Learning Abstract Disentangled Factors from Entangled Conjunctive Codes through Compositional Tasks

Abstract, or disentangled, representations in neural networks encode latent factors in separate subspaces and can support compositional generalization. Yet latent factors are often observed only through entangled combinations, posing a challenge for networks to disentangle them. Here we study compositional tasks whose inputs and outputs consist of conjunctions of discrete latent factors (e.g., shape $\times$ color). Each combination of factor values in a conjunction (e.g., *square* $\times$ *blue*) receives a distinct one-hot code. We find that even when a latent factor $X$ is always entangled with other factors in the input and the output, it can become abstract in task-trained networks through **rebinding**. Rebinding occurs when $X$ is *bound* to (i.e. encoded in a conjunction with) one factor in the input and a different factor in the output. We illustrate this mechanism in a rule transfer task inspired by Raven's Progressive Matrices, for which we analytically derive the optimal hidden representation of single-hidden-layer ReLU networks. The solution uses subpopulations of mixed-selective neurons that each supports abstraction for a subset of factor values. We then derive the optimal linear network representation for arbitrary tasks in the family. The theory formalizes the rebinding principle and predicts that abstraction increases when a factor is reused across many distinct conjunctions. The predicted degree of abstraction qualitatively matches that observed in nonlinear networks and closely tracks their generalization performance to held-out contexts in a transfer task. Together, these results show how compositional task structure can drive networks to learn abstract representations from entangled observations.