Artificial neural networks (ANNs), inspired by the interconnection of real neurons, have achieved unprecedented success in various fields such as computer vision and natural language processing. Recently, a novel mathematical ANN model, known as the dendritic neuron model (DNM), has been proposed to address nonlinear problems by more accurately reflecting the structure of real neurons. However, the single-output design limits its capability to handle multi-output tasks, significantly lowering its applications. In this paper, we propose a novel multi-in and multi-out dendritic neuron model (MODN) to tackle multi-output tasks. Our core idea is to introduce a filtering matrix to the soma layer to adaptively select the desired dendrites to regress each output. Because such a matrix is designed to be learnable, MODN can explore the relationship between each dendrite and output to provide a better solution to downstream tasks. We also model a telodendron layer into MODN to simulate better the real neuron behavior. Importantly, MODN is a more general and unified framework that can be naturally specialized as the DNM by customizing the filtering matrix. To explore the optimization of MODN, we investigate both heuristic and gradient-based optimizers and introduce a 2-step training method for MODN. Extensive experimental results performed on 11 datasets on both binary and multi-class classification tasks demonstrate the effectiveness of MODN, with respect to accuracy, convergence, and generality.

翻译：人工神经网络（ANNs）受真实神经元互联结构的启发，在计算机视觉和自然语言处理等多个领域取得了前所未有的成功。近年来，一种称为树突神经元模型（DNM）的新型数学ANN模型被提出，其通过更精确地反映真实神经元结构来解决非线性问题。然而，单输出设计限制了其处理多输出任务的能力，显著降低了该模型的应用价值。本文提出一种新型多输入多输出树突神经元模型（MODN）以应对多输出任务。核心思想是在胞体层引入过滤矩阵，通过自适应方式选择所需树突来回归每个输出。由于该矩阵被设计为可学习的，MODN能够探索每个树突与输出之间的关系，从而为下游任务提供更优解决方案。我们还在MODN中构建了终树突层以更真实地模拟神经元行为。值得注意的是，MODN是一个更通用的统一框架，通过定制过滤矩阵可自然地特化为DNM。为探究MODN的优化方法，我们研究了启发式优化器和基于梯度的优化器，并提出了适用于MODN的两步训练法。在11个数据集上针对二分类和多分类任务开展的大量实验结果表明，MODN在精度、收敛性和泛化能力方面均展现出显著有效性。