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Using Laplace Transform To Optimize the Hallucination of Generation Models

arXiv cs.AI / 3/20/2026

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Key Points

  • They formalize generation models as stochastic dynamical systems and use control theory to analyze factors contributing to hallucination.
  • They propose using Laplace transform analysis to optimize hallucination, noting that analytical solutions are intractable but a macroscopic, source-response simulation offers a viable alternative.
  • They observe that training progress correlates with the corresponding system response, suggesting a diagnostic link to improve optimization components.
  • The approach provides a virtual framework to mitigate hallucination that complements traditional optimization methods.

Abstract

To explore the feasibility of avoiding the confident error (or hallucination) of generation models (GMs), we formalise the system of GMs as a class of stochastic dynamical systems through the lens of control theory. Numerous factors can be attributed to the hallucination of the learning process of GMs, utilising knowledge of control theory allows us to analyse their system functions and system responses. Due to the high complexity of GMs when using various optimization methods, we cannot figure out their solution of Laplace transform, but from a macroscopic perspective, simulating the source response provides a virtual way to address the hallucination of GMs. We also find that the training progress is consistent with the corresponding system response, which offers us a useful way to develop a better optimization component. Finally, the hallucination problem of GMs is fundamentally optimized by using Laplace transform analysis.