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We consider Upper Domination, the problem of finding the minimal dominating set of maximum cardinality. Very few exact algorithms have been described for solving Upper Domination. In particular, no binary programming formulations for Upper Domination have been described in literature, although such formulations have proved quite successful for other kinds of domination problems. We introduce two such binary programming formulations, and show that both can be improved with the addition of extra constraints which reduce the number of feasible solutions. We compare the performance of the formulations on various kinds of graphs, and demonstrate that (a) the additional constraints improve the performance of both formulations, and (b) the first formulation outperforms the second in most cases, although the second performs better for very sparse graphs. Also included is a short proof that the upper domination number of any generalized Petersen graph P(n,k) is equal to n.

Public blockchains group submitted transactions into batches, called blocks. A natural question is how to determine which transactions are included in these batches. In this note, we show a gap between the welfare of so-called `fair' ordering, namely first-in-first-out (an ideal that a number of blockchain protocols strive to achieve), where the first transactions to arrive are the ones put into the block, and the welfare of `optimal' inclusion that is, at least approximately, welfare-maximizing, such as choosing which transactions are included in a block via an auction. We show this gap is positive under a simple model with mild assumptions where we assume transactions are, roughly speaking, uniformly drawn from a reasonable distribution. Our results formalize a performance metric for blockchain inclusion rules and consequently provide a framework to help design and compare these rules. The results can be directly extended to ordering mechanisms as well.

Throughout the analytical revolution that has occurred in the NBA, the development of specific metrics and formulas has given teams, coaches, and players a new way to see the game. However - the question arises - how can we verify any metrics? One method would simply be eyeball approximation (trying out many different gameplans) and/or trial and error - an estimation-based and costly approach. Another approach is to try to model already existing metrics with a unique set of features using machine learning techniques. The key to this approach is that with these features that are selected, we can try to gauge the effectiveness of these features combined, rather than using individual analysis in simple metric evaluation. If we have an accurate model, it can particularly help us determine the specifics of gameplan execution. In this paper, the statistic ORTG (Offensive Rating, developed by Dean Oliver) was found to have a correlation with different NBA playtypes using both a linear regression model and a neural network regression model, although ultimately, a neural network worked slightly better than linear regression. Using the accuracy of the models as a justification, the next step was to optimize the output of the model with test examples, which would demonstrate the combination of features to best achieve a highly functioning offense.

Achieving success in agricultural activities heavily relies on precise navigation in row crop fields. Recently, segmentation-based navigation has emerged as a reliable technique when GPS-based localization is unavailable or higher accuracy is needed due to vegetation or unfavorable weather conditions. It also comes in handy when plants are growing rapidly and require an online adaptation of the navigation algorithm. This work applies a segmentation-based visual agnostic navigation algorithm to lavender fields, considering both simulation and real-world scenarios. The effectiveness of this approach is validated through a wide set of experimental tests, which show the capability of the proposed solution to generalize over different scenarios and provide highly-reliable results.

Functional encryption is a powerful paradigm for public-key encryption which allows for controlled access to encrypted data. This primitive is generally impossible in the standard setting so we investigate possibilities in the bounded quantum storage model (BQSM) and the bounded classical storage model (BCSM). In these models, ciphertexts potentially disappear which nullifies impossibility results and allows us to obtain positive outcomes. Firstly, in the BQSM, we construct information-theoretically secure functional encryption with $\texttt{q}=O(\sqrt{\texttt{s}/\texttt{r}})$ where $\texttt{r}$ can be set to any value less than $\texttt{s}$. Here $\texttt{r}$ denotes the number of times that an adversary is restricted to $\texttt{s}$--qubits of quantum memory in the protocol and $\texttt{q}$ denotes the required quantum memory to run the protocol honestly. We then show that our scheme is optimal by proving that it is impossible to attain information-theoretically secure functional encryption with $\texttt{q} < \sqrt{\texttt{s}/\texttt{r}}$. However, by assuming the existence of post-quantum one-way functions, we can do far better and achieve functional encryption with classical keys and with $\texttt{q}=0$ and $\texttt{r}=1$. Secondly, in the BCSM, we construct $(O(\texttt{n}),\texttt{n}^2)$ functional encryption assuming the existence of $(\texttt{n},\texttt{n}^2)$ virtual weak grey-box obfuscation. Here, the pair $(\texttt{n},\texttt{n}^2)$ indicates the required memory to run honestly and the needed memory to break security, respectively. This memory gap is optimal and the assumption is minimal. In particular, we also construct $(O(\texttt{n}),\texttt{n}^2)$ virtual weak grey-box obfuscation assuming $(\texttt{n},\texttt{n}^2)$ functional encryption.

Recent work in algorithmic fairness has highlighted the challenge of defining racial categories for the purposes of anti-discrimination. These challenges are not new but have previously fallen to the state, which enacts race through government statistics, policies, and evidentiary standards in anti-discrimination law. Drawing on the history of state race-making, we examine how longstanding questions about the nature of race and discrimination appear within the algorithmic fairness literature. Through a content analysis of 60 papers published at FAccT between 2018 and 2020, we analyze how race is conceptualized and formalized in algorithmic fairness frameworks. We note that differing notions of race are adopted inconsistently, at times even within a single analysis. We also explore the institutional influences and values associated with these choices. While we find that categories used in algorithmic fairness work often echo legal frameworks, we demonstrate that values from academic computer science play an equally important role in the construction of racial categories. Finally, we examine the reasoning behind different operationalizations of race, finding that few papers explicitly describe their choices and even fewer justify them. We argue that the construction of racial categories is a value-laden process with significant social and political consequences for the project of algorithmic fairness. The widespread lack of justification around the operationalization of race reflects institutional norms that allow these political decisions to remain obscured within the backstage of knowledge production.

Diffusion models have demonstrated impressive generative capabilities, but their 'exposure bias' problem, described as the input mismatch between training and sampling, lacks in-depth exploration. In this paper, we systematically investigate the exposure bias problem in diffusion models by first analytically modelling the sampling distribution, based on which we then attribute the prediction error at each sampling step as the root cause of the exposure bias issue. Furthermore, we discuss potential solutions to this issue and propose an intuitive metric for it. Along with the elucidation of exposure bias, we propose a simple, yet effective, training-free method called Epsilon Scaling to alleviate the exposure bias. We show that Epsilon Scaling explicitly moves the sampling trajectory closer to the vector field learned in the training phase by scaling down the network output (Epsilon), mitigating the input mismatch between training and sampling. Experiments on various diffusion frameworks (ADM, DDPM/DDIM, EDM, LDM), unconditional and conditional settings, and deterministic vs. stochastic sampling verify the effectiveness of our method. The code is available at //github.com/forever208/ADM-ES; //github.com/forever208/EDM-ES

The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.

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.

A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.