Deep-learning approaches in data-driven modeling relies on learning a finite number of transformations (and representations) of the data that are structured in a hierarchy and are often instantiated as deep neural networks (and their internal activations). State-of-the-art models for visual data usually implement deep residual learning: the network learns to predict a finite number of discrete updates that are applied to the internal network state to enrich it. Pushing the residual learning idea to the limit, ODE Net—a novel network formulation involving continuously evolving internal representations that gained the best paper award at NeurIPS 2018—has been recently proposed. Differently from traditional neural networks, in this model the dynamics of the internal states are defined by an ordinary differential equation with learnable parameters that defines a continuous transformation of the input representation. These representations can be computed using standard ODE solvers, and their dynamics can be steered to learn the input-output mapping by adjusting the ODE parameters via standard gradient-based optimization. In this work, we investigate the image representation learned in the continuous hidden states of ODE Nets. In particular, we train image classifiers including ODE-defined continuous layers and perform preliminary experiments to assess the quality, in terms of transferability and generality, of the learned image representations and compare them to standard representation extracted from residual networks. Experiments on CIFAR-10 and Tiny-ImageNet-200 datasets show that representations extracted from ODE Nets are more transferable and suggest an improved robustness to overfit.
Carrara, F., Amato, G., Falchi, F., & Gennaro, C. (2019). Evaluation of continuous image features learned by ODE nets. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11751 LNCS, pp. 432–442). Springer Verlag. https://doi.org/10.1007/978-3-030-30642-7_39