ArrowFlow：排列空间中的层次化机器学习
ArrowFlow: Hierarchical Machine Learning in the Space of Permutations
AI总结：
提出ArrowFlow架构，在排列空间中通过排序滤波器和置换矩阵累积实现无浮点参数的层次化排序表示学习，并利用社会选择公理违反作为归纳偏置，实验表明在多个基准上具有竞争力且具备噪声鲁棒性、隐私保护等特性。
摘要：
我们引入了ArrowFlow，一种完全在排列空间中运行的机器学习架构。其计算单元是排序滤波器，即学习到的排序，通过Spearman's footrule距离比较输入，并通过置换矩阵累积（一种基于位移证据的非梯度规则）进行更新。层以层次方式组合：每一层的输出排序成为下一层的输入，从而在核心计算中无需任何浮点参数即可实现深度序数表示学习。我们将该架构与Arrow不可能定理联系起来，表明社会选择公平性公理（上下文依赖性、专业化、对称性破坏）的违反作为非线性、稀疏性和稳定性的归纳偏置。实验涵盖UCI表格基准、MNIST、基因表达癌症分类（TCGA）和偏好数据，均与GridSearchCV调优的基线进行比较。ArrowFlow在Iris上击败所有基线（2.7% vs. 3.3%），并在大多数UCI数据集上具有竞争力。单个参数多项式次数充当主开关：次数1带来噪声鲁棒性（退化减少8-28%）、隐私保护（成本增加0.5个百分点）和缺失特征弹性；更高次数则牺牲这些特性以换取更高的干净准确率。ArrowFlow并非旨在超越基于梯度的方法。它是一个存在性证明，表明在一种根本不同的计算范式（将序数结构提升为一等公民，且与纯整数和神经形态硬件自然对齐）中实现有竞争力的分类是可能的。
英文摘要：
We introduce ArrowFlow, a machine learning architecture that operates entirely in the space of permutations. Its computational units are ranking filters, learned orderings that compare inputs via Spearman's footrule distance and update through permutation-matrix accumulation, a non-gradient rule rooted in displacement evidence. Layers compose hierarchically: each layer's output ranking becomes the next layer's input, enabling deep ordinal representation learning without any floating-point parameters in the core computation. We connect the architecture to Arrow's impossibility theorem, showing that violations of social-choice fairness axioms (context dependence, specialization, symmetry breaking) serve as inductive biases for nonlinearity, sparsity, and stability. Experiments span UCI tabular benchmarks, MNIST, gene expression cancer classification (TCGA), and preference data, all against GridSearchCV-tuned baselines. ArrowFlow beats all baselines on Iris (2.7% vs. 3.3%) and is competitive on most UCI datasets. A single parameter, polynomial degree, acts as a master switch: degree 1 yields noise robustness (8-28% less degradation), privacy preservation (+0.5pp cost), and missing-feature resilience; higher degrees trade these for improved clean accuracy. ArrowFlow is not designed to surpass gradient-based methods. It is an existence proof that competitive classification is possible in a fundamentally different computational paradigm, one that elevates ordinal structure to a first-class citizen, with natural alignment to integer-only and neuromorphic hardware.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
