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Non-Commutative State Tracking with Input-Dependent Low-Rank Updates in Mamba-3

arXiv · AI, language, vision and robotics · article · Sep 23, 2026 · UTC

State tracking from sequential observations can require both retaining information and updating it by composing observed operations. We extend Mamba-3's diagonal transition with an input-dependent low-rank reflection term to support noncommutative state tracking, in which the order of operations matters. The rank-one update couples state coordinates along an input-dependent direction, enabling non-diagonal state transitions within a single Mamba-3 block. The extension preserves Mamba-3's exponential-trapezoidal discretization, rotary embeddings (RoPE), and readout. For training, we adapt chunk

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