Related papers: Expressive Power of Hypergraph Lambek Grammars
Hierarchical graph rewriting is a highly expressive computational formalism that manipulates graphs enhanced with box structures for representing hierarchies. It has provided the foundations of various graph-based modeling tools, but the…
Reinforcement learning (RL) has been applied to improve large language model (LLM) reasoning, yet the systematic study of how training scales with task difficulty has been hampered by the lack of controlled, scalable environments. Observed…
Hypergraphs, as a generalization of traditional graphs, naturally capture high-order relationships. In recent years, hypergraph neural networks (HNNs) have been widely used to capture complex high-order relationships. However, most existing…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout…
Recent progress in Large Language Models (LLMs) and language agents has demonstrated significant promise for various future applications across multiple disciplines. While traditional approaches to language agents often rely on fixed,…
The recent advancements in Large Language Models (LLMs) have attracted interest in exploring their in-context learning abilities and chain-of-thought capabilities. However, there are few studies investigating the specific traits related to…
Hypergraphs are vital in modelling data with higher-order relations containing more than two entities, gaining prominence in machine learning and signal processing. Many hypergraph neural networks leverage message passing over hypergraph…
Knowledge graphs (KGs) are large datasets with specific structures representing large knowledge bases (KB) where each node represents a key entity and relations amongst them are typed edges. Natural language queries formed to extract…
We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega$-rule, and prove that the derivability problem in this calculus is…
The expressive power of graph neural network formalisms is commonly measured by their ability to distinguish graphs. For many formalisms, the k-dimensional Weisfeiler-Leman (k-WL) graph isomorphism test is used as a yardstick. In this paper…
Large language models (LLMs), such as GPT3.5, GPT4 and LLAMA2 perform surprisingly well and outperform human experts on many tasks. However, in many domain-specific evaluations, these LLMs often suffer from hallucination problems due to…
Multi-step retrieval-augmented generation (RAG) has become a widely adopted strategy for enhancing large language models (LLMs) on tasks that demand global comprehension and intensive reasoning. Although many RAG systems incorporate a…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
Both syntax-phonology and syntax-semantics interfaces in Higher Order Grammar (HOG) are expressed as axiomatic theories in higher-order logic (HOL), i.e. a language is defined entirely in terms of provability in the single logical system.…
Morpho-syntactic lexicons provide information about the morphological and syntactic roles of words in a language. Such lexicons are not available for all languages and even when available, their coverage can be limited. We present a…
Despite significant advances in Graph Neural Networks (GNNs), their limited expressivity remains a fundamental challenge. Research on GNN expressivity has produced many expressive architectures, leading to architecture hierarchies with…
Human infants can discover words directly from unsegmented speech signals without any explicitly labeled data. In this paper, we develop a novel machine learning method called nonparametric Bayesian double articulation analyzer (NPB-DAA)…
Generating synthetic variants of a document is often posed as text-to-text transformation. We propose an alternate LLM based method that first decomposes a document into semantic frames and then generates text using this interim sparse…
This paper delves into the capabilities of large language models (LLMs), specifically focusing on advancing the theoretical comprehension of chain-of-thought prompting. We investigate how LLMs can be effectively induced to generate a…