Concept Representations in Vector Space: Quantifying Sharedness and Idiosyncrasy of Meaning

arXiv:2610.15496v1 Announce Type: new Abstract: Concepts are the basic units through which we navigate the world and communicate meaning. But do you and I really mean the same thing when we think or speak about a concept? The present study develops a measurement framework for modeling and analyzing interindividual variation in concept representations through sentence embeddings, dense vector representations mapping entire utterances into a shared geometric space. The framework is developed in a theoretical argument and validated, demonstrated, and subjected to robustness checks in a pre-registered study. Short personal definitions, elicited from $N = 125$ participants, are encoded as sentence embeddings and submitted pairwise to a crossed random effects model yielding two concept-level quantities: sharedness ($S_b$), the expected dissimilarity between two randomly drawn individuals, and idiosyncrasy ($I_b$), the person-specific share of total dyadic variance. Two validity tests support the approach: the embedding space fully recovers concept and domain organization from participant definitions even with the target word excluded, and a parameter-free classifier achieves 0.630 accuracy in a within-participant extensional prediction task against a chance baseline of 0.500 and a consistency ceiling of 0.893. The framework finds theoretically interpretable variation in $S_b$ and establishes $I_b$ as a reliable source of dyadic variance across concepts. Results replicate across three encoders varying in architecture and capacity, providing a reproducible and scalable instrument for the empirical study of meaning variation.