更多数据无法打破对称性：设计驱动的可识别性
More Data Cannot Break a Symmetry: Identifiability by Design
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中文总结 AI 辅助
该研究针对无监督表征对齐的退化问题，将已知不变性转化为设计时诊断方法，通过选择非对称颜色集，大幅降低了灾难性对齐失败率，且仅需一次函数调用即可完成数据收集前的检查。
中文摘要 AI 辅助
无监督表征对齐仅通过几何结构即可恢复刺激与刺激间的对应关系，但在有数据之前，刺激几何结构的自同构群就已限制了此类对齐所能识别的内容。针对这种退化情况的明显诊断指标——成本最低的非身份重标记，对两项已发表设计的排名是错误的，因为密集采样会产生近重复样本，其转置几乎是自由的。我们将这一已知的不变性（Demetci等人，2024年）转化为设计时的诊断和干预手段。在颜色领域，候选几何结构具有闭式形式，我们表明这种失败是结构性的：64倍的重启预算仍无法改变对称设计，而相同样本量（N）的非对称集每次都能成功恢复。区分表征模型与恢复对应关系本质上是不相关的目标（在3000个子集上的相关系数r=-0.02）。仅通过该诊断指标选择9种颜色，无需参考任何学习到的表征，即可将全部93个模型表征从退化点移开，并在模型、层、样本量N和求解器均保持固定的情况下，将灾难性对齐失败率从75%降至2%。当规则设计遇到其候选几何结构的等距群时，就会出现同样的风险，包括均匀间隔的方向、色调或运动方向，且该检查仅需一次函数调用，发生在数据收集之前。
英文摘要
Unsupervised representational alignment recovers a stimulus-by-stimulus correspondence from geometry alone, but the automorphism group of the stimulus geometry bounds what any such alignment can identify, before data exist. The obvious diagnostic for this degeneracy, the cheapest non-identity relabelling, ranks two published designs in the wrong order, because dense sampling creates near-duplicates whose transposition is nearly free. We turn this known invariance (Demetci et al., 2024) into a design-time diagnostic and intervention. In colour, where candidate geometries have closed form, we show that the failure is structural: sixty-four times the restart budget leaves a symmetric design unmoved while an asymmetric set at the same N recovers every time. Discriminating representational models and recovering a correspondence are essentially uncorrelated objectives (r = -0.02 over 3,000 subsets). Choosing nine colours by this diagnostic alone, without consulting any learned representation, moves all 93 model representations away from the degenerate point and cuts catastrophic alignment failures from 75% to 2% with the models, the layers, N and the solver all held fixed. The same risk arises wherever a regular design meets its candidate geometry's isometry group, including evenly spaced orientations, tones, or motion directions, and the check costs one function call before data collection.
发表机构
- University of Rochester（罗切斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
