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arXiv 1601.00720q-bio.NCcs.AI
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神经元如何在稀疏分布表示上操作?稀疏性、神经元和活跃树突的数学理论

How do neurons operate on sparse distributed representations? A mathematical theory of sparsity, neurons and active dendrites

Numenta, Inc.(Numenta 公司)

Subutai Ahmad, Jeff Hawkins

摘要:

我们提出了一个形式化的数学模型稀疏表示和活跃的树突在新皮层。我们的模型的灵感来自于最近的实验发现,积极的树突状处理和NMDA尖峰锥体神经元。这些实验和建模研究表明,在新皮层的模式记忆的基本单位是由本地化的非线性树突状过程操作的小簇突触实例化。我们推导出一些标度律,这些标度律表征了在不利条件下检测神经元群体中的激活模式的这种树突的准确性。我们引入了联合属性,该属性表明多个模式的突触可以在一个段内随机混合在一起,并且仍然导致高度准确的识别。我们描述的模拟结果,提供了进一步的洞察稀疏表示以及两个主要的结果。首先,我们表明,模式识别的神经元与活跃的树突可以是非常准确和强大的高维稀疏输入,即使使用少量的突触识别大的模式。其次,表示识别精度的树突预测最佳NMDA尖峰阈值下的一组慷慨的假设方程。该预测与文献中测量的NMDA尖峰阈值紧密匹配。我们的模型与锥体神经元的许多已知特性相匹配。因此,该理论为理解皮质网络中稀疏表示的好处和局限性提供了一个数学框架。

英文摘要:

We propose a formal mathematical model for sparse representations and active dendrites in neocortex. Our model is inspired by recent experimental findings on active dendritic processing and NMDA spikes in pyramidal neurons. These experimental and modeling studies suggest that the basic unit of pattern memory in the neocortex is instantiated by small clusters of synapses operated on by localized non-linear dendritic processes. We derive a number of scaling laws that characterize the accuracy of such dendrites in detecting activation patterns in a neuronal population under adverse conditions. We introduce the union property which shows that synapses for multiple patterns can be randomly mixed together within a segment and still lead to highly accurate recognition. We describe simulation results that provide further insight into sparse representations as well as two primary results. First we show that pattern recognition by a neuron with active dendrites can be extremely accurate and robust with high dimensional sparse inputs even when using a tiny number of synapses to recognize large patterns. Second, equations representing recognition accuracy of a dendrite predict optimal NMDA spiking thresholds under a generous set of assumptions. The prediction tightly matches NMDA spiking thresholds measured in the literature. Our model matches many of the known properties of pyramidal neurons. As such the theory provides a mathematical framework for understanding the benefits and limits of sparse representations in cortical 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。

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