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RG-LRU Recurrence Gate

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Authors:

(1) Soham De, Google DeepMind and with Equal contributions;

(2) Samuel L. Smith, Google DeepMind and with Equal contributions;

(3) Anushan Fernando, Google DeepMind and with Equal contributions;

(4) Aleksandar Botev, Google DeepMind and with Equal contributions;

(5) George Cristian-Muraru, Google DeepMind and with Equal contributions;

(6) Albert Gu, Work done while at Google DeepMind;

(7) Ruba Haroun, Google DeepMind;

(8) Leonard Berrada, Google DeepMind;

(9) Yutian Chen, Google DeepMind;

(10) Srivatsan Srinivasan, Google DeepMind;

(11) Guillaume Desjardins, Google DeepMind;

(12) Arnaud Doucet, Google DeepMind;

(13) David Budden, Google DeepMind;

(14) Yee Whye Teh, Google DeepMind;

(15) David Budden, Google DeepMind;

(16) Razvan Pascanu, Google DeepMind;

(17) Nando De Freitas, Google DeepMind;

(18) Caglar Gulcehre, Google DeepMind.

Table of Links

1 Introduction

2 Model Architecture

3 Recurrent Models Scale as Efficiently as Transformers

3.1. Scaling curves

3.2. Evaluation on downstream tasks

4 Training Recurrent Models Efficiently on Device and 4.1. Model parallelism for large scale training

4.2. Efficient linear recurrences on device

4.3. Training speed on longer sequences

5. Inference Speed

5.1. A simple model of the decode step

5.2. Results

6. Long Context Modeling and 6.1. Improving next token prediction with longer contexts

6.2. Copy and retrieval capabilities

7. Related Works

8. Conclusion, Acknowledgements, and References


A. RG-LRU Recurrence Gate

B. Complex-Gated Linear Recurrent Unit (CG-LRU)

C. Model Scale Hyper-Parameters

D. Efficient Linear Recurrences on Device

E. The Local Attention Window Size of Griffin

F. Inference Speeds

G. Improving Next Token Prediction with Longer Contexts: Additional Results

H. Additional Details of the Copy and Retrieval Tasks

A. RG-LRU Recurrence Gate

In Figure 7, we demonstrate the behavior of different gating mechanisms applied on the recurrent weight a.


Figure 7 | The behaviour of different gating mechanisms applied on the recurrent weight 𝑎 (note that in the Mamba’s notations this is −𝐴).


Implementation We implement our recurrence gate, as defined in Section 2.4, in a slightly different, but mathematically equivalent form, for numerical stability. In particular, we compute the logarithm of 𝑎𝑡 and then we exponentiate it, instead of computing a sigmoid and then taking a power:



This paper is available on arxiv under CC BY 4.0 DEED license.


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