Related papers: Probability Bracket Notation, Term Vector Space, C…
In this paper, we continue to explore the consistence and usability of Probability Bracket Notation (PBN) proposed in our previous articles. After a brief review of PBN with dimensional analysis, we investigate probability spaces in terms…
Using Dirac Notation as a powerful tool, we investigate the three classical Information Retrieval (IR) models and some their extensions. We show that almost all such models can be described by vectors in Occupation Number Representations…
Following the Dirac Notation in Quantum Mechanics (QM), we propose the Bracket Notation (PBN) by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectations in…
We extend Probability Bracket Notation (PBN), inspired by the Dirac notation in quantum mechanics, to multivariable probability systems and static Bayesian networks (BNs). By defining probability distributions and conditional expectations…
In this article, we continue to explore Probability Bracket Notation (PBN), proposed in our previous article. Using both Dirac vector bracket notation (VBN) and PBN, we define induced Hilbert space and induced sample space, and propose that…
Inspired by the Dirac vector probability notation (VPN), we propose the Probability Bracket Notation (PBN), a new set of symbols defined similarly (but not identically) as in the VPN. Applying the PBN to fundamental definitions and theorems…
After a brief introduction to Probability Bracket Notation (PBN), indicator operator and conditional density operator (CDO), we investigate probability spaces associated with various quantum systems: system with one observable (discrete or…
In order to adopt deep learning for information retrieval, models are needed that can capture all relevant information required to assess the relevance of a document to a given user query. While previous works have successfully captured…
In this work, we advance the development of the Probability Bracket Notation (PBN), a formalism inspired by Dirac's notation in quantum mechanics, to provide a unified framework for probability modeling. We demonstrate that under a Special…
Classical information retrieval (IR) methods, such as query likelihood and BM25, score documents independently w.r.t. each query term, and then accumulate the scores. Assuming query term independence allows precomputing term-document scores…
A fundamental goal of search engines is to identify, given a query, documents that have relevant text. This is intrinsically difficult because the query and the document may use different vocabulary, or the document may contain query words…
Mechanistic interpretation has greatly contributed to a more detailed understanding of generative language models, enabling significant progress in identifying structures that implement key behaviors through interactions between internal…
Most efforts in interpreting neural relevance models have focused on local explanations, which explain the relevance of a document to a query but are not useful in predicting the model's behavior on unseen query-document pairs. We propose a…
Recent advances in neural word embedding provide significant benefit to various information retrieval tasks. However as shown by recent studies, adapting the embedding models for the needs of IR tasks can bring considerable further…
Learning a high-dimensional dense representation for vocabulary terms, also known as a word embedding, has recently attracted much attention in natural language processing and information retrieval tasks. The embedding vectors are typically…
Large Language Models (LLMs) have shown strong capabilities in document re-ranking, a key component in modern Information Retrieval (IR) systems. However, existing LLM-based approaches face notable limitations, including ranking…
Most work in the area of statistical relational learning (SRL) is focussed on discrete data, even though a few approaches for hybrid SRL models have been proposed that combine numerical and discrete variables. In this paper we distinguish…
Latent semantic representations of words or paragraphs, namely the embeddings, have been widely applied to information retrieval (IR). One of the common approaches of utilizing embeddings for IR is to estimate the document-to-query (D2Q)…
Information Retrieval (IR) is the task of obtaining pieces of data (such as documents) that are relevant to a particular query or need from a large repository of information. IR is a valuable component of several downstream Natural Language…
We present a new Convolutional Neural Network (CNN) model for text classification that jointly exploits labels on documents and their component sentences. Specifically, we consider scenarios in which annotators explicitly mark sentences (or…