Vision-Language Models (VLMs) learn a shared feature space for text and images, enabling the comparison of inputs of different modalities. While prior works demonstrated that VLMs organize natural language representations into regular structures encoding composite meanings, it remains unclear if compositional patterns also emerge in the visual embedding space. In this work, we investigate compositionality in the image domain, where the analysis of compositional properties is challenged by noise and sparsity of visual data. We address these problems and propose a framework, called Geodesically Decomposable Embeddings (GDE), that approximates image representations with geometry-aware compositional structures in the latent space. We demonstrate that visual embeddings of pre-trained VLMs exhibit a compositional arrangement, and evaluate the effectiveness of this property in the tasks of compositional classification and group robustness. GDE achieves stronger performance in compositional classification compared to its counterpart method that assumes linear geometry of the latent space. Notably, it is particularly effective for group robustness, where we achieve higher results than task-specific solutions. Our results indicate that VLMs can automatically develop a human-like form of compositional reasoning in the visual domain, making their underlying processes more interpretable. Code is available at https://github.com/BerasiDavide/vlm_image_compositionality.

An old-school recipe for training a classifier is to (i) learn a good feature extractor and (ii) optimize a linear layer atop. When only a handful of samples are available per category, as in Few-Shot Adaptation (FSA), data are insufficient to fit a large number of parameters, rendering the above impractical. This is especially true with large pre-trained Vision-Language Models (VLMs), which motivated successful research at the intersection of Parameter-Efficient Fine-tuning (PEFT) and FSA. In this work, we start by analyzing the learning dynamics of PEFT techniques when trained on few-shot data from only a subset of categories, referred to as the ``base'' classes. We show that such dynamics naturally splits into two distinct phases: (i) task-level feature extraction and (ii) specialization to the available concepts. To accommodate this dynamic, we then depart from prompt- or adapter-based methods and tackle FSA differently. Specifically, given a fixed computational budget, we split it to (i) learn a task-specific feature extractor via PEFT and (ii) train a linear classifier on top. We call this scheme Two-Stage Few-Shot Adaptation (2SFS). Differently from established methods, our scheme enables a novel form of selective inference at a category level, i.e., at test time, only novel categories are embedded by the adapted text encoder, while embeddings of base categories are available within the classifier. Results with fixed hyperparameters across two settings, three backbones, and eleven datasets, show that 2SFS matches or surpasses the state-of-the-art, while established methods degrade significantly across settings.

Vision-Language Models seamlessly discriminate among arbitrary semantic categories, yet they still suffer from poor generalization when presented with challenging examples. For this reason, Episodic Test-Time Adaptation (TTA) strategies have recently emerged as powerful techniques to adapt VLMs in the presence of a single unlabeled image. The recent literature on TTA is dominated by the paradigm of prompt tuning by Marginal Entropy Minimization, which, relying on online backpropagation, inevitably slows down inference while increasing memory. In this work, we theoretically investigate the properties of this approach and unveil that a surprisingly strong TTA method lies dormant and hidden within it. We term this approach ZERO (TTA with "zero" temperature), whose design is both incredibly effective and frustratingly simple: augment N times, predict, retain the most confident predictions, and marginalize after setting the Softmax temperature to zero. Remarkably, ZERO requires a single batched forward pass through the vision encoder only and no backward passes. We thoroughly evaluate our approach following the experimental protocol established in the literature and show that ZERO largely surpasses or compares favorably w.r.t. the state-of-the-art while being almost 10x faster and 13x more memory-friendly than standard Test-Time Prompt Tuning. Thanks to its simplicity and comparatively negligible computation, ZERO can serve as a strong baseline for future work in this field. The code is available at https://github.com/FarinaMatteo/zero.