Deep Convolutional Neural Networks (DCNNs) have demonstrated impressive robustness to recognize objects under transformations (eg. blur or noise) when these transformations are included in the training set. A hypothesis to explain such robustness is that DCNNs develop invariant neural representations that remain unaltered when the image is transformed. However, to what extent this hypothesis holds true is an outstanding question, as robustness to transformations could be achieved with properties different from invariance, eg. parts of the network could be specialized to recognize either transformed or non-transformed images. This paper investigates the conditions under which invariant neural representations emerge by leveraging that they facilitate robustness to transformations beyond the training distribution. Concretely, we analyze a training paradigm in which only some object categories are seen transformed during training and evaluate whether the DCNN is robust to transformations across categories not seen transformed. Our results with state-of-the-art DCNNs indicate that invariant neural representations do not always drive robustness to transformations, as networks show robustness for categories seen transformed during training even in the absence of invariant neural representations. Invariance only emerges as the number of transformed categories in the training set is increased. This phenomenon is much more prominent with local transformations such as blurring and high-pass filtering than geometric transformations such as rotation and thinning, which entail changes in the spatial arrangement of the object. Our results contribute to a better understanding of invariant neural representations in deep learning and the conditions under which it spontaneously emerges.

The information transmission rate (ITR), or effective bit rate, is a popular and widely used information measurement metric, particularly popularized for SSVEP-based Brain-Computer (BCI) interfaces. By combining speed and accuracy into a single-valued parameter, this metric aids in the evaluation and comparison of various target identification algorithms across different BCI communities. In order to calculate ITR, it is customary to assume a uniform input distribution and an oversimplified channel model that is memoryless, stationary, and symmetrical in nature with discrete alphabet sizes. To accurately depict performance and inspire an end-to-end design for futuristic BCI designs, a more thorough examination and definition of ITR is therefore required. We model the symbiotic communication medium, hosted by the retinogeniculate visual pathway, as a discrete memoryless channel and use the modified capacity expressions to redefine the ITR. We leverage a result for directed graphs to characterize the relationship between the asymmetry of the transition statistics and the ITR gain due to the new definition, leading to potential bounds on data rate performance. On two well-known SSVEP datasets, we compared two cutting-edge target identification methods. Results indicate that the induced DM channel asymmetry has a greater impact on the actual perceived ITR than the change in input distribution. Moreover, it is demonstrated that the ITR gain under the new definition is inversely correlated with the asymmetry in the channel transition statistics. Individual input customizations are further shown to yield perceived ITR performance improvements. Finally, an algorithm is proposed to find the capacity of binary classification and further discussions are given to extend such results to multi-class case through ensemble techniques.

The training data distribution is often biased towards objects in certain orientations and illumination conditions. While humans have a remarkable capability of recognizing objects in out-of-distribution (OoD) orientations and illuminations, Deep Neural Networks (DNNs) severely suffer in this case, even when large amounts of training examples are available. In this paper, we investigate three different approaches to improve DNNs in recognizing objects in OoD orientations and illuminations. Namely, these are (i) training much longer after convergence of the in-distribution (InD) validation accuracy, i.e., late-stopping, (ii) tuning the momentum parameter of the batch normalization layers, and (iii) enforcing invariance of the neural activity in an intermediate layer to orientation and illumination conditions. Each of these approaches substantially improves the DNN's OoD accuracy (more than 20% in some cases). We report results in four datasets: two datasets are modified from the MNIST and iLab datasets, and the other two are novel (one of 3D rendered cars and another of objects taken from various controlled orientations and illumination conditions). These datasets allow to study the effects of different amounts of bias and are challenging as DNNs perform poorly in OoD conditions. Finally, we demonstrate that even though the three approaches focus on different aspects of DNNs, they all tend to lead to the same underlying neural mechanism to enable OoD accuracy gains -- individual neurons in the intermediate layers become more selective to a category and also invariant to OoD orientations and illuminations.

The capability of Deep Neural Networks (DNNs) to recognize objects in orientations outside the distribution of the training data, ie. out-of-distribution (OoD) orientations, is not well understood. For humans, behavioral studies showed that recognition accuracy varies across OoD orientations, where generalization is much better for some orientations than for others. In contrast, for DNNs, it remains unknown how generalization abilities are distributed among OoD orientations. In this paper, we investigate the limitations of DNNs' generalization capacities by systematically inspecting patterns of success and failure of DNNs across OoD orientations. We use an intuitive and controlled, yet challenging learning paradigm, in which some instances of an object category are seen at only a few geometrically restricted orientations, while other instances are seen at all orientations. The effect of data diversity is also investigated by increasing the number of instances seen at all orientations in the training set. We present a comprehensive analysis of DNNs' generalization abilities and limitations for representative architectures (ResNet, Inception, DenseNet and CORnet). Our results reveal an intriguing pattern -- DNNs are only capable of generalizing to instances of objects that appear like 2D, ie. in-plane, rotations of in-distribution orientations.

A key question in neuroscience is how to encode sensory stimuli such as images and sounds. Motivated by studies of response properties of neurons in the early cortical areas, we propose an encoding scheme that dispenses with absolute measures of signal intensity or contrast and uses, instead, only local ordinal measures. In this scheme, the structure of a signal is represented by a set of equalities and inequalities across adjacent regions. In this paper, we focus on characterizing the fidelity of this representation strategy. We develop a regularization approach for image reconstruction from ordinal measures and thereby demonstrate that the ordinal representation scheme can faithfully encode signal structure. We also present a neurally plausible implementation of this computation that uses only local update rules.

Infinitely many reconstruction functions could satisfy the given ordinal constraints.