Universal Approximation Theorem for Input-Connected Multilayer Perceptrons
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917358943076352 |
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| author | Ismailov, Vugar |
| author_facet | Ismailov, Vugar |
| contents | 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 $\mathbb{R}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_14026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Approximation Theorem for Input-Connected Multilayer Perceptrons Ismailov, Vugar Machine Learning Neural and Evolutionary Computing Functional Analysis 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 $\mathbb{R}^n$. |
| title | Universal Approximation Theorem for Input-Connected Multilayer Perceptrons |
| topic | Machine Learning Neural and Evolutionary Computing Functional Analysis |
| url | https://arxiv.org/abs/2601.14026 |