Affective Predictive Graph Theory

Abstract

This working paper treats affective regulation as a modeling problem, not as a settled claim about consciousness. Predictive processing gives a useful computational vocabulary for perception and action, but it often leaves three practical questions underspecified: how affective expectations propagate, how bodily state changes the impact of those expectations, and how attention to one’s own state can alter subsequent dynamics. Affective predictive graph theory (APGT) is proposed as a formal toy model for those questions. It represents cognitive-affective state as recurrence over a directed weighted graph, modulates effective coupling by latent physiology, and includes a partial self-observation operator for meta-awareness. The manuscript proves four model-level 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 sufficiently rich trajectory — and checks them in simulations on a canonical six-node graph and an ensemble of 120-node small-world graphs (n = 60 seeds). In those simulations, 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 result is best read as a falsifiable scaffold for future empirical work linking physiology, attention, and affect, rather than as evidence that the model captures the full structure of mental life.

Contributions

1. 01

   A compact graph formalism for studying how affective expectations might propagate under changing physiological state.

2. 02

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

3. 03

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

4. 04

   Three falsifiable empirical predictions linking bodily state, attention deployment, and recovery from emotional perturbation.

Empirical results

Meta-awareness effect

In simulation, 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

In the toy model, 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, suggesting a candidate personalized stress-reactivity threshold to test empirically.

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
• metacognitive awareness

Cite

Seddiqi, R. (2026). Affective Predictive Graph Theory: An exploratory computational model of physiology, attention, and affective dynamics. Working paper.