Towards a universal language of concepts: A survey

How humans grow and maintain abstract knowledge from the sparse, streaming noisy data of experience is a longstanding challenge in cognitive science. Any computational account must satisfy at least three desiderata: It must be (1) data-efficient and compute-efficient, (2) capture gradations of uncertainty to support intelligent inquiry and information gathering, and (3) be flexible enough to mentally represent the endless range of concepts people can learn and think about. Here we introduce a computational model that captures these three properties, by encoding symbolic knowledge as mental programs that combine natural language with source code, and sequentially inferring mental programs using LLM-guided Bayesian learning algorithms. Across a range of behavioral studies this model successfully reproduces quantitative signatures of human inductive learning and active inquiry, such as anchoring, garden-pathing, and other effects. In contrast, pure LLMs and classic Bayesian models either fail at the underlying task, or do not reproduce human behavior, or succeed only at exorbitant computational cost. These results suggest that one way humans continually grow their knowledge is by mentally representing many hypotheses spanning language-like and program-like representations, then revising those hypotheses to approximate Bayesian updates, while a bottom-up neural mechanism (an LLM) makes inference both tractable and learnable.

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.

Techniques for concept extraction, such as sparse autoencoders and transcoders, aim to extract high-level symbolic concepts from low-level nonsymbolic representations. When these extracted concepts are used for downstream tasks such as model steering and unlearning, it is essential to understand their guarantees, or lack thereof. In this work, we present a unified theoretical framework for unsupervised concept extraction, in which we frame the task of concept extraction as identifying a generative model. We present a general meta-theorem for identifiability, which reduces the problem of establishing identifiability guarantees to the problem of characterizing the intersection of two sets. As we demonstrate on a range of widely-used approaches, this meta-theorem substantially simplifies the task of proving such guarantees, thus paving the way for the development of new, principled approaches for concept extraction.