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

• URL: http://arxiv.org/abs/2604.05923v1
• Date: Tue, 07 Apr 2026 14:23:40 GMT
• Title: The UNDO Flip-Flop: A Controlled Probe for Reversible Semantic State Management in State Space Model
• Abstract summary: State space models (SSMs) have been shown to possess the theoretical capacity to model both star-free sequential tasks and bounded hierarchical structures.<n>We introduce the UNDO Flip-Flop task to fill this gap.<n>We evaluate one-layer and two-layer Mamba-2 under this framework.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 length distribution, the two-layer model collapses to 41.10% accuracy, which is below random chance. The results confirm systematic rather than incidental failure. Causal ablation shows that the bottleneck lies in retrieval, not storage. These results draw a clear line between what an architecture can in principle represent and what gradient descent reliably learns, a distinction that theoretical expressivity analyses alone cannot capture.

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