arXiv:2607.10506cs.LGcond-mat.dis-nn2026-07

让受限玻尔兹曼机学会拒绝异常图像,靠的是重塑能量景观。

Learning from Noise: Effective-Rank Collapse and Out-of-Distribution Rejection in Restricted Boltzmann Machines

论文配图:Learning from Noise: Effective-Rank Collapse and Out-of-Distribution Rejection in Restricted Boltzmann Machines
图 1 · 摘自论文原文
  • 用随机辅助图像训练,使模型权重谱集中到少数主方向。
  • 有效秩下降后,对异常图像的分类准确率保持不变但拒绝率提升。
  • 适合想提升模型鲁棒性的机器学习研究者参考。

受限玻尔兹曼机(RBMs)通过可见层与隐层配置的能量景观表示数据,但在分布外(OOD)输入下判别能力脆弱:非训练分布的样本可能被误吸收进已学类别谷底而非被拒绝。本文通过分析诱导的可见-可见互作矩阵 $J=WW^{T}$ 的谱特性,揭示此问题根源。相对于马尔琴科-帕斯图随机矩阵参考,常规训练使谱权重分散于多个弱且批量兼容的方向,导致 $J$ 的有效秩较高。当训练中引入辅助随机二值图像并分配至拒绝标签时,学习到的互作矩阵发生有效秩坍缩:弱批量模式被抑制,谱权重集中于更少的主导特征方向,有效秩趋近于实测数据协方差矩阵。由此构建的RBMs可有效拒绝结构化分布外图像数据集,同时保持对MNIST的分类准确率,表明随机辅助曝光能重塑能量基分类器的互作谱与自由能景观。

原文摘要 · Abstract (English)

Restricted Boltzmann machines (RBMs) represent data by shaping an energy landscape over visible and hidden configurations, but their discriminative use is fragile under out-of-distribution (OOD) inputs: samples outside the training distribution can be absorbed into one of the learned class basins rather than rejected. Here, we analyze this failure mode through the spectrum of the induced visible--visible interaction $J=WW^{T}$, where \(W\) is the visible--hidden weight matrix. Relative to a Marchenko--Pastur random-matrix reference, conventional training spreads spectral weight into many weak, bulk-compatible directions, increasing the effective rank of $J$. When auxiliary random binary images are assigned to a rejection label during training, the learned interaction undergoes effective-rank collapse: weak bulk-like modes are depleted, spectral weight concentrates into fewer dominant eigendirections, and the effective rank of $J$ approaches that of the empirical data covariance matrix. The resulting RBM rejects structured OOD image datasets while preserving MNIST classification accuracy, showing that random auxiliary exposure can reshape both the interaction spectrum and the free-energy landscape of an energy-based classifier.

能量模型分布外检测神经网络鲁棒性

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