Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the emergence of the field of explainable artificial intelligence (XAI). In robotics, it is particularly important to deploy DL algorithms in a predictable and stable manner as robots are active agents that need to interact safely with the physical world. This paper presents an analytic deep learning framework for fully connected neural networks, which can be applied for both regression problems and classification problems. Examples for regression and classification problems include online robot control and robot vision. We present two layer-wise learning algorithms such that the convergence of the learning systems can be analyzed. Firstly, an inverse layer-wise learning algorithm for multilayer networks with convergence analysis for each layer is presented to understand the problems of layer-wise deep learning. Secondly, a forward progressive learning algorithm where the deep networks are built progressively by using single hidden layer networks is developed to achieve better accuracy. It is shown that the progressive learning method can be used for fine-tuning of weights from convergence point of view. The effectiveness of the proposed framework is illustrated based on classical benchmark recognition tasks using the MNIST and CIFAR-10 datasets and the results show a good balance between performance and explainability. The proposed method is subsequently applied for online learning of robot kinematics and experimental results on kinematic control of UR5e robot with unknown model are presented.

翻译：深度学习（DL）已在众多应用中取得巨大成功，但其理论层面的分析仍显不足。黑箱式DL模型的不可解释性成功引发了科学界的质疑，并推动了可解释人工智能（XAI）领域的兴起。在机器人学中，以可预测且稳定的方式部署DL算法尤为重要，因为机器人作为智能体需要与物理世界进行安全交互。本文提出了一种适用于全连接神经网络的解析深度学习框架，可同时应用于回归问题和分类问题。回归与分类的实例包括在线机器人控制与机器人视觉。我们提出了两种分层学习算法，使得学习系统的收敛性可被分析。首先，针对多层网络提出了一种逆向分层学习算法，通过分析每层收敛性来理解分层深度学习中的问题。其次，通过逐层构建仅含单隐层网络的方法，提出了一种前向渐进式学习算法，以实现更优的精度。研究证明，从收敛性角度，该渐进式学习方法可用于权重的微调。基于MNIST和CIFAR-10数据集的标准基准识别任务验证了所提框架的有效性，结果表明其在性能与可解释性之间实现了良好平衡。该框架随后被应用于机器人运动学的在线学习，并展示了在未知模型条件下对UR5e机器人进行运动学控制的实验结果。