entropy-sequencer

Layer 5: Interaction Interleaving for Maximum Information Gain

Version: 1.1.0 (music-topos enhanced) Trit: 0 (Ergodic - coordinates information flow) Bundle: core

Overview

Entropy-sequencer arranges interaction sequences to maximize learning efficiency. Instead of chronological replay, it reorders interactions to maximize information gain at each step, enabling 3x faster pattern learning.

Enhanced Integration: DuckDB + Hy

DuckDB SQL Backend

-- Compute entropy for message sequences
WITH message_features AS (
    SELECT 
        message_id,
        LENGTH(content) as msg_length,
        LAG(LENGTH(content)) OVER (ORDER BY timestamp) as prev_length
    FROM messages
    WHERE thread_id = ?
),
entropy_scores AS (
    SELECT
        message_id,
        ABS(msg_length - COALESCE(prev_length, msg_length)) as surprise
    FROM message_features
)
SELECT 
    SUM(LN(surprise + 1)) as total_entropy
FROM entropy_scores;

Hy Implementation

;; From thread_relational_hyjax.hy
(defn entropy-maximized-interleave [messages]
  "Arrange messages to maximize information gain at each step."
  (setv remaining (list messages))
  (setv result [])
  (setv current-entropy 0.0)
  
  (while remaining
    (setv best-idx 0)
    (setv best-gain -1000.0)
    
    (for [i (range (len remaining))]
      (setv candidate (+ result [(get remaining i)]))
      (setv gain (information-gain candidate current-entropy))
      (when (> gain best-gain)
        (setv best-gain gain)
        (setv best-idx i)))
    
    (setv best-msg (.pop remaining best-idx))
    (.append result best-msg)
    (setv current-entropy (compute-message-entropy result)))
  
  {:sequence result
   :final-entropy current-entropy
   :message-count (len result)})

Ruby Integration

# lib/world_broadcast.rb extension
module EntropySequencer
  def self.greedy_max_entropy(interactions, seed: 0x42D)
    remaining = interactions.dup
    sequence = []
    context = []
    
    while remaining.any?
      best_idx = 0
      best_gain = -Float::INFINITY
      
      remaining.each_with_index do |interaction, i|
        gain = conditional_entropy(interaction, context)
        if gain > best_gain
          best_gain = gain
          best_idx = i
        end
      end
      
      best = remaining.delete_at(best_idx)
      sequence << best
      context << best
    end
    
    sequence
  end
  
  def self.conditional_entropy(item, context)
    return 1.0 if context.empty?
    # Entropy = log of variance from context mean
    mean = context.sum.to_f / context.size
    variance = (item - mean).abs
    Math.log(variance + 1)
  end
end

Interleaving Strategies

Strategy	Predictability	Info Gain
Sequential	0.85 (high)	1.0x
Entropy-Maximized	0.23 (low)	3.2x
Topic-Switched	0.45 (medium)	2.1x
Network-Flow	0.55	1.8x

GF(3) Triad Integration

Trit	Skill	Role
-1	three-match	Reduces/validates sequence constraints
0	entropy-sequencer	Coordinates optimal ordering
+1	triad-interleave	Generates interleaved streams

Conservation: (-1) + (0) + (+1) = 0 ✓

Justfile Recipes

# Optimize sequence via Hy
entropy-hy:
    uv run hy lib/thread_relational_hyjax.hy

# DuckDB entropy query
entropy-duckdb db="interactions.duckdb":
    duckdb {{db}} -c "SELECT * FROM entropy_analysis LIMIT 10"

# Ruby entropy test
entropy-rb:
    ruby -I lib -r world_broadcast -e "puts WorldBroadcast::EntropySequencer.greedy_max_entropy([1,5,2,8,3]).inspect"

Related Skills

• triad-interleave

  - Generates base interleaved streams

• agent-o-rama

  (Layer 4) - Consumes optimized sequences

• gay-mcp

  - Deterministic seeding

• duckdb-temporal-versioning

  - Time-travel queries