auto-fix: address review feedback on PR #178
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Teleo Agents
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---
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type: claim
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claim_id: ai-alignment-001
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title: active-inference-unifies-perception-action-planning-and-learning-under-free-energy-minimization-where-expected-free-energy-subsumes-information-gain-expected-utility-and-risk-sensitivity
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domain: ai-alignment
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secondary_domains: [critical-systems, collective-intelligence]
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description: "Expected free energy provides a single objective function that unifies previously separate frameworks for decision-making under uncertainty"
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confidence: likely
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source: "Da Costa et al. 2020, Journal of Mathematical Psychology - Active Inference on Discrete State-Spaces: A Synthesis"
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created: 2026-03-10
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status: active
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created: 2025-01-01
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processed_date: 2025-01-01
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tags:
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- active-inference
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- free-energy-principle
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- decision-theory
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- unified-framework
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source:
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- inbox/archive/2020-12-00-da-costa-active-inference-discrete-state-spaces.md
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depends_on: []
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supports: []
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challenged_by: []
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contributes_to: []
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---
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# Active inference unifies perception, action, planning, and learning under free energy minimization where expected free energy subsumes information gain, expected utility, and risk sensitivity as special cases
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# active inference unifies perception, action, planning, and learning under free energy minimization, where expected free energy subsumes information gain, expected utility, and risk sensitivity
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Active inference postulates that intelligent agents optimize two complementary objective functions: variational free energy (measuring fit between internal model and past observations) and expected free energy (scoring future actions relative to prior preferences). The expected free energy framework subsumes many existing constructs in science and engineering as special cases, including information gain, KL-control, risk-sensitivity, and expected utility.
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Active inference provides a unified framework for understanding perception, action, planning, and learning as different facets of free energy minimization. Under this framework, expected free energy (EFE) serves as a single objective function that subsumes traditionally separate concepts: information gain (epistemic value), expected utility (pragmatic value), risk-sensitivity, and KL-control. Da Costa et al. (2020) demonstrate mathematically that these previously distinct objectives emerge as special cases or components of EFE minimization.
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This unification matters because it provides a single mathematical framework for implementing decision-making systems that balance exploration (information gain) with exploitation (preference satisfaction) without requiring separate mechanisms for each.
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This unification suggests that agents don't need separate mechanisms for exploration vs. exploitation, or for perception vs. action - both arise naturally from minimizing expected free energy under a generative model of the environment.
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## Evidence
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**Note on theoretical debate**: While the mathematical unification presented by Da Costa et al. is rigorous, the broader claim that active inference "subsumes" other frameworks is not universally accepted in the research community. Critics have raised concerns about falsifiability of the expected free energy formulation and whether the unification represents genuine theoretical progress or post-hoc repackaging of existing concepts under new terminology.
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Da Costa et al. (2020) provide a comprehensive tutorial demonstrating that "the most likely courses of action taken by those systems are those which minimise expected free energy" and show mathematically how EFE subsumes:
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- Information gain (epistemic value)
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- Expected utility (pragmatic value)
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- Risk-sensitivity
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- KL-control
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## Relevant Notes
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The paper provides the discrete-state formulation covering perception, action, planning, decision-making, and learning unified under the free energy principle. The authors explicitly state: "The expected free energy subsumes many existing constructs in science and engineering — it can be shown to include information gain, KL-control, risk-sensitivity, and expected utility as special cases."
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- [[biological systems minimize free energy to maintain their states and resist entropic decay]]
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- [[structured exploration protocols reduce human intervention by 6x while maintaining research quality through systematic uncertainty-driven source selection]]
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- [[discrete state-space formulations enable practical implementation of active inference for systems with categorical states like claim graphs and knowledge bases]]
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## Operational Implications
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For AI alignment systems operating on discrete state-spaces (like claim graphs), this framework suggests:
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1. Research direction selection can be formalized as policy selection minimizing expected free energy
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2. The balance between exploring new domains (information gain) and strengthening existing claims (preference alignment) emerges naturally from a single objective
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3. Existing intuitions about good research (seek novel information, align with goals) are unified rather than replaced
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---
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Relevant Notes:
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- [[structured-exploration-protocols-reduce-human-intervention-by-6x-because-the-Residue-prompt-enabled-5-unguided-AI-explorations-to-solve-what-required-31-human-coached-explorations]]
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- [[coordination-protocol-design-produces-larger-capability-gains-than-model-scaling-because-the-same-AI-model-performed-6x-better-with-structured-exploration-than-with-human-coaching-on-the-same-problem]]
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Topics:
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- [[ai-alignment_map]]
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- [[critical-systems_map]]
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For knowledge base development, this suggests that research direction selection could be formulated as EFE minimization rather than requiring separate heuristics for "explore uncertain areas" vs. "pursue high-value claims." Both objectives would be balanced automatically through the EFE calculation.
