[2604.05923] The UNDO Flip-Flop: A Controlled Probe for Reversible Semantic State Management in State Space Model

Computer Science > Machine Learning arXiv:2604.05923 (cs) [Submitted on 7 Apr 2026] Title:The UNDO Flip-Flop: A Controlled Probe for Reversible Semantic State Management in State Space Model Authors:Hongxu Zhou View a PDF of the paper titled The UNDO Flip-Flop: A Controlled Probe for Reversible Semantic State Management in State Space Model, by Hongxu Zhou View PDF HTML (experimental) Abstract:State space models (SSMs) have been shown to possess the theoretical capacity to model both star-free sequential tasks and bounded hierarchical structures Sarrof et al. (2024). However, formal expressivity results do not guarantee that gradient-based optimisation will reliably discover the corresponding solutions. Existing benchmarks probe either monotonic state tracking, as in the standard Flip-Flop task, or structural nesting, as in the Dyck languages, but neither isolates reversible semantic state retrieval. We introduce the UNDO Flip-Flop task to fill this gap. By extending the standard Flip-Flop with an UNDO, the task requires a model to maintain an implicit bounded stack and recover historical states under non-monotonic update sequences. We evaluate one-layer and two-layer Mamba-2 under this framework. Both variants fail to acquire the provably expressible stack-based rollback mechanism, converging instead on a local toggle heuristic that inverts the current state rather than retrieving stored history. Under an adversarial retraction pressure test held within the training lengt...