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Despite recent theoretical progress on the non-convex optimization of two-layer neural networks, it is still an open question whether gradient descent on neural networks without unnatural modifications can achieve better sample complexity than kernel methods. This paper provides a clean mean-field analysis of projected gradient flow on polynomial-width two-layer neural networks. Different from prior works, our analysis does not require unnatural modifications of the optimization algorithm. We prove that with sample size $n = O(d^{3.1})$ where $d$ is the dimension of the inputs, the network converges in polynomially many iterations to a non-trivial error that is not achievable by kernel methods using $n \ll d^4$ samples, hence demonstrating a clear separation between unmodified gradient descent and NTK.

In this paper, we investigate computational power of threshold circuits and other theoretical models of neural networks in terms of the following four complexity measures: size (the number of gates), depth, weight and energy. Here the energy complexity of a circuit measures sparsity of their computation, and is defined as the maximum number of gates outputting non-zero values taken over all the input assignments. As our main result, we prove that any threshold circuit $C$ of size $s$, depth $d$, energy $e$ and weight $w$ satisfies $\log (rk(M_C)) \le ed (\log s + \log w + \log n)$, where $rk(M_C)$ is the rank of the communication matrix $M_C$ of a $2n$-variable Boolean function that $C$ computes. Thus, such a threshold circuit $C$ is able to compute only a Boolean function of which communication matrix has rank bounded by a product of logarithmic factors of $s,w$ and linear factors of $d,e$. This implies an exponential lower bound on the size of even sublinear-depth threshold circuit if energy and weight are sufficiently small. For other models of neural networks such as a discretized ReLE circuits and decretized sigmoid circuits, we prove that a similar inequality also holds for a discretized circuit $C$: $rk(M_C) = O(ed(\log s + \log w + \log n)^3)$.

Satellites have become more widely available due to the reduction in size and cost of their components. As a result, there has been an advent of smaller organizations having the ability to deploy satellites with a variety of data-intensive applications to run on them. One popular application is image analysis to detect, for example, land, ice, clouds, etc. for Earth observation. However, the resource-constrained nature of the devices deployed in satellites creates additional challenges for this resource-intensive application. In this paper, we present our work and lessons-learned on building an Image Processing Unit (IPU) for a satellite. We first investigate the performance of a variety of edge devices (comparing CPU, GPU, TPU, and VPU) for deep-learning-based image processing on satellites. Our goal is to identify devices that can achieve accurate results and are flexible when workload changes while satisfying the power and latency constraints of satellites. Our results demonstrate that hardware accelerators such as ASICs and GPUs are essential for meeting the latency requirements. However, state-of-the-art edge devices with GPUs may draw too much power for deployment on a satellite. Then, we use the findings gained from the performance analysis to guide the development of the IPU module for an upcoming satellite mission. We detail how to integrate such a module into an existing satellite architecture and the software necessary to support various missions utilizing this module.

For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations across the total number of linear system solves in the sequence. However, for general (i.e., non-identity) shifted systems with the shift value varying over a wide range, the properties of the linear systems vary widely as well, which makes recycling less effective. If such a sequence of systems is embedded in a nonlinear iteration, the problem is compounded, and special approaches are needed to use recycling effectively. In this paper, we develop new, more efficient, Krylov subspace recycling approaches for large-scale image reconstruction and restoration techniques that employ a nonlinear iteration to compute a suitable regularization matrix. For each new regularization matrix, we need to solve regularized linear systems, ${\bf A} + \gamma_\ell {\bf E}_k$, for a sequence of regularization parameters, $\gamma_\ell$, to find the optimally regularized solution that, in turn, will be used to update the regularization matrix. In this paper, we analyze system and solution characteristics to choose appropriate techniques to solve each system rapidly. Specifically, we use an inner-outer recycling approach with a larger, principal recycle space for each nonlinear step and smaller recycle spaces for each shift. We propose an efficient way to obtain good initial guesses from the principle recycle space and smaller shift-specific recycle spaces that lead to fast convergence. Our method is substantially reduces the total number of matrix-vector products that would arise in a naive approach. Our approach is more generally applicable to sequences of shifted systems where the matrices in the sum are positive semi-definite.

