Rapidly learning abstract concepts from limited examples is a hallmark of human intelligence. This work investigates whether gradient-based meta-learning can equip neural networks with inductive biases for efficient few-shot acquisition of discrete concepts. We compare meta-learning with meta-SGD against a supervised learning baseline on Boolean tasks generated by a probabilistic context-free grammar (PCFG). By systematically varying concept dimensionality (number of features) and compositionality (depth of grammar recursion), we identify regimes in which meta-learning robustly improves few-shot concept learning. We find improved performance and sample efficiency by training a multilayer perceptron (MLP) across concept spaces increasing in dimensional and compositional complexity. We are able to show that meta-learners are much better able to handle compositional complexity than featural complexity and establish an empirical analysis demonstrating how featural complexity shapes 'concept basins' of the loss landscape, allowing curvature-aware optimization to be more effective than first order methods. We see that we can robustly increase generalization on complex concepts by increasing the number of adaptation steps in meta-SGD, encouraging exploration of rougher loss basins. Overall, this work highlights the intricacies of learning compositional versus featural complexity in high dimensional concept spaces and provides a road to understanding the role of curvature and extended gradient adaptation in meta-concept-learning. \end{abstract}