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Despite their elegant formulation and lightweight memory cost, neural ordinary differential equations (NODEs) suffer from known representational limitations. In particular, the single flow learned by NODEs cannot express all homeomorphisms from a given data space to itself, and their static weight parameterization restricts the type of functions they can learn compared to discrete architectures with layer-dependent weights. Here, we describe a new module called neurally-controlled ODE (N-CODE) designed to improve the expressivity of NODEs. The parameters of N-CODE modules are dynamic variables governed by a trainable map from initial or current activation state, resulting in forms of open-loop and closed-loop control, respectively. A single module is sufficient for learning a distribution on non-autonomous flows that adaptively drive neural representations. We provide theoretical and empirical evidence that N-CODE circumvents limitations of previous NODEs models and show how increased model expressivity manifests in several supervised and unsupervised learning problems. These favorable empirical results indicate the potential of using data- and activity-dependent plasticity in neural networks across numerous domains. 

The goal of this review is to bring together material from cognitive psychology with recent machine vision studies to identify plausible neural mechanisms for visual same-different discrimination and relational understanding. We highlight how developments in the study of artificial neural networks provide computational evidence implicating attention and working memory in the ascertaining of visual relations, including same- different relations. We review some recent attempts to incorporate these mechanisms into flexible models of visual reasoning. Particular attention is given to recent models jointly trained on visual and linguistic information. These recent systems are promising, but they still fall short of the biological standard in several ways, which we outline in a final section. 

The development of deep convolutional neural networks (CNNs) has recently led to great successes in computer vision and CNNs have become de facto computational models of vision. However, a growing body of work suggests that they exhibit critical limitations beyond image categorization. Here, we study one such fundamental limitation, for judging whether two simultaneously presented items are the same or different (SD) compared to a baseline assessment of their spatial relationship (SR). In both human subjects and artificial neural networks, we test the prediction that SD tasks recruit additional cortical mechanisms which underlie critical aspects of visual cognition that are not explained by current computational models. We thus recorded EEG signals from human participants engaged in the same tasks as the computational models. Importantly, in humans the two tasks were matched in terms of difficulty by an adaptive psychometric procedure: yet, on top of a modulation of evoked potentials, our results revealed higher activity in the low beta (16-24Hz) band in the SD compared to the SR conditions. We surmise that these oscillations reflect the crucial involvement of additional mechanisms, such as working memory and attention, which are missing in current feed-forward CNNs.