teleo-codex/inbox/archive/2020-12-00-da-costa-active-inference-discrete-state-spaces.md
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---
type: source
source_id: da-costa-2020-active-inference
title: "Active inference on discrete state-spaces: A synthesis"
authors:
- Lancelot Da Costa
- Thomas Parr
- Noor Sajid
- Sebastijan Veselic
- Victorita Neacsu
- Karl Friston
publication: Journal of Mathematical Psychology
year: 2020
volume: 99
url: https://doi.org/10.1016/j.jmp.2020.102447
processed_date: 2025-01-01
status: processed
claims_extracted:
- ai-alignment-001
- ai-alignment-002
---
# Source Summary
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.
Key contributions:
1. Complete mathematical formulation of active inference for categorical state spaces
2. Proof that EFE subsumes information gain, expected utility, and other decision-theoretic objectives
3. Discrete-state formulation using matrix operations over categorical distributions
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.
## Extraction Notes
- Theoretical unification is well-established in the paper
- Application to KB systems is our inference, not claimed by authors
- Implementation challenges (model specification, computational tractability) not addressed in source