Just Say No to Single Embeddings: Why Your AI Needs Multiple Perspectives

Note: This is a work in progress document We present empirical evidence that conversations exhibit consistent geometric signatures when projected into different embedding spaces, alongside surprising variability in local feature detection. Analyzing 229 multi-agent AI dialogues from our prior study on social dynamics [Garcia, 2025], we examine whether geometric properties of conversational trajectories remain consistent across 5 fundamentally different embedding models. Our analysis reveals a striking dichotomy: while global geometric patterns (distance matrices, trajectory shapes) show remarkable consistency across both transformer-based and classical embeddings (correlations ranging from 0.521 to 0.957), local phase detection exhibits extreme variability (F1 scores from 0.08 to 0.36, agreement correlations from -0.14 to 0.76). This pattern of high global consistency with low local agreement suggests that different embedding models may capture distinct projections of conversations existing in a higher-dimensional semantic space. Transport-based analysis supports this interpretation, showing threefold increases in cross-paradigm distances compared to within-paradigm distances. These findings establish that while geometric analysis of conversation captures genuine structural properties, the global-local dichotomy implies fundamental limits on fine-grained analysis and raises intriguing questions about the true dimensionality of conversational dynamics.