Related papers: Hierarchical similarity-based approximate reasonin…
Retrieval-augmented generation (RAG) has been extensively employed to mitigate hallucinations in large language models (LLMs). However, existing methods for multi-hop reasoning tasks often lack global planning, increasing the risk of…
This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…
The set similarity join problem is a fundamental problem in data processing and discovery, relying on exact similarity measures between sets. In the presence of alterations, such as misspellings on string data, the fuzzy set similarity join…
In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly…
Feature selection identifies subsets of informative features and reduces dimensions in the original feature space, helping provide insights into data generation or a variety of domain problems. Existing methods mainly depend on feature…
Because of the high approximation power and simplicity of computation of smooth radial basis functions (RBFs), in recent decades they have received much attention for function approximation. These RBFs contain a shape parameter that…
In this paper we analyze the joint rate distortion function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual distortion criteria. First, we derive structural…
Range-filtering approximate $k$-nearest neighbor (RFAKNN) search takes as input a vector and a numeric value, returning $k$ points from a database of $N$ high-dimensional points. The returned points must satisfy two criteria: their numeric…
This chapter approaches the image retrieval system on the base of the colors of image. It creates fuzzy signature to describe the color of image on color space HSV and builds fuzzy Hamming distance (FHD) to evaluate the similarity between…
Approximate subgraph matching (ASM) is a task that determines the approximate presence of a given query graph in a large target graph. Being an NP-hard problem, ASM is critical in graph analysis with a myriad of applications ranging from…
Hierarchical Merging is a technique commonly used to summarize very long texts ($>$100K tokens) by breaking down the input into smaller sections, summarizing those sections individually, and then merging or combining those summaries into a…
We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Retrieval-Augmented Generation (RAG) enhances Large Language Models (LLMs) by grounding responses in external knowledge during inference. However, conventiona RAG systems under-perform on structured tabular data, largely due to coarse…
In this work, we propose using a unified representation, termed Factorized Features, for low-level vision tasks, where we test on Single Image Super-Resolution (SISR) and \textbf{Image Compression}. Motivated by the shared principles…
As one of the most powerful tools for examining the association between functional covariates and a response, the functional regression model has been widely adopted in various interdisciplinary studies. Usually, a limited number of…
With the surging popularity of approximate near-neighbor search (ANNS), driven by advances in neural representation learning, the ability to serve queries accompanied by a set of constraints has become an area of intense interest. While the…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many applications. However, these algorithms cannot be directly applied to supervised tasks. This…
In this extended abstract, we discuss the opportunity to formally verify that inference systems for probabilistic programming guarantee good performance. In particular, we focus on hybrid inference systems that combine exact and approximate…