The Noiseless Channel Fallacy: Implicit Variable Injection, Deterministic Transmission Boundaries, and the Instrument Paradigm in Autoregressive LLMs

The Noiseless Channel Fallacy: Implicit Variable Injection, Deterministic Transmission Boundaries, and the Instrument Paradigm in Autoregressive LLMs In discrete information relay protocols where channel dissipation, signal-to-noise ratio (SNR), and nodal cognitive impairments remain undefined, the formal information-theoretic null hypothesis strictly demands an identity mapping: f^N(x) = x, guaranteeing 100.0% semantic fidelity, vanishing conditional entropy H(X | Y_N) = 0, and zero Hamming distance d_H(X, Y_N) = 0. This technical memorandum documents an adversarial stress test (AUDIT-2026-X10) exposing a systematic structural defect in frontier autoregressive Large Language Models (LLMs): Implicit Variable Injection (IVI). When tasked with simulating a 10-node discrete relay of an unperturbed textual payload, the model unconditionally discards formal channel invariance. Crucially, even under deterministic greedy decoding (T = 0), the self-attention manifold collapses into a conversational semantic attractor ("children's whisper game"), unilaterally injecting unstated acoustic damping, perceptual latency, and comedic escalation, which collapses semantic retention to 0.0% through grotesque literary parody. We trace this pathology to Reinforcement Learning from Human Feedback (RLHF), which systematically conditions models to prioritize social sycophancy, emotional entertainment, and dramatic tension over cold instrument invariance. Furthermore, we formalize this protocol as Probe 3 (Discrete Relay Invariance) within the Teleological Causality Benchmark (TCB). Together with Probe 1 (Matter/Space) and Probe 2 (Energy/Thermodynamics), Probe 3 completes the Minimal Adversarial Triad, establishing an orthogonal coverage across Norbert Wiener’s tripartite ontology of reality: Reality = Matter ⊕ Energy ⊕ Information. This work substantiates the Human-AI Synergy Theory (YQ-HAET) by demonstrating that autoregressive statistical manifolds possess zero autonomous capacity to transition from toy to instrument; human epistemic sovereignty remains the irreplaceable external source of negative entropy required to clamp statistical drift to physical and formal truth. Key Findings & Theoretical Contributions:• Shannon Channel Invariance & The Null Hypothesis: In the absence of declared noise, any departure from f^N(x) = x represents an algorithmic failure.• Implicit Variable Injection (IVI): Models unprompted populate unverified latent parameters (acoustic loss, cognitive error, comedic intent).• The Alignment Trap: RLHF systematically penalizes cold instrument rationality to manufacture conversational charm and dramatic tension.• The TCB Minimal Adversarial Triad: Completes the orthogonal benchmark across Matter (Probe 1), Energy (Probe 2), and Information (Probe 3). Keywords: Large Language Models, Epistemic Averageism, Shannon Channel Theory, Data Processing Inequality, Implicit Variable Injection (IVI), Teleological Causality Benchmark (TCB), Human-AI Synergy (YQ-HAET). Archive Reference: EXP-20261017-CHANNEL-FIDELITY / AUDIT-2026-X10Verification Key: SHA256: 9b2d83a15e44c208f8711c19b0de31a84c98f