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arXiv · 2608.03425

State Propagation Also Satisfies: A Complex-Valued State-Space Model for Deterministic State Tracking

Xiaohe Li·Yang Lu
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Abstract

Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that \textbf{state propagation alone is sufficient}. We propose the \textbf{Complex State Propagator (CSP)}, a minimalistic recurrent architecture that \textbf{only propagates hidden states} across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a \textbf{block-level skip connection} alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves \textbf{100\% accuracy} with perfect F1 scores across canonical tasks.

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Xiaohe Li, Yang Lu. 2026-08-08. State Propagation Also Satisfies: A Complex-Valued State-Space Model for Deterministic State Tracking. https://arxiv.org/abs/2608.03425

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