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Approximating the Mathematical Structure of Psychodynamics

Bryce-Allen Bagley, Navin Khoshnan

TL;DR

The paper addresses the challenge of quantifying psychodynamics by introducing a diagrammatic, process-theoretic formulation based on a Symmetric Monoidal Category to model cognitive dynamics as interlinked processes. It defines cogits and outputs, internal/external measurement processes, and operator-valued distributions, and formalizes the Wittgenstein–Lion language game as a hierarchical Bayesian entropy-reduction problem with recursive Bayesian updates and optimal experiment design via expected information gain. The key contributions are (i) a rigorously defined psychodynamics process theory with multiparty interactions, (ii) a concrete W-L framework that unifies cognitive states and private-language dynamics under $ ho_t \,\in\, \\mathcal{D}_D$ and $U(D)$-based evolution, and (iii) connections to AI safety through analysis of cognition-targeting attacks, AI alignment, and representation agents (including cognitive dossiers and gogols). This framework offers a mathematically precise, scale-flexible approach to modeling cognition with potential practical impact on clinical psychology, neurotechnology, and AI safety, while outlining future work on inferring OVDs and implementing efficient Bayesian optimization in real data settings.

Abstract

The complexity of human cognition has meant that psychology makes more use of theory and conceptual models than perhaps any other biomedical field. To enable precise quantitative study of the full breadth of phenomena in psychological and psychiatric medicine as well as cognitive aspects of AI safety, there is a need for a mathematical formulation which is both mathematically precise and equally accessible to experts from numerous fields. In this paper we formalize human psychodynamics via the diagrammatic framework of process theory, describe its key properties, and explain the links between a diagrammatic representation and central concepts in analysis of cognitive processes in contexts such as psychotherapy, neurotechnology, AI alignment, AI agent representation of individuals in autonomous negotiations, developing human-like AI systems, and other aspects of AI safety.

Approximating the Mathematical Structure of Psychodynamics

TL;DR

The paper addresses the challenge of quantifying psychodynamics by introducing a diagrammatic, process-theoretic formulation based on a Symmetric Monoidal Category to model cognitive dynamics as interlinked processes. It defines cogits and outputs, internal/external measurement processes, and operator-valued distributions, and formalizes the Wittgenstein–Lion language game as a hierarchical Bayesian entropy-reduction problem with recursive Bayesian updates and optimal experiment design via expected information gain. The key contributions are (i) a rigorously defined psychodynamics process theory with multiparty interactions, (ii) a concrete W-L framework that unifies cognitive states and private-language dynamics under and -based evolution, and (iii) connections to AI safety through analysis of cognition-targeting attacks, AI alignment, and representation agents (including cognitive dossiers and gogols). This framework offers a mathematically precise, scale-flexible approach to modeling cognition with potential practical impact on clinical psychology, neurotechnology, and AI safety, while outlining future work on inferring OVDs and implementing efficient Bayesian optimization in real data settings.

Abstract

The complexity of human cognition has meant that psychology makes more use of theory and conceptual models than perhaps any other biomedical field. To enable precise quantitative study of the full breadth of phenomena in psychological and psychiatric medicine as well as cognitive aspects of AI safety, there is a need for a mathematical formulation which is both mathematically precise and equally accessible to experts from numerous fields. In this paper we formalize human psychodynamics via the diagrammatic framework of process theory, describe its key properties, and explain the links between a diagrammatic representation and central concepts in analysis of cognitive processes in contexts such as psychotherapy, neurotechnology, AI alignment, AI agent representation of individuals in autonomous negotiations, developing human-like AI systems, and other aspects of AI safety.

Paper Structure

This paper contains 20 sections, 17 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Necessary Properties of a Process theory
  4. Constructing a Process Theory Description of Psychodynamics
  5. Multiparty Processes
  6. W-L Language Games
  7. Formulation of W-L Games as Hierarchical Bayesian Inference
  8. Cognitive States and Dynamics
  9. Operator-Valued Distributions
  10. The Hierarchical Bayesian Framework
  11. Recursive Bayesian Update
  12. Optimal Experiment Design for Entropy Reduction
  13. Connections to AI Safety
  14. Analysis of AI-driven Attacks on Cognition
  15. Application to AI Alignment
  16. ...and 5 more sections

Figures (5)

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Theorems & Definitions (3)

  • Definition 1: Cognitive State
  • Definition 2: Public Language Operators
  • Definition 3: Operator-Valued Distribution