# Using Laplace Transform To Optimize the Hallucination of Generation Models

arXiv: https://arxiv.org/abs/2603.18022 · HTML: https://mlsanity.com/paper/2603.18022/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 5 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Retrieval Augmentation Reduces Hallucination in Conversation](https://mlsanity.com/paper/2104.07567/) (2021)
- [Mitigating Object Hallucinations in Large Vision-Language Models through Visual Contrastive Decoding](https://mlsanity.com/paper/2311.16922/) (2023)
- [A Survey of Hallucination in Large Foundation Models](https://mlsanity.com/paper/2309.05922/) (2023)
- [On the Origin of Hallucinations in Conversational Models: Is it the Datasets or the Models?](https://mlsanity.com/paper/2204.07931/) (2022)
- [An Improved Analysis of Stochastic Gradient Descent with Momentum](https://mlsanity.com/paper/2007.07989/) (2020)
- [Neural Path Hunter: Reducing Hallucination in Dialogue Systems via Path Grounding](https://mlsanity.com/paper/2104.08455/) (2021)
- [On the convergence properties of a K-step averaging stochastic gradient descent algorithm for nonconvex optimization](https://mlsanity.com/paper/1708.01012/) (2017)
- [Understanding Hallucinations in Diffusion Models through Mode Interpolation](https://mlsanity.com/paper/2406.09358/) (2024)
- [CIEM: Contrastive Instruction Evaluation Method for Better Instruction Tuning](https://mlsanity.com/paper/2309.02301/) (2023)
- [CycleGAN, a Master of Steganography](https://mlsanity.com/paper/1712.02950/) (2017)
- [Low-Pass Filtering SGD for Recovering Flat Optima in the Deep Learning Optimization Landscape](https://mlsanity.com/paper/2201.08025/) (2022)
- [Tackling Structural Hallucination in Image Translation with Local Diffusion](https://mlsanity.com/paper/2404.05980/) (2024)
- [An improvement of the convergence proof of the ADAM-Optimizer](https://mlsanity.com/paper/1804.10587/) (2018)

## Abstract (arXiv)

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.