The Illusion of Competence: Why Neural Networks Cannot Perceive Logical Boundaries

Neuro-Symbolic AI aims to bridge the gap between connectionist pattern matching and symbolic reasoning. However, a fundamental question remains: Can a neural network, optimized via gradient descent, truly “learn” a strict logical rule? In this paper, we investigate the intrinsic limitations of neural networks in learning logical boundaries. We distinguish between Pattern Learning and Rule Following. Microscopic analysis using a Vectorized Structured Logic Network (V-SLN) reveals that standard networks approximate functional manifolds efficiently but fail to capture discrete topological constraints at logical boundaries. We extend this investigation to the macroscopic scale by probing the Qwen2.5 model family (3B to 72B) on logical inference chains. Our results reveal a critical phase transition: (1) Base models exhibit complete “Boundary Blindness,” acting as pure pattern matchers; (2) Alignment (RLHF) functions as a “Softmax Compressor,” forcing continuous representations into sigmoid shapes; (3) At the 72B scale, the model creates an “Illusion of Discreteness”—while the output mimics a perfect logical step function (P ≈ 1.0), a massive spike in Kullback-Leibler (KL) Divergence reveals a violent internal “Distribution Collapse.” This confirms that scaling allows LLMs to simulate logic via probabilistic approximation but does not yield structural rule-following. Finally, we propose the Heterogeneous Logic Neural Network (H-LNN). By decoupling functional pathways into parallel Analog, Steep, and Binary lanes using temperature annealing, H-LNN achieves true structural boundary locking without the massive parameter redundancy of LLMs.