Self-referential feedback in chaotic reservoirs with preserved dynamics: a minimal architecture and the role of feedback type

The idea that an internal model's predictions return to the system and shape what they predict is centralto predictive coding (Rao and Ballard 1999) and was recently developed in the active-inference theory ofconsciousness by Laukkonen, Friston, and Chandaria (2025). Existing implementations of this idea —hierarchical predictive coding networks and world models (Ha and Schmidhuber 2018) — operate inregimes where internal dynamics converge to a stable representation. This work asks a differentquestion: can such feedback be maintained in a chaotic regime, without collapsing the chaos?I propose a minimal architecture, new anima, based on reservoir computing. Two specialized reservoirs(chaos, spectral radius 1.8; memory, spectral radius 1.05) are coupled to a dual-head self-model withasymmetric compression 1000 to 32. The self-model can influence the reservoirs in two ways:parametrically (prediction error modulates noise and leak), and via content (the decoded predictedlatent is fed back into memory as a weak input).On ten random seeds, the content loop raises the cosine similarity between the latent predicted 30steps ago and the current latent (the prediction match metric) from 0.33 in an observation-only modeto 0.66 in the closed-loop mode — a difference of 0.33 (Cohen's d about 2.0, 10/10 seeds positive). TheLyapunov exponent stays positive and stable across modes (0.020 ± 0.002). Systematic ablation showsthat the content loop alone is sufficient (pmatch 0.65), the parametric loop alone is insufficient and infact slightly degrades pmatch (0.30, 9/10 seeds worsen), and adding the parametric loop on top of thecontent loop contributes only +0.02.This yields three results: (1) a minimal architecture where predictive feedback coexists with chaoswithout collapse; (2) prediction match as an operational measure of self-consistency, distinct fromtraining loss; (3) an empirical decomposition of the two feedback types — parametric modulation(similar in spirit to SM-RC, Sakemi et al. 2024) and content-based (similar to predictive coding). Code anddata are open under MIT.