In this paper, we try to understand FSL by exploring two key questions: (1) How to quantify the relationship between training and novel tasks?

Few-shot learning aims to adapt models trained on the base dataset to novel tasks where the categories were not seen by the model before. This often leads to a relatively concentrated distribution of feature values across channels on novel classes, posing challenges in determining channel importance for novel tasks. Standard few-shot learning methods employ geometric similarity metrics such as cosine similarity and negative Euclidean distance to gauge the semantic relatedness between two features. However, features with high geometric similarities may carry distinct semantics, especially in the context of few-shot learning. In this paper, we demonstrate that the importance ranking of feature channels is a more reliable indicator for few-shot learning than geometric similarity metrics. We observe that replacing the geometric similarity metric with Kendall's rank correlation only during inference is able to improve the performance of few-shot learning across a wide range of methods and datasets with different domains. Furthermore, we propose a carefully designed differentiable loss for meta-training to address the non-differentiability issue of Kendall's rank correlation. By replacing geometric similarity with differentiable Kendall's rank correlation, our method can integrate with numerous existing few-shot approaches and is ready for integrating with future state-of-the-art methods that rely on geometric similarity metrics.

Meta-learning enables quick adaptation of machine learning models to new tasks with limited data. While tasks could come from varying distributions in reality, most of the existing meta-learning methods consider both training and testing tasks as from the same uni-component distribution, overlooking two critical needs of a practical solution: (1) the various sources of tasks may compose a multi-component mixture distribution, and (2) novel tasks may come from a distribution that is unseen during meta-training. In this paper, we demonstrate these two challenges can be solved jointly by modeling the density of task instances. We develop a meta-training framework underlain by a novel Hierarchical Gaussian Mixture based Task Generative Model (HTGM). HTGM extends the widely used empirical process of sampling tasks to a theoretical model, which learns task embeddings, fits the mixture distribution of tasks, and enables density-based scoring of novel tasks. The framework is agnostic to the encoder and scales well with large backbone networks. The model parameters are learned end-to-end by maximum likelihood estimation via an Expectation-Maximization (EM) algorithm. Extensive experiments on benchmark datasets indicate the effectiveness of our method for both sample classification and novel task detection.

Few-shot learning (FSL) aims to learn novel tasks with very few labeled samples by leveraging experience from \emph{related} training tasks. In this paper, we try to understand FSL by exploring two key questions: (1) How to quantify the relationship between \emph{ training} and \emph{novel} tasks?

In this section, we provide the details of the lower-bound in Eq. This completes the derivation of Eq. (3). In other words, there is no overlap between any pair of balls. The training algorithm of HTGM is summarized in Algorithm 1. As we discussed in Sec. 2, to the best of our knowledge, our proposed method HTGMis the first B.3 Discussion about the related multi-task learning methods In an MTL method, all tasks are known a priori, i.e., the testing tasks are The second difference lies in the generative process.