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Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…
PDDL-based symbolic task planning remains pivotal for robot autonomy yet struggles with dynamic human-robot collaboration due to scalability, re-planning demands, and delayed plan availability. Although a few neurosymbolic frameworks have…
Motivated by interpretability and reliability, we investigate whether large language models (LLMs) deploy universal geometric structures to encode discrete, graph-structured knowledge. To this end, we present two complementary experimental…
The Unified Modeling Language is a standardized visual language widely used for modeling and documenting the design of software systems. Although many tools generate UML diagrams from UML code, generating executable UML code from…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Cryptographic protocols play a fundamental role in securing modern digital infrastructure, but they are often deployed without prior formal verification. This could lead to the adoption of distributed systems vulnerable to attack vectors.…
Recent work has shown that integrating large language models (LLMs) with theorem provers (TPs) in neuro-symbolic pipelines helps with entailment verification and proof-guided refinement of explanations for natural language inference (NLI).…
Generating accurate and consistent visual aids is a critical challenge in mathematics education, where visual representations like geometric shapes and functions play a pivotal role in enhancing student comprehension. This paper introduces…
Formal verification via interactive theorem proving is increasingly used to ensure the correctness of critical systems, yet constructing large proof scripts remains highly manual and limits scalability. Advances in large language models…
Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
The development of artificial intelligence systems capable of understanding and reasoning about complex real-world scenarios is a significant challenge. In this work we present a novel approach to enhance and exploit LLM reactive capability…
This paper introduces and formally verifies a novel geometric framework for first-order stochastic dominance (FSD) in $N$ dimensions using the Lean 4 theorem prover. Traditional analytical approaches to multi-dimensional stochastic…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…
Existing end-to-end autonomous driving models rely heavily on purely data-driven inductive reasoning. This "black-box" nature leads to a lack of interpretability and absolute safety guarantees in complex, long-tail scenarios. To overcome…
Despite the superior performance of large language models to generate natural language texts, it is hard to generate texts with correct logic according to a given task, due to the difficulties for neural models to capture implied rules from…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…