Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914573636861952 |
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| author | Barnfield, Nicholas Sen, Subhabrata Sur, Pragya |
| author_facet | Barnfield, Nicholas Sen, Subhabrata Sur, Pragya |
| contents | Recent progress has rapidly advanced our understanding of the mechanisms underlying in-context learning in modern attention-based neural networks. However, existing results focus exclusively on unimodal data; in contrast, the theoretical underpinnings of in-context learning for multi-modal data remain poorly understood. We introduce a mathematically tractable framework for studying multi-modal learning and explore when transformer-like architectures can recover Bayes-optimal performance in-context. To model multi-modal problems, we assume the observed data arises from a latent factor model. Our first result comprises a negative take on expressibility: we prove that single-layer, linear self-attention fails to recover the Bayes-optimal predictor uniformly over the task distribution. To address this limitation, we introduce a novel, linearized cross-attention mechanism, which we study in the regime where both the number of cross-attention layers and the context length are large. We show that this cross-attention mechanism is provably Bayes optimal when optimized using gradient flow. Our results underscore the benefits of depth for in-context learning and establish the provable utility of cross-attention for multi-modal distributions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_04872 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning Barnfield, Nicholas Sen, Subhabrata Sur, Pragya Machine Learning Artificial Intelligence Recent progress has rapidly advanced our understanding of the mechanisms underlying in-context learning in modern attention-based neural networks. However, existing results focus exclusively on unimodal data; in contrast, the theoretical underpinnings of in-context learning for multi-modal data remain poorly understood. We introduce a mathematically tractable framework for studying multi-modal learning and explore when transformer-like architectures can recover Bayes-optimal performance in-context. To model multi-modal problems, we assume the observed data arises from a latent factor model. Our first result comprises a negative take on expressibility: we prove that single-layer, linear self-attention fails to recover the Bayes-optimal predictor uniformly over the task distribution. To address this limitation, we introduce a novel, linearized cross-attention mechanism, which we study in the regime where both the number of cross-attention layers and the context length are large. We show that this cross-attention mechanism is provably Bayes optimal when optimized using gradient flow. Our results underscore the benefits of depth for in-context learning and establish the provable utility of cross-attention for multi-modal distributions. |
| title | Multi-layer Cross-attention is Provably Optimal for Multi-modal In-context Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.04872 |