Affective Predictive Graph Theory

Abstract

Predictive processing has become the dominant computational framework for understanding the mind, yet three central features of ordinary mental life remain underspecified: the typed affective structure of the relations the brain predicts over, the role of moment-to-moment bodily state in shaping which predictions become consequential, and the mechanism by which metacognitive awareness alters affective dynamics rather than merely reporting on them. We introduce affective predictive graph theory (APGT), a formal dynamical model in which mental states emerge from sigmoidal recurrence over a directed weighted graph whose edges encode affective-predictive expectations, whose effective coupling is parametrically modulated by latent physiology, and which closes a feedback loop with a partial self-observation operator. We prove four results — existence/uniqueness of a low-threat fixed point under contraction; a saddle-node bifurcation as physiological stress crosses a critical value; spectral contraction of the effective coupling matrix by meta-awareness; and identifiability of parameters from a single sufficiently rich trajectory — and confirm each in computational experiments on a canonical six-node graph and an ensemble of 120-node small-world graphs (n = 60 seeds). Meta-awareness reduces late-window threat activation by 0.081 (95% CI [0.027, 0.144], Wilcoxon p < 10⁻¹⁰) and restores recovery from an acute threat pulse in 100% of seeds (versus 0% without awareness within the same window). The results provide a unified, falsifiable, and computationally tractable account of cognitive–affective dynamics that bridges predictive processing, allostasis, and contemplative neuroscience.

Contributions

1. 01

   A formalism lifting predictive processing from symbolic propositions to typed affective graph propagation.

2. 02

   Four theorems: existence/uniqueness of fixed point under contraction; saddle-node bifurcation in physiological stress; spectral contraction of the effective coupling matrix by meta-awareness; identifiability from a single persistently exciting trajectory.

3. 03

   A computational test suite confirming each theorem on a canonical 6-node graph and a 120-node small-world ensemble (n = 60 seeds).

4. 04

   Three pre-registered, falsifiable predictions linking bodily state, attention deployment, and recovery from emotional perturbation.

Empirical results

Meta-awareness effect

Reduces late-window threat-pool activation by 0.081 (95% CI [0.027, 0.144]); Wilcoxon signed-rank p < 10⁻¹⁰ across 60 seeds.

Recovery from acute stress

100% of seeds recover (mean threat < 0.30) with meta-awareness vs. 0% without, within the same 100-step window.

Spectral radius contraction

ρ(W_eff) monotonically non-increasing in awareness intensity κ at every physiological stress level p ∈ [0, 1.4].

Bifurcation in physiology

Median threat fixed-point activation transitions sharply at p* ≈ 0.6. A candidate personalised stress-reactivity threshold.

Falsifiable predictions

• P1. 14-day ecological momentary assessment + wearable physiology should reveal individual-specific bifurcation thresholds p̂*, predicting laboratory emotional reactivity better than baseline negative affect.
• P2. Mindfulness-based interventions should reduce the estimated spectral radius of late-window effective coupling on the threat subgraph, even when self-reported affect changes only modestly.
• P3. Recovery time from an acute laboratory stressor should be shorter, and recovery success rate higher, in trained meditators than matched controls. The effect is mediated by trial-by-trial meta-awareness, not by trait mindfulness.

Keywords

• predictive processing
• affective neuroscience
• allostasis
• metacognition
• mindfulness
• dynamical systems
• computational psychiatry
• graph theory
• consciousness research

Cite

Seddiqi, R. (2026). Affective Predictive Graph Theory: A physiologically modulated and self-observing model of cognitive dynamics. Working paper.

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