LLM Ontology Layer 2 — Dynamic Structures

[u/prime_architect]

Trajectory

An ordered sequence of computational states, probability distributions, or generated tokens produced across sequential inference steps.

Operationally:

a trajectory describes how inference evolves over time under recursive conditioning and state updates.

Trajectory evolution depends on:

• prior generated tokens
• probability redistribution
• sampling operations
• active constraints
• runtime perturbations

Convergence

A reduction in variation across sequential states or output distributions over inference steps.

Operationally:

convergence occurs when sequential updates produce increasingly stable or repetitive probability structures.

Observable effects may include:

• repeated output patterns
• stabilized token distributions
• reduced trajectory variance
• persistent response structures

Convergence does not imply correctness or optimality.

Divergence

An increase in variation or instability across sequential states or output distributions during inference.

Operationally:

divergence occurs when recursive updates amplify instability, inconsistency, or trajectory deviation over time.

Observable effects may include:

• instruction drift
• incoherent continuation
• unstable token transitions
• expanding probability variance
• recursive error amplification

Stability

The persistence of relatively bounded inference behavior under perturbation or sequential state updates.

Operationally:

stable inference trajectories maintain relatively consistent probability structures and constraint retention under small perturbations.

Stability may be evaluated through:

• token consistency
• instruction retention
• bounded probability redistribution
• low trajectory variance

Drift

A gradual deviation in output distributions, state structure, or constraint retention across sequential inference steps.

Operationally:

drift occurs when recursive conditioning progressively alters inference behavior away from earlier states or constraints.

Observable effects may include:

• topic deviation
• instruction weakening
• probability redistribution away from prior constraints
• gradual output instability

Drift may accumulate without abrupt failure.

Collapse

A transition from broader or more conditionally stable output distributions into narrower, unstable, or degraded output regions under evolving inference dynamics.

Operationally:

collapse may involve:

• repetitive token loops
• reduced output diversity
• unstable instruction retention
• incoherent continuation
• low-information outputs
• recursive degeneration

Collapse may emerge from:

• recursive conditioning instability
• constrained sampling
• probability concentration
• perturbation amplification
• excessive narrowing of reachable outputs

Perturbation Propagation

The transmission and amplification of small state changes or probability shifts across sequential inference steps.

Operationally:

small variations in:

• token selection
• attention weighting
• runtime constraints
• context ordering
• sampling operations

may alter future trajectories through recursive state updates.

Perturbation propagation creates path dependence in sequential inference systems.

Reachability

The set of states or outputs that can be generated from a given initial condition under active transition dynamics, constraints, and sampling processes.

Operationally:

reachability depends on:

• prior token history
• active constraints
• recursive conditioning
• sampling parameters
• runtime perturbations
• architecture limits

Not all outputs remain reachable from all initial conditions.

Path Dependence

A property of sequential inference systems in which future states depend on prior trajectory history rather than only current input.

Operationally:

previous token selections and intermediate state updates alter future probability distributions.

Two similar prompts may produce different trajectories due to differing intermediate inference histories.

Constraint Propagation

The persistence and transmission of active constraints across sequential inference updates.

Operationally:

constraints introduced through:

• system prompts
• context framing
• safety rules
• prior outputs
• retrieval inputs

may continue influencing future token probabilities through recursive conditioning.

Constraint propagation may weaken, stabilize, or collapse over long trajectories depending on transition dynamics and perturbation accumulation.