A remarkable characteristic of overparameterized deep neural networks (DNNs) is that their accuracy does not degrade when the network width is increased. Recent evidence suggests that developing compressible representations allows the complexity of large networks to be adjusted for the learning task at hand. However, these representations are poorly understood. A promising strand of research inspired from biology involves studying representations at the unit level as it offers a more granular interpretation of the neural mechanisms. In order to better understand what facilitates increases in width without decreases in accuracy, we ask: Are there mechanisms at the unit level by which networks control their effective complexity? If so, how do these depend on the architecture, dataset, and hyperparameters? We identify two distinct types of “frivolous” units that proliferate when the network’s width increases: prunable units which can be dropped out of the network without significant change to the output and redundant units whose activities can be expressed as a linear combination of others. These units imply complexity constraints as the function the network computes could be expressed without them. We also identify how the development of these units can be influenced by architecture and a number of training factors. Together, these results help to explain why the accuracy of DNNs does not degrade when width is increased and highlight the importance of frivolous units toward understanding implicit regularization in DNNs.

In the last two decades rodents have been on the rise as a dominant model for visual neuroscience. This is particularly true for earlier levels of information processing, but a number of studies have suggested that also higher levels of processing such as invariant object recognition occur in rodents. Here we provide a quantitative and comprehensive assessment of this claim by comparing a wide range of rodent behavioral and neural data with convolutional deep neural networks. These networks have been shown to capture hallmark properties of information processing in primates through a succession of convolutional and fully connected layers. We find that performance on rodent object vision tasks can be captured using low to mid-level convolutional layers only, without any convincing evidence for the need of higher layers known to simulate complex object recognition in primates. Our approach also reveals surprising insights on assumptions made before, for example, that the best performing animals would be the ones using the most abstract representations-which we show to likely be incorrect. Our findings suggest a road ahead for further studies aiming at quantifying and establishing the richness of representations underlying information processing in animal models at large.

Recent studies suggest that deep Convolutional Neural Network (CNN) models show higher representational similarity, compared to any other existing object recognition models, with macaque inferior temporal (IT) cortical responses, human ventral stream fMRI activations and human object recognition. These studies employed natural images of objects. A long research tradition employed abstract shapes to probe the selectivity of IT neurons. If CNN models provide a realistic model of IT responses, then they should capture the IT selectivity for such shapes. Here, we compare the activations of CNN units to a stimulus set of 2D regular and irregular shapes with the response selectivity of macaque IT neurons and with human similarity judgements. The shape set consisted of regular shapes that differed in nonaccidental properties, and irregular, asymmetrical shapes with curved or straight boundaries. We found that deep CNNs (Alexnet, VGG-16 and VGG-19) that were trained to classify natural images show response modulations to these shapes that were similar to those of IT neurons. Untrained CNNs with the same architecture than trained CNNs, but with random weights, demonstrated a poorer similarity than CNNs trained in classification. The difference between the trained and untrained CNNs emerged at the deep convolutional layers, where the similarity between the shape-related response modulations of IT neurons and the trained CNNs was high. Unlike IT neurons, human similarity judgements of the same shapes correlated best with the last layers of the trained CNNs. In particular, these deepest layers showed an enhanced sensitivity for straight versus curved irregular shapes, similar to that shown in human shape judgments. In conclusion, the representations of abstract shape similarity are highly comparable between macaque IT neurons and deep convolutional layers of CNNs that were trained to classify natural images, while human shape similarity judgments correlate better with the deepest layers.