Embeddings have emerged as a standard representational interface linking foundation models with downstream systems. Most embedding benchmarks assess representations through discriminative tasks or geometric criteria centered on separability in embedding space. However, strong performance on such evaluations does not establish whether content compressed into an embedding remains accessible to a downstream generator. To address this gap, we introduce the Generative Embedding Benchmark (GEB), in which a decoder answers questions using only a frozen embedding and question text, without access to the original image or intermediate visual features. Answer quality under this readout measures generative information: the answer-relevant content recoverable from an embedding. GEB includes a curated visual-question-answering dataset with a 1,800-item development split and a held-out 900-item test split covering natural images, scene text, and visual documents. Using a common decoder and training recipe, we evaluate seven public embedding models in visual-only and vision-language joint modes. On the test set, visual-only scores range from 28.25 to 33.21; with image-question joint encoding, all five VLM-based embedding models score higher, and the best reaches 65.56. Matched embeddings also outperform text-only inputs, zero embeddings, and shuffled embeddings. Natural-image information is much easier to recover than scene text or visual-document information, while a Qwen3-VL-2B reference with access to the original image reaches 84.30. Together, these results show that generative readout exposes information bottlenecks that separability-based evaluation does not capture.
Large vision-language models exhibit strong in-context learning (ICL) capabilities, yet when and why visual context helps multimodal ICL remains poorly understood. Empirical studies show a puzzling dichotomy: models sometimes effectively leverage visual demonstrations, yet often neglect them entirely. We propose VIB-ICL, an information-theoretic framework that resolves this dichotomy through the Information Bottleneck principle. We introduce the Cross-Modal Information Gain (CMIG), which quantifies the additional mutual information that visual context provides about the target beyond textual context. We derive a generalization bound showing that multimodal ICL's excess risk over text-only ICL is governed by the CMIG, proving that multimodal ICL provably outperforms text-only ICL when visual information is non-redundant. We further prove that visual context neglect, often viewed as a failure mode, is the Information Bottleneck-optimal solution when visual information is redundant, yielding a closed-form Attention Reallocation Principle that prescribes how visual attention weights should be adaptively adjusted. We instantiate this principle in the VIB-ICL algorithm, which estimates CMIG via variational bounds and dynamically reallocates attention. Experiments on five benchmarks demonstrate consistent improvements of up to 4.7\% accuracy gains and 35\% reduction in required demonstrations, validating our theoretical predictions.