Deep learning has become a crucial technology for making breakthroughs in many fields. Nevertheless, it still faces two important challenges in theoretical and applied aspects. The first lies in the shortcomings of gradient descent based learning schemes which are time-consuming and difficult to determine the learning control hyperparameters. Next, the architectural design of the model is usually tricky. In this paper, we propose a semi-adaptive synergetic two-way pseudoinverse learning system, wherein each subsystem encompasses forward learning, backward learning, and feature concatenation modules. The whole system is trained using a non-gradient descent learning algorithm. It simplifies the hyperparameter tuning while improving the training efficiency. The architecture of the subsystems is designed using a data-driven approach that enables automated determination of the depth of the subsystems. We compare our method with the baselines of mainstream non-gradient descent based methods and the results demonstrate the effectiveness of our proposed method. The source code for this paper is available at http://github.com/B-berrypie/Semi-adaptive-Synergetic-Two-way-Pseudoinverse-Learning-System}{http://github.com/B-berrypie/Semi-adaptive-Synergetic-Two-way-Pseudoinverse-Learning-System.
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