Precision-Weighted Belief Updating in Instruction-Tuned Transformers: A Comparative Analysis with Biological Predictive Coding

The free-energy principle and predictive coding frameworks characterise biological cognition as inference under uncertainty, in which belief updating is gated by the precision (inverse variance) of prior expectations: ΔV ∝ Π · ε. We test whether this computational strategy extends to an instruction-tuned transformer language model. Under deterministic inference, a 2×2×2 factorial experiment on Llama 3 8B Instruct (360 trials) initially appears to support a gap-proportional account dominated by a fixed update rate (β ≈ 0.76), with only a small residual precision-modulation effect (interaction p = 0.036). However, we identify a fundamental design-theory mismatch: deterministic inference produces zero output variance, making the precision parameter Π = 1/Var mathematically undefined. When we instead use temperature sampling (T = 0.7, N = 30 samples per trial) to instantiate variance empirically, precision-weighted belief updating emerges with decisive statistical support. The Π × ε interaction coefficient is −0.47 (averaged across two independent replications), p < 10⁻⁶, with ΔBIC = 129 favouring the full precision-weighted model over the pure gap-proportional account. This effect is robust under hostile statistical scrutiny: it survives stratification by prior position on the rating scale, and it remains significant and substantial (coefficient = −0.80, p < 10⁻⁶) after orthogonalising precision against ev_before to remove scale-geometry confounds. The effective update rate ranges from β ≈ 0.96 under low empirical precision to β ≈ 0.28 under high empirical precision, exactly matching the biological prediction that high precision attenuates the influence of new evidence. Mechanistic analysis on Llama 3.2 1B identifies sixteen attention heads with condition-sensitive entropy after length-matched prompt controls, and locates layer 14 as a significant correlate of absolute gap magnitude (ρ = 0.51, p = 0.012). We frame these findings as cross-substrate evidence for the predictive coding framework, with substantial implications for understanding LLM belief revision under conflicting evidence and for the ethical question of how this understanding could be used in adversarial contexts.