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Behaviour Surprisal Analysis
Basé sur la classification professionnelle SOC
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ACSets (Attributed C-Sets): Algebraic databases with Specter-style bidirectional navigation. Category-theoretic formalism for relational databases.
Attributed C-Sets as algebraic databases. Category-theoretic data structures generalizing graphs and dataframes with Gay.jl color integration.
ACSets (Attributed C-Sets): Algebraic databases with Specter-style bidirectional
Bridge active inference theory with robot control using K-Scale's JAX/MuJoCo stack. Use when connecting predictive coding to locomotion policies, mapping KL divergence minimization to RL training, applying mean field approximation to robotics state estimation, or implementing sim2real as inference about future observations.
Implement affective valence as directional derivative of interoceptive energy landscapes for AI alignment. Use when building alignment-aware RL agents, validating GF(3) conservation in reward signals, training Langevin-based policies, or analyzing fold-change detection signals in POMDP environments.
| name | behaviour-surprisal-analysis |
| description | Behaviour Surprisal Analysis |
| version | 1.0.0 |
Status: Production Ready (v3.0 - Cat# Integration) Trit: 0 (ERGODIC - measurement/observation) Principle: S(x) = -log₂(P(x|attention_mode)) Frame: Tri-channel prediction evaluation with AGM belief revision + Cat# bicomodule structure
Behaviour Surprisal Analysis calculates information-theoretic surprise between predictions and observed outcomes using three complementary attention channels mapped to Cat# = Comod(P) structure:
| Channel | Trit | Home | Poly Op | Kan Role | Description |
|---|---|---|---|---|---|
| Direct (α) | −1 | Span | × (product) | Ran_K | Exact artifact matching |
| Diffuse (β) | 0 | Prof | ⊗ (parallel) | Adj | Thematic/structural matching |
| Meta (γ) | +1 | Presheaves | ◁ (substitution) | Lan_K | Capability/infrastructure tracking |
Total Surprisal = α·S_direct + β·S_diffuse + γ·S_meta
where α + β + γ = 1 and typically α=0.3, β=0.5, γ=0.2
This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Concepts: eval, apply, interpreter, environment
behaviour-surprisal-analysis (−) + SDF.Ch5 (−) + [balancer] (−) = 0
Skill Trit: -1 (MINUS - verification)
Evaluation interprets expressions. This skill processes or generates evaluable forms.
The Direct and Meta channels form a Galois adjunction through the Diffuse bridge:
α (abstract)
Direct ─────────────→ Diffuse
↑ │
│ CatSharp │ γ (concretize)
│ Scale │
└──────────────────────┘
Meta
GF(3): (−1) + (0) + (+1) = 0 ✓
Each channel lives in a specific Cat# home:
┌────────────┬─────────────┬──────────┬───────────────┬────────────┐
│ Channel │ Poly Op │ Kan Role │ Structure │ Home │
├────────────┼─────────────┼──────────┼───────────────┼────────────┤
│ Direct │ × (prod) │ Ran_K │ cofree t_p │ Span │
│ Diffuse │ ⊗ (para) │ Adj │ bicomodule │ Prof │
│ Meta │ ◁ (subst) │ Lan_K │ free m_p │ Presheaves │
└────────────┴─────────────┴──────────┴───────────────┴────────────┘
Predictions and observations form bicomodule pairs. Coherence is verified by:
Surprisal values map to pitch classes via the CatSharp scale:
| Trit | Pitch Classes | Chord Type | Hz Range |
|---|---|---|---|
| +1 (PLUS) | {0, 4, 8} | Augmented triad | C-E-G# |
| 0 (ERGODIC) | {3, 6, 9} | Diminished 7th | D#-F#-A-C |
| −1 (MINUS) | {1,2,5,7,10,11} | Fifths cycle | C#,D,F,G,A#,B |
;; Surprisal → Pitch class → Frequency
(defn surprisal->pitch-class [surp]
(mod (Math/round (* (min surp 10.0) 1.2)) 12))
(defn pitch-class->freq [pc]
(* 261.63 (Math/pow 2 (/ pc 12.0)))) ;; C4 = 261.63 Hz
Enable with --sonify flag to hear the surprisal as tones via sox.
Based on Baker 2023:
K * φ = (K − ¬φ) + φ (Levi Identity)
Predictions ranked by entrenchment:
(defn kappa-rank [belief]
(- (Math/log (/ 1 (max 0.01 (:confidence belief))))))
Lower κ = more entrenched = harder to revise.
