Related papers: Fast Context-Free Grammar Parsing Requires Fast Bo…
Automated Test Case Generation (ATCG) is crucial for evaluating software reliability, particularly in competitive programming where robust algorithm assessments depend on diverse and accurate test cases. However, existing ATCG methods often…
Phrase-structure grammars are effective models for important syntactic and semantic aspects of natural languages, but can be computationally too demanding for use as language models in real-time speech recognition. Therefore, finite-state…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. Boolean-width is similar to rank-width, which is related to the number of $GF[2]$-sums (1+1=0) of…
Large language models (LLMs) are increasingly used to solve complex tasks where they must retrieve and compose many pieces of in-context information in long reasoning chains. For many real-world tasks it is hard to accurately gauge how…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…
Understanding the query complexity for testing linear-invariant properties has been a central open problem in the study of algebraic property testing. Triangle-freeness in Boolean functions is a simple property whose testing complexity is…
The proliferation of agentic systems has thrust the reasoning capabilities of AI into the forefront of contemporary machine learning. While it is known that there \emph{exist} neural networks which can reason through any Boolean task…
An arbitrary $m\times n$ Boolean matrix $M$ can be decomposed {\em exactly} as $M =U\circ V$, where $U$ (resp. $V$) is an $m\times k$ (resp. $k\times n$) Boolean matrix and $\circ$ denotes the Boolean matrix multiplication operator. We…
Since its introduction Boson Sampling has been the subject of intense study in the world of quantum computing. The task is to sample independently from the set of all $n \times n$ submatrices built from possibly repeated rows of a larger $m…
Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense…
The rapid progress of large language models (LLMs) has laid the foundation for multimodal models. However, visual language models (VLMs) still face heavy computational costs when extended from images to videos due to high frame rates and…
Language-based testing combines context-free grammar definitions with semantic constraints over grammar elements to generate test inputs. By pairing context-free grammars with constraints, users have the expressiveness of unrestricted…
There has been recent interest in applying cognitively or empirically motivated bounds on recursion depth to limit the search space of grammar induction models (Ponvert et al., 2011; Noji and Johnson, 2016; Shain et al., 2016). This work…
This paper proposes the use of ``pattern-based'' context-free grammars as a basis for building machine translation (MT) systems, which are now being adopted as personal tools by a broad range of users in the cyberspace society. We discuss…
A constant-workspace algorithm has read-only access to an input array and may use only O(1) additional words of $O(\log n)$ bits, where $n$ is the size of the input. We assume that a simple $n$-gon is given by the ordered sequence of its…
Dictionary learning is a branch of signal processing and machine learning that aims at finding a frame (called dictionary) in which some training data admits a sparse representation. The sparser the representation, the better the…
Many loss functions in representation learning are invariant under a continuous symmetry transformation. For example, the loss function of word embeddings (Mikolov et al., 2013) remains unchanged if we simultaneously rotate all word and…