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The Math Behind Selective State Space Models
by The Serialization PublicationDecember 18th, 2024
Too Long; Didn't Read
This section examines the mechanics of Selective SSMs, detailing the discretization process, the role of learnable biases, and how the zero-order hold (ZOH) formulas shape efficient AI recurrences.
Authors:
(1) Albert Gu, Machine Learning Department, Carnegie Mellon University and with equal contribution;
(2) Tri Dao, Department of Computer Science, Princeton University and with equal contribution.
Table of Links
3 Selective State Space Models and 3.1 Motivation: Selection as a Means of Compression
3.2 Improving SSMs with Selection
3.3 Efficient Implementation of Selective SSMs
3.4 A Simplified SSM Architecture
3.5 Properties of Selection Mechanisms
4 Empirical Evaluation and 4.1 Synthetic Tasks
4.4 Audio Modeling and Generation
4.5 Speed and Memory Benchmarks
A Discussion: Selection Mechanism
D Hardware-aware Algorithm For Selective SSMs
E Experimental Details and Additional Results
C Mechanics of Selective SSMs
The discretization step size is
where we observe that the parameter can be viewed as a learnable bias and folded into the linear projection. Now applying the zero-order hold (ZOH) discretization formulas:
Thus the final discrete recurrence (2a) is
as desired.
This paper is available on arxiv under CC BY 4.0 DEED license.
L O A D I N G
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