Problem
Research questions and friction points this paper is trying to address.
Neural Quantum States
Transformer
Generalization
In-Context Learning
Quantum Many-Body Systems
Generalization of Transformer-Based Neural Quantum States via In-Context Learning
🤖 AI Summary
This study addresses the lack of generalization theory for Transformer-based neural quantum states by constructing a theoretical framework grounded in in-context learning. Through deriving mean squared error (MSE) generalization bounds, it establishes rigorous guarantees during the inference phase for the first time, revealing an inverse relationship between network depth and prediction error alongside linear scaling with system size. The analysis is further extended to density operators. Numerical simulations conducted in both continuous and discrete domains validate these theoretical findings. Ultimately, this work provides a solid theoretical foundation for understanding the generalization properties of neural quantum state representations under the Transformer architecture.
📝 Abstract
Neural quantum states based on modern deep learning architectures have emerged as powerful representations for quantum many-body systems. In particular, Transformer-based neural quantum states provide expressive models capable of capturing long-range correlations, and their empirical generalization performance has recently been demonstrated. However, a theoretical understanding of their generalization behavior remains largely unexplored. In this paper, we develop a theoretical framework to analyze the generalization properties of Transformer-based neural quantum states under in-context learning. We establish a rigorous inference-time generalization error bound in terms of mean squared error (MSE), showing that the pointwise prediction error decreases inversely with both the number of in-context examples and the depth of the Transformer. We further show that the Transformer depth required to achieve this guarantee scales only linearly with the system size--namely, the number of particles in continuous systems or the number of qudits in discrete systems. Building on this result, we extend our analysis to full quantum states formulated as rank-one density operators, and derive MSE-based generalization bounds over both continuous and discrete domains under physical constraints. Finally, numerical simulations corroborate our theoretical analysis.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Neural Quantum States
In-Context Learning
Generalization Bounds
Transformer
Quantum Many-Body Systems
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