Exact semantic readout from compressed vector representations

We propose Latent Terms, a method revealing that models trained for dense retrieval, whether single- or multi-vector, learn representations that can trivially be decomposed into retrieval-ready sparse features. When trained on frozen retrievers, Sparse Autoencoders without any retrieval-specific adjustments extract a latent vocabulary with approximately Zipfian collection statistics, directly suitable for classical sparse retrieval scoring via BM25. This approach enables sparse retrieval while requiring no learned expansion objective or sparse retrieval supervision whatsoever, and can be readily applied to any dense retriever. Latent Terms is able to match or outperform single-vector scoring methods from its own base model as well as comparable SPLADE variants. In addition, it substantially outperforms its base model on LIMIT, a task specifically designed to highlight the failures of single-vector retrieval. Overall, our results highlight that neural retrievers contain more expressive and indexable structure than their default scoring functions expose, but that other methods can nonetheless be leveraged.

Linear properties are ubiquitous in the representations of language models; however, testing them experimentally remains a challenging task. This work focuses on relational linearity: the hypothesis that, for a fixed relation (e.g., "plays"), the unembedding of an object (e.g., "trumpet") can be predicted from the embedding of its subject (e.g.,"Miles Davis") by a linear map. We present an experimental method to test the formulation of relational linearity by Marconato et al. (2025). Specifically, we introduce a probing method, based on Kullback-Leibler divergence, to evaluate this property and examine its variation across layers and paraphrased relational queries. It is also more efficient than previous work; for example, it avoids the crude Jacobian approximations used in Linear Relational Embeddings by Hernandez et al. (2024). Our findings across four datasets show that relational linearity varies across models, exhibits layer-wise patterns consistent with prior observations about linguistic information in model representations, and is differently affected by changes in how the relation is phrased.

In this study, we identify depth-dependent prefix redundancy in final-readout LLM embedding models, notably across representative backbones including Qwen3-Embedding and Qwen3-VL-Embedding. We find that removing prefix states is substantially more damaging in shallow layers than at greater depth, showing that prefix states become increasingly compressible as the prefix and readout states propagate through the network. To this end, we introduce FastE, a training-free, plug-and-play method. FastE uses a shared fixed threshold on batch-mean readout-prefix alignment as a lightweight online heuristic for selecting when compression occurs, and ranks prefix states by the attention scores they receive from the readout position to determine which states are retained in subsequent layers. Our evaluations demonstrate FastE's ability to substantially reduce computational costs: on NarrativeQA with Qwen3-Embedding-0.6B, it reduces decoder-backbone FLOPs by 40.11% while retaining 99.53% of Full Forward nDCG@10. Across five text embedding benchmarks, two backbone scales, and three cross-modal retrieval tasks, the quality-efficiency trade-off is directly customizable through the maximum removal ratio without retraining. We believe FastE offers practical value for scalable embedding generation in retrieval, indexing, clustering, and multimodal representation systems.