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Similarity analysis is one of the crucial steps in most fMRI studies. Representational Similarity Analysis (RSA) can measure similarities of neural signatures generated by different cognitive states. This paper develops Deep Representational Similarity Learning (DRSL), a deep extension of RSA that is appropriate for analyzing similarities between various cognitive tasks in fMRI datasets with a large number of subjects, and high-dimensionality -- such as whole-brain images. Unlike the previous methods, DRSL is not limited by a linear transformation or a restricted fixed nonlinear kernel function -- such as Gaussian kernel. DRSL utilizes a multi-layer neural network for mapping neural responses to linear space, where this network can implement a customized nonlinear transformation for each subject separately. Furthermore, utilizing a gradient-based optimization in DRSL can significantly reduce runtime of analysis on large datasets because it uses a batch of samples in each iteration rather than all neural responses to find an optimal solution. Empirical studies on multi-subject fMRI datasets with various tasks -- including visual stimuli, decision making, flavor, and working memory -- confirm that the proposed method achieves superior performance to other state-of-the-art RSA algorithms.