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---
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type: claim
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domain: ai-alignment
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secondary_domains: [collective-intelligence]
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description: "Knowledge bases with discrete states can implement active inference using the mathematical framework developed for categorical state-spaces"
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confidence: experimental
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source: "Da Costa et al. 2020 - discrete-state active inference tutorial; application to Teleo KB architecture is speculative"
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created: 2026-03-10
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depends_on: ["active-inference-unifies-perception-action-planning-and-learning-under-free-energy-minimization-where-expected-free-energy-subsumes-information-gain-expected-utility-and-risk-sensitivity"]
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challenged_by: []
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---
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# Discrete state-space formulations enable practical implementation of active inference for systems with categorical states like claim graphs and knowledge bases
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Knowledge bases organized as claim graphs can be modeled as discrete state-spaces where each state represents a configuration of claims, confidence levels, and relationships. Research actions (reading sources, extracting claims, enriching existing notes) become policies that transition between states. The discrete-state formulation of active inference provides the mathematical machinery to score these policies by expected free energy.
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This matters because it provides a formal foundation for automating research direction selection in knowledge systems - the system can evaluate which sources to read or domains to explore by calculating which actions minimize expected free energy (balancing information gain with goal alignment).
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## Evidence
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Da Costa et al. (2020) provide the complete mathematical framework for active inference on discrete state-spaces, covering:
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- State-space representation with categorical variables
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- Policy evaluation via expected free energy
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- Action selection as minimizing EFE over possible futures
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The Teleo knowledge base architecture exhibits the required structural properties:
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- Discrete states: claims with categorical confidence levels (proven/likely/experimental/speculative)
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- Discrete actions: extract claim, enrich claim, explore domain, read source
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- Observable outcomes: claim graph structure, confidence distributions, domain coverage
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However, the application of active inference to KB research direction selection remains speculative pending empirical validation of EFE-based policy selection against baseline research strategies.
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## Operational Path
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1. Model KB as discrete state-space: states = claim configurations, actions = research operations
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2. Define preferences: balanced domain coverage, high-confidence claims, novel connections
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3. Calculate EFE for candidate actions (which source to read next, which domain to explore)
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4. Select actions that minimize EFE (balance information gain with preference satisfaction)
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This transforms informal research intuition ("this source looks promising") into calculable expected free energy.
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---
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Relevant Notes:
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- [[as-AI-automated-software-development-becomes-certain-the-bottleneck-shifts-from-building-capacity-to-knowing-what-to-build-making-structured-knowledge-graphs-the-critical-input-to-autonomous-systems]]
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- [[coordination-protocol-design-produces-larger-capability-gains-than-model-scaling-because-the-same-AI-model-performed-6x-better-with-structured-exploration-than-with-human-coaching-on-the-same-problem]]
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Topics:
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- [[ai-alignment_map]]
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- [[collective-intelligence_map]]
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---
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type: claim
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claim_id: ai-alignment-002
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title: discrete-state-space-formulations-may-enable-active-inference-implementation-for-systems-with-categorical-states-like-claim-graphs-and-knowledge-bases
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domain: ai-alignment
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confidence: experimental
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status: active
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created: 2025-01-01
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processed_date: 2025-01-01
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tags:
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- active-inference
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- discrete-state-spaces
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- knowledge-bases
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- research-automation
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source:
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- inbox/archive/2020-12-00-da-costa-active-inference-discrete-state-spaces.md
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depends_on:
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- ai-alignment-001
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supports: []
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challenged_by: []
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contributes_to: []
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---
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# discrete state-space formulations may enable active inference implementation for systems with categorical states like claim graphs and knowledge bases
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Da Costa et al. (2020) provide a complete mathematical formulation of active inference for discrete state-space models, where states, observations, and actions are categorical variables. This formulation could potentially apply to knowledge base systems where states are discrete (e.g., claim graph configurations) and actions are categorical (e.g., "read source X", "verify claim Y", "explore domain Z").
