Cognition as Geometry: Building Minds from Branching Prediction Errors

The brain functions as a fractal of anticipation, perpetually generating predictions across various dimensions —sensory, conceptual, and temporal. Although predictive processing (PP) has emerged as a prominent framework in cognitive science, its structures frequently lack the self-similarity and energy-efficient geometry found in biological systems. This paper presents the Fractal Predictive Processing Network (FPPN): a recursive, self-similar tree of predictive units, where each node is responsible for modeling expectations, calculating errors, and dynamically distributing inference resources through active inference. Structural parameters —depth, branching factor, angular spread —are optimized using Cuckoo Search, aligning computational efficiency with energetic constraints akin to neurovascular fractals. FPPN employs bidirectional hierarchical PP, allowing abstract predictions to flow downward while errors ascend. We illustrate that this configuration inherently supports temporal abstraction, with lower branches sensitive to rapid changes and deeper nodes representing long-term patterns —providing a computational analogy to cortical timescale hierarchies. By integrating active inference, each node assesses expected free energy, activating or suppressing its subtree based on informational value. This results in an adaptive attention mechanism that reduces redundancy and enhances informational flow. Simulations indicate that FPPN not only improves predictive accuracy but also achieves significant energy savings. Beyond the realm of neuroscience, we propose that this architecture serves as a model for developing artificial agents where inference and structure evolve together. By connecting various fields —neuroanatomy, computational neuroscience, AI, psychology, and philosophy of mind —our framework reconceptualizes cognition as a fractal forest of recursive anticipation rather than a linear pipeline. In this conceptualization of thought, prediction transcends mere mechanism to become a shape —a self-similar whisper resonating throughout the levels of the mind. (Friston. ۲۰۱۰, Clark. ۲۰۱۳; Bullmore and Sporns. ۲۰۰۹