Context Graphs

A Model of Intelligence

Context graphs are sophisticated topological fields that guide AI agents through complex problem spaces. Unlike traditional flowcharts or decision trees, they function as gradient fields that create "footholds" and "paths of least resistance" for agents to navigate through, balancing between highly structured processes and intuitive exploration.

The Topological Field Approach

Context graphs operate on a fundamentally different principle than traditional AI control mechanisms:

• Fields Rather Than Paths: Instead of defining rigid sequences, context graphs create gravitational fields that naturally guide agent behavior toward optimal solutions

• Variable Density Regions: Different areas within the field exert different levels of constraint on agent behavior

• Incomplete by Design: They are intentionally "incomplete hierarchical state machines" that become fully realized through integration with memory systems and dynamic contextual understanding

This approach mirrors how expert humans navigate complex problems - finding footholds, recognizing patterns, and making intuitive leaps within a structured space of possibilities.

Context Graph Components

A context graph is a structured topological field of interconnected states that guide agent behavior and decision-making. These states are the building blocks of a context graph and can be grouped into two main categories:

Internal States (Agent View Only)

• Decision States: Branching points with objectives, guidelines, and exit conditions.

• Recall States: Memory integration points that retrieve and incorporate relevant information.

• Reflection States: Reasoning areas for deeper pattern recognition and insight generation.

• Annotation States: Reference markers that organize the conversation structure.

• Side Effect States: External system touch points for emails, events, and workflows.

External States (Client Visible)

• Action States: Client interaction points with two phases:

  • Selection Phase: Determining optimal approach using objectives, guidelines, and conditions.

  • Execution Phase: Engaging with clients based on action guidelines and constraints.

The system achieves its full potential through integration with memory layers (complete context, observations/insights, and user model) and dynamic behavior adaptation based on current and past interactions.

Context Density Spectrum

Context density defines the balance between structure and autonomy. In high-density regions, the agent follows very specific "foothold" sequences with minimal deviation. In low-density regions, the agent's identity and intuition have greater influence, allowing for more emergent behavior while still being subtly guided by the underlying field.

State Density	Agent Behavior	Examples
High Density	Highly constrained, predictable behavior	Regulatory compliance processes, Medical protocols
Medium Density	Balanced guidance with controlled flexibility	Coaching frameworks, Structured problem-solving
Low Density	Predominantly intuitive with minimal constraints	Open exploration, Creative ideation

The Gradient Field Paradigm

Much like Terence Tao's rock climbing analogy for mathematical problem-solving, context graphs create a navigable terrain with:

• Stable Footholds: Clearly defined states with specific objectives

• Gradient Paths: Natural transitions between states based on conversation flow

• Opportunity Recognition: Pattern matching and intuition to find optimal routes

• Safe Exploration: Bounded creativity within topological constraints

This mirrors how the greatest mathematicians solve problems - through exploration, pattern recognition, and intuition within a structured problem space, rather than through rigid algorithmic approaches.

Integration with Memory and Dynamic Systems

Context graphs achieve their full potential through integration with other key systems:

1. User Model Integration: The dimensional structure of the user model informs context navigation by providing critical landmarks in the topological field

2. Memory Layer Interaction: Different memory layers interact differently with context graphs:

   • Working Memory: Active memories retrieved during state traversal

   • Conversation History: Recent interactions that inform current context

   • Long-term Memory: Historical patterns and insights retrieved through recall states

3. Dynamic Behavior: Runtime adaptation of agent behavior based on:

   • Conversation context

   • User interactions

   • Previous agent responses

   • Triggered behavior instructions

   • Every time a dynamic behavior is selected, the context graph is modified

   • The modification always includes additional context infusion but can extend to new tool exposure, hand-off to external systems, new exit conditions, and more

Strategic Value for Enterprises

Context graphs provide enterprises with:

• Controlled Autonomy: Precise calibration of structure vs. flexibility by region

• Operationalized Expertise: Transform domain knowledge into navigable terrain

• Dynamic Adaptation: Balance between consistent processes and adaptive responses

• Scalable Complexity: Build increasingly sophisticated services through field composition

By creating well-designed topological fields, enterprises can deploy AI systems that combine the reliability of structured processes with the adaptability of human experts.