We initiate the study of applications of machine learning to Seiberg duality, focusing on the case of quiver gauge theories, a problem also of interest in mathematics in the context of cluster algebras. Within the general theme of Seiberg duality, we define and explore a variety of interesting questions, broadly divided into the binary determination of whether a pair of theories picked from a series of duality classes are dual to each other, as well as the multi-class determination of the duality class to which a given theory belongs. We study how the performance of machine learning depends on several variables, including number of classes and mutation type (finite or infinite). In addition, we evaluate the relative advantages of Naive Bayes classifiers versus Convolutional Neural Networks. Finally, we also investigate how the results are affected by the inclusion of additional data, such as ranks of gauge/flavor groups and certain variables motivated by the existence of underlying Diophantine equations. In all questions considered, high accuracy and confidence can be achieved.

In recent years, surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. The current state-of-the-art performance for this task has been achieved by Bayesian Optimization with Gaussian Processes (GPs). While this combination works well for unimodal target distributions, it is restricting the flexibility and applicability of Bayesian Optimization for accelerating likelihood-free inference more generally. We address this problem by proposing a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases. This confirms that DGPs as surrogate models can extend the applicability of Bayesian Optimization for likelihood-free inference (BOLFI), while adding computational overhead that remains negligible for computationally intensive simulators.

Learning the distribution of observed data is a basic task in unsupervised learning which has been studied for decades. The recently-introduced concept of Generative Adversarial Networks (GANs) [1] has demonstrated great success in various distribution learning tasks. Unlike the traditional maximum-likelihood-based approaches, GANs learn the distribution of observed data through a zero-sum game between two machine players, a generator G mimicking the true distribution of data and a discriminator D distinguishing the generator's produced samples from real data points. This zero-sum game is typically formulated through a minimax optimization problem where G and D optimize a minimax objective quantifying how dissimilar G's generated samples and real training samples are. In GAN minimax optimization problems, the generator and discriminator functions are commonly chosen as two deep neural networks (DNNs). Leveraging the expressive power of DNNs, GANs have achieved state-of-the-art performance in learning complex distributions of image data [2, 3, 4]. This success, however, is achieved at the cost of their notoriously difficult training procedure which has introduced several challenges to the machine learning community. Addressing these challenges requires a deeper theoretical understanding of GANs, including their approximation, generalization, and optimization properties. Specifically, GANs have been frequently observed to fail in learning multi-modal distributions [5].

In most of the transfer learning approaches to reinforcement learning (RL) the distribution over the tasks is assumed to be stationary. Therefore, the target and source tasks are i.i.d. samples of the same distribution. In the context of this work, we consider the problem of transferring value functions through a variational method when the distribution that generates the tasks is time-variant, proposing a solution that leverages this temporal structure inherent in the task generating process. Furthermore, by means of a finite-sample analysis, the previously mentioned solution is theoretically compared to its time-invariant version. Finally, we will provide an experimental evaluation of the proposed technique with three distinct temporal dynamics in three different RL environments.

Ising machines (IMs) are a potential breakthrough in the NP-hard problem of score-based Bayesian network (BN) learning. To utilize the power of IMs, encoding of BN learning into quadratic unconstrained binary optimization (QUBO) has been proposed using up to $\mathcal{O}(N^2)$ bits, for $N$ variables in BN and $M = 2$ parents each. However, this approach is usually infeasible owing to the upper bound of IM bits when $M \geq 3$. In this paper, we propose an efficient conversion method for BN learning into QUBO with a maximum of $\sum_n (\Lambda_n - 1) + \binom N2$ bits, for $\Lambda_n$ parent set candidates each. The advance selection of parent set candidates plays an essential role in reducing the number of required bits. We also develop a pre-processing algorithm based on the capabilities of a classification and regression tree (CART), which allows us to search for parent set candidates consistent with score minimization in a realistic timeframe.Our conversion method enables us to more significantly reduce the upper bound of the required bits in comparison to an existing method, and is therefore expected to make a significant contribution to the advancement of scalable score-based BN learning.

Computers have been used to analyze and create music since they were first introduced in the 1950s and 1960s. Beginning in the late 1990s, the rise of the Internet and large scale platforms for music recommendation and retrieval have made music an increasingly prevalent domain of machine learning and artificial intelligence research. While still nascent, several different approaches have been employed to tackle what may broadly be referred to as "musical intelligence." This article provides a definition of musical intelligence, introduces a taxonomy of its constituent components, and surveys the wide range of AI methods that can be, and have been, brought to bear in its pursuit, with a particular emphasis on machine learning methods.

This paper investigates how a Bayesian reinforcement learning method can be used to create a tactical decision-making agent for autonomous driving in an intersection scenario, where the agent can estimate the confidence of its recommended actions. An ensemble of neural networks, with additional randomized prior functions (RPF), are trained by using a bootstrapped experience replay memory. The coefficient of variation in the estimated $Q$-values of the ensemble members is used to approximate the uncertainty, and a criterion that determines if the agent is sufficiently confident to make a particular decision is introduced. The performance of the ensemble RPF method is evaluated in an intersection scenario, and compared to a standard Deep Q-Network method. It is shown that the trained ensemble RPF agent can detect cases with high uncertainty, both in situations that are far from the training distribution, and in situations that seldom occur within the training distribution. In this study, the uncertainty information is used to choose safe actions in unknown situations, which removes all collisions from within the training distribution, and most collisions outside of the distribution.

Active learning is able to reduce the amount of labelling effort by using a machine learning model to query the user for specific inputs. While there are many papers on new active learning techniques, these techniques rarely satisfy the constraints of a real-world project. In this paper, we analyse the main drawbacks of current active learning techniques and we present approaches to alleviate them. We do a systematic study on the effects of the most common issues of real-world datasets on the deep active learning process: model convergence, annotation error, and dataset imbalance. We derive two techniques that can speed up the active learning loop such as partial uncertainty sampling and larger query size. Finally, we present our open-source Bayesian active learning library, BaaL.

The goal of item response theoretic (IRT) models is to provide estimates of latent traits from binary observed indicators and at the same time to learn the item response functions (IRFs) that map from latent trait to observed response. However, in many cases observed behavior can deviate significantly from the parametric assumptions of traditional IRT models. Nonparametric IRT models overcome these challenges by relaxing assumptions about the form of the IRFs, but standard tools are unable to simultaneously estimate flexible IRFs and recover ability estimates for respondents. We propose a Bayesian nonparametric model that solves this problem by placing Gaussian process priors on the latent functions defining the IRFs. This allows us to simultaneously relax assumptions about the shape of the IRFs while preserving the ability to estimate latent traits. This in turn allows us to easily extend the model to further tasks such as active learning. GPIRT therefore provides a simple and intuitive solution to several longstanding problems in the IRT literature.

We study PAC-Bayesian generalization bounds for Multilayer Perceptrons (MLPs) with the cross entropy loss. Above all, we introduce probabilistic explanations for MLPs in two aspects: (i) MLPs formulate a family of Gibbs distributions, and (ii) minimizing the cross-entropy loss for MLPs is equivalent to Bayesian variational inference, which establish a solid probabilistic foundation for studying PAC-Bayesian bounds on MLPs. Furthermore, based on the Evidence Lower Bound (ELBO), we prove that MLPs with the cross entropy loss inherently guarantee PAC- Bayesian generalization bounds, and minimizing PAC-Bayesian generalization bounds for MLPs is equivalent to maximizing the ELBO. Finally, we validate the proposed PAC-Bayesian generalization bound on benchmark datasets.