Table of Links
Abstract and 1 Introduction
2 Related Work
3 Model and 3.1 Associative memories
3.2 Transformer blocks
4 A New Energy Function
4.1 The layered structure
5 Cross-Entropy Loss
6 Empirical Results and 6.1 Empirical evaluation of the radius
6.2 Training GPT-2
6.3 Training Vanilla Transformers
7 Conclusion and Acknowledgments
Appendix A. Deferred Tables
Appendix B. Some Properties of the Energy Functions
Appendix C. Deferred Proofs from Section 5
Appendix D. Transformer Details: Using GPT-2 as an Example
References
Appendix B. Some Properties of the Energy Functions
We introduce some useful properties of the LogSumExp function defined below. This is particularly useful because The softmax function, widely utilized in the Transformer models, is the gradient of the LogSumExp function. As shown in (Grathwohl et al., 2019), the LogSumExp corresponds to the energy function of the a classifier.
Lemma 1 LogSumExp(x) is convex.
Proof
Consequently, we have the following smooth approximation for the min function.
B.1 Proof of Proposition 2
Authors:
(1) Xueyan Niu, Theory Laboratory, Central Research Institute, 2012 Laboratories, Huawei Technologies Co., Ltd.;
(2) Bo Bai baibo ([email protected]);
(3) Lei Deng ([email protected]);
(4) Wei Han ([email protected]).
This paper is
