通过模型副本的排列路由提升泛化能力
Improving Generalization by Permutation Routing Across Model Copies
AI总结：
本文提出通过排列路由提升模型泛化能力，利用结构化混合核Q定义消息传输拓扑，避免参数耦合，适用于感知机、委员会机和多层感知机。
摘要：
我们介绍了一种M-cover（或M层）变换在机器学习中的应用。该方法复制模型M次，但不通过参数平均或显式吸引力力，而是重新路由局部学习消息的计算上下文。每个局部损失在路由模型上评估，其参数从不同副本中根据从结构化混合核Q采样的排列获取。训练使用原始局部更新规则，而结果学习消息通过这些路由计算路径重新分布。因此Q定义了消息传输的拓扑结构，并控制提升因子图的长循环结构。我们为感知机、委员会机和多层感知机制定了这一构造，显示从离散模型到可微神经网络均适用相同原理。所得到的框架提供了一种通过结构化消息共享而非复制坍缩或参数空间耦合来提升泛化能力的机制。
英文摘要：
We introduce a use of the \(M\)-cover (or \(M\)-layer) transform for machine learning. The method replicates a model \(M\) times, but instead of coupling the copies through parameter averaging or an explicit attractive force, as in replicated SGD or Elastic SGD, it rewires the contexts in which local learning messages are computed. Each local loss is evaluated on a routed model whose parameters are drawn from different copies according to permutations sampled from a structured mixing kernel \(Q\). Training then uses the original local update rule, while the resulting learning messages are redistributed across the copies through these routed computational paths. Thus \(Q\) defines a topology for message transport and controls the long-loop structure of the lifted factor graph. We formulate this construction for perceptrons, committee machines, and multilayer perceptrons, showing that the same principle applies from discrete models to differentiable neural networks. The resulting framework provides a mechanism for improving generalization through structured message sharing rather than replica collapse or parameter-space coupling.
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