Gradient-based meta-learning algorithms offer promising solutions to the challenge of swift adaptation to new tasks, especially when faced with limited sample data. One pivotal concern in few-shot classification tasks is striking the right balance between interpretability and accuracy within the meta-learning framework. This study introduces a novel methodology titled Fast, Interpretable, and Adaptive meta-Learning based on Logistic Regression (FIAML-LR). Distinctively, FIAML-LR employs logistic regression to craft a meta-network in the inner loop. This design facilitates faster generation of the learning rate and weight attenuation coefficient, enhancing the interpretability of meta-learning for new task adaptation. An adaptable parameter update strategy is also embedded, initializing with a broader hyperparameter adjustment scope and fine-tuning progressively throughout the experiment. Experimental evidence reveals that, when implemented on a 4-CONV architecture, FIAML-LR not only bolsters the model's interpretability but also amplifies its accuracy for few-shot classification tasks. A focused investigation on the diabetic retinopathy dataset demonstrated that FIAML-LR, even with limited data, could boost classification accuracy by a significant 14.28% against the benchmark model. This heightened accuracy could aid medical professionals in more precisely diagnosing diabetic retinopathy.