Related papers: The Liouville Generator for Producing Integrable E…

Search-based test generators are effective at producing unit tests with high coverage. However, such automatically generated tests have no meaningful test and variable names, making them hard to understand and interpret by developers. On…

A Hamiltonian system is completely integrable (in the sense of Liouville) if there exist as many independent integrals of motion in involution as the dimension of the configuration space. Under certain regularity conditions,…

Despite the broad applicability of large language models (LLMs), their reliance on probabilistic inference makes them vulnerable to errors such as hallucination in generated facts and inconsistent output structure in natural language…

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated…

In this paper, we present the current progress of the project Verif.ai, an open-source scientific generative question-answering system with referenced and verified answers. The components of the system are (1) an information retrieval…

We introduce an abductive method for a coherent integration of independent data-sources. The idea is to compute a list of data-facts that should be inserted to the amalgamated database or retracted from it in order to restore its…

We consider a three dimensional complex polynomial, or rational, vector field (equivalently, a two-form in three variables) which admits a Liouvillian first integral. We prove that there exists a first integral whose differential is the…

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact"…

We present Liquid, an auto-regressive generation paradigm that seamlessly integrates visual comprehension and generation by tokenizing images into discrete codes and learning these code embeddings alongside text tokens within a shared…

Generative systems have a significant potential to synthesize innovative design alternatives. Still, most of the common systems that have been adopted in design require the designer to explicitly define the specifications of the procedures…

Large Language Models (LLMs) have shown promise as robotic planners but often struggle with long-horizon and complex tasks, especially in specialized environments requiring external knowledge. While hierarchical planning and…

Symbolic model checkers can construct proofs of properties over very complex models. However, the results reported by the tool when a proof succeeds do not generally provide much insight to the user. It is often useful for users to have…

We propose a symbolic generative task description language and a corresponding inference engine capable of representing arbitrary multimodal tasks as structured symbolic flows. Unlike conventional generative models that rely on large-scale…

The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for…

Numerous process discovery techniques exist for generating process models that describe recorded executions of business processes. The models are meant to generalize executions into human-understandable modeling patterns, notably…

Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…

We introduce Prototype Generation, a stricter and more robust form of feature visualisation for model-agnostic, data-independent interpretability of image classification models. We demonstrate its ability to generate inputs that result in…

Generative models typically sample outputs independently, and recent inference-time guidance and scaling algorithms focus on improving the quality of individual samples. However, in real-world applications, users are often presented with a…

Code generation with large language models (LLMs), often termed vibe coding, is increasingly adopted in production but fails to ensure code quality, particularly in security (e.g., SQL injection vulnerabilities) and maintainability (e.g.,…

Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method…