--Hardware complexity continues to strain verification resources, motivating the adoption of machine learning (ML) methods to improve debug efficiency. However, ML-assisted debugging critically depends on diverse and scalable bug datasets, which existing manual or automated bug insertion methods fail to reliably produce. We introduce BugGen, a first of its kind, fully autonomous, multi-agent pipeline leveraging Large Language Models (LLMs) to systematically generate, insert, and validate realistic functional bugs in RTL. BugGen partitions modules, selects mutation targets via a closed-loop agentic architecture, and employs iterative refinement and rollback mechanisms to ensure syntactic correctness and functional detectability. Evaluated across five OpenTitan IP blocks, BugGen produced 500 unique bugs with 94% functional accuracy and achieved a throughput of 17.7 validated bugs per hour--over five times faster than typical manual expert insertion. Additionally, BugGen identified 104 previously undetected bugs in Open-Titan regressions, highlighting its utility in exposing verification coverage gaps. Compared against Certitude, BugGen demonstrated over twice the syntactic accuracy, deeper exposure of testbench blind spots, and more functionally meaningful and complex bug scenarios. Furthermore, when these BugGen-generated datasets were employed to train MLbased failure triage models, we achieved high classification accuracy (88.1%-93.2%) BugGen thus provides a scalable solution for generating high-quality bug datasets, significantly enhancing verification efficiency and ML-assisted debugging. Modern hardware systems continue to grow in complexity, often incorporating billions of transistors on a single chip. This increased complexity significantly expands the scope and difficulty of design verification tasks. V erification efforts already consume more than half of the total hardware development time [1], with this fraction steadily increasing each year. The heightened complexity also results in large volumes of test failures, particularly during early front-end development and initial volume regressions, placing severe demands on debugging resources to pinpoint root causes or effectively triage these failures.

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze. In this work, we use graph neural networks to investigate quiver mutation -- an operation that transforms one quiver (or directed multigraph) into another -- which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics. In the study of cluster algebras, the question of mutation equivalence is of fundamental concern: given two quivers, can one efficiently determine if one quiver can be transformed into the other through a sequence of mutations? Currently, this question has only been resolved in specific cases. In this paper, we use graph neural networks and AI explainability techniques to discover mutation equivalence criteria for the previously unknown case of quivers of type $\tilde{D}_n$. Along the way, we also show that even without explicit training to do so, our model captures structure within its hidden representation that allows us to reconstruct known criteria from type $D_n$, adding to the growing evidence that modern machine learning models are capable of learning abstract and general rules from mathematical data.

Machine learning (ML) has emerged as a powerful tool in mathematical research in recent years. This paper applies ML techniques to the study of quivers--a type of directed multigraph with significant relevance in algebra, combinatorics, computer science, and mathematical physics. Specifically, we focus on the challenging problem of determining the mutation-acyclicity of a quiver on 4 vertices, a property that is pivotal since mutation-acyclicity is often a necessary condition for theorems involving path algebras and cluster algebras. Although this classification is known for quivers with at most 3 vertices, little is known about quivers on more than 3 vertices. We give a computer-assisted proof of a theorem to prove that mutation-acyclicity is decidable for quivers on 4 vertices with edge weight at most 2. By leveraging neural networks (NNs) and support vector machines (SVMs), we then accurately classify more general 4-vertex quivers as mutation-acyclic or non-mutation-acyclic. Our results demonstrate that ML models can efficiently detect mutation-acyclicity, providing a promising computational approach to this combinatorial problem, from which the trained SVM equation provides a starting point to guide future theoretical development.

The ubiquitous interrelations between algebraic geometry and physics has for centuries flourished fruitful phenomena in both fields. With connections made as far back as Archimedes whose work on conic sections aided development of concepts surrounding the motion under gravity, physical understanding has largely relied upon the mathematical tools available. In the modern era, these two fields are still heavily intertwined, with particular relevance in addressing one of the most significant problems of our time - quantising gravity. String theory as a candidate for this theory of everything, relies heavily on algebraic geometry constructions to define its spacetime and to interpret its matter. However, where new mathematical tools arise their implementation is not always simple.

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.