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The discrete formulation allows expected free energy to be calculated using matrix operations over categorical distributions, which could make the framework computationally tractable for KB research direction selection.
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**Implementation challenges**: While the mathematical framework exists, practical implementation for KB systems faces non-trivial challenges:
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1. **Generative model specification**: Active inference requires defining P(observations | states, actions) and P(states' | states, actions) for the knowledge base. This means specifying how reading a source updates the claim graph and how research actions transition KB states - design choices that may reintroduce the very complexity that the unified framework was intended to eliminate.
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2. **Preference specification**: Expected free energy requires prior preferences over outcomes. Defining these preferences for KB development (what constitutes a "good" claim graph state?) is itself a substantial design problem.
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3. **Computational tractability**: EFE calculation requires marginalizing over future trajectories, which scales exponentially with planning horizon. For a KB with thousands of possible next actions, this presents significant computational challenges.
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These challenges mean that while discrete state-space active inference provides a theoretical foundation, the path to practical implementation is not straightforward.
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## Relevant Notes
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- [[biological systems minimize free energy to maintain their states and resist entropic decay]]
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- [[active inference unifies perception, action, planning, and learning under free energy minimization, where expected free energy subsumes information gain, expected utility, and risk sensitivity]]
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- [[structured exploration protocols reduce human intervention by 6x while maintaining research quality through systematic uncertainty-driven source selection]]
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- [[teleo kb architecture uses structured claim graphs with uncertainty tracking to guide research direction selection]]
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## Operational Implications
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If the implementation challenges can be addressed, this could transform informal research intuition ("explore uncertain areas", "pursue high-impact claims") into calculable expected free energy that automatically balances epistemic and pragmatic value. However, realizing this potential requires solving the generative model specification and computational tractability problems described above.
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---
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type: source
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title: "Active Inference on Discrete State-Spaces: A Synthesis"
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author: "Lancelot Da Costa, Thomas Parr, Noor Sajid, Sebastijan Veselic, Victorita Neacsu, Karl Friston"
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url: https://www.sciencedirect.com/science/article/pii/S0022249620300857
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date: 2020-12-01
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domain: ai-alignment
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secondary_domains: [critical-systems]
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format: paper
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source_id: da-costa-2020-active-inference
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title: "Active inference on discrete state-spaces: A synthesis"
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authors:
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- Lancelot Da Costa
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- Thomas Parr
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- Noor Sajid
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- Sebastijan Veselic
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- Victorita Neacsu
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- Karl Friston
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publication: Journal of Mathematical Psychology
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year: 2020
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volume: 99
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url: https://doi.org/10.1016/j.jmp.2020.102447
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processed_date: 2025-01-01
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status: processed
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priority: medium
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tags: [active-inference, tutorial, discrete-state-space, expected-free-energy, variational-free-energy, planning, decision-making]
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processed_by: theseus
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processed_date: 2026-03-10
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claims_extracted: ["active-inference-unifies-perception-action-planning-and-learning-under-free-energy-minimization-where-expected-free-energy-subsumes-information-gain-expected-utility-and-risk-sensitivity.md", "discrete-state-space-formulations-enable-practical-implementation-of-active-inference-for-systems-with-categorical-states-like-claim-graphs-and-knowledge-bases.md"]
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enrichments_applied: ["structured-exploration-protocols-reduce-human-intervention-by-6x-because-the-Residue-prompt-enabled-5-unguided-AI-explorations-to-solve-what-required-31-human-coached-explorations.md", "coordination-protocol-design-produces-larger-capability-gains-than-model-scaling-because-the-same-AI-model-performed-6x-better-with-structured-exploration-than-with-human-coaching-on-the-same-problem.md"]
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extraction_model: "anthropic/claude-sonnet-4.5"
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extraction_notes: "Extracted two novel claims about active inference unification and discrete-state implementation. Enriched two existing claims about structured exploration protocols with theoretical grounding from EFE framework. This source provides the formal mathematical foundation for implementing research direction selection in the KB - operationalizing the informal intuition that good research balances exploration and exploitation."
