Quantification and Control of LSTM Resilience Based on Stability Theory

TMLR Paper7945 Authors

Abstract: This paper proposes a novel theoretical framework for guaranteeing and evaluating the resilience of long short-term memory (LSTM) networks in control systems. We introduce *recovery time* as a new metric of resilience in order to quantify the time required for an LSTM to return to its normal state after anomalous inputs. By mathematically refining incremental input-to-state stability ($\delta$ISS) theory for LSTM, we derive a practical data-independent upper bound on recovery time. This upper bound gives us resilience-aware training. Experimental validation on simple models demonstrates the effectiveness of our resilience estimation and control methods, enhancing a foundation for rigorous quality assurance in safety-critical AI applications.

Submission Type: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

1. Move Section D between Section 7 and Section 8.
2. Correct $\mu$ to $\mu(t)$ all of these errors in proof of theorem A.4. (previous version: page 20, revision version: page 22)

Assigned Action Editor: ~John_Timothy_Halloran1

Submission Number: 7945