This paper proposes a novel approach to few-shot learning by integrating fast and differentiable solvers, such as ridge regression and logistic regression, into a meta-learning framework. The main idea is to teach deep networks to use standard machine learning tools as part of their internal model, enabling them to quickly adapt to new data. By leveraging the Woodbury identity, the computational cost of matrix operations is significantly reduced, making the method efficient even with a small number of examples. The authors introduce two types of solvers: closed-form and iterative, both of which are based on ridge regression and logistic regression components. Extensive experiments on three benchmarks (Omniglot, CIFAR-100, and miniImageNet) demonstrate that the proposed methods achieve competitive or superior performance compared to state-of-the-art techniques. The paper also discusses the efficiency and adaptability of the proposed methods, showing that they can effectively handle high-dimensional feature spaces and perform per-episode adaptation.This paper proposes a novel approach to few-shot learning by integrating fast and differentiable solvers, such as ridge regression and logistic regression, into a meta-learning framework. The main idea is to teach deep networks to use standard machine learning tools as part of their internal model, enabling them to quickly adapt to new data. By leveraging the Woodbury identity, the computational cost of matrix operations is significantly reduced, making the method efficient even with a small number of examples. The authors introduce two types of solvers: closed-form and iterative, both of which are based on ridge regression and logistic regression components. Extensive experiments on three benchmarks (Omniglot, CIFAR-100, and miniImageNet) demonstrate that the proposed methods achieve competitive or superior performance compared to state-of-the-art techniques. The paper also discusses the efficiency and adaptability of the proposed methods, showing that they can effectively handle high-dimensional feature spaces and perform per-episode adaptation.