The multiple-choice knapsack problem (MCKP) is a classic NP-hard combinatorial optimization problem. Motivated by several significant practical applications, this work investigates a novel variant of MCKP called data-driven chance-constrained multiple-choice knapsack problem (DDCCMCKP), where the item weight is a random variable with unknown probability distribution. We first present the problem formulation of DDCCMCKP, and then establish two benchmark sets. The first set contains synthetic instances, and the second set is devised to simulate a real-world application scenario of a certain telecommunication company. To solve DDCCMCKP, we propose a data-driven adaptive local search (DDALS) algorithm. The main merit of DDALS lies in evaluating solutions with chance constraints by data-driven methods, under the condition of unknown distributions and only historical sample data being available. The experimental results demonstrate the effectiveness of the proposed algorithm and show that it is superior to other baselines. Additionally, ablation experiments confirm the necessity of each component in the algorithm. Our proposed algorithm can serve as the baseline for future research, and the code and benchmark sets will be open-sourced to further promote research on this challenging problem.

Feature-Imitating-Networks (FINs) are neural networks with weights that are initialized to approximate closed-form statistical features. In this work, we perform the first-ever evaluation of FINs for biomedical image processing tasks. We begin by training a set of FINs to imitate six common radiomics features, and then compare the performance of networks with and without the FINs for three experimental tasks: COVID-19 detection from CT scans, brain tumor classification from MRI scans, and brain-tumor segmentation from MRI scans; we find that FINs provide best-in-class performance for all three tasks, while converging faster and more consistently when compared to networks with similar or greater representational power. The results of our experiments provide evidence that FINs may provide state-of-the-art performance for a variety of other biomedical image processing tasks.

Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap in the literature by proposing a novel coevolutionary model, in which each individual selects an action from a binary set and has an opinion on which action they prefer. Actions and opinions coevolve on a two-layer network. For homogeneous parameters, undirected networks, and under reasonable assumptions on the asynchronous updating mechanics, we prove that the coevolutionary dynamics is an ordinal potential game, enabling analysis via potential game theory. Specifically, we establish global convergence to the Nash equilibria of the game, proving that actions converge in a finite number of time steps, while opinions converge asymptotically. Next, we provide sufficient conditions for the existence of, and convergence to, polarized equilibria, whereby the population splits into two communities, each selecting and supporting one of the actions. Finally, we use simulations to examine the social psychological phenomenon of pluralistic ignorance.

This paper introduces a novel approach to active feature acquisition for classification, which is the task of sequentially selecting the most informative subset of features to achieve optimal prediction performance during testing while minimizing cost. The proposed approach involves a new lazy model that is significantly faster and more efficient compared to existing methods, while still producing comparable accuracy results. During the test phase, the proposed approach utilizes Fisher scores for feature ranking to identify the most important feature at each step. In the next step the training dataset is filtered based on the observed value of the selected feature and then we continue this process to reach to acceptable accuracy or limit of the budget for feature acquisition. The performance of the proposed approach was evaluated on synthetic and real datasets, including our new synthetic dataset, CUBE dataset and also real dataset Forest. The experimental results demonstrate that our approach achieves competitive accuracy results compared to existing methods, while significantly outperforming them in terms of speed. The source code of the algorithm is released at github with this link: //github.com/alimirzaei/FCwSFS.

We consider the problem of recovering conditional independence relationships between $p$ jointly distributed Hilbertian random elements given $n$ realizations thereof. We operate in the sparse high-dimensional regime, where $n \ll p$ and no element is related to more than $d \ll p$ other elements. In this context, we propose an infinite-dimensional generalization of the graphical lasso. We prove model selection consistency under natural assumptions and extend many classical results to infinite dimensions. In particular, we do not require finite truncation or additional structural restrictions. The plug-in nature of our method makes it applicable to any observational regime, whether sparse or dense, and indifferent to serial dependence. Importantly, our method can be understood as naturally arising from a coherent maximum likelihood philosophy.

Fine-grained image analysis (FGIA) is a longstanding and fundamental problem in computer vision and pattern recognition, and underpins a diverse set of real-world applications. The task of FGIA targets analyzing visual objects from subordinate categories, e.g., species of birds or models of cars. The small inter-class and large intra-class variation inherent to fine-grained image analysis makes it a challenging problem. Capitalizing on advances in deep learning, in recent years we have witnessed remarkable progress in deep learning powered FGIA. In this paper we present a systematic survey of these advances, where we attempt to re-define and broaden the field of FGIA by consolidating two fundamental fine-grained research areas -- fine-grained image recognition and fine-grained image retrieval. In addition, we also review other key issues of FGIA, such as publicly available benchmark datasets and related domain-specific applications. We conclude by highlighting several research directions and open problems which need further exploration from the community.