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:

text

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:

text

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:

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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:

text

KO(A,B) = |T_A ∩ T_B| / |T_A ∪ T_B|

Jaccard similarity of knowledge domains.

API#

js

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#

MetricLow (Good)High (Bad)MeaningRedundancy R< 0.2> 0.6Low = diverse info; High = echo chamberMutual Info I< 0.3> 0.7Low = independent; High = redundantKnowledge Overlap< 0.3> 0.7Low = complementary; High = duplicationEntropy H> 0.7·H_max< 0.3·H_maxHigh = 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.