What Breaks in Multi-Image Schema Application? Factorial Oracle Interventions Reveal an Instance-Information Bottleneck

Vision-Language Models (VLMs) have advanced across multimodal benchmarks but still show clear gaps in ordinal number understanding, i.e., the ability to track relative positions and generalize to large indices. We present OrdinalBench, a diagnostic benchmark that standardizes ordinal number understanding as an evaluation task for VLMs. The core task is N-th object identification, defined by a starting reference and traversal rule. Task difficulty is controlled along three axes: (i) ordinal magnitude, from small numbers to extreme cases up to 300; (ii) arrangement complexity, from single loops to maze-like paths; and (iii) object count. The benchmark provides 39,000 question-answer pairs, each annotated with a ground-truth reasoning trajectory and balanced across difficulty levels for controlled large-scale testing. Beyond answer-only evaluation, our framework requires models to generate structured stepwise traces of the counting process and provides an open evaluation toolkit that measures both final accuracy and step-level path consistency. Zero-shot evaluations of GPT-5, Gemini 2.5 Flash Lite, Qwen2.5-VL, InternVL3.5, and Molmo reveal sharp degradation under large-ordinal and complex-path conditions, highlighting weak generalization despite strong scores on standard multimodal tasks. By framing ordinal number understanding as a core target, OrdinalBench provides a reproducible benchmark and diagnostic framework for developing VLMs with stronger sequential reasoning. All data and code are available at https://ordinalbench.github.io/

Vision-language models (VLMs) increasingly reason over visual evidence that is cropped, segmented, retrieved, or revealed over time. Yet most VQA benchmarks present the complete image and question at once. We ask what models lose when the same information is fragmented. We introduce Layered-VQA, with 93 scenes and 300 questions. Each image is decomposed into ordered RGBA layers that exactly recompose the original scene, and each question is annotated with supporting, minimal-sufficient, and distractor layers. We evaluate eleven open-weight VLMs from 3B to 32B parameters and two proprietary models with a scale of 187,200 conversations, graded by 1.74M open-model cross-judgments. We find three consistent failures. Loss in Composition: fragmenting the question has a small effect, but fragmenting the scene substantially reduces accuracy; recomposing the same layers largely restores performance. Oracle Inversion: even oracle-selected sufficient evidence can perform worse than the complete scene. Loss in Grounding: as more evidence is required, grounding degrades much faster than answer accuracy. Together, these results show that having the right visual evidence is not enough. How that evidence is composed and presented determines whether models can use and ground it. The right evidence is not enough: VLMs need the scene it came from.

Dual-encoder vision-language models (VLMs) expose a similarity interface that enables zero-shot retrieval but fails compositional constraints: queries like "umbrella and no person" retrieve images containing both, even when concept detection is reliable. We trace this to an interface-level Bag-of-Concepts effect, where similarity scores approximate mean pooling of concept evidence regardless of operators. Although operator-dependent signals exist in text embeddings, they are too weak or misaligned to affect rankings. Fine-tuning does not reliably resolve this failure because the dominant bottleneck is how similarity aggregates evidence rather than what encoders represent. We propose factored inference, which separates evidence extraction from constraint execution, and introduce LCSE (Logic-Constrained Score Editing), a training-free method that executes constraints externally using concept scores from frozen encoders. We also introduce FACTOR-Bench, where LCSE achieves 85.5% accuracy versus 73.2% for the best fine-tuned baseline, 90.7% when applied to SigLIP 2, and improves NegBench COCO MCQ accuracy from 27.2% to 65.2% while preserving retrieval performance.