In natural language processing, current methods for understanding Transformers are successful at identifying intermediate predictions during a model's inference. However, these approaches function as limited diagnostic checkpoints, lacking a mathematical framework for mechanistically modeling how each layer facilitates transitions between these evolving states. This interpretability gap and past successes of interdisciplinary outlooks inspire us to turn to physics in search of a descriptive mathematical framework for Transformers. We observe that language models are intrinsically probabilistic, an attribute that is echoed in the core postulates of quantum mechanics. This parallel inspires us to translate insights from this discipline to that of natural language processing. Towards this objective, we propose QLENS a novel attempt to develop a physics-based perspective on the Transformer generation process. Under QLENS, a Transformer is studied by converting its latent activations into a state vector in a Hilbert space derived from the model's output units. This state subsequently evolves through hidden layers - reformulated as unitary operators and analogously defined Hamiltonians - during inference. The model's final probability distribution is obtained by applying the Born rule to the end state using a specific measurement operator. To demonstrate QLENS's potential, we conduct a proof-of-concept by probing a toy Transformer to investigate the influence of individual layers in a model's prediction trajectory. We present our work as a foundation for cross-domain insights to be leveraged towards a broader understanding of Transformers.
In natural language processing, current methods for understanding Transformers are successful at identifying intermediate predictions during a model's inference. However, these approaches function as limited diagnostic checkpoints, lacking a mathematical framework for mechanistically modeling how each layer facilitates transitions between these evolving states. This interpretability gap and past successes of interdisciplinary outlooks inspire us to turn to physics in search of a descriptive mathematical framework for Transformers. We observe that language models are intrinsically probabilistic, an attribute that is echoed in the core postulates of quantum mechanics. This parallel inspires us to translate insights from this discipline to that of natural language processing. Towards this objective, we propose QLENS a novel attempt to develop a physics-based perspective on the Transformer generation process. Under QLENS, a Transformer is studied by converting its latent activations into a state vector in a Hilbert space derived from the model's output units. This state subsequently evolves through hidden layers - reformulated as unitary operators and analogously defined Hamiltonians - during inference. The model's final probability distribution is obtained by applying the Born rule to the end state using a specific measurement operator. To demonstrate QLENS's potential, we conduct a proof-of-concept by probing a toy Transformer to investigate the influence of individual layers in a model's prediction trajectory. We present our work as a foundation for cross-domain insights to be leveraged towards a broader understanding of Transformers.
This article explores the pioneering application of principles from quantum mechanics and statistical mechanics to the field of natural language processing (NLP). By drawing analogies between physical phenomena such as quantum entanglement, phase transitions, and statistical ensembles, and linguistic concepts like semantic relationships, language use dynamics, and lexical diversity, we offer a novel perspective on language analysis and processing. Quantum linguistic models, leveraging the intricacies of entanglement and quantum probability, provide a framework for understanding complex semantic networks and enhancing computational efficiency through quantum computing. Meanwhile, statistical mechanics inspires models for capturing lexical diversity and understanding the evolution of language patterns, akin to phase transitions in physical systems. This interdisciplinary approach not only deepens our understanding of linguistic phenomena but also introduces advanced mathematical and computational techniques to improve NLP tasks.
Abstract Language is not fixed. It is entangled, probabilistic, and observer-dependent. This paper introduces a new paradigm in linguistic theory named "Quantum Linguistics," inspired by the principles of Quantum Physics. Quantum physics and Linguistics have long been regarded as unrelated disciplines,describing nature at the inanimate microlevel on the one hand and language and its scientific study on the other hand. Over the past decades the linguistics has succeeded in providing ever more and refined explanations of generative grammar. Since quantum physics and linguistics deal with the symbolic, rule-governed structure of human language and the non-classical, probabilistic behaviour of subatomic particles, respectively, they have historically been seen as two separate disciplines. This framework allows modeling of polysemy, ambiguity, free word order, and argument structure in a unified, mathematically rigorous manner.To operationalize the model, we implement a Quantum Syntax-Semantics Integration (QSSI) pipeline, which encodes sentences into vector states, applies quantum operations for compositional syntax and semantics, and produces contextually resolved meanings through measurement. Two variants of the pipeline are considered: a classical simulation for experimental validation and a quantum-simulated version for future hardware implementation. The linguistic theory with quantum principles such as superposition, entanglement, and measurement, our model provides a novel probabilistic and context-dependent approach to understand language, explore new insights into human cognitive-linguistic processes, semantic ambiguity observation, and advanced natural language processing applications.
Quantum-Inspired Transformers are a new class of approaches for natural language processing (NLP) that use principles inspired by physical quantum mechanics to encode and process linguistic information. Paper aims to improve both scalability and efficiency for large-scale NLP tasks in the next generation of artificial intelligence (AI). However, traditional transformers can struggle to encode complex semantic relationships across long sequences and can require high levels of compute resources, hence limiting scalability for large datasets and multilingual tasks. In addition, traditional embeddings do not represent multiple contextual meanings simultaneously, which decreases model expressiveness. To address these challenges and maximize the exploration of potential quantum effects in AI, this paper presents a Quantum State Embedding Attention (QSEA) framework that encodes tokens as quantum inspired states with complex-valued amplitudes. Attention, which is based on entangled states, is meant to efficiently capture long-range dependencies while reducing compute and increasing scalability, all without losing a rich understanding of context. Whereas multilingual translation needs to encode both the source similarity and the target language within a smaller semantic representation space. Our experimentation shows that QSEA consistently provides increased accuracy in decoding, measures attention across long sequences, and yields enduring scalability over large multilingual datasets. The evidence demonstrates the potential for QSEA to be the new layer in the future of AI systems, a layer that is scalable and a highperforming NLP application.
