为现代霍普菲尔德网络设计新拉格朗日函数，实现对分布外样本的精准检测。
Rectified Lagrangian for Out-of-Distribution Detection in Modern Hopfield Networks
- 引入修正拉格朗日函数，显式构建分布外样本的吸引子。
- 在九个图像数据集上优于主流基于能量的分布外检测方法。
- 适合需要高可靠性异常检测的AI系统开发者。
现代霍普菲尔德网络（MHNs）因具备指数级存储容量而受到关注，能存储并检索大量模式。传统MHNs将分布内（ID）样本的特征表示为特征空间中的吸引子，但无法有效处理分布外（OOD）样本，因假设所有输入均为ID样本。为此，本文提出修正拉格朗日函数（RegLag），在记忆神经元中显式引入一个用于表示OOD样本的平凡吸引子。该机制使任意交互矩阵下均存在一个稳定的零点吸引子，可通过识别落入该吸引子的样本判定为分布外。通过优化交互矩阵以估计概率密度，实现精确的ID/OOD分类。实验表明，基于RegLag的MHN在九个图像数据集上的表现优于现有基于能量的分布外检测方法，包括使用前沿霍普菲尔德能量的方案。
原文摘要 · Abstract (English)
Modern Hopfield networks (MHNs) have recently gained significant attention in the field of artificial intelligence because they can store and retrieve a large set of patterns with an exponentially large memory capacity. A MHN is generally a dynamical system defined with Lagrangians of memory and feature neurons, where memories associated with in-distribution (ID) samples are represented by attractors in the feature space. One major problem in existing MHNs lies in managing out-of-distribution (OOD) samples because it was originally assumed that all samples are ID samples. To address this, we propose the rectified Lagrangian (RegLag), a new Lagrangian for memory neurons that explicitly incorporates an attractor for OOD samples in the dynamical system of MHNs. RecLag creates a trivial point attractor for any interaction matrix, enabling OOD detection by identifying samples that fall into this attractor as OOD. The interaction matrix is optimized so that the probability densities can be estimated to identify ID/OOD. We demonstrate the effectiveness of RecLag-based MHNs compared to energy-based OOD detection methods, including those using state-of-the-art Hopfield energies, across nine image datasets.
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