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Using Laplace Transform To Optimize the Hallucination of Generation Models

Cheng Kang, Xinye Chen, Daniel Novak, Xujing Yao

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.

Using Laplace Transform To Optimize the Hallucination of Generation Models

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.
Paper Structure (22 sections, 28 equations, 10 figures, 2 tables)

This paper contains 22 sections, 28 equations, 10 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. The Connection Between Control Theory and Learning Progress of GMs
  3. The Laplace Transform of Optimization Methods
  4. SGD Optimization Method
  5. SGDM Optimization Method
  6. PID Optimization Method
  7. Adam Optimization Method
  8. Filter Processed SGD Optimization Method
  9. FuzzyPID Optimization Method
  10. The Laplace Transform of GAN
  11. The Laplace Transform of CycleGAN
  12. Experiments
  13. Experiment Settings
  14. Simulation
  15. Results and Analysis
  16. ...and 7 more sections

Figures (10)

  • Figure 1: Evolution process of the weight $\theta({t})$ for each component under the generation task.
  • Figure 2: The control system of classical GAN.
  • Figure 3: The system response of Classical GAN on various optimizers. Optimizer from left to right is respectively SGD, SGDM, Adam, PID, LPFSGD, HPFSGD, and FuzzyPID. The input of generator is a random Gaussian noise, and the input of discriminator is a square wave. (Blue wave comes from the discriminator, and yellow wave is the response of the generator.)
  • Figure 4: The control system of CycleGAN.
  • Figure 5: The system response of CycleGAN on different optimizers, such as SGD, SGDM, Adam, PID, LPF-SGD, HPF-SGD and FuzzyPID optimizers. For $G_{a}$, the source is a sinusoidal wave (green), and the dashed green wave comes from $D_{a}$. For $G_{a}$, the source is a cosine wave (red), and the dashed red wave comes from $D_{b}$.
  • ...and 5 more figures