Abstract. Do convolutional networks really need a fixed feed-forward structure? What if, after identifying the high-level concept of an image, a network could move directly to a layer that can distinguish finegrained differences? Currently, a network would first need to execute sometimes hundreds of intermediate layers that specialize in unrelated aspects. Ideally, the more a network already knows about an image, the better it should be at deciding which layer to compute next. In this work, we propose convolutional networks with adaptive inference graphs (ConvNet-AIG) that adaptively define their network topology conditioned on the input image. Following a high-level structure similar to residual networks (ResNets), ConvNet-AIG decides for each input image on the fly which layers are needed. In experiments on ImageNet we show that ConvNet-AIG learns distinct inference graphs for different categories. Both ConvNet-AIG with 50 and 101 layers outperform their ResNet counterpart, while using 20% and 33% less computations respectively. By grouping parameters into layers for related classes and only executing relevant layers, ConvNet-AIG improves both efficiency and overall classification quality. Lastly, we also study the effect of adaptive inference graphs on the susceptibility towards adversarial examples. We observe that ConvNet-AIG shows a higher robustness than ResNets, complementing other known defense mechanisms