Related papers: MRA-Wavelet subspace architecture for logic, proba…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

The widespread application of pre-trained language models (PLMs) in natural language processing (NLP) has led to increasing concerns about their explainability. Selective rationalization is a self-explanatory framework that selects…

A matrix algorithm runs at {\em sublinear cost} if it uses much fewer memory cells and arithmetic operations than the input matrix has entries. Such algorithms are indispensable for Big Data Mining and Analysis. Quite typically in that area…

We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic…

With the emergence of 3D foundation models, there is growing interest in fine-tuning them for downstream tasks, where LoRA is the dominant fine-tuning paradigm. As 3D datasets exhibit distinct variations in texture, geometry, camera motion,…

This paper proposes a probabilistic model of subspaces based on the probabilistic principal component analysis (PCA). Given a sample of vectors in the embedding space -- commonly known as a snapshot matrix -- this method uses quantities…

Since most of music has repetitive structures from motifs to phrases, repeating musical ideas can be a basic operation for music composition. The basic block that we focus on is conceptualized as loops which are essential ingredients of…

Large-scale generative models like DeepSeek-R1 and OpenAI-O1 benefit substantially from chain-of-thought (CoT) reasoning, yet pushing their performance typically requires vast data, large model sizes, and full-parameter fine-tuning. While…

From molecular imaging to wireless communications, the ability to align and reconstruct signals from multiple misaligned observations is crucial for system performance. We study the problem of multi-reference alignment (MRA), which arises…

Low-rank matrices are pervasive throughout statistics, machine learning, signal processing, optimization, and applied mathematics. In this paper, we propose a novel and user-friendly Euclidean representation framework for low-rank matrices.…

For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…

We propose Modal Logical Neural Networks (MLNNs), a neurosymbolic framework that integrates deep learning with the formal semantics of modal logic, enabling reasoning about necessity and possibility. Drawing on Kripke semantics, we…

Low-Rank Adaptation (LoRA) is a widely adopted parameter-efficient fine-tuning (PEFT) method validated across NLP and CV domains. However, LoRA faces an inherent low-rank bottleneck: narrowing its performance gap with full finetuning…

Ensuring reliable data-driven decisions is crucial in domains where analytical accuracy directly impacts safety, compliance, or operational outcomes. Decision support in such domains relies on large tabular datasets, where manual analysis…

We contribute a theoretical and operational framework for neurosymbolic AI called DeepLog. DeepLog introduces building blocks and primitives for neurosymbolic AI that make abstraction of commonly used representations and computational…

Despite their linguistic competence, Large Language Models (LLMs) often struggle to reason reliably and flexibly. To identify these shortcomings, we introduce the Non-Linear Reasoning (NLR) dataset, a collection of 55 unique, hand-designed…

The Layout Analysis (LA) stage is of vital importance to the correct performance of an Optical Music Recognition (OMR) system. It identifies the regions of interest, such as staves or lyrics, which must then be processed in order to…

Time series modeling holds significant importance in many real-world applications and has been extensively studied. While pre-trained foundation models have made impressive strides in the fields of natural language processing (NLP) and…

We propose a novel neural network architecture for visual saliency detections, which utilizes neurophysiologically plausible mechanisms for extraction of salient regions. The model has been significantly inspired by recent findings from…

This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its…