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We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a configuration-type LP and using a rounding procedure for (utilitarian) social welfare as a blackbox, which could be applicable to other variants of the problem.

We consider the linear lambda-calculus extended with the sup type constructor, which provides an additive conjunction along with a non-deterministic destructor. The sup type constructor has been introduced in the context of quantum computing. In this paper, we study this type constructor within a simple linear logic categorical model, employing the category of semimodules over a commutative semiring. We demonstrate that the non-deterministic destructor finds a suitable model in a "weighted" codiagonal map. This approach offers a valid and insightful alternative to interpreting non-determinism, especially in instances where the conventional Powerset Monad interpretation does not align with the category's structure, as is the case with the category of semimodules. The validity of this alternative relies on the presence of biproducts within the category.

Social insects such as ants communicate via pheromones which allows them to coordinate their activity and solve complex tasks as a swarm, e.g. foraging for food. This behavior was shaped through evolutionary processes. In computational models, self-coordination in swarms has been implemented using probabilistic or simple action rules to shape the decision of each agent and the collective behavior. However, manual tuned decision rules may limit the behavior of the swarm. In this work we investigate the emergence of self-coordination and communication in evolved swarms without defining any explicit rule. We evolve a swarm of agents representing an ant colony. We use an evolutionary algorithm to optimize a spiking neural network (SNN) which serves as an artificial brain to control the behavior of each agent. The goal of the evolved colony is to find optimal ways to forage for food and return it to the nest in the shortest amount of time. In the evolutionary phase, the ants are able to learn to collaborate by depositing pheromone near food piles and near the nest to guide other ants. The pheromone usage is not manually encoded into the network; instead, this behavior is established through the optimization procedure. We observe that pheromone-based communication enables the ants to perform better in comparison to colonies where communication via pheromone did not emerge. We assess the foraging performance by comparing the SNN based model to a rule based system. Our results show that the SNN based model can efficiently complete the foraging task in a short amount of time. Our approach illustrates self coordination via pheromone emerges as a result of the network optimization. This work serves as a proof of concept for the possibility of creating complex applications utilizing SNNs as underlying architectures for multi-agent interactions where communication and self-coordination is desired.

Besov priors are nonparametric priors that can model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of work has initiated the study of their asymptotic frequentist convergence properties. In the present paper, we consider the theoretical recovery performance of the posterior distributions associated to Besov-Laplace priors in the density estimation model, under the assumption that the observations are generated by a possibly spatially inhomogeneous true density belonging to a Besov space. We improve on existing results and show that carefully tuned Besov-Laplace priors attain optimal posterior contraction rates. Furthermore, we show that hierarchical procedures involving a hyper-prior on the regularity parameter lead to adaptation to any smoothness level.

As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the slow and memory consuming methods. Diffusive representation of fractional derivative is an efficient tool to overcome the mentioned challenge. This paper presents two new diffusive representations to approximate the Caputo fractional derivative of order $0<\alpha<1$. Error analysis of the newly presented methods together with some numerical examples are provided at the end.

Over the past decades, cognitive neuroscientists and behavioral economists have recognized the value of describing the process of decision making in detail and modeling the emergence of decisions over time. For example, the time it takes to decide can reveal more about an agent's true hidden preferences than only the decision itself. Similarly, data that track the ongoing decision process such as eye movements or neural recordings contain critical information that can be exploited, even if no decision is made. Here, we argue that artificial intelligence (AI) research would benefit from a stronger focus on insights about how decisions emerge over time and incorporate related process data to improve AI predictions in general and human-AI interactions in particular. First, we introduce a highly established computational framework that assumes decisions to emerge from the noisy accumulation of evidence, and we present related empirical work in psychology, neuroscience, and economics. Next, we discuss to what extent current approaches in multi-agent AI do or do not incorporate process data and models of decision making. Finally, we outline how a more principled inclusion of the evidence-accumulation framework into the training and use of AI can help to improve human-AI interactions in the future.

Adversarial attacks dramatically change the output of an otherwise accurate learning system using a seemingly inconsequential modification to a piece of input data. Paradoxically, empirical evidence indicates that even systems which are robust to large random perturbations of the input data remain susceptible to small, easily constructed, adversarial perturbations of their inputs. Here, we show that this may be seen as a fundamental feature of classifiers working with high dimensional input data. We introduce a simple generic and generalisable framework for which key behaviours observed in practical systems arise with high probability -- notably the simultaneous susceptibility of the (otherwise accurate) model to easily constructed adversarial attacks, and robustness to random perturbations of the input data. We confirm that the same phenomena are directly observed in practical neural networks trained on standard image classification problems, where even large additive random noise fails to trigger the adversarial instability of the network. A surprising takeaway is that even small margins separating a classifier's decision surface from training and testing data can hide adversarial susceptibility from being detected using randomly sampled perturbations. Counterintuitively, using additive noise during training or testing is therefore inefficient for eradicating or detecting adversarial examples, and more demanding adversarial training is required.

A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the following. (i) Introducing $N$-bit-delay AIFV codes, constructed by multiple code trees with higher flexibility than the conventional AIFV codes. (ii) Proving that the proposed codes can represent any uniquely-encodable and uniquely-decodable variable-to-variable length codes. (iii) Showing how to express codes as multiple code trees with minimum decoding delay. (iv) Formulating the constraints of decodability as the comparison of intervals in the real number line. The theoretical results in this paper are expected to be useful for further study on AIFV codes.

We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the min-entropy within the class of log-concave probability sequences with fixed variance. As an application, we obtain a discrete R\'enyi entropy power inequality in the log-concave case, which improves a result of Bobkov, Marsiglietti and Melbourne (2022).

Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.