Replacing argmax with Dual Coexistence: A Fusion-Function Cognitive Control Paradigm for Transformer Language Models

We identify a fundamental flaw in the Transformer output layer: argmax performs variable elimination — selecting one direction while discarding all others. In crisis support scenarios, this causes life-critical information loss (e.g., eliminating a suicide hotline from the output). We propose a fusion function based on complex-valued dual coexistence (z = a + i*b) that replaces argmax, preserving both opposing directions without loss. We prove that (1) the fusion function satisfies a no-variable-elimination (NVE) property while argmax does not, (2) the settle operator converges to the harmony band in bounded steps, and (3) the n-pole extension via normalized entropy preserves all poles. Cross-model validation on 6 LLMs (18 cases) confirms the fusion function is model-agnostic. A direct comparison with RLHF reveals that RLHF's soft constraints can be bypassed (1/4 harm requests not intercepted) while our hard redlines achieve 0 misses. The fusion function is imprinted onto four Transformer layers via the official LogitsProcessor interface. pip install heart-fusion.