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 Abstract and 1 Introduction 2 State Space Models 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 3.6 Additional Model Details 4 Empirical Evaluation and 4.1 Synthetic Tasks 4.2 Language Modeling 4.3 DNA Modeling 4.4 Audio Modeling and Generation 4.5 Speed and Memory Benchmarks 4.6 Model Ablations 5 Discussion 6 Conclusion and References A Discussion: Selection Mechanism B Related Work C Mechanics of Selective SSMs 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. 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. Authors: 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 Abstract and 1 Introduction Abstract and 1 Introduction 2 State Space Models 2 State Space Models 3 Selective State Space Models and 3.1 Motivation: Selection as a Means of Compression 3 Selective State Space Models and 3.1 Motivation: Selection as a Means of Compression 3.2 Improving SSMs with Selection 3.2 Improving SSMs with Selection 3.3 Efficient Implementation of Selective SSMs 3.3 Efficient Implementation of Selective SSMs 3.4 A Simplified SSM Architecture 3.4 A Simplified SSM Architecture 3.5 Properties of Selection Mechanisms 3.5 Properties of Selection Mechanisms 3.6 Additional Model Details 3.6 Additional Model Details 4 Empirical Evaluation and 4.1 Synthetic Tasks 4 Empirical Evaluation and 4.1 Synthetic Tasks 4.2 Language Modeling 4.2 Language Modeling 4.3 DNA Modeling 4.3 DNA Modeling 4.4 Audio Modeling and Generation 4.4 Audio Modeling and Generation 4.5 Speed and Memory Benchmarks 4.5 Speed and Memory Benchmarks 4.6 Model Ablations 4.6 Model Ablations 5 Discussion 5 Discussion 6 Conclusion and References 6 Conclusion and References A Discussion: Selection Mechanism A Discussion: Selection Mechanism B Related Work B Related Work C Mechanics of Selective SSMs C Mechanics of Selective SSMs D Hardware-aware Algorithm For Selective SSMs D Hardware-aware Algorithm For Selective SSMs E Experimental Details and Additional Results 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. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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The Math Behind Selective State Space Models

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