Vugar Ismailov's IC-MLP architecture proves universal approximation with direct input links

Researcher Vugar Ismailov has published a formal proof establishing the universal approximation capabilities of a novel neural network architecture called the Input-Connected Multilayer Perceptron (IC-MLP). Unlike standard MLPs where information flows strictly from one layer to the next, the IC-MLP introduces direct affine connections from the raw input vector to every hidden neuron in the network. This creates a more densely connected information pathway, allowing each processing unit to reference the original input data directly, not just a transformed version from the previous layer.

In the 19-page paper (arXiv:2601.14026v2), Ismailov first analyzes the architecture in a univariate setting, providing explicit formulas for network functions across an arbitrary number of hidden layers. The core theoretical contribution is a proven universal approximation theorem: a deep IC-MLP with a nonlinear activation function can approximate any continuous function on a compact subset of ℝⁿ. This extends the famous, foundational universal approximation theorems for standard neural networks to this new, more connected architecture. The work provides a rigorous mathematical justification for exploring these types of models, which could lead to networks that learn certain functions more efficiently or with different internal representations than conventional designs.