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With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic autoencoder architecture that includes a lightweight nonlinear encoder, a convex combination decoder, and a smooth clustering network. Supported by several proofs, the model architecture ensures that all reconstructed states lie within a polytope, accompanied by a metric indicating the quality of the constructed polytopes, referred to as polytope error. Additionally, it offers a minimal number of convex coordinates for polytopic linear-parameter varying systems while achieving acceptable reconstruction errors compared to proper orthogonal decomposition (POD). To validate our proposed model, we conduct simulations involving two flow scenarios with the incompressible Navier-Stokes equation. Numerical results demonstrate the guaranteed properties of the model, low reconstruction errors compared to POD, and the improvement in error using a clustering network.

In this paper, we formulate the multi-agent graph bandit problem as a multi-agent extension of the graph bandit problem introduced by Zhang, Johansson, and Li [CISS 57, 1-6 (2023)]. In our formulation, $N$ cooperative agents travel on a connected graph $G$ with $K$ nodes. Upon arrival at each node, agents observe a random reward drawn from a node-dependent probability distribution. The reward of the system is modeled as a weighted sum of the rewards the agents observe, where the weights capture the decreasing marginal reward associated with multiple agents sampling the same node at the same time. We propose an Upper Confidence Bound (UCB)-based learning algorithm, Multi-G-UCB, and prove that its expected regret over $T$ steps is bounded by $O(N\log(T)[\sqrt{KT} + DK])$, where $D$ is the diameter of graph $G$. Lastly, we numerically test our algorithm by comparing it to alternative methods.

In the quest for unveiling novel categories at test time, we confront the inherent limitations of traditional supervised recognition models that are restricted by a predefined category set. While strides have been made in the realms of self-supervised and open-world learning towards test-time category discovery, a crucial yet often overlooked question persists: what exactly delineates a category? In this paper, we conceptualize a category through the lens of optimization, viewing it as an optimal solution to a well-defined problem. Harnessing this unique conceptualization, we propose a novel, efficient and self-supervised method capable of discovering previously unknown categories at test time. A salient feature of our approach is the assignment of minimum length category codes to individual data instances, which encapsulates the implicit category hierarchy prevalent in real-world datasets. This mechanism affords us enhanced control over category granularity, thereby equipping our model to handle fine-grained categories adeptly. Experimental evaluations, bolstered by state-of-the-art benchmark comparisons, testify to the efficacy of our solution in managing unknown categories at test time. Furthermore, we fortify our proposition with a theoretical foundation, providing proof of its optimality. Our code is available at //github.com/SarahRastegar/InfoSieve.

To ensure the fairness and trustworthiness of machine learning (ML) systems, recent legislative initiatives and relevant research in the ML community have pointed out the need to document the data used to train ML models. Besides, data-sharing practices in many scientific domains have evolved in recent years for reproducibility purposes. In this sense, the adoption of these practices by academic institutions has encouraged researchers to publish their data and technical documentation in peer-reviewed publications such as data papers. In this study, we analyze how this scientific data documentation meets the needs of the ML community and regulatory bodies for its use in ML technologies. We examine a sample of 4041 data papers of different domains, assessing their completeness and coverage of the requested dimensions, and trends in recent years, putting special emphasis on the most and least documented dimensions. As a result, we propose a set of recommendation guidelines for data creators and scientific data publishers to increase their data's preparedness for its transparent and fairer use in ML technologies.

In this paper, we consider an unmanned aerial vehicle (UAV)-enabled emergency communication system, which establishes temporary communication link with users equipment (UEs) in a typical disaster environment with mountainous forest and obstacles. Towards this end, a joint deployment, power allocation, and user association optimization problem is formulated to maximize the total transmission rate, while considering the demand of each UE and the disaster environment characteristics. Then, an alternating optimization algorithm is proposed by integrating coalition game and virtual force approach which captures the impact of the demand priority of UEs and the obstacles to the flight path and consumed power. Simulation results demonstrate that the computation time consumed by our proposed algorithm is only $5.6\%$ of the traditional heuristic algorithms, which validates its effectiveness in disaster scenarios.

In this paper, we propose an efficient approach for the compression and representation of volumetric data utilizing coordinate-based networks and multi-resolution hash encoding. Efficient compression of volumetric data is crucial for various applications, such as medical imaging and scientific simulations. Our approach enables effective compression by learning a mapping between spatial coordinates and intensity values. We compare different encoding schemes and demonstrate the superiority of multi-resolution hash encoding in terms of compression quality and training efficiency. Furthermore, we leverage optimization-based meta-learning, specifically using the Reptile algorithm, to learn weight initialization for neural representations tailored to volumetric data, enabling faster convergence during optimization. Additionally, we compare our approach with state-of-the-art methods to showcase improved image quality and compression ratios. These findings highlight the potential of coordinate-based networks and multi-resolution hash encoding for an efficient and accurate representation of volumetric data, paving the way for advancements in large-scale data visualization and other applications.

In this paper, we investigate the complexity of feed-forward neural networks by examining the concept of functional equivalence, which suggests that different network parameterizations can lead to the same function. We utilize the permutation invariance property to derive a novel covering number bound for the class of feedforward neural networks, which reveals that the complexity of a neural network can be reduced by exploiting this property. We discuss the extensions to convolutional neural networks, residual networks, and attention-based models. We demonstrate that functional equivalence benefits optimization, as overparameterized networks tend to be easier to train since increasing network width leads to a diminishing volume of the effective parameter space. Our findings offer new insights into overparameterization and have significant implications for understanding generalization and optimization in deep learning.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.