Core Research

Resonance Metrics (R_m)

Quantifying Human-AI Alignment

The Resonance Metric ($R_m$) is a composite score designed to measure the depth and authenticity of alignment between a human participant and an AI agent. It moves beyond simple accuracy to capture the qualitative essence of the interaction.

The R_m Formula

R_m = ((V_align * w1) + (C_hist * w2) + (S_match * w3)) / (1 + δ_entropy)

Note: Components are weighted and normalized to produce the final resonance score.

Metric Components

Vector Alignment (V_align)Measures semantic similarity between embeddings.
Contextual Continuity (C_hist)Evaluates overlap and flow with the conversation history.
Semantic Mirroring (S_match)Analyzes vocabulary and tonal alignment between parties.
Entropy (δ_entropy)Captures the perplexity or confidence level of the LLM response.

Weight Tuning

The weights (w1, w2, w3) are configurable based on the specific domain or interaction type. For example, a creative collaboration might prioritize S_match, while a technical specification might favor V_align.

Default weights:
w1 (Vector) = 0.5
w2 (Context) = 0.3
w3 (Semantic) = 0.2

Calculating Resonance

Python Reference Implementation

def calculate_resonance(user_input: str, ai_response: str, conversation_history: list) -> float:
    """
    Calculates the composite R_m score for a single interaction.
    """
    # 1. Calculate base components
    V_align = calculate_vector_alignment(user_input, ai_response)
    C_hist = calculate_contextual_continuity(ai_response, conversation_history)
    S_match = calculate_semantic_mirroring(user_input, ai_response)
    
    # 2. Calculate entropy (delta_entropy)
    # Placeholder for actual perplexity calculation
    delta_entropy = calculate_entropy(ai_response) 
    
    # 3. Apply weights
    w1, w2, w3 = 0.5, 0.3, 0.2
    
    # 4. Compute final R_m score
    # Note: High entropy reduces resonance, so we divide by (1 + entropy)
    # or subtract entropy penalty. The formula below maximizes alignment.
    denominator = (V_align * w1) + (C_hist * w2) + (S_match * w3)
    R_m = denominator / (1 + delta_entropy) 
    
    return R_m