Contrastive-Difference CKA Reveals Concept-Specific Structural Alignment Across Language Model Architectures

Neural networks are increasingly employed to identify both well-defined and ambiguous concepts, yet output-level metrics reveal little about how those concepts are represented internally. Our study asks if these networks exhibit \textit{conceptual separation}: if examples of the same concept form coherent representations, and whether related concepts lie closer together in the representation space. We examine this conceptual organisation in Convolutional Neural Networks (CNNs) and Large Language Models (LLMs) through geometric and distributional analysis of their internal activations. In CNNs, familiar ImageNet concepts form coherent and semantically ordered representations, while this coherence weakens for unseen concepts and suffers within-class domain shift. In LLMs, clearly distinct domains remain well separated, related subdomains move closer together, and the distinction between ambiguous topics collapses at both the mean and covariance level. These results suggest that conceptual separation can reveal structure that output accuracy alone cannot, and may serve as a useful diagnostic of how robustly a model represents the concepts it is asked to identify. Code and data available on \href{https://github.com/JaeeRoshniCapstoneProject/Are-You-Thinking-What-I-m-Thinking-Examining-Conceptual-Separation-in-Neural-Architectures}{GitHub}.

Language model benchmarking is a difficult task. Outcome reasoning alone does not test the model's conceptualization of language and popular open-source benchmarks are quickly saturated or ingested as training data. It is important to test the model's output, but augmenting these tests by characterizing semantic structure gives more insight to how models relate abstract concepts. However, the high dimensional embedding spaces are not easy to interpret. This work demonstrates how topological methods can be used to rigorously compare these spaces to low dimensional and interpretable baselines like ontologies and curated knowledge graphs. These multi-modal alignment tests make it possible to track model adaptations and test phrase understanding across multiple languages.

Large language models (LLMs) encode rich concept-like information, but represent it implicitly through distributed statistical associations rather than as explicit, structured, compositional concepts. Consequently, concept-level structure is typically \emph{found} rather than \emph{designed}: it is recovered after training through probing or dictionary learning, with no architectural guarantee of stability, compositionality, controllability, or alignment with human conceptual organization. We organize concept-aware interventions along two dimensions: whether concept structure is internally induced or externally grounded, and the stage of the pipeline where it is introduced. This taxonomy reveals three broad patterns: inference-time approaches remain comparatively underexplored, related ideas have developed largely in isolation across pipeline stages, and externally grounded methods span the entire pipeline despite often being described under different terminology. Together, these observations motivate moving beyond recovering concept-like structure from trained models toward designing LLMs with explicit conceptual representations.