深度网络总是更偏好简单数据,而非复杂数据。
Deep Networks Favor Simple Data
- 用雅可比和自回归方法分离模型与密度估计,跨架构分析数据复杂度
- 无论训练数据如何,简单样本始终被赋予更高密度估计值
- 现象普遍存在于多种模型和任务中,适合关注模型偏差的研究者
深度模型在训练后对分布外(OOD)的简单数据赋予比真实测试数据更高的密度估计,这种现象称为OOD异常。以往研究多局限于单一架构或基准,我们则将模型与密度估计解耦,提出雅可比基和自回归自估计两种方法,使密度分析适用于多种模型。在iGPT、PixelCNN++、Glow、基于得分的扩散模型、DINOv2和I-JEPA等模型上均发现一致规律:低复杂度样本获得更高密度估计,高复杂度样本则更低。该排序不仅存在于测试集内部,也跨数据集如CIFAR-10与SVHN保持一致,且在独立训练的模型间高度稳定。通过斯皮尔曼等级相关系数量化,结果与外部复杂度指标高度吻合。即使仅用最复杂样本(甚至单个样本)训练,模型仍会将更简单的图像判定为更高密度。这揭示了深层网络普遍存在对简单数据的偏好,超出传统OOD异常范畴。
原文摘要 · Abstract (English)
Estimated density is often interpreted as indicating how typical a sample is under a model. Yet deep models trained on one dataset can assign higher density to simpler out-of-distribution (OOD) data than to in-distribution test data. We refer to this behavior as the OOD anomaly. Prior work typically studies this phenomenon within a single architecture, detector, or benchmark, implicitly assuming certain canonical densities. We instead separate the trained network from the density estimator built from its representations or outputs. We introduce two estimators: Jacobian-based estimators and autoregressive self-estimators, making density analysis applicable to a wide range of models. Applying this perspective to a range of models, including iGPT, PixelCNN++, Glow, score-based diffusion models, DINOv2, and I-JEPA, we find the same striking regularity that goes beyond the OOD anomaly: lower-complexity samples receive higher estimated density, while higher-complexity samples receive lower estimated density. This ordering appears within a test set and across OOD pairs such as CIFAR-10 and SVHN, and remains highly consistent across independently trained models. To quantify these orderings, we introduce Spearman rank correlation and find striking agreement both across models and with external complexity metrics. Even when trained only on the lowest-density (most complex) samples - or even a single such sample - the resulting models still rank simpler images as higher density. These observations lead us beyond the original OOD anomaly to a more general conclusion: deep networks consistently favor simple data. Our goal is not to close this question, but to define and visualize it more clearly. We broaden its empirical scope and show that it appears across architectures, objectives, and density estimators.
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