Hierarchical sparse coding of objects in deep convolutional neural networks

Abstract

Recently, deep convolutional neural networks (DCNNs) have attained human-level performances on challenging object recognition tasks owing to their complex internal representation. However, it remains unclear how objects are represented in DCNNs with an overwhelming number of features and non-linear operations. In parallel, the same question has been extensively studied in primates brain, and three types of coding schemes have been found: one object is coded by entire neuronal population (distributed coding), or by one single neuron (local coding), or by a subset of neuronal population (sparse coding). Here we asked whether DCNNs adopted any of these coding schemes to represent objects. Specifically, we used the population sparseness index, which is widely-used in neurophysiological studies on primates brain, to characterize the degree of sparseness at each layer in two representative DCNNs pretrained for object categorization, AlexNet and VGG11. We found that the sparse coding scheme was adopted at all layers of the DCNNs, and the degree of sparseness increased along the hierarchy. That is, the coding scheme shifted from distributed-like coding at lower layers to local-like coding at higher layers. Further, the degree of sparseness was positively correlated with DCNNs performance in object categorization, suggesting that the coding scheme was related to behavioral performance. Finally, with the lesion approach, we demonstrated that both external learning experiences and built-in gating operations were necessary to construct such a hierarchical coding scheme. In sum, our study provides direct evidence that DCNNs adopted a hierarchically-evolved sparse coding scheme as the biological brain does, suggesting an implementation-independent principle of representing a myriad of objects efficiently.