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[2602.18364] Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings
Summary
This paper presents a novel perspective on in-context learning in large language models (LLMs) through the lens of quantum mechanics, proposing a framework that integrates classical and quantum models for maximum likelihood prediction.
Why It Matters
As LLMs become increasingly integral to various applications, understanding their underlying mechanisms is crucial. This research offers insights into the intersection of quantum theory and machine learning, potentially paving the way for advancements in AI and information theory.
Key Takeaways
- Introduces a quantum approach to maximum likelihood prediction in LLMs.
- Models training as embedding probability distributions into quantum density operators.
- Provides non-asymptotic performance guarantees for quantum models.
- Unifies classical and quantum frameworks for LLMs.
- Explores implications for information theory and statistical learning.
Computer Science > Information Theory arXiv:2602.18364 (cs) [Submitted on 20 Feb 2026] Title:Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings Authors:Sreejith Sreekumar, Nir Weinberger View a PDF of the paper titled Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings, by Sreejith Sreekumar and Nir Weinberger View PDF HTML (experimental) Abstract:Recent works have proposed various explanations for the ability of modern large language models (LLMs) to perform in-context prediction. We propose an alternative conceptual viewpoint from an information-geometric and statistical perspective. Motivated by Bach[2023], we model training as learning an embedding of probability distributions into the space of quantum density operators, and in-context learning as maximum-likelihood prediction over a specified class of quantum models. We provide an interpretation of this predictor in terms of quantum reverse information projection and quantum Pythagorean theorem when the class of quantum models is sufficiently expressive. We further derive non-asymptotic performance guarantees in terms of convergence rates and concentration inequalities, both in trace norm and quantum relative entropy. Our approach provides a unified framework to handle both classical and quantum LLMs. Comments: Subjects: Information Theory (cs.IT); Machine Learning (cs.LG); Quantum Physics (quant-ph); Machine Learning (stat.ML) Cite as: arXiv:2602.18364 [cs.IT] (or arXiv:2602.18364v1 [...