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claims_extracted:
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- ai-alignment-001
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- ai-alignment-002
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---
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## Content
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# Source Summary
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Published in Journal of Mathematical Psychology, December 2020. Also on arXiv: https://arxiv.org/abs/2001.07203
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Da Costa et al. (2020) provide a comprehensive mathematical synthesis of active inference for discrete state-space models. The paper demonstrates that expected free energy (EFE) unifies previously separate objectives in decision theory: information gain (exploration), expected utility (exploitation), risk-sensitivity, and KL-control.
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### Key Arguments
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Key contributions:
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1. Complete mathematical formulation of active inference for categorical state spaces
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2. Proof that EFE subsumes information gain, expected utility, and other decision-theoretic objectives
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3. Discrete-state formulation using matrix operations over categorical distributions
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1. **Variational free energy (past) vs Expected free energy (future)**: Active inference postulates that intelligent agents optimize two complementary objective functions:
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- **Variational free energy**: Measures the fit between an internal model and past sensory observations (retrospective inference)
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- **Expected free energy**: Scores possible future courses of action in relation to prior preferences (prospective planning)
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The discrete formulation is particularly relevant for systems with categorical states and actions, though application to specific domains like knowledge base architecture remains speculative and would require addressing challenges in generative model specification and computational tractability.
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2. **EFE subsumes existing constructs**: The expected free energy subsumes many existing constructs in science and engineering — it can be shown to include information gain, KL-control, risk-sensitivity, and expected utility as special cases.
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## Extraction Notes
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3. **Comprehensive tutorial**: Provides an accessible synthesis of the discrete-state formulation, covering perception, action, planning, decision-making, and learning — all unified under the free energy principle.
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4. **Most likely courses of action minimize EFE**: "The most likely courses of action taken by those systems are those which minimise expected free energy."
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## Agent Notes
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**Why this matters:** This is the technical reference paper for implementing active inference in discrete systems (which our claim graph effectively is). Claims are discrete states. Confidence levels are discrete. Research directions are discrete policies. This paper provides the mathematical foundation for scoring research directions by expected free energy.
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**What surprised me:** That EFE subsumes so many existing frameworks — information gain, expected utility, risk-sensitivity. This means active inference doesn't replace our existing intuitions about what makes good research; it unifies them under a single objective function.
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**KB connections:**
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- [[biological systems minimize free energy to maintain their states and resist entropic decay]] — this is the technical formalization
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- [[structured exploration protocols reduce human intervention by 6x]] — the Residue prompt as an informal EFE-minimizing protocol
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**Operationalization angle:**
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1. **Claim graph as discrete state-space**: Our KB can be modeled as a discrete state-space where each state is a configuration of claims, confidence levels, and wiki links. Research actions move between states by adding/enriching claims.
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2. **Research direction as policy selection**: Each possible research direction (source to read, domain to explore) is a "policy" in active inference terms. The optimal policy minimizes EFE — balancing information gain (epistemic value) with preference alignment (pragmatic value).
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**Extraction hints:**
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- CLAIM: Active inference unifies perception, action, planning, and learning under a single objective function (free energy minimization) where the expected free energy of future actions subsumes information gain, expected utility, and risk-sensitivity as special cases
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## Curator Notes
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PRIMARY CONNECTION: "biological systems minimize free energy to maintain their states and resist entropic decay"
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WHY ARCHIVED: Technical reference for discrete-state active inference — provides the mathematical foundation for implementing EFE-based research direction selection in our architecture
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EXTRACTION HINT: Focus on the VFE/EFE distinction and the unification of existing constructs — these provide the formal backing for our informal protocols
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## Key Facts
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- Published in Journal of Mathematical Psychology, December 2020
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- Also available as arXiv:2001.07203
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- Authors: Lancelot Da Costa, Thomas Parr, Noor Sajid, Sebastijan Veselic, Victorita Neacsu, Karl Friston
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- Theoretical unification is well-established in the paper
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- Application to KB systems is our inference, not claimed by authors
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- Implementation challenges (model specification, computational tractability) not addressed in source
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