利用核回归映射连通结构到功能（在类似小脑的网络中）
Mapping Connectomic Structure to Function(s) in Cerebellar-like Networks using Kernel Regression
AI总结：
本文通过扩展简化核回归模型，揭示了小脑网络中连接模式与学习能力之间的数学联系，发现投影权重的结构影响网络的归纳偏置。
摘要：
类似小脑的网络，其中输入活动模式在分类前被投射到更高维空间，是神经生物学中反复出现的motif，存在于小脑、海马齿状回、昆虫嗅觉系统和电鱼的电感受系统中。其相对了解的设计为探测生物学习原理提供了有希望的测试案例。电路的广泛投射长期以来被建模为随机的，使有效的一般性模式分离成为可能。然而，电子显微镜研究在果蝇蘑菇体和小鼠小脑中发现了有趣的结构线索。最近的数值工作表明，这种非随机连接性使电路能够优先学习某些、 presumably 自然的任务。在这里，我们而不是数值结果，呈现了一个稳健的数学链接，将观察到的连接模式与小脑电路的学习能力联系起来。特别是，我们扩展了系统的简化核回归模型，并利用最近的机器学习理论结果将连接性与学习联系起来。我们发现，报告的投影权重结构以直观的方式影响网络的归纳偏置：如果函数依赖于被过度采样的输入或倾向于连接到相同隐藏层神经元的神经元集合，则更容易学习。我们的方法是分析上可处理且令人满意的简单，我们希望它继续作为理解其他处理motif在类似小脑网络的功能影响的模型。
英文摘要：
Cerebellar-like networks, in which input activity patterns are separated by projection to a much higher-dimensional space before classification, are a recurring neurobiological motif, present in the cerebellum, dentate gyrus, insect olfactory system, and electrosensory system of the electric fish. Their relatively well-understood design presents a promising test-case for probing principles of biological learning. The circuits' expansive projections have long been modelled as random, enabling effective general purpose pattern separation. However, electron-microscopy studies have discovered interesting hints of structure in both the fly mushroom body and mouse cerebellum. Recent numerical work suggested that this non-random connectivity enables the circuit to prioritise learning of some, presumably natural, tasks over others. Here, rather than numerical results, we present a robust mathematical link between the observed connectivity patterns and the cerebellar circuit's learning ability. In particular, we extend a simplified kernel regression model of the system and use recent machine learning theory results to relate connectivity to learning. We find that the reported structure in the projection weights shapes the network's inductive bias in intuitive ways: functions are easier to learn if they depend on inputs that are oversampled, or on collections of neurons that tend to connect to the same hidden layer neurons. Our approach is analytically tractable and pleasingly simple, and we hope it continues to serve as a model for understanding the functional implications of other processing motifs in cerebellar-like networks.
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。
