Modeling Quantum Entanglements in Quantum Language Models

Recently, a Quantum Language Model (QLM) was proposed to model term dependencies upon Quantum Theory (QT) framework and successively applied in Information Retrieval (IR). Nevertheless, QLM's dependency is based on co-occurrences of terms and has not yet taken into account the Quantum Entanglement (QE), which is a key quantum concept and has a significant cognitive implication. In QT, an entangled state can provide a more complete description for the nature of realities, and determine intrinsic correlations of considered objects globally, rather than those co-occurrences on the surface. It is, however, a real challenge to decide and measure QE using the classical statistics of texts in a post-measurement configuration. In order to circumvent this problem, we theoretically prove the connection between QE and statistically Unconditional Pure Dependence (UPD). Since UPD has an implementable deciding algorithm, we can in turn characterize QE by extracting the UPD patterns from texts. This leads to a measurable QE, based on which we further advance the existing QLM framework. We empirically compare our model with related models, and the results demonstrate the effectiveness of our model

End-to-End Quantum-like Language Models with Application to Question Answering

Language Modeling (LM) is a fundamental research topic ina range of areas. Recently, inspired by quantum theory, a novel Quantum Language Model (QLM) has been proposed for Information Retrieval (IR). In this paper, we aim to broaden the theoretical and practical basis of QLM. We develop a Neural Network based Quantum-like Language Model (NNQLM) and apply it to Question Answering. Specifically, based on word embeddings, we design a new density matrix, which represents a sentence (e.g., a question or an answer) and encodes a mixture of semantic subspaces. Such a density matrix, together with a joint representation of the question and the answer, can be integrated into neural network architectures (e.g., 2-dimensional convolutional neural networks). Experiments on the TREC-QA and WIKIQA datasets have verified the effectiveness of our proposed models

The solution of the Sixth Hilbert Problem: the Ultimate Galilean Revolution

I argue for a full mathematisation of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: "physics from no physics". Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either don't have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as "clock", "rigid rod ", "force", "inertial mass" (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the Sixth Hilbert's Problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.Comment: Opinion paper. Special issue of Philosophical Transaction A, devoted to the VI Hilbert problem, after the Workshop "Hilbert's Sixth Problem", University of Leicester, May 02-04 201