Deep Continuous Networks
Nergis Tomen Silvia L. Pintea Jan C. van Gemert
CNNs and computational models of biological vision share some fundamental
principles, which opened new avenues of research. However, fruitful cross-field
research is hampered by conventional CNN architectures being based on spatially
and depthwise discrete representations, which cannot accommodate certain
aspects of biological complexity such as continuously varying receptive field
sizes and dynamics of neuronal responses. Here we propose deep continuous
networks (DCNs), which combine spatially continuous filters, with the
continuous depth framework of neural ODEs. This allows us to learn the spatial
support of the filters during training, as well as model the continuous
evolution of feature maps, linking DCNs closely to biological models. We show
that DCNs are versatile and highly applicable to standard image classification
and reconstruction problems, where they improve parameter and data efficiency,
and allow for meta-parametrization. We illustrate the biological plausibility
of the scale distributions learned by DCNs and explore their performance in a
neuroscientifically inspired pattern completion task. Finally, we investigate
an efficient implementation of DCNs by changing input contrast.