DIFFCZSL: Compositional Zero-Shot Learning Regularized by Diffusion Representations

Compositional Zero-Shot Learning (CZSL) aims to recognize unseen attribute-object compositions by leveraging knowledge of primitive concepts learned from seen compositions. Although recent works achieve impressive performance in CZSL by leveraging large vision-language models, they primarily rely on discriminative representations that may not explicitly preserve the structured relationships between primitive concepts and their compositions. Motivated by the recent success of diffusion-based classifiers and their competitive performance relative to discriminative models, we investigate whether intermediate diffusion representations can provide complementary cues for CZSL. To this end, we propose DIFFCZSL, a diffusion-augmented framework that injects generative priors from pre-trained diffusion models into CLIP-based CZSL pipelines. We extract intermediate diffusion representations and project them into the CLIP embedding space to provide auxiliary supervision on both image and text modalities. Through contrastive alignment between CLIP embeddings and diffusion features during training, our method encourages the embedding geometry toward richer composition-aware semantics, while introducing no additional cost at inference time. Extensive experiments on three public CZSL benchmarks demonstrate consistent improvements over strong CLIP-based baselines under both closed-world and open-world settings. Our results highlight the complementary strengths of generative diffusion representations and discriminative vision-language models for compositional generalization.

A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel

A persistent empirical observation is that trained neural networks outperform their neural tangent kernel (NTK) limit on tasks with compositional structure, yet a quantitative account of $\textbf{when}$ and $\textbf{by how much}$ has been lacking. Working on the unit circle, we give such an account through a dichotomy between two complexity measures of the target: its $\textbf{Fourier complexity}$, which controls NTK kernel regression, and its $\textbf{architectural complexity}$, which controls learning over depth-$L$, width-$w$ ReLU networks with the variation norm of the weights bounded by $R$. We first characterize the minimax rate of the architecture class $\mathcal{C}_{L,w,R}$, pinning it down up to a single factor of $L$: between $Ω(Lw^2R^2/n)$ and $\tilde{O}(L^2w^2R^2/n)$. We then show the NTK estimator sits $\textbf{exponentially}$ above this floor whenever the two complexities decouple: for the depth-$L$ iterated sawtooth, NTK regression needs $Ω(4^L)$ samples while the minimax floor is polynomial in $L$. Numerical experiments confirm the theoretical claims: on bandlimited smooth targets, the NTK is competitive or better, while on the hypercube sparse-parity model, a standard two-layer network beats the NTK by four to six orders of magnitude in test error. The gap is thus a function-space property, a mismatch between the kernel's smoothness bias and the target's compositional structure, rather than a generic kernel-versus-network phenomenon.

Dimensionality Controls When Modularity Helps in Continual Learning

Compositional learning systems must balance plasticity, the ability to acquire new knowledge, with stability, the preservation of previously learned components, especially when tasks share structure and risk interference. We study how modular architecture, task similarity, and representational dimensionality jointly shape compositional continual learning in a sequential A-B-A paradigm, comparing a task-partitioned recurrent network to a single-network baseline while inducing high- and low-dimensional regimes via weight-scale manipulations. In a high-dimensional "lazy" regime, both architectures achieve similar performance and internal geometry, suggesting that explicit modular structure has little impact when representations are weakly constrained. In a lower-dimensional "rich" regime, modularity becomes decisive: the modular network develops graded task-specific subspaces that overlap for similar tasks, partially align for moderately dissimilar tasks, and separate for dissimilar tasks, yielding a more compositional and interpretable organization than the single network. These findings identify the representational regime induced by initialization scale, which co-varies with representational dimensionality, as a key factor governing when compositional, modular structure is functionally beneficial in continual learning, and support viewing safety and robustness as problems of adaptive allocation of representational subspaces rather than fixed separation versus sharing.