The Neural Tangent Kernel is an important milestone in the ongoing effort to build a theory for deep learning. Its prediction that sufficiently wide neural networks behave as kernel methods, or equivalently as random feature models arising from linearized networks, has been confirmed empirically for certain wide architectures. In this paper, we compare the performance of two common finite-width convolutional neural networks, LeNet and AlexNet, to their linearizations on common benchmark datasets like MNIST and modified versions of it, CIFAR-10 and an ImageNet subset. We demonstrate empirically that finite-width neural networks, generally, greatly outperform the finite-width linearization of these architectures. When increasing the problem difficulty of the classification task, we observe a larger gap which is in line with common intuition that finite-width neural networks perform feature learning which finite-width linearizations cannot. At the same time, finite-width linearizations improve dramatically with width, approaching the behavior of the wider standard networks which in turn perform slightly better than their standard width counterparts. Therefore, it appears that feature learning for non-wide standard networks is important but becomes less significant with increasing width. We furthermore identify cases where both standard and linearized networks match in performance, in agreement with NTK theory, and a case where a wide linearization outperforms its standard width counterpart.

Abstract Archetypes represent extreme manifestations of a population with respect to specific characteristic traits or features. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. As mixing of archetypes is performed directly on the input data, linear Archetypal Analysis requires additivity of the input, which is a strong assumption unlikely to hold e.g. in case of image data. To address this problem, we propose learning an appropriate latent feature space while simultaneously identifying suitable archetypes. We thus introduce a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a deep variational information bottleneck and an optimal representation, together with the archetypes, can be learned end-to-end. Moreover, the information bottleneck framework allows for a natural incorporation of arbitrarily complex side information during training. As a consequence, learned archetypes become easily interpretable as they derive their meaning directly from the included side information. Applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. By using different kinds of side information we demonstrate how identified archetypes, along with their interpretation, largely depend on the side information provided.