Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that allows some neurons to remain unmatched, yielding rotation-sensitive but robust correspondences. This partial soft-matching distance provides theoretical advantages -- relaxing strict mass conservation while maintaining interpretable transport costs -- and practical benefits through efficient neuron ranking in terms of cross-network alignment without costly iterative recomputation. In simulations, it preserves correct matches under outliers and reliably selects the correct model in noise-corrupted identification tasks. On fMRI data, it automatically excludes low-reliability voxels and produces voxel rankings by alignment quality that closely match computationally expensive brute-force approaches. It achieves higher alignment precision across homologous brain areas than standard soft-matching, which is forced to match all units regardless of quality. In deep networks, highly matched units exhibit similar maximally exciting images, while unmatched units show divergent patterns. This ability to partition by match quality enables focused analyses, e.g., testing whether networks have privileged axes even within their most aligned subpopulations. Overall, partial soft-matching provides a principled and practical method for representational comparison under partial correspondence.

翻译：表征相似性度量通常强制匹配所有单元，使其易受神经表征中常见的噪声和离群值影响。我们将软匹配距离扩展至部分最优传输框架，允许部分神经元保持未匹配状态，从而产生对旋转敏感但鲁棒的对应关系。该部分软匹配距离具有理论优势——在保持可解释传输成本的同时放松严格的质量守恒约束——并通过高效的神经元排序（依据跨网络对齐质量）提供实际效益，无需昂贵的迭代重计算。在仿真实验中，该方法能在离群值干扰下保持正确匹配，并在噪声污染识别任务中可靠选择正确模型。在fMRI数据上，该方法自动排除低可靠性体素，并生成按对齐质量排序的体素列表，其结果与计算成本高昂的暴力穷举法高度一致。相较于强制匹配所有单元（无论质量如何）的标准软匹配方法，该方法在同源脑区实现了更高的对齐精度。在深度网络中，高度匹配的单元呈现相似的最大激发图像，而未匹配单元则显示发散模式。这种按匹配质量进行划分的能力支持聚焦分析，例如检验网络是否在其最对齐的子群中仍存在特权轴。总体而言，部分软匹配为部分对应关系下的表征比较提供了原则性且实用的方法。