Contextual Self-Modulation (CSM) is a potent regularization mechanism for the Neural Context Flow (NCF) framework which demonstrates powerful meta-learning of physical systems. However, CSM has limitations in its applicability across different modalities and in high-data regimes. In this work, we introduce two extensions: $i$CSM, which expands CSM to infinite-dimensional tasks, and StochasticNCF, which improves scalability. These extensions are demonstrated through comprehensive experimentation on a range of tasks, including dynamical systems with parameter variations, computer vision challenges, and curve fitting problems. $i$CSM embeds the contexts into an infinite-dimensional function space, as opposed to CSM which uses finite-dimensional context vectors. StochasticNCF enables the application of both CSM and $i$CSM to high-data scenarios by providing an unbiased approximation of meta-gradient updates through a sampled set of nearest environments. Additionally, we incorporate higher-order Taylor expansions via Taylor-Mode automatic differentiation, revealing that higher-order approximations do not necessarily enhance generalization. Finally, we demonstrate how CSM can be integrated into other meta-learning frameworks with FlashCAVIA, a computationally efficient extension of the CAVIA meta-learning framework (Zintgraf et al. 2019). FlashCAVIA outperforms its predecessor across various benchmarks and reinforces the utility of bi-level optimization techniques. Together, these contributions establish a robust framework for tackling an expanded spectrum of meta-learning tasks, offering practical insights for out-of-distribution generalization. Our open-sourced library, designed for flexible integration of self-modulation into contextual meta-learning workflows, is available at \url{github.com/ddrous/self-mod}.

翻译：上下文自调制（CSM）是神经上下文流（NCF）框架中一种有效的正则化机制，该框架展现了物理系统强大的元学习能力。然而，CSM在不同模态间的适用性及高数据机制中存在局限性。本研究提出两项扩展：$i$CSM将CSM推广至无限维任务，StochasticNCF则提升了可扩展性。通过涵盖参数变化动力系统、计算机视觉挑战及曲线拟合问题的一系列任务实验，验证了这些扩展的有效性。$i$CSM将上下文嵌入无限维函数空间，而非CSM采用的有限维上下文向量。StochasticNCF通过采样最近邻环境集合提供元梯度更新的无偏近似，使得CSM与$i$CSM能够适用于高数据场景。此外，我们通过泰勒模式自动微分引入高阶泰勒展开，揭示高阶近似未必能提升泛化性能。最后，我们展示了如何通过FlashCAVIA将CSM整合至其他元学习框架——FlashCAVIA是CAVIA元学习框架（Zintgraf等人，2019）的计算高效扩展版本。FlashCAVIA在多项基准测试中超越其前身，并强化了双层优化技术的实用性。这些贡献共同构建了一个应对更广泛元学习任务的鲁棒框架，为分布外泛化提供了实践洞见。我们开源了专为自调制灵活集成至上下文元学习流程设计的代码库，访问地址为\url{github.com/ddrous/self-mod}。