Few-Shot Learning via Learning the Representation, Provably (2002.09434v2)

Abstract: This paper studies few-shot learning via representation learning, where one uses $T$ source tasks with $n_1$ data per task to learn a representation in order to reduce the sample complexity of a target task for which there is only $n_2 (\ll n_1)$ data. Specifically, we focus on the setting where there exists a good \emph{common representation} between source and target, and our goal is to understand how much of a sample size reduction is possible. First, we study the setting where this common representation is low-dimensional and provide a fast rate of $O\left(\frac{\mathcal{C}\left(\Phi\right)}{n_1T} + \frac{k}{n_2}\right)$; here, $\Phi$ is the representation function class, $\mathcal{C}\left(\Phi\right)$ is its complexity measure, and $k$ is the dimension of the representation. When specialized to linear representation functions, this rate becomes $O\left(\frac{dk}{n_1T} + \frac{k}{n_2}\right)$ where $d (\gg k)$ is the ambient input dimension, which is a substantial improvement over the rate without using representation learning, i.e. over the rate of $O\left(\frac{d}{n_2}\right)$. This result bypasses the $\Omega(\frac{1}{T})$ barrier under the i.i.d. task assumption, and can capture the desired property that all $n_1T$ samples from source tasks can be \emph{pooled} together for representation learning. Next, we consider the setting where the common representation may be high-dimensional but is capacity-constrained (say in norm); here, we again demonstrate the advantage of representation learning in both high-dimensional linear regression and neural network learning. Our results demonstrate representation learning can fully utilize all $n_1T$ samples from source tasks.

• The paper demonstrates that learning shared representations from multiple source tasks provably reduces the number of samples needed for new target tasks.
• It establishes precise theoretical bounds for both low-dimensional and high-dimensional settings, highlighting norm-based improvements in sample efficiency.
• The work extends these insights to neural networks, providing a foundation for more effective multitask and transfer learning in practical applications.

An Academic Overview of "Few-Shot Learning via Learning the Representation, Provably"

Few-shot learning has gained significant attention in machine learning due to its potential to perform well with minimal data in target tasks. The paper "Few-Shot Learning via Learning the Representation, Provably" introduces promising methods to address this challenge using representation learning. The work focuses on theoretically underpinning the effectiveness of representation learning and demonstrates significant sample complexity reduction in target tasks by leveraging shared representations learned from multiple source tasks.

Key Contributions

The authors provide a thorough theoretical analysis of few-shot learning by focusing on two primary settings: low-dimensional and high-dimensional representation learning. Both settings aim to determine the extent to which learning a common representation from several source tasks can minimize the number of samples required for learning new tasks.

1. Low-Dimensional Representations:
   • The paper shows that if a common low-dimensional representation can be learned effectively from source tasks, the sample complexity for a new task can be significantly reduced from $O(d/n_2)$ to $O((dk/n_1T) + (k/n_2))$, where $d$ is the dimensionality of the input space, $k$ is the dimension of the representation, $n_1$ is the number of samples per source task, $n_2$ is the number of samples for the target task, and $T$ is the number of source tasks.
2. High-Dimensional Representations:
   • For high-dimensional settings, where the representation might be overparametrized, the authors provide a norm-based bound. They demonstrate that representation learning can utilize all $n_1T$ samples from the source tasks, thereby reducing the sample complexity for target tasks proportionally.
3. Generalization to Neural Networks:
   • Extending their analysis to neural networks, the authors analyze two-layer ReLU networks and show that a good representation can mitigate the complexity in new tasks, adhering to similar bounds achieved in the linear settings.

Implications and Results

The implications of these findings are substantial for both theory and practice:

• Theoretical Implications:
  • The results challenge the traditional view constrained by the i.i.d. task assumption, bypassing the $\Omega(1/T)$ barrier. The findings emphasize the importance of task diversity and the structural alignment of tasks in enhancing representation learning.
  • They propose new structural conditions among tasks that can enable more effective few-shot learning.
• Practical Implications:
  • These theoretical guarantees are crucial for the practical design of multitask and transfer learning systems, specifically in scenarios where acquiring vast datasets for new tasks is infeasible.
  • This work suggests robust methodologies for effectively deploying AI models in real-world applications such as personalized medicine, environmental monitoring, and beyond, where data might be scarce or costly.

Future Directions

The paper leaves open several avenues for further research:

• Exploring different types of representation learning methodologies and their impact on few-shot learning paradigms.
• Extending these theoretical insights to more complex, real-world applications that may involve structured data, sequential data, or varied forms of uncertainty.
• Investigating the interactions between representation learning and other advanced machine learning fields such as meta-learning, semi-supervised learning, and self-supervised learning.

In conclusion, this paper provides a foundational framework for understanding and applying representation learning in few-shot settings, promising a fruitful direction for future research and application in artificial intelligence.