In this article, we’ll talk about TF signatures(TF签). We’ll look at what they are, why they’re important to machine learning researchers, and how to use them in your work.
The Group Matrix Signature
The Group Matrix signature is the most general and encompasses all of the other tensor signatures. It allows you to specify a set of generators, which may be symmetric or non-symmetric. The generator group can have as many elements as you like, but if it has too many elements then it won’t be easy to calculate with.
It’s also possible for you to use different bases for each generator: compact one and another that’s not so compact! You can even mix these up in any way you like!
The Unified Signature
The Unified Signature(统一签名) is a generalization of the group matrix signature. It’s a tensor signature with an additional function parameter, which allows us to represent it as a tensorial product.
This additional parameter acts as a “group” operation in our representation and allows us to extend the range of possible signatures by adding new transformations on unique signatures.
The Tensor Signature
The Tensor Signature
The Tensor Signature is a generalization of the group matrix signature, which is a generalization of the unified signature.
Let’s start with an example. We have a graph where all vertices are labeled with integers between 1 and 10 (1 being the first vertex, 2 being the second vertex, etc.). The edges are labeled by pairs of these numbers (1-2, 3-8). Each edge connects two vertices such that they differ by at least two steps from each other; for example, edges 0 – 1 and 3 – 4 connect vertices 0 and 3 which differ in steps by 2.
The Group Matrix signature is the most general and encompasses all of the other tensor signatures
The group matrix signature is the most general tensor signature, and as such, it is a generalization of the tensor signatures. It’s also a generalization of the unified signature.
Conclusion
At the end of the day, it’s important to keep in mind that these are just three different ways of constructing a signature. If you want to learn more about this topic, check out my blog post on TF signatures!
