Related papers: On the Complexity of CCG Parsing
The paper demonstrates that exponential complexities with respect to grammar size and input length have little impact on the performance of three unification-based parsing algorithms, using a wide-coverage grammar. The results imply that…
While context-free grammars are characterized by a simple proof-theoretic grammatical formalism namely categorial grammar and its logic the Lambek calculus, no such characterizations were known for tree-adjoining grammars, and even for any…
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the…
Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences $X$ and $Y$. We present a framework which relies on…
We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent,…
The effectiveness of Retrieval-Augmented Generation (RAG) is highly dependent on how documents are chunked, that is, segmented into smaller units for indexing and retrieval. Yet, commonly used "one-size-fits-all" approaches often fail to…
Causal reasoning and compositional reasoning are two core aspirations in AI. Measuring the extent of these behaviors requires principled evaluation methods. We explore a unified perspective that considers both behaviors simultaneously,…
Retrieval-Augmented Generation (RAG), while serving as a viable complement to large language models (LLMs), often overlooks the crucial aspect of text chunking within its pipeline. This paper initially introduces a dual-metric evaluation…
We introduce Transformer Grammars (TGs), a novel class of Transformer language models that combine (i) the expressive power, scalability, and strong performance of Transformers and (ii) recursive syntactic compositions, which here are…
We study methods for automated parsing of informal mathematical expressions into formal ones, a main prerequisite for deep computer understanding of informal mathematical texts. We propose a context-based parsing approach that combines…
Long-context large language models remain computationally expensive to run and often fail to reliably process very long inputs, which makes context compression an important component of many systems. Existing compression approaches…
Deep generative models have achieved remarkable success in various data domains, including images, time series, and natural languages. There remain, however, substantial challenges for combinatorial structures, including graphs. One of the…
Several methods have been proposed for processing a corpus to induce a tagset for the sub-language represented by the corpus. This paper examines a structured-tag word classification method introduced by McMahon (1994) and discussed further…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Self-explaining text categorization requires a classifier to make a prediction along with supporting evidence. A popular type of evidence is sub-sequences extracted from the input text which are sufficient for the classifier to make the…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
The state-of-the-art semantic communication (SC) schemes typically rely on end-to-end deep learning frameworks that lack interpretability and struggle with robust semantic selection and reconstruction under noisy conditions. To address this…
This paper was was first drafted in 2001 as a formalization of the system described in U.S. patent U.S. 7,392,174. It describes a system for implementing a parser based on a kind of cross-product over vectors of contextually similar words.…