Threshold-Affine Normal Form

How it works

Comparisons

Highlighted claims

• Threshold-affine normal form uses affine maps and integer-coefficient tests controlled by a threshold function. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• LOOP programs are compiled into finite-dimensional integer states whose updates and control can be expressed using affine assignments and threshold gates. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• Primitive recursive functions, recurrent ReLU computations, and threshold-affine normal forms are equivalent according to Theorem 14. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs
• Threshold-affine normal form is described as the central mediator between LOOP-style recursion and bounded dynamical iteration. — Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs