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arXiv · 2507.07574

Beyond the Linear Separability Ceiling: Aligning Representations in VLMs

Enrico Vompa·Tanel Tammet·Mohit Vaishnav
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Abstract

A challenge in advancing Visual-Language Models (VLMs) is determining whether their failures on abstract reasoning tasks, such as Bongard problems, stem from flawed perception or faulty top-down reasoning. To disentangle these factors, we introduce a diagnostic framework centered on the Linear Separability Ceiling (LSC), the performance achievable by a linear classifier on a VLM's raw visual embeddings. Applying this framework to state-of-the-art VLMs, we uncover a pervasive ''alignment gap'', where most models fail to generatively outperform the linear separability of their representations. We find that the few models surpassing this ceiling do so via two mechanisms: by further refining visual representations into a more linearly separable format or by executing non-linear decision logic. We demonstrate that this bottleneck is not a fundamental limitation but a solvable visual alignment issue. Our method augments standard next-token prediction with a contrastive objective to restructure the visual manifold into a more one-dimensionally linear geometry, improving image-to-image comparison and enabling models to significantly surpass the LSC on abstract compositional reasoning tasks.

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Enrico Vompa, Tanel Tammet, Mohit Vaishnav. 2025-07-10. Beyond the Linear Separability Ceiling: Aligning Representations in VLMs. https://arxiv.org/abs/2507.07574

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