← 研踪 PaperTrailarXiv:2611.11336 · v1
Where Should a Gate Look? Input vs. State Gating in Diagonal State Space Models
首次提交 2026-11-08 20:27
版本更新 2026-11-08 20:27
雷达观测 2026-11-10 12:16
摘要
Modern state-space models owe much of their computational efficiency to their linear, often diagonal, dynamics. Classical recurrent neural networks instead allow nonlinear state-to-state interactions, which can be beneficial when memory updates need to depend on the past context. In this paper, we ask whether state feedback through a simple gate regulating memory updates can enhance the expressivity of diagonal state-space models. To investigate this question, we compare gates that depend on the current input, the recurrent state, or both. We establish a strict expressivity separation: for scalar models, state gating solves induction-head tasks for arbitrary vocabulary size and sequence length, whereas input gating fails on a finite instance under standard stability assumptions on the state transition matrix. Experiments show that state gating retains its advantage on induction-head tasks in higher-dimensional models, whereas input gating performs better on selective copying tasks. Together, our results show that even a simple, diagonal form of state-feedback gating can unlock capabilities unavailable to input-controlled models, while input and state gating offer complementary strengths and achieve the strongest overall performance when combined.
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v1 · 2026-11-08 20:27 · 最新观测版本
Where Should a Gate Look? Input vs. State Gating in Diagonal State Space Models
Modern state-space models owe much of their computational efficiency to their linear, often diagonal, dynamics. Classical recurrent neural networks instead allow nonlinear state-to-state interactions, which can be beneficial when memory updates need to depend on the past context. In this paper, we ask whether state feedback through a simple gate regulating memory updates can enhance the expressivity of diagonal state-space models. To investigate this question, we compare gates that depend on the current input, the recurrent state, or both. We establish a strict expressivity separation: for scalar models, state gating solves induction-head tasks for arbitrary vocabulary size and sequence length, whereas input gating fails on a finite instance under standard stability assumptions on the state transition matrix. Experiments show that state gating retains its advantage on induction-head tasks in higher-dimensional models, whereas input gating performs better on selective copying tasks. Together, our results show that even a simple, diagonal form of state-feedback gating can unlock capabilities unavailable to input-controlled models, while input and state gating offer complementary strengths and achieve the strongest overall performance when combined.
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