Computation as Constrained Transport: A Geometric Perspective on Information Processing

Abstract We propose a unifying perspective in which computation is understood as constrained transport of information over a structured state space. In this view, constraints on allowable transitions—arising from logical structure, architectural priors, or biological control mechanisms—induce an effective geometry that governs the efficiency and organization of information flow. We formalize this intuition by linking constrained dynamics to induced metrics over state spaces and distributions, drawing connections to optimal transport and information geometry. We show how this lens captures common structure across contemporary machine learning systems and biological neural networks, and distinguish between systems with fixed geometric priors and those capable of dynamically modulating their geometry. This framework does not replace classical models of computation, but provides a complementary, substrate-level interpretation that links representation, dynamics, and control. Overview This work proposes a geometric interpretation of computation based on constrained transport over structured state spaces. We argue that constraints on admissible transitions induce effective geometries that govern the dynamics of information flow. This formulation is developed using concepts from optimal transport and extended to distributional settings, with connections to information geometry. The framework is applied conceptually across machine learning and biological systems, including latent predictive models, transformer-based architectures, and neural circuits, revealing a common structure linking constraints, geometry, and dynamics. We distinguish between systems with fixed geometric priors and those capable of dynamically modulating their geometry, and outline potential empirical predictions relating constraint modulation to measurable changes in network structure. This perspective is intended as a unifying interpretive framework rather than a replacement for existing computational formalisms. Related Works Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. https://doi.org/10.5281/zenodo.18615180 Pender, M. A. (2026). Formal Constraint and Routing Reorganization: A Constrained-Transport View of Transformer Attention. https://doi.org/10.5281/zenodo.19363506 Pender, M. A. (2026). A Control-Law Extension of the Curvature Adaptation Hypothesis in Hierarchical Transport Networks. https://doi.org/10.5281/zenodo.19270110 Pender, M. A. (2026). Beyond Mean Curvature: Lower-Tail Routing Structure in Controlled Hierarchical Networks. https://doi.org/10.5281/zenodo.19341335 Pender, M. A. (2026). The Manifold Chip: Silicon Architecture for Dynamic Curvature Adaptation via Dual-Gated Analog Shunting. https://doi.org/10.5281/zenodo.18717807 Pender, M. A. (2026). Geometry-Aware Plasticity: Thermodynamic Weight Updates in Non-Euclidean Hardware. https://doi.org/10.5281/zenodo.18761137