Compositional Representation Learning

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the combinatorial space of possible inputs, raising the question of what structure representations must have to support generalization to unseen combinations. We formalize three desiderata for compositional generalization under standard training (divisibility, transferability, stability) and show they impose necessary geometric constraints: representations must decompose linearly into per-concept components, and these components must be orthogonal across concepts. This provides theoretical grounding for the Linear Representation Hypothesis: the linear structure widely observed in neural representations is a necessary consequence of compositional generalization. We further derive dimension bounds linking the number of composable concepts to the embedding geometry. Empirically, we evaluate these predictions across modern vision models (CLIP, SigLIP, DINO) and find that representations exhibit partial linear factorization with low-rank, near-orthogonal per-concept factors, and that the degree of this structure correlates with compositional generalization on unseen combinations. As models continue to scale, these conditions predict the representational geometry they may converge to. Code is available at https://github.com/oshapio/necessary-compositionality.

Zero-Shot Compositional Action Recognition (ZS-CAR) requires recognizing novel verb-object combinations composed of previously observed primitives. In this work, we tackle a key failure mode: models predict verbs via object-driven shortcuts (i.e., relying on the labeled object class) rather than temporal evidence. We argue that sparse compositional supervision and verb-object learning asymmetry can promote object-driven shortcut learning. Our analysis with proposed diagnostic metrics shows that existing methods overfit to training co-occurrence patterns and underuse temporal verb cues, resulting in weak generalization to unseen compositions. To address object-driven shortcuts, we propose Robust COmpositional REpresentations (RCORE) with two components. Co-occurrence Prior Regularization (CPR) adds explicit supervision for unseen compositions and regularizes the model against frequent co-occurrence priors by treating them as hard negatives. Temporal Order Regularization for Composition (TORC) enforces temporal-order sensitivity to learn temporally grounded verb representations. Across Sth-com and EK100-com, RCORE reduces shortcut diagnostics and consequently improves compositional generalization.

Sparse Autoencoders (SAEs) decompose language-model activations into sparse, interpretable features, but standard encoders usually treat the latent dictionary as a flat set of independent coordinates, leaving hierarchy and feature interactions to emerge only implicitly. We propose KronSAE, a design that factorizes the latent space into heads and forms post-latent features as pairwise compositions of lower-dimensional pre-latents using mAND, a differentiable AND-like interaction. This imposes a compositional co-activation prior while remaining compatible with standard SAE objectives and variants such as TopK, Matryoshka, and Switch SAEs. KronSAE matches strong baselines on the EV-FLOPs frontier, improves interpretability of the latents, better captures the underlying correlated feature structure, and reduces encoder computational cost as an additional benefit. Code is available at https://github.com/corl-team/kronsae.

Out-of-distribution (OOD) generalisation through composition requires a system to discover invariant properties from input-output associations and transfer them to novel inputs and unseen tasks. We argue that confirming compositional learning requires more than OOD evaluation alone: one must also verify that the learned features are genuinely compositional and that the system encodes their compositional rules. We demonstrate this through two tasks with clearly defined OOD metrics, generated via composable high-level abstractions, on which three standard architectures (MLP, CNN, Transformer) and an object-centric, slot-based architecture fail to generalise OOD. We pair these tasks with two novel attention-based architectures featuring an interpretable final hidden layer designed to expose whether compositional representations emerge. One architecture carries an engineered inductive bias that enables near-perfect OOD performance on one task. Our results show that even with appropriate biases and near-perfect OOD accuracy, a model can fail to learn the compositional feature structures necessary for systematic generalisation. The interpretable layer reveals that successful OOD performance is driven by task-specific biases rather than the discovery of reusable compositional primitives. These findings indicate that OOD benchmarks alone are insufficient for evaluating compositionality in neural networks.