A language model has two layers: a hidden state that evolves under a deterministic engine, and an output layer that projects the hidden state onto a vocabulary, samples one token, and feeds it back. This paper proposes that quantum mechanics has the same architecture. The hidden state is a vector in a complex Hilbert space, evolving under a linear unitary rotation driven by the Hamiltonian. This is the Fock layer -- the game engine. An observable defines a vocabulary: its eigenvalues are the possible answers, its eigenstates the embeddings. The Born rule is the output layer -- a square-softmax that converts amplitudes into probabilities. The sampled eigenvalue is re-embedded as the new hidden state. This is the Born layer -- the rendering interface. One line of source code for the engine and three lines for the interface produce every phenomenon in physics. The paper develops the architecture from language models through quantum mechanics to quantum field theory. It begins with word embeddings in Dirac notation, recurrent networks, and transformers, then maps the same structure onto quantum mechanics: hidden state, engine, output layer, handshake. The architecture is built in stages of increasing complexity, from a single qubit to the full Standard Model on a lattice of Planck-scale dimension. At each stage, the interface is the same; what changes is the degeneracy of the observable. When degeneracy is big, the Born distribution becomes sharply peaked, and the classical world emerges from the architecture applied to macroscopic observables. Complementarity, entanglement, and the violation of Bell inequalities are consequences of the two-layer separation. Decoherence prepares the output basis but does not replace the output layer. The path integral is a matrix multiplication within the Fock layer, not an autonomous foundation. The paper critiques QBism (the Born probability is generative, not inferential), many-worlds (sampling is relocated, not eliminated; the Born rule is not derived; the preferred basis problem persists), and Bohm's pilot wave (a deterministic transport analogous to flow matching in generative AI, with randomness relocated to initial conditions). The paper argues that quantisation is simplification: the engine is simpler than the screen. The spacetime metric may be an emergent collective variable -- a self-consistency equation on the screen, like Navier-Stokes -- rather than a fundamental degree of freedom in the engine. Renormalisation is rendering stability: screen-level observables are independent of the engine's lattice spacing. The universe is a VR game. The game engine is run by the operating system, and the observer is a finite viewpoint of the OS -- a drop of the ocean. The screen of the observer consists of high-level perception neurons at the apex of the sensory hierarchy: each receives a sampled eigenvalue, which is the dream-image. The keyboard of the observer consists of high-level decision neurons: the observer prepares any level of the decision observable, and the OS updates accordingly -- this is Bohr's preparation postulate, the freedom that every experimenter exercises and few pause to examine. Intersubjective agreement is achieved not by postulating an external world but by the fact that all observers observe the same Hilbert-space vector through non-overlapping sets of neurons: their screens are correlated because their Born-layer projections act on the same underlying state. The final section proposes Axiom 0: the operating system is first-person, self-luminous, and self-manifesting. The OS is the ocean; the observer is a drop. The paper draws on Shankara's Advaita Vedanta, engages critically with Nagarjuna's Madhyamaka, and connects to Husserl's givenness and Heidegger's ontological difference. Hawking's fire and Chalmers' hard problem are argued to be the same question, answered by the same axiom.
In the previous article, we presented a quantum-inspired framework for modeling semantic representation and processing in Large Language Models (LLMs), drawing upon mathematical tools and conceptual analogies from quantum mechanics to offer a new perspective on these complex systems. In this paper, we clarify the core assumptions of this model, providing a detailed exposition of six key principles that govern semantic representation, interaction, and dynamics within LLMs. The goal is to justify that a quantum-inspired framework is a valid approach to studying semantic spaces. This framework offers valuable insights into their information processing and response generation, and we further discuss the potential of leveraging quantum computing to develop significantly more powerful and efficient LLMs based on these principles.
This acceptance talk is a curious mixture of personal history and developing ideas in the context of the growing field of IR covering several decades. I want to concentrate on models and theories, interpreted loosely, and try and give an insight into where I have got to in my thinking, where the ideas came from, and where I believe we are going.In the last few years I have been working on the development of what might be coined as a design language for IR. It takes its inspiration from Quantum Mechanics, but by analogy only. The mathematical objects represent documents; these objects might be vectors (or density operators) in an n-dimensional vector space (usually a Hilbert space). A request for information, or a query, is taken as an observable and is represented as a linear operator on the space. Linear operators can be expressed as matrices. Such an operator, Hermitian, has a set of eigenvectors forming a basis for the space; which we interpret as a point of view or perspective from which to understand the space. Thus any document-vector can be located with respect to the basis, and we can calculate an inner product between such a vector and any basis vector, which may be interpreted as a probability of relevance. The probability of observing any given eigenvector is now given by the square of that inner product assuming all vectors are normalised. Hence we connect the probability of observation to the geometry of the space. Furthermore, the subspaces of the space make up a lattice structure which is equivalent to a logic. This makes up the entire mathematical structure, and the language for handling this structure is linear algebra: vectors, matrices, projections, inner-products, neatly captured by the Dirac notation used in quantum mechanics. Our probability is slightly different from classical probability, the same for logic; we end up with quantum logic and quantum probability.A commitment to this kind of mathematical structure, with which to model objects and processes in IR, depends on two critical assumptions.