FractalNet: Ultra-Deep Neural Networks without Residuals

We introduce a design strategy for neural network macro-architecture based on selfsimilarity. Repeated application of a single expansion rule generates an extremely deep network whose structural layout is precisely a truncated fractal. Such a network contains interacting subpaths of different lengths, but does not include any pass-through connections: every internal signal is transformed by a filter and nonlinearity before being seen by subsequent layers. This property stands in stark contrast to the current approach of explicitly structuring very deep networks so that training is a residual learning problem. Our experiments demonstrate that residual representation is not fundamental to the success of extremely deep convolutional neural networks. A fractal design achieves an error rate of 22.85% on CIFAR-100, matching the state-of-the-art held by residual networks. Fractal networks exhibit intriguing properties beyond their high performance. They can be regarded as a computationally efficient implicit union of subnetworks of every depth. We explore consequences for training, touching upon connection with student-teacher behavior, and, most importantly, demonstrating the ability to extract high-performance fixed-depth subnetworks. To facilitate this latter task, we develop drop-path, a natural extension of dropout, to regularize co-adaptation of subpaths in fractal architectures. With such regularization, fractal networks exhibit an anytime property: shallow subnetworks provide a quick answer, while deeper subnetworks, with higher latency, provide a more accurate answer.