ERank in Latent Space as an Image-Complexity and Richness Measure

Large vision-language models used as listwise rerankers must jointly process visual tokens from tens of candidates per query, making token pruning essential for practical deployment. Existing pruning methods retain tokens by attention saliency, yet we show that saliency is systematically misaligned with ranking contribution: visually prominent tokens often capture order-neutral patterns shared across candidates. This mismatch is layer-dependent: saliency becomes informative only where attention is concentrated, and normalized attention entropy diagnoses the reliability shift (Pearson r=0.87). We propose RaDiCal (Rank-Discriminative Calibration), a training-free framework that uses normalized attention entropy to decide when saliency can be trusted, fusing it with an attention-free rank-discriminative prior and selecting pruning layers from the same trust landscape. Across three retrieval benchmarks and multiple VLM architectures, RaDiCal matches Dense MRR@10 on Flickr30K and surpasses it on MSCOCO at a 20% token budget, ranks first among all pruning methods on FashionIQ, and holds within 1.2 pp on Flickr30K and MSCOCO at 10% retention. It cuts FLOPs by 39--45% and delivers 1.28--1.45$\times$ measured speedups across two VLM architectures without dataset-specific retuning.

Deep networks trained with label noise often learn clean structure before memorizing corrupted labels. We show that this transition leaves a spectral signature in the centered scatter of per-example last-layer gradients. Its effective rank transiently expands during memorization and contracts after corrupted labels are fit. We call this phenomenon Fisher Rank Inflation. Corrupted labels increase effective rank by injecting spectral mass into low-energy or previously unused eigendirections, increasing the entropy of the gradient spectrum. We derive a first-order leave-one-out attribution formula, identify conditions under which corrupted examples contribute more strongly than clean examples, and explain why attribution signals weaken once the normalized Fisher-gradient spectrum stabilizes. We test these predictions on CIFAR-10, CIFAR-100, and CIFAR-10N using SmallCNN, ResNet18, and Vision Transformers. Across settings, Fisher effective rank exhibits a consistent inflation--collapse trajectory aligned with memorization. At peak-rank checkpoints, corrupted examples are enriched among the highest rank-contributing samples, with top-100 noisy fractions from $69.2\%$ to $96.2\%$ across five-seed synthetic-corruption experiments and $94.4\%\pm1.9\%$ on CIFAR-10N. First-order spectral attribution closely matches exact leave-one-out contributions in convolutional models and remains enriched in the Vision Transformer. Peak effective rank increases monotonically with corruption severity, from $28.88\pm1.95$ under clean training to $97.09\pm1.78$ at $60\%$ corruption. In several settings, the retrospectively identified onset of rank inflation precedes observable test degradation. These results establish Fisher Rank Inflation as a spectral signature connecting corrupted-example enrichment, corruption severity, and the transition from structure learning to memorization.

Composed Image Retrieval (CIR) constitutes a pivotal paradigm requiring models to perform joint reasoning on reference images and modification texts. However, the prevalence of Noisy Triplet Correspondence (NTC) in large-scale datasets severely constrains model performance. Existing denoising methods either target binary mismatches or rely on scalar-based point-wise estimation, neglecting rich global structural correlations among sample populations and dynamic value variations during training, thereby yielding suboptimal results. This paper identifies two critical unresolved challenges: Global Structural Inconsistency of Semantic Correlations and Hard Sample Discrimination Uncertainty. To address these, we propose RankVR, a framework designed to construct a robust CIR model via global structure consistency and dynamic value perception. Specifically, we introduce the Global Structure Consistency Perception (GSCP) module, which utilizes the Effective Rank of the Correlation Matrix to decouple clean samples from structural noise. By measuring rank difference, GSCP identifies samples disrupting macroscopic semantic symmetry. Furthermore, we develop the Adaptive Semantic Value Calibration (ASVC) module to distinguish high-value hard clean samples. By integrating training potential and reliability, it dynamically quantifies the semantic value of each triplet, ensuring effective utilization of hard samples while suppressing noise characterized by logical conflicts. Extensive experiments on the FashionIQ and CIRR benchmark datasets demonstrate that RankVR significantly outperforms existing state-of-the-art methods, validating its superior robustness in noisy environments.