Compositional Generalization Requires More Than Disentangled Representations

Composition-the ability to generate myriad variations from finite means-is believed to underlie powerful generalization. However, compositional generalization remains a key challenge for deep learning. A widely held assumption is that learning disentangled (factorized) representations naturally supports this kind of extrapolation. Yet, empirical results are mixed, with many generative models failing to recognize and compose factors to generate out-of-distribution (OOD) samples. In this work, we investigate a controlled 2D Gaussian "bump" generation task, demonstrating that standard generative architectures fail in OOD regions when training with partial data, even when supplied with fully disentangled $(x, y)$ coordinates, re-entangling them through subsequent layers. By examining the model's learned kernels and manifold geometry, we show that this failure reflects a "memorization" strategy for generation through the superposition of training data rather than by combining the true factorized features. We show that models forced-through architectural modifications with regularization or curated training data-to create disentangled representations in the full-dimensional representational (pixel) space can be highly data-efficient and effective at learning to compose in OOD regions. These findings underscore that bottlenecks with factorized/disentangled representations in an abstract representation are insufficient: the model must actively maintain or induce factorization directly in the representational space in order to achieve robust compositional generalization.