| _version_ | 1866901876952268800 |
|---|---|
| author | Pender, Matthew A |
| author_facet | Pender, Matthew A |
| contents | <p><strong>Abstract</strong></p> <p>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.</p> <h3>Overview</h3> <p>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.</p> <p>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.</p> <p>This perspective is intended as a unifying interpretive framework rather than a replacement for existing computational formalisms.</p> <h3> </h3> <h3>Related Works</h3> <ul> <li>Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. <a href="https://doi.org/10.5281/zenodo.18615180">https://doi.org/10.5281/zenodo.18615180</a></li> <li>Pender, M. A. (2026). Formal Constraint and Routing Reorganization: A Constrained-Transport View of Transformer Attention. <a href="https://doi.org/10.5281/zenodo.19363506">https://doi.org/10.5281/zenodo.19363506</a></li> <li>Pender, M. A. (2026). A Control-Law Extension of the Curvature Adaptation Hypothesis in Hierarchical Transport Networks. <a href="https://doi.org/10.5281/zenodo.19270110">https://doi.org/10.5281/zenodo.19270110</a></li> <li>Pender, M. A. (2026). Beyond Mean Curvature: Lower-Tail Routing Structure in Controlled Hierarchical Networks. <a href="https://doi.org/10.5281/zenodo.19341335" target="_blank" rel="noopener">https://doi.org/10.5281/zenodo.19341335</a></li> <li>Pender, M. A. (2026). The Manifold Chip: Silicon Architecture for Dynamic Curvature Adaptation via Dual-Gated Analog Shunting. <a href="https://doi.org/10.5281/zenodo.18717807">https://doi.org/10.5281/zenodo.18717807</a></li> <li>Pender, M. A. (2026). Geometry-Aware Plasticity: Thermodynamic Weight Updates in Non-Euclidean Hardware. <a href="https://doi.org/10.5281/zenodo.18761137">https://doi.org/10.5281/zenodo.18761137</a></li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19410118 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Computation as Constrained Transport: A Geometric Perspective on Information Processing Pender, Matthew A Computation Information Transport Geometry of Computation Constrained Dynamics Network Geometry Optimal Transport Wasserstein Distance Information Geometry Metric Spaces Graph Curvature Deep Learning Transformer Models Attention Mechanisms Representation Learning Latent Space Computational Neuroscience Brain Dynamics Complex Systems Dynamical Systems Information Processing Emergent Behavior Theoretical Framework <p><strong>Abstract</strong></p> <p>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.</p> <h3>Overview</h3> <p>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.</p> <p>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.</p> <p>This perspective is intended as a unifying interpretive framework rather than a replacement for existing computational formalisms.</p> <h3> </h3> <h3>Related Works</h3> <ul> <li>Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. <a href="https://doi.org/10.5281/zenodo.18615180">https://doi.org/10.5281/zenodo.18615180</a></li> <li>Pender, M. A. (2026). Formal Constraint and Routing Reorganization: A Constrained-Transport View of Transformer Attention. <a href="https://doi.org/10.5281/zenodo.19363506">https://doi.org/10.5281/zenodo.19363506</a></li> <li>Pender, M. A. (2026). A Control-Law Extension of the Curvature Adaptation Hypothesis in Hierarchical Transport Networks. <a href="https://doi.org/10.5281/zenodo.19270110">https://doi.org/10.5281/zenodo.19270110</a></li> <li>Pender, M. A. (2026). Beyond Mean Curvature: Lower-Tail Routing Structure in Controlled Hierarchical Networks. <a href="https://doi.org/10.5281/zenodo.19341335" target="_blank" rel="noopener">https://doi.org/10.5281/zenodo.19341335</a></li> <li>Pender, M. A. (2026). The Manifold Chip: Silicon Architecture for Dynamic Curvature Adaptation via Dual-Gated Analog Shunting. <a href="https://doi.org/10.5281/zenodo.18717807">https://doi.org/10.5281/zenodo.18717807</a></li> <li>Pender, M. A. (2026). Geometry-Aware Plasticity: Thermodynamic Weight Updates in Non-Euclidean Hardware. <a href="https://doi.org/10.5281/zenodo.18761137">https://doi.org/10.5281/zenodo.18761137</a></li> </ul> |
| title | Computation as Constrained Transport: A Geometric Perspective on Information Processing |
| topic | Computation Information Transport Geometry of Computation Constrained Dynamics Network Geometry Optimal Transport Wasserstein Distance Information Geometry Metric Spaces Graph Curvature Deep Learning Transformer Models Attention Mechanisms Representation Learning Latent Space Computational Neuroscience Brain Dynamics Complex Systems Dynamical Systems Information Processing Emergent Behavior Theoretical Framework |
| url | https://doi.org/10.5281/zenodo.19410118 |