## 2 Proposed Method
### Rethinking the Meta-Learning Paradigm  
In the deep learning domain, the standard approach necessitates voluminous datasets to effectively train models with a high predictive accuracy. This stands in stark contrast with the innate human ability to acquire and generalize new concepts from minimal exposure. An illustrative example of this is a child's ability to differentiate between species, such as cats and dogs, after only a handful of observations. Meta-learning, or learning to learn, takes inspiration from this human cognitive trait and aims to emulate it within the realm of machine learning. This paradigm shift towards designing algorithms that require fewer examples to adapt and learn new skills embodies the core principle of meta-learning.  
Meta-learning algorithms aspire to facilitate the acquisition of generalizable knowledge from a limited set of training examples, enabling the model to apply this knowledge to novel tasks. The objective is to construct a computational framework that allows machines to observe the strategies employed by various machine learning algorithms across a diverse set of tasks, assimilate the underlying patterns, and utilize this consolidated experience to solve new, unseen problems. Consider a machine learning classification task defined by a dataset \(D=\{(x_{1},y_{1}),\ldots,(x_{n},y_{n})\}\), where \(x\) denotes the input sample and \(y\) its corresponding label. The goal is to optimize the model parameters \(\theta\), such that the model \(y=f_{\theta}(x)\) minimizes the loss function over the dataset, formulated as follows:  
\[\theta^{*}=\operatorname*{argmin}_{\theta}\mathcal{L}(D;\theta,\omega) \tag{1}\]Here, \(\mathcal{L}\) represents the loss function and \(\omega\) the learning strategy. In meta-learning, this is extended to a series of tasks \(D_{\text{train}}=\{(D^{1}_{\text{train}},D^{1}_{\text{test}}),\ldots,(D^{m}_{ \text{train}},D^{m}_{\text{test}})\}\), classified into training and testing phases, where the model's efficacy is evaluated across these tasks using the expected loss:  
\[\omega^{*}=\min_{\omega}\mathbb{E}_{\tau\sim p(T)}[\mathcal{L}(D;\omega)] \tag{2}\]  
In this equation, \(p(T)\) refers to the distribution over all tasks and \(\omega\) encapsulates the meta-knowledge, which is the knowledge representation that the model aims to generalize across different tasks.  
The meta-learning framework employs a dual-layer learning structure. The meta-level (outer layer) is dedicated to learning a generalized knowledge representation (\(\omega\)), which evolves as it encounters new tasks. The task-level (inner layer) mirrors traditional machine learning models, focusing on updating the model with respect to individual tasks through training and testing. Every task, whether a training or testing instance, utilizes the meta-learner to facilitate a learning process that incorporates both the training data \(D_{\text{train}}\) and the testing data \(D_{\text{test}}\). To differentiate the primary dataset \(D\) used for the overall learning process from the meta-task specific data, we introduce the terms'support set' for the training data and 'query set' for the testing data of the meta-tasks.  
The meta-learner is trained on the support set and evaluated on the query set, with the objective of classifying samples into \(N\) categories. In an \(N\)-way classification, the meta-task is to classify data into \(N\) distinct categories. The term \(K\)-shot refers to the number of examples in the support set for each category, which results in \(N\times K\) samples for training in each meta-task. Because of the random selection process, some overlap between the support and query sets of different tasks is expected, which does not compromise the model's generalization capability due to the intrinsic fast adaptation feature of meta-learning. As long as there are distinctive differences in the training samples of each task, complete independence of tasks is not a prerequisite for effective meta-learning.