# Full Cat# analysis with sonification
bb ~/.claude/skills/behaviour-surprisal-analysis/analyse.bb \
--predictions predictions.json \
--observed observed.json \
--alpha 0.3 --beta 0.5 --gamma 0.2 \
--sonify
# With capability tracking
bb analyse.bb \
--predictions predictions.json \
--observed observed.json \
--skills-before skills_t0.txt \
--skills-after skills_t30.txt
# Direct-heavy (Span home focus)
bb analyse.bb --alpha 0.7 --beta 0.2 --gamma 0.1
# Meta-heavy (Presheaves home focus)
bb analyse.bb --alpha 0.1 --beta 0.3 --gamma 0.6 --sonify
{
"predictions": {
"direct": [
{"content": "Ruby MCP SDK for skill markets", "confidence": 0.8},
{"content": "VirtualizationBridge sandbox test", "confidence": 0.7}
],
"diffuse": [
{"theme": "GF(3) conservation", "keywords": ["trit", "lattice", "conservation"]},
{"theme": "skill markets", "keywords": ["confidential", "commitment", "beacon"]}
],
"meta": {
"skills_before": 45,
"mcp_servers_before": 12,
"config_hash": "a3f2c1"
}
},
"observed": {
"threads": [
"Ruby MCP SDK for confidential skill markets",
"GF(3) skill composition and Galois connection verification",
"Derangement operators and GF(3) entropy management"
],
"capability_events": [
{"type": "skill_install", "count": 373, "source": "plurigrid/asi"},
{"type": "mcp_addition", "server": "world_a_aptos"}
]
}
}
╔══════════════════════════════════════════════════════════════════╗
║ BEHAVIOUR SURPRISAL ANALYSIS v3.0 (Cat# + AGM) ║
║ α=0.30 (Span/Ran) β=0.50 (Prof/Adj) γ=0.20 (Presh/Lan) ║
╚══════════════════════════════════════════════════════════════════╝
DIRECT ATTENTION (Home: Span, Kan: Ran_K)
───────────────────────────────────────────────────────────────
Prediction │ Match │ S_dir │ Trit │ PC │ Home
────────────────────────────────┼───────┼───────┼──────┼────┼─────
VirtualizationBridge sandbox │ 34.9% │ 1.52 │ + │ 2 │ Span
...
CAT# COHERENCE
───────────────────────────────────────────────────────────────
Galois adjunction α ⊣ γ: ✓ coherent
Bicomodule compatibility: 85.0% (✓)
CATSHARP SONIFICATION
───────────────────────────────────────────────────────────────
♪ Direct (Ran_K): 293.7 Hz
♪ Diffuse (Adj): 329.6 Hz
♪ Meta (Lan_K): 261.6 Hz
The skill participates in balanced triads:
behaviour-surprisal-analysis (0) ⊗ catsharp-galois (0) ⊗ gay-mcp (-1) + operad-compose (+1) = 0 ✓
# Internal channel triad
Direct (−1) + Diffuse (0) + Meta (+1) = 0 ✓
| Prediction Style | Recommended (α,β,γ) | Cat# Focus |
|---|---|---|
| Specific artifacts | (0.6, 0.3, 0.1) | Span heavy |
| Thematic directions | (0.2, 0.6, 0.2) | Prof heavy |
| Capability exploration | (0.2, 0.3, 0.5) | Presheaves heavy |
| Mixed/balanced | (0.3, 0.5, 0.2) | Bicomodule equilibrium |
(require '[behaviour-surprisal-analysis :as bsa])
;; Full Cat# analysis
(bsa/combined-analysis
predictions observed
0.3 0.5 0.2 ;; α β γ
before-state after-state
capability-events
true) ;; sonify?
;; Galois adjunction verification
(bsa/verify-galois-unit direct-result)
;; Bicomodule coherence check
(bsa/check-bicomodule-coherence direct diffuse meta)
;; Sonify channel
(bsa/sonify-channel results "Direct" 0.3)
The tri-channel Cat# model reflects:
GF(3) conservation IS the naturality condition of Cat# equipment:
For a triad (s₋₁, s₀, s₊₁):
Ran_K(s₋₁) →[bicomodule]→ s₀ →[bicomodule]→ Lan_K(s₊₁)
The commuting square:
G(f) ∘ η_A = η_B ∘ F(f)
Becomes the GF(3) equation:
(−1) + (0) + (+1) ≡ 0 (mod 3)
Skill Name: behaviour-surprisal-analysis Version: 3.0.0 (Cat# Integration) Type: Prediction Evaluation / Information Theory / Belief Revision / Category Theory Trit: 0 (ERGODIC) GF(3): Conserved via Cat# bicomodule structure Dependencies: sox (optional, for sonification) Sources: