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Deep feedforward and recurrent rate-based neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions, and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

We consider hypergraph network design problems where the goal is to construct a hypergraph satisfying certain properties. In graph network design problems, the number of edges in an arbitrary solution is at most the square of the number of vertices. In contrast, in hypergraph network design problems, the number of hyperedges in an arbitrary solution could be exponential in the number of vertices and hence, additional care is necessary to design polynomial-time algorithms. The central theme of this work is to show that certain hypergraph network design problems admit solutions with polynomial number of hyperedges and moreover, can be solved in strongly polynomial time. Our work improves on the previous fastest pseudo-polynomial run-time for these problems. In addition, we develop algorithms that return (near-)uniform hypergraphs as solutions. The hypergraph network design problems that we focus upon are splitting-off operation in hypergraphs, connectivity augmentation using hyperedges, and covering skew-supermodular functions using hyperedges. Our definition of the splitting-off operation in hypergraphs and our proof showing the existence of the operation using a strongly polynomial-time algorithm to compute it are likely to be of independent graph-theoretical interest.

Efficient and robust control using spiking neural networks (SNNs) is still an open problem. Whilst behaviour of biological agents is produced through sparse and irregular spiking patterns, which provide both robust and efficient control, the activity patterns in most artificial spiking neural networks used for control are dense and regular -- resulting in potentially less efficient codes. Additionally, for most existing control solutions network training or optimization is necessary, even for fully identified systems, complicating their implementation in on-chip low-power solutions. The neuroscience theory of Spike Coding Networks (SCNs) offers a fully analytical solution for implementing dynamical systems in recurrent spiking neural networks -- while maintaining irregular, sparse, and robust spiking activity -- but it's not clear how to directly apply it to control problems. Here, we extend SCN theory by incorporating closed-form optimal estimation and control. The resulting networks work as a spiking equivalent of a linear-quadratic-Gaussian controller. We demonstrate robust spiking control of simulated spring-mass-damper and cart-pole systems, in the face of several perturbations, including input- and system-noise, system disturbances, and neural silencing. As our approach does not need learning or optimization, it offers opportunities for deploying fast and efficient task-specific on-chip spiking controllers with biologically realistic activity.

We study the validity of the Neumann or Born series approach in solving the Helmholtz equation and coefficient identification in related inverse scattering problems. Precisely, we derive a sufficient and necessary condition under which the series is strongly convergent. We also investigate the rate of convergence of the series. The obtained condition is optimal and it can be much weaker than the traditional requirement for the convergence of the series. Our approach makes use of reduction space techniques proposed by Suzuki \cite{Suzuki-1976}. Furthermore we propose an interpolation method that allows the use of the Neumann series in all cases. Finally, we provide several numerical tests with different medium functions and frequency values to validate our theoretical results.

We present a neural network approach to compute stream functions, which are scalar functions with gradients orthogonal to a given vector field. As a result, isosurfaces of the stream function extract stream surfaces, which can be visualized to analyze flow features. Our approach takes a vector field as input and trains an implicit neural representation to learn a stream function for that vector field. The network learns to map input coordinates to a stream function value by minimizing the inner product of the gradient of the neural network's output and the vector field. Since stream function solutions may not be unique, we give optional constraints for the network to learn particular stream functions of interest. Specifically, we introduce regularizing loss functions that can optionally be used to generate stream function solutions whose stream surfaces follow the flow field's curvature, or that can learn a stream function that includes a stream surface passing through a seeding rake. We also discuss considerations for properly visualizing the trained implicit network and extracting artifact-free surfaces. We compare our results with other implicit solutions and present qualitative and quantitative results for several synthetic and simulated vector fields.

Binary neural networks leverage $\mathrm{Sign}$ function to binarize weights and activations, which require gradient estimators to overcome its non-differentiability and will inevitably bring gradient errors during backpropagation. Although many hand-designed soft functions have been proposed as gradient estimators to better approximate gradients, their mechanism is not clear and there are still huge performance gaps between binary models and their full-precision counterparts. To address these issues and reduce gradient error, we propose to tackle network binarization as a binary classification problem and use a multi-layer perceptron (MLP) as the classifier in the forward pass and gradient estimator in the backward pass. Benefiting from the MLP's theoretical capability to fit any continuous function, it can be adaptively learned to binarize networks and backpropagate gradients without any prior knowledge of soft functions. From this perspective, we further empirically justify that even a simple linear function can outperform previous complex soft functions. Extensive experiments demonstrate that the proposed method yields surprising performance both in image classification and human pose estimation tasks. Specifically, we achieve $65.7\%$ top-1 accuracy of ResNet-34 on ImageNet dataset, with an absolute improvement of $2.6\%$. Moreover, we take binarization as a lightweighting approach for pose estimation models and propose well-designed binary pose estimation networks SBPN and BHRNet. When evaluating on the challenging Microsoft COCO keypoint dataset, the proposed method enables binary networks to achieve a mAP of up to $60.6$ for the first time. Experiments conducted on real platforms demonstrate that BNN achieves a better balance between performance and computational complexity, especially when computational resources are extremely low.

Artificial Intelligence is present in the generation and distribution of culture. How do artists exploit neural networks? What impact do these algorithms have on artistic practice? Through a practice-based research methodology, this paper explores the potentials and limits of current AI technology, more precisely deep neural networks, in the context of image, text, form and translation of semiotic spaces. In a relatively short time, the generation of high-resolution images and 3D objects has been achieved. There are models, like CLIP and text2mesh, that do not need the same kind of media input as the output; we call them translation models. Such a twist contributes toward creativity arousal, which manifests itself in art practice and feeds back to the developers' pipeline. Yet again, we see how artworks act as catalysts for technology development. Those creative scenarios and processes are enabled not solely by AI models, but by the hard work behind implementing these new technologies. AI does not create a 'push-a-button' masterpiece but requires a deep understanding of the technology behind it, and a creative and critical mindset. Thus, AI opens new avenues for inspiration and offers novel tool sets, and yet again the question of authorship is asked.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.

Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.