methods to medical image analysis. Few-shot learning methods aim to recognize new classes from only a small number of labeled examples. These methods are typically studied under the standard few-shot learning setting, where all classes in a task are new. However, medical applications such as pathology classification from chest X-rays often require learning new classes while simultaneously leveraging knowledge of previously known ones, a scenario more closely aligned with generalized few-shot classification. Despite its practical relevance, few-shot learning has been scarcely studied in this context. In this work, we present MetaChest, a large-scale dataset of 479,215 chest X-rays collected from four public databases. MetaChest includes a meta-set partition specifically designed for standard few-shot classification, as well as an algorithm for generating multi-label episodes. We conduct extensive experiments evaluating both a standard transfer learning approach and an extension of ProtoNet across a wide range of few-shot multi-label classification tasks. Our results demonstrate that increasing the number of classes per episode and the number of training examples per class improves classification performance. Notably, the transfer learning approach consistently outperforms the ProtoNet extension, despite not being tailored for few-shot learning. We also show that higher-resolution images improve accuracy at the cost of additional computation, while efficient model architectures achieve comparable performance to larger models with significantly reduced resource requirements.

Few-shot node classification on hypergraphs requires models that generalize from scarce labels while capturing high-order structures. Existing hypergraph neural networks (HNNs) effectively encode such structures but often suffer from overfitting and scalability issues due to complex, black-box architectures. In this work, we propose ZEN (Zero-Parameter Hypergraph Neural Network), a fully linear and parameter-free model that achieves both expressiveness and efficiency. Built upon a unified formulation of linearized HNNs, ZEN introduces a tractable closed-form solution for the weight matrix and a redundancy-aware propagation scheme to avoid iterative training and to eliminate redundant self information. On 11 real-world hypergraph benchmarks, ZEN consistently outperforms eight baseline models in classification accuracy while achieving up to 696x speedups over the fastest competitor. Moreover, the decision process of ZEN is fully interpretable, providing insights into the characteristic of a dataset. Our code and datasets are fully available at https://github.com/chaewoonbae/ZEN.

One of the central questions in statistical learning theory is to determine the conditions under which agents can learn from experience. This includes the necessary and sufficient conditions for generalization from a given finite training set to new observations. In this paper, we prove that algorithmic stability in the inference process is equivalent to uniform generalization across all parametric loss functions. We provide various interpretations of this result. For instance, a relationship is proved between stability and data processing, which reveals that algorithmic stability can be improved by post-processing the inferred hypothesis or by augmenting training examples with artificial noise prior to learning. In addition, we establish a relationship between algorithmic stability and the size of the observation space, which provides a formal justification for dimensionality reduction methods. Finally, we connect algorithmic stability to the size of the hypothesis space, which recovers the classical P AC result that the size (complexity) of the hypothesis space should be controlled in order to improve algorithmic stability and improve generalization.

An adaptive bandwidth selection procedure for the mixture kernel in the maximum mean discrepancy (MMD) for fitting generative moment matching networks (GMMNs) is introduced, and its ability to improve the learning of copula random number generators is demonstrated. Based on the relative error of the training loss, the number of kernels is increased during training; additionally, the relative error of the validation loss is used as an early stopping criterion. While training time of such adaptively trained GMMNs (AGMMNs) is similar to that of GMMNs, training performance is increased significantly in comparison to GMMNs, which is assessed and shown based on validation MMD trajectories, samples and validation MMD values. Superiority of AGMMNs over GMMNs, as well as typical parametric copula models, is demonstrated in terms of three applications. First, convergence rates of quasi-random versus pseudo-random samples from high-dimensional copulas are investigated for three functionals of interest and in dimensions as large as 100 for the first time. Second, replicated validation MMDs, as well as Monte Carlo and quasi-Monte Carlo applications based on the expected payoff of a basked call option and the risk measure expected shortfall as functionals are used to demonstrate the improved training of AGMMNs over GMMNs for a copula model fitted to the standardized residuals of the 50 constituents of the S&P 500 index after deGARCHing. Last, both the latter dataset and 50 constituents of the FTSE~100 are used to demonstrate that the improved training of AGMMNs over GMMNs and in comparison to the fitting of classical parametric copula models indeed also translates to an improved model prediction.

Transformation invariances are present in many real-world problems.