Related papers: Basic Elements of Logical Graphs
We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…
The analysis of graphs has become increasingly important to a wide range of applications. Graph analysis presents a number of unique challenges in the areas of (1) software complexity, (2) data complexity, (3) security, (4) mathematical…
By taking the semantic object parsing task as an exemplar application scenario, we propose the Graph Long Short-Term Memory (Graph LSTM) network, which is the generalization of LSTM from sequential data or multi-dimensional data to general…
The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
With the increasing popularity of large language models (LLMs), reasoning on basic graph algorithm problems is an essential intermediate step in assessing their abilities to process and infer complex graph reasoning tasks. Existing methods…
Despite enormous progress in Natural Language Processing (NLP), our field is still lacking a common deep semantic representation scheme. As a result, the problem of meaning and understanding is typically sidestepped through more simple,…
The increasing complexity of computing systems places a tremendous burden on optimizing compilers, requiring ever more accurate and aggressive optimizations. Machine learning offers significant benefits for constructing optimization…
We present a formal language with expressions denoting general symbol structures and queries which access information in those structures. A sequence-to-sequence network processing this language learns to encode symbol structures and query…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
Recent efforts leverage Large Language Models (LLMs) for modeling text-attributed graph structures in node classification tasks. These approaches describe graph structures for LLMs to understand or aggregate LLM-generated textual attribute…
Graph Neural Networks (GNNs) have become a standard approach for learning from graph-structured data. However, their reliance on parametric classifiers (most often linear softmax layers) limits interpretability and sometimes hinders…
We focus on a conversational question answering task which combines the challenges of understanding questions in context and reasoning over evidence gathered from heterogeneous sources like text, knowledge graphs, tables, and infoboxes. Our…
The advancement of Large Language Models (LLMs) has remarkably pushed the boundaries towards artificial general intelligence (AGI), with their exceptional ability on understanding diverse types of information, including but not limited to…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale…
How can we best encode structured data into sequential form for use in large language models (LLMs)? In this work, we introduce a parameter-efficient method to explicitly represent structured data for LLMs. Our method, GraphToken, learns an…
Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers…
We demonstrate a deep learning framework which is inherently based in the highly expressive language of relational logic, enabling to, among other things, capture arbitrarily complex graph structures. We show how Graph Neural Networks and…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…