Related papers: Implementing Tensor Logic: Unifying Datalog and Ne…

Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…

The transition from standard generative AI to \emph{reasoning-centric architectures}, exemplified by models capable of extensive Chain-of-Thought~(CoT) processing, marks a fundamental paradigm shift in system requirements. Unlike…

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty…

Compositionality is a pivotal property of symbolic reasoning. However, how well recent neural models capture compositionality remains underexplored in the symbolic reasoning tasks. This study empirically addresses this question by…

Neuro-symbolic methods integrate neural architectures, knowledge representation and reasoning. However, they have been struggling at both dealing with the intrinsic uncertainty of the observations and scaling to real-world applications.…

DeepSeek R1 has significantly advanced complex reasoning for large language models (LLMs). While recent methods have attempted to replicate R1's reasoning capabilities in multimodal settings, they face limitations, including inconsistencies…

Tensor algebra is a crucial component for data-intensive workloads such as machine learning and scientific computing. As the complexity of data grows, scientists often encounter a dilemma between the highly specialized dense tensor algebra…

Representation learning of knowledge graphs encodes entities and relation types into a continuous low-dimensional vector space, learns embeddings of entities and relation types. Most existing methods only concentrate on knowledge triples,…

Solving topological grid puzzles requires reasoning over global spatial invariants such as connectivity, loop closure, and region symmetry and remains challenging for even the most powerful large language models (LLMs). To study these…

Semantic image interpretation can vastly benefit from approaches that combine sub-symbolic distributed representation learning with the capability to reason at a higher level of abstraction. Logic Tensor Networks (LTNs) are a class of…

Datalog$^\neg$ is a central formalism used in a variety of domains ranging from deductive databases and abstract argumentation frameworks to answer set programming. Its model theory is the finite counterpart of the logical semantics…

Large Language Models (LLMs) have demonstrated impressive progress in complex reasoning tasks, largely driven by the Chain-of-Thought (CoT) paradigm, which decomposes difficult problems into intermediate steps. However, CoT reasoning…

Recent research has highlighted the role of relational inductive biases in building learning agents that can generalize and reason in a compositional manner. However, while relational learning algorithms such as graph neural networks (GNNs)…

Computing derivatives of tensor expressions, also known as tensor calculus, is a fundamental task in machine learning. A key concern is the efficiency of evaluating the expressions and their derivatives that hinges on the representation of…

Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…

Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks…

Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at…

This paper aims to give an epistemic interpretation to the tensor disjunction in dependence logic, through a rather surprising connection to the so-called weak disjunction in Medvedev's early work on intermediate logic under the…

Chain-of-thought prompting has emerged as a powerful technique for enabling large language models (LLMs) to solve complex reasoning tasks. However, these reasoning chains can be verbose, raising concerns about efficiency. In response,…

Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…