Two direct mappings (healthcare, agent systems) using the Function Model's two-layer structure-base function f₀ + patch layer g-so we can see exactly how to apply it in each domain. Healthcare: "Guideline engine + patient-specific overrides"
What f₀ is
A stable clinical logic layer:
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evidence-based guidelines (e.g., HTN/DM algorithms)
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drug–drug interaction rules
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risk calculators (ASCVD, CHA₂DS₂-VASc)
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your organization's standing orders / pathways
What g (patches) are
Deterministic overrides learned from real cases, expert review, or patient-specific facts:
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"For this patient, ACE inhibitor caused angioedema → never suggest again."
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"This patient's baseline creatinine trend is stable despite high value → don't auto-flag as AKI unless delta criteria met."
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"This clinic uses pathway v3.2; prior rule v3.1 no longer applies."
Input signature (key idea)
Instead of raw "x," use a context signature:
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(patient_id, problem_id, setting, guideline_version, meds_hash, labs_hash, timeframe)
This keeps patches precise and auditable.
How learning happens (streaming)
Each reviewed decision becomes an event:
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(time, signature, output, clinician_id, reason_code, evidence_link)
Stored as patch. No retraining. Immediate effect.
Why it's valuable
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Eliminates "drift" from silent model updates
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Supports "never forget this contraindication" memory
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Creates an auditable trail for QA, medico-legal review, and safety governance FunctionModel_Simple
Agent systems: "Policy/skills + exact state-action corrections"
What f₀ is
The agent's general policy stack:
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planner (task decomposition)
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tool-use policy (when to call a tool)
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general heuristics (prioritization, safety checks)
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base model prompting / templates
What g (patches) are
Hard corrections to stop repeated failure modes:
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"When user asks X, do NOT do Y; do Z."
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"If tool call fails with error E, use fallback F."
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"If this customer environment has limitation L, skip action A."
Input signature
Use a compact, hashed state representation:
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(agent_goal, tool_context, user_intent, environment_flags, failure_code)
Optionally add a "customer_id / deployment_id" to prevent cross-tenant leakage.
Learning events
Sent: 12/25/2025 3:27:00 PM
From: John Harby
Subject: Function Models - a new approach
The function model family includes models of most any type: neural nets, DNNs, transforms, etc. These models learn by modification of the function(s) in the model rather than parametric.
The result is considerable savings in energy usage, one-shot streaming learning is a natural capability, cost is very low for these models and transparency/audit capabilities increase. Rollbacks are created and logged for any learning so learning can be reversed if needed. Many of these models using Kafka is a great option.
See:
https://zenodo.org/uploads/18056053
Two documents - one an overview the other is detailed with mathematical justification
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John Harby
CEO
Autonomic AI, LLC
Temecula CA
9513835000
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