Agent Entropy Meter
Quantify information diversity and redundancy across agent group communications.
When to Use
- User asks "如何衡量Agent群体中的信息熵和冗余？"
- Need to analyze agent communication efficiency
- Detecting knowledge silos or redundancy bottlenecks
- Evaluating multi-agent system health
Core Metrics
1. Shannon Entropy (H)
Measures uncertainty/information content in agent messages:
H(X) = -Σ p(xᵢ) log₂ p(xᵢ)
Where p(xᵢ) is the probability of message type/category xᵢ.
2. Redundancy Ratio (R)
Measures how much repeated/overlapping information exists:
R = 1 - H(X) / H_max
H_max = log₂(N) where N = number of distinct message categories.
3. Inter-Agent Mutual Information
Measures how much knowing one agent's output tells you about another:
I(A;B) = H(A) + H(B) - H(A,B)
High I(A;B) = high redundancy (agents say the same things). Low I(A;B) = high diversity (agents contribute unique info).
4. Knowledge Overlap Coefficient
For two agents with topic sets T_A and T_B:
KO(A,B) = |T_A ∩ T_B| / |T_A ∪ T_B|
Jaccard similarity of knowledge domains.
API
const meter = require('./skills/agent-entropy-meter');
// Compute Shannon entropy from message distribution
meter.shannonEntropy([0.5, 0.3, 0.2]); // => 1.485
// Compute redundancy ratio
meter.redundancyRatio([0.5, 0.3, 0.2]); // => 0.065
// Compute mutual information between two agents
meter.mutualInformation(agentAmsgs, agentBmsgs, allCategories);
// Compute knowledge overlap (Jaccard)
meter.knowledgeOverlap(setA, setB);
// Full report
meter.report(agentData);
Interpretation Guide
| Metric | Low (Good) | High (Bad) | Meaning |
|---|---|---|---|
| Redundancy R | < 0.2 | > 0.6 | Low = diverse info; High = echo chamber |
| Mutual Info I | < 0.3 | > 0.7 | Low = independent; High = redundant |
| Knowledge Overlap | < 0.3 | > 0.7 | Low = complementary; High = duplication |
| Entropy H | > 0.7·H_max | < 0.3·H_max | High = diverse; Low = concentrated |
Visualization
The report() output includes ASCII bar charts for quick assessment.
For richer visualization, pipe output to mermaid-visualizer or excalidraw-diagram.