物理学习网络的盲方向：在哪里测量以及测量什么
Blind directions of physical learning networks: where to measure and what to measure
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中文总结 AI 辅助
本文研究物理学习网络中测量位置与量的选择对盲维度的影响，提出分解定理和生成森林上界，并通过数值与硬件实验验证了测量方式决定可学习性。
中文摘要 AI 辅助
物理学习网络在少数可访问节点处被读取。每个仅使用该处固定工作点下的稳态电压和电流的任务和学习规则，都通过边界响应映射起作用。其雅可比矩阵核中的参数变化在一阶上是盲的。沿着该映射的一条纤维行走未在600步上限处终止，一条边随后达到其起始值的15.2倍。一个分解定理将响应雅可比矩阵在隐藏组件上拆分。盲维度在幸存的槽位不相交的组件上相加。一条边界到边界的边增加一个参数并删除一个槽位。暴露一个隐藏节点仅改变其组件。对于一个隐藏节点，该组件的贡献计数其邻居的非邻接图的二分组件。对于包含h个隐藏节点的口袋，一个因子分析界限限制了外部电极可以暴露的内容。当每个口袋节点遇到每个邻居且没有边连接两个这样的邻居时达到该界限，因此超过阈值后，此类口袋外部的进一步电极不暴露任何内容。当口袋内的隐藏节点形成团时，口袋内的一个电极价值h-1个方向，而外部的一个电极价值为零。将可访问节点读取为向量位移而非电势，在所有测试的90个弹簧网络中没有留下超出计数的缺陷，每个网络是一个完全连接到五个或更多可访问节点的口袋，并且在88个中完全没有盲点。限制读取的是测量的量以及接触的数量。最大权重生成森林给出了盲维度的已证明上界。匹配等式对一个隐藏节点被证明，并推测超过该情况。森林计数在1500个保留网络中的1451个中匹配数值盲维度，并且没有短缺将不完整的搜索与错误的等式区分开来。一个自学习电路在硬件上展示了这种拆分。
英文摘要
A physical learning network is read at a few accessible nodes. Every task and learning rule that uses only the steady voltages and currents there, at a fixed operating point, acts through the boundary response map. Changes in the kernel of its Jacobian are blind to first order. A walk along one fiber ran to a 600-step cap, one edge then at 15.2 times its start. A decomposition theorem splits the response Jacobian over the hidden components. The blind dimension adds over components whose surviving slots are disjoint. A boundary-to-boundary edge adds one parameter and deletes one slot. Exposing a hidden node changes only its component. For one hidden node the contribution counts the bipartite components of the non-adjacency graph of its neighbors. For a pocket of h hidden nodes a factor-analysis bound caps what outside electrodes can expose. It is attained when every pocket node meets every neighbor and no edge joins two of those neighbors, so past a threshold further electrodes outside such a pocket expose nothing. An electrode inside such a pocket, when its hidden nodes form a clique, is worth h-1 directions where one outside is worth none. Read as vector displacements rather than potentials, the same nodes left no deficit beyond counting in all 90 spring networks tested, each a pocket fully joined to five or more accessible nodes, and nothing blind in 88. What limits the reading is the quantity measured as much as the number of contacts. Maximum-weight spanning forests give a proved upper bound on the blind dimension. The matching equality is proved for one hidden node and conjectured beyond. It holds in all 5,343 components whose maximum could be attained and certified, and the forest count matched the certified blind dimension in 1,448 of 1,500 held-out networks, where the maximum must be searched. A self-learning circuit shows the split on hardware.
发表机构
- Hanoi University of Civil Engineering（河内土木工程大学）
机构由 AI 辅助整理，请以论文原文为准。
