Learning to Adapt Without Gradients: Emergence of Mental Representations via Second-Order Learning

Mental representation, characterized by structured internal models that mirror external environments, is fundamental to advanced cognition but remains challenging to investigate empirically. Existing theory suggests that second-order learning mechanisms that adapt first-order learning, i.e., learning about the underlying task or domain, can promote the emergence of environment–cognition isomorphism. In this work, we empirically validate this hypothesis using a hierarchical framework with a Graph Convolutional Network (GCN) as a first-order learner and an MLP-based controller as a second-order learner. The controller dynamically adapts the GCN’s parameters in response to structurally novel environments, enabling fast adaptation without gradient-based optimization. Across synthetic maze tasks and real-world road network graphs, we show that second-order learning improves generalization under distributional shift. Notably, the approach achieves performance comparable to gradient-based meta-learning methods such as MAML, while requiring no test-time gradients or labeled data and performing adaptation in a single forward pass. We further show that effective adaptation is linked to the emergence of structured latent representations that are isomorphic to the environment; when this isomorphism is disrupted, performance degrades significantly. These results provide empirical evidence for the role of structured representations in second-order learning and establish a practical alternative to gradient-based meta-learning for graph-structured environments.