The Triple Alignment Test

The Triple Alignment Test

RSA correlation between information-theoretic affect vectors and embedding-predicted affect vectors should exceed the null (the Geometric Alignment hypothesis). What does the experiment actually look like, what are the failure modes, and how do we distinguish them?

Three measurement streams:

1. Structure: Affect vector $\mathbf{a}_i$ from internal dynamics (Part II, Transformer Affect Extraction protocol)
2. Signal: Affect embedding $\mathbf{e}_i$ from VLM translation of emergent communication (see sidebar below)
3. Action: Behavioral action vector $\mathbf{b}_i$ from observable behavior (movement patterns, resource decisions, social interactions)

The Geometric Alignment hypothesis predicts $\rho_{\text{RSA}}(D^{(a)}, D^{(e)}) > \rho_{\text{null}}$. But we can go further. With three streams, we get three pairwise RSA tests: structure–signal, structure–action, signal–action. All three should exceed the null. And the structure–signal alignment should be at least as strong as the structure–action alignment, because the signal encodes the agent’s representation of its situation, not just its motor response.

Failure modes and their diagnostics:

• No alignment anywhere: The framework’s operationalization is wrong, or the environment lacks the relevant forcing functions. Diagnose via forcing function ablation (Priority 3).
• Structure–action alignment without structure–signal: Communication is not carrying affect-relevant content. The agents may be signaling about coordination without encoding experiential state.
• Signal–action alignment without structure: The VLM translation is picking up behavioral cues (what the agent does) rather than structural cues (what the agent is). The translation is contaminated by action observation.
• All pairwise alignments present but weak: The affect dimensions are real but noisy. Increase $N$, improve probes, refine translation protocol.