We present the Input-Connected Multilayer Perceptron (IC-MLP), a feedforward neural network architecture in which each hidden neuron receives, in addition to the outputs of the preceding layer, a direct affine connection from the raw input. We first study this architecture in the univariate setting and give an explicit and systematic description of IC-MLPs with an arbitrary finite number of hidden layers, including iterated formulas for the network functions. In this setting, we prove a universal approximation theorem showing that deep IC-MLPs can approximate any continuous function on a closed interval of the real line if and only if the activation function is nonlinear. We then extend the analysis to vector-valued inputs and establish a corresponding universal approximation theorem for continuous functions on compact subsets of $\mathbb{R}^n$.

翻译：我们提出输入连接多层感知机（IC-MLP），一种前馈神经网络架构，其中每个隐藏层神经元除了接收前一层的输出外，还直接从原始输入获得仿射连接。我们首先在单变量设置下研究该架构，并给出具有任意有限层隐藏层的IC-MLP的显式且系统化的描述，包括网络函数的迭代公式。在此设置下，我们证明了一个通用逼近定理：当且仅当激活函数是非线性时，深层IC-MLP可以逼近实轴闭区间上的任意连续函数。随后，我们将分析扩展到向量值输入，并建立了关于$\mathbb{R}^n$紧致子集上连续函数的相应通用逼近定理。