$\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval

This paper studies the minimal dimension required to embed subset memberships ($m$ elements and ${m\choose k}$ subsets of at most $k$ elements) into vector spaces, denoted as Minimal Embeddable Dimension (MED). The tight bounds of MED are derived theoretically and supported empirically for various notions of "distances" or "similarities," including the $\ell_2$ metric, inner product, and cosine similarity. In addition, we conduct numerical simulation in a more achievable setting, where the ${m\choose k}$ subset embeddings are chosen as the centroid of the embeddings of the contained elements. Our simulation easily realizes a logarithmic dependency between the MED and the number of elements to embed. These findings imply that embedding-based retrieval limitations stem primarily from learnability challenges, not geometric constraints, guiding future algorithm design.

MMLongBench: Benchmarking Long-Context Vision-Language Models Effectively and Thoroughly

The rapid extension of context windows in large vision-language models has given rise to long-context vision-language models (LCVLMs), which are capable of handling hundreds of images with interleaved text tokens in a single forward pass. In this work, we introduce MMLongBench, the first benchmark covering a diverse set of long-context vision-language tasks, to evaluate LCVLMs effectively and thoroughly. MMLongBench is composed of 13,331 examples spanning five different categories of downstream tasks, such as Visual RAG and Many-Shot ICL. It also provides broad coverage of image types, including various natural and synthetic images. To assess the robustness of the models to different input lengths, all examples are delivered at five standardized input lengths (8K-128K tokens) via a cross-modal tokenization scheme that combines vision patches and text tokens. Through a thorough benchmarking of 46 closed-source and open-source LCVLMs, we provide a comprehensive analysis of the current models' vision-language long-context ability. Our results show that: i) performance on a single task is a weak proxy for overall long-context capability; ii) both closed-source and open-source models face challenges in long-context vision-language tasks, indicating substantial room for future improvement; iii) models with stronger reasoning ability tend to exhibit better long-context performance. By offering wide task coverage, various image types, and rigorous length control, MMLongBench provides the missing foundation for diagnosing and advancing the next generation of LCVLMs.

Self-Consistent Narrative Prompts on Abductive Natural Language Inference

Abduction has long been seen as crucial for narrative comprehension and reasoning about everyday situations. The abductive natural language inference ($\alpha$NLI) task has been proposed, and this narrative text-based task aims to infer the most plausible hypothesis from the candidates given two observations. However, the inter-sentential coherence and the model consistency have not been well exploited in the previous works on this task. In this work, we propose a prompt tuning model $\alpha$-PACE, which takes self-consistency and inter-sentential coherence into consideration. Besides, we propose a general self-consistent framework that considers various narrative sequences (e.g., linear narrative and reverse chronology) for guiding the pre-trained language model in understanding the narrative context of input. We conduct extensive experiments and thorough ablation studies to illustrate the necessity and effectiveness of $\alpha$-PACE. The performance of our method shows significant improvement against extensive competitive baselines.