论文标题
在神经调整景观的水平和不变性上
On the Level Sets and Invariance of Neural Tuning Landscapes
论文作者
论文摘要
视觉表示可以定义为响应图像的神经元种群的激活。神经元在所有图像空间上的功能的激活都被描述为“调谐景观”。作为在高维空间上的功能，该景观的结构是什么？在这项研究中，我们通过水平集和莫尔斯理论的镜头来表征调整景观。最近的一项研究测量了不同大脑区域神经元的体内二维调谐图。在这里，我们根据级别集合中拓扑的变化为这些地图开发了一个统计上可靠的签名。我们发现，在整个皮质层次结构中，这种拓扑签名逐渐变化，在卷积神经网络（CNN）中发现了相似的趋势。此外，我们分析了CNN单元调整景观上的水平集的几何形状。我们提出了一个假设，即高阶单元可以局部被视为各向同性径向基函数，但在全球范围内则不能。这显示了水平集的力量作为理解图像空间上神经元激活的概念工具。
Visual representations can be defined as the activations of neuronal populations in response to images. The activation of a neuron as a function over all image space has been described as a "tuning landscape". As a function over a high-dimensional space, what is the structure of this landscape? In this study, we characterize tuning landscapes through the lens of level sets and Morse theory. A recent study measured the in vivo two-dimensional tuning maps of neurons in different brain regions. Here, we developed a statistically reliable signature for these maps based on the change of topology in level sets. We found this topological signature changed progressively throughout the cortical hierarchy, with similar trends found for units in convolutional neural networks (CNNs). Further, we analyzed the geometry of level sets on the tuning landscapes of CNN units. We advanced the hypothesis that higher-order units can be locally regarded as isotropic radial basis functions, but not globally. This shows the power of level sets as a conceptual tool to understand neuronal activations over image space.
