Multilayer feedforward networks are universal approximators

Proved the Universal Approximation Theorem: standard multilayer feedforward networks with a single hidden layer and squashing activation can approximate any continuous Borel measurable function on compact subsets of R^n.

Serves as qualified theoretical and empirical reference for task-regression, task-multiclass-classification.

Assumptions

• Mathematical convexity, regularity, and empirical consistency hold across problem configurations

Limitations

• Theoretical bounds and benchmark saturation characteristics vary across model architectures and training scales