Semiconductor circuits and multilayer perceptrons (MLPs) can both perform computations, but they differ greatly in how gate count scales with input dimensionality.

 Semiconductor circuits and multilayer perceptrons (MLPs) can both perform computations, but they differ greatly in how gate count scales with input dimensionality. Semiconductors excel at low-dimensional, simple tasks: a 2-input AND/OR takes only a few gates, an 8-bit adder ~200–300 gates, and a 32-bit adder ~1,000–2,000 gates. However, for arbitrary functions, gate counts grow exponentially with inputs: n=10 may require thousands to tens of thousands of gates, while n=100 implies 2^100 ≈ 10^30 cases—physically impossible. MLPs scale polynomially: a 784-dim input (28×28 pixels) can be handled by a hidden layer of several hundred to 1,000 units (10^5–10^6 parameters). Even 3,000-dim inputs are manageable with a few thousand units, and 10,000-dim inputs can be tackled with tens of thousands of units and tens of millions of parameters. Thus, for n≦32, semiconductors remain superior—fast, efficient, exact. But for n≧100, high-dimensional, nonlinear problems, MLPs are practical, avoiding gate explosion. The true dividing line lies where dimensionality surpasses dozens and gate requirements surge exponentially.