Comments (3)
Besides, I'm also curious about you say " It is obvious that F is a contraction mapping", how can you guarentee it is a contraction mapping.
from enjoy-hamburger.
Hi @BraveDrXuTF ,
Thank you for your interest in this work! Regarding your questions,
- This codebase does not contain the naming of "fixed point." The discussion presented in blog series 2 is for generic cases. As for further analysis, check this paper on training more generalized fixed point systems/deep equilibrium models. In addition, you can find Hamburger's code here, which treats the optimization algorithm as fixed point iteration.
- This is the assumption for analysis in Section 2.3. Please take a look at the sentence below Figure 2: One-Step Gradient on page 5. People established toolkits leaner toward optimization to prove the convergence of optimization algorithms rather than Lipschitzness in fixed point analysis. See this paper for the convergence of MU, for example.
Please let me know if you have additional questions!
Thanks!
Zhengyang
from enjoy-hamburger.
Thanks you for providing rich details and references. So there may be a certain guarentee of convergence in matrix decomposition. And If we do not use factorization method to replace the attention mechanism, for example, we use other common neural arch, like fc, conv, and rnn, without any additional constraint, we would not have the guarentee of the good property that iteration will converge, right? In WGAN and Lipschitzness-GAN, they tend to clip the weights (WGAN) or penalize the gradients (Lipschitzness-GAN) of the discriminator, and by doing so they have the Lipschitzness.
from enjoy-hamburger.
Related Issues (11)
- Applying Hamburger to other models makes the training collapse soon HOT 2
- Confusion on update rules of Ham HOT 1
- question about the implementation of one-step gradient
- ZeroDivisionError: float division by zero
- Arxiv version or blog HOT 5
- BatchNormalization HOT 1
- KeyError: 'van_tiny is not in the models registry' HOT 4
- 缺少主干网络 HOT 2
- Default process group has not been initialized HOT 4
- Difference between the code and Eq(13) in the paper about the gradient calculation HOT 5
Recommend Projects
-
React
A declarative, efficient, and flexible JavaScript library for building user interfaces.
-
Vue.js
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
-
Typescript
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
-
TensorFlow
An Open Source Machine Learning Framework for Everyone
-
Django
The Web framework for perfectionists with deadlines.
-
Laravel
A PHP framework for web artisans
-
D3
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
-
Recommend Topics
-
javascript
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
-
web
Some thing interesting about web. New door for the world.
-
server
A server is a program made to process requests and deliver data to clients.
-
Machine learning
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
-
Visualization
Some thing interesting about visualization, use data art
-
Game
Some thing interesting about game, make everyone happy.
Recommend Org
-
Facebook
We are working to build community through open source technology. NB: members must have two-factor auth.
-
Microsoft
Open source projects and samples from Microsoft.
-
Google
Google ❤️ Open Source for everyone.
-
Alibaba
Alibaba Open Source for everyone
-
D3
Data-Driven Documents codes.
-
Tencent
China tencent open source team.
from enjoy-hamburger.