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A Transition System Abstraction Framework for Neural Network Dynamical System Models

Yejiang Yang, Zihao Mo, Hoang-Dung Tran, Weiming Xiang

TL;DR

The paper addresses the opacity of neural network dynamical systems by introducing a transition-system abstraction that maps a localized, data-driven working zone into a discrete graph via Maximum Entropy partitioning. Transitions between partitions are computed with set-valued reachability, enabling offline, CTL-verifiable reasoning about the system's behaviors. Key contributions include the data-driven ME partitioning framework, offline transition computation with a guaranteed-distance link to the true dynamics, and empirical validation on LASA handwriting dynamics showing interpretable transition graphs and verifiable properties. This approach provides a practical path toward interpretable verification of complex neural dynamical models in real-world, safety-critical contexts.

Abstract

This paper proposes a transition system abstraction framework for neural network dynamical system models to enhance the model interpretability, with applications to complex dynamical systems such as human behavior learning and verification. To begin with, the localized working zone will be segmented into multiple localized partitions under the data-driven Maximum Entropy (ME) partitioning method. Then, the transition matrix will be obtained based on the set-valued reachability analysis of neural networks. Finally, applications to human handwriting dynamics learning and verification are given to validate our proposed abstraction framework, which demonstrates the advantages of enhancing the interpretability of the black-box model, i.e., our proposed framework is able to abstract a data-driven neural network model into a transition system, making the neural network model interpretable through verifying specifications described in Computational Tree Logic (CTL) languages.

A Transition System Abstraction Framework for Neural Network Dynamical System Models

TL;DR

The paper addresses the opacity of neural network dynamical systems by introducing a transition-system abstraction that maps a localized, data-driven working zone into a discrete graph via Maximum Entropy partitioning. Transitions between partitions are computed with set-valued reachability, enabling offline, CTL-verifiable reasoning about the system's behaviors. Key contributions include the data-driven ME partitioning framework, offline transition computation with a guaranteed-distance link to the true dynamics, and empirical validation on LASA handwriting dynamics showing interpretable transition graphs and verifiable properties. This approach provides a practical path toward interpretable verification of complex neural dynamical models in real-world, safety-critical contexts.

Abstract

This paper proposes a transition system abstraction framework for neural network dynamical system models to enhance the model interpretability, with applications to complex dynamical systems such as human behavior learning and verification. To begin with, the localized working zone will be segmented into multiple localized partitions under the data-driven Maximum Entropy (ME) partitioning method. Then, the transition matrix will be obtained based on the set-valued reachability analysis of neural networks. Finally, applications to human handwriting dynamics learning and verification are given to validate our proposed abstraction framework, which demonstrates the advantages of enhancing the interpretability of the black-box model, i.e., our proposed framework is able to abstract a data-driven neural network model into a transition system, making the neural network model interpretable through verifying specifications described in Computational Tree Logic (CTL) languages.
Paper Structure (10 sections, 1 theorem, 17 equations, 2 figures, 1 table, 2 algorithms)

This paper contains 10 sections, 1 theorem, 17 equations, 2 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Variation of the Shannon Entropy
  4. Neural Network Dynamical System Model and Reachability Analysis
  5. Problem Formulation
  6. Transition System Abstraction via ME Partitioning and Reachability Analysis
  7. ME Partitioning
  8. Transition Computation via Reachability Analysis
  9. Application to Learning and Verification on Human Handwriting Dynamics
  10. Conclusions

Key Result

Proposition 1

Given an output reachable set estimation in $\mathcal{X}'=[\Phi](P_i)$ and $\mathcal{X}'\subset P_j$, $\dim (\mathcal{X}')=m$, the estimation for transitions of the neural transition system will be the same as the dynamics $f$, there is a transition in neural transition system as is in the ideal dyn

Figures (2)

  • Figure 1: There are $28$ partitions from (a) while $27$ partitions from (b), information-rich areas are allocated more partitions.
  • Figure 2: The transition relationships are denoted by red arrows. Based on (a) and (b) we can clearly see the model's working flow, which means the learning model's interpretability is enhanced, such as results in Table \ref{['tab5']} where complex CTL formulae can be verified.

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 1
  • Remark 2
  • Definition 4
  • Definition 5
  • Remark 3
  • Definition 6
  • Proposition 1
  • ...and 1 more