用可解释的模糊规则建模，让深度学习既准确又透明。

Representation learning has emerged as a crucial focus in machine and deep learning, involving the extraction of meaningful and useful features and patterns from the input data, thereby enhancing the performance of various downstream tasks such as classification, clustering, and prediction. Current mainstream representation learning methods primarily rely on non-linear data mining techniques such as kernel methods and deep neural networks to extract abstract knowledge from complex datasets. However, most of these methods are black-box, lacking transparency and interpretability in the learning process, which constrains their practical utility. To this end, this paper introduces a novel representation learning method grounded in an interpretable fuzzy rule-based model. Specifically, it is built upon the Takagi-Sugeno-Kang fuzzy system (TSK-FS) to initially map input data to a high-dimensional fuzzy feature space through the antecedent part of the TSK-FS. Subsequently, a novel differentiable optimization method is proposed for the consequence part learning which can preserve the model's interpretability and transparency while further exploring the nonlinear relationships within the data. This optimization method retains the essence of traditional optimization, with certain parts of the process parameterized corresponding differentiable modules constructed, and a deep optimization process implemented. Consequently, this method not only enhances the model's performance but also ensures its interpretability. Moreover, a second-order geometry preservation method is introduced to further improve the robustness of the proposed method. Extensive experiments conducted on various benchmark datasets validate the superiority of the proposed method, highlighting its potential for advancing representation learning methodologies.