This editorial summarizes selected key contributions of Prof. Stephen Grossberg and describes the papers in this 80th birthday special issue in his honor. His productivity, creativity, and vision would each be enough to mark a scientist of the first caliber. In combination, they have resulted in contributions that have changed the entire discipline of neural networks. Grossberg has been tremendously influential in engineering, dynamical systems, and artificial intelligence as well. Indeed, he has been one of the most important mentors and role models in my career, and has done so with extraordinary generosity and encouragement. All authors in this special issue have taken great pleasure in hereby commemorating his extraordinary career and contributions.

We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation. The input to our method is a dataset (or ensemble of datasets) corresponding to a particular solution (or ensemble of particular solutions) of a differential equation. The output is a human-readable differential equation with parameters calibrated to the individual particular solutions provided. The key to our method is to learn differentiable models of the data that subsequently serve as inputs to a genetic programming algorithm in which graphs specify computation over arbitrary compositions of functions, parameters, and (potentially differential) operators on functions. Differential operators are composed and evaluated using recursive application of automatic differentiation, allowing our algorithm to explore arbitrary compositions of operators without the need for human intervention. We also demonstrate an active learning process to identify and remedy deficiencies in the proposed governing equations.

With the recent success of deep neural networks in computer vision, it is important to understand the internal working of these networks. What does a given neuron represent? The concepts captured by a neuron may be hard to understand or express in simple terms. The approach we propose in this paper is to characterize the region of input space that excites a given neuron to a certain level; we call this the inverse set. This inverse set is a complicated high dimensional object that we explore by an optimization-based sampling approach. Inspection of samples of this set by a human can reveal regularities that help to understand the neuron. This goes beyond approaches which were limited to finding an image which maximally activates the neuron or using Markov chain Monte Carlo to sample images, but this is very slow, generates samples with little diversity and lacks control over the activation value of the generated samples. Our approach also allows us to explore the intersection of inverse sets of several neurons and other variations.

In this paper we consider the problem of video-based person re-identification, which is the task of associating videos of the same person captured by different and non-overlapping cameras. We propose a Siamese framework in which video frames of the person to re-identify and of the candidate one are processed by two identical networks which produce a similarity score. We introduce an attention mechanisms to capture the relevant information both at frame level (spatial information) and at video level (temporal information given by the importance of a specific frame within the sequence). One of the novelties of our approach is given by a joint concurrent processing of both frame and video levels, providing in such a way a very simple architecture. Despite this fact, out approach achieves better performance than the state-of-the-art on the challenging iLIDS-VID dataset.

In this paper, we study the novel problem of not only predicting ingredients from a food image, but also predicting the relative amounts of the detected ingredients. We propose two prediction-based models using deep learning that output sparse and dense predictions, coupled with important semi-automatic multi-database integrative data pre-processing, to solve the problem. Experiments on a dataset of recipes collected from the Internet show the models generate encouraging experimental results.

Arbitrary style transfer is an important problem in computer vision that aims to transfer style patterns from an arbitrary style image to a given content image. However, current methods either rely on slow iterative optimization or fast pre-determined feature transformation, but at the cost of compromised visual quality of the styled image; especially, distorted content structure. In this work, we present an effective and efficient approach for arbitrary style transfer that seamlessly transfers style patterns as well as keep content structure intact in the styled image. We achieve this by aligning style features to content features using rigid alignment; thus modifying style features, unlike the existing methods that do the opposite. We demonstrate the effectiveness of the proposed approach by generating high-quality stylized images and compare the results with the current state-of-the-art techniques for arbitrary style transfer.

Machine learning models for medical image analysis often suffer from poor performance on important subsets of a population that are not identified during training or testing. For example, overall performance of a cancer detection model may be high, but the model still consistently misses a rare but aggressive cancer subtype. We refer to this problem as hidden stratification, and observe that it results from incompletely describing the meaningful variation in a dataset. While hidden stratification can substantially reduce the clinical efficacy of machine learning models, its effects remain difficult to measure. In this work, we assess the utility of several possible techniques for measuring and describing hidden stratification effects, and characterize these effects both on multiple medical imaging datasets and via synthetic experiments on the well-characterised CIFAR-100 benchmark dataset. We find evidence that hidden stratification can occur in unidentified imaging subsets with low prevalence, low label quality, subtle distinguishing features, or spurious correlates, and that it can result in relative performance differences of over 20% on clinically important subsets. Finally, we explore the clinical implications of our findings, and suggest that evaluation of hidden stratification should be a critical component of any machine learning deployment in medical imaging.

We study the problem of training machine learning models incrementally using active learning with access to imperfect or noisy oracles. We specifically consider the setting of batch active learning, in which multiple samples are selected as opposed to a single sample as in classical settings so as to reduce the training overhead. Our approach bridges between uniform randomness and score based importance sampling of clusters when selecting a batch of new samples. Experiments on benchmark image classification datasets (MNIST, SVHN, and CIFAR10) shows improvement over existing active learning strategies. We introduce an extra denoising layer to deep networks to make active learning robust to label noises and show significant improvements.

In the total least squares problem, one is given an $m \times n$ matrix $A$, and an $m \times d$ matrix $B$, and one seeks to "correct" both $A$ and $B$, obtaining matrices $\hat{A}$ and $\hat{B}$, so that there exists an $X$ satisfying the equation $\hat{A}X = \hat{B}$. Typically the problem is overconstrained, meaning that $m \gg \max(n,d)$. The cost of the solution $\hat{A}, \hat{B}$ is given by $\|A-\hat{A}\|_F^2 + \|B - \hat{B}\|_F^2$. We give an algorithm for finding a solution $X$ to the linear system $\hat{A}X=\hat{B}$ for which the cost $\|A-\hat{A}\|_F^2 + \|B-\hat{B}\|_F^2$ is at most a multiplicative $(1+\epsilon)$ factor times the optimal cost, up to an additive error $\eta$ that may be an arbitrarily small function of $n$. Importantly, our running time is $\tilde{O}( \mathrm{nnz}(A) + \mathrm{nnz}(B) ) + \mathrm{poly}(n/\epsilon) \cdot d$, where for a matrix $C$, $\mathrm{nnz}(C)$ denotes its number of non-zero entries. Importantly, our running time does not directly depend on the large parameter $m$. As total least squares regression is known to be solvable via low rank approximation, a natural approach is to invoke fast algorithms for approximate low rank approximation, obtaining matrices $\hat{A}$ and $\hat{B}$ from this low rank approximation, and then solving for $X$ so that $\hat{A}X = \hat{B}$. However, existing algorithms do not apply since in total least squares the rank of the low rank approximation needs to be $n$, and so the running time of known methods would be at least $mn^2$. In contrast, we are able to achieve a much faster running time for finding $X$ by never explicitly forming the equation $\hat{A} X = \hat{B}$, but instead solving for an $X$ which is a solution to an implicit such equation. Finally, we generalize our algorithm to the total least squares problem with regularization.

One of the primary challenges of visual storytelling is developing techniques that can maintain the context of the story over long event sequences to generate human-like stories. In this paper, we propose a hierarchical deep learning architecture based on encoder-decoder networks to address this problem. To better help our network maintain this context while also generating long and diverse sentences, we incorporate natural language image descriptions along with the images themselves to generate each story sentence. We evaluate our system on the Visual Storytelling (VIST) dataset and show that our method outperforms state-of-the-art techniques on a suite of different automatic evaluation metrics. The empirical results from this evaluation demonstrate the necessities of different components of our proposed architecture and shows the effectiveness of the architecture for visual storytelling.