LaTeX-OCR VS Graphormer

I didn't know that such tools exists (completly new to LaTex). Thanks to your suggestion I looked for an open source althernative (to avoid anoyances of freemium) and I found pix2tex That works really like a charm.

I have recently discovered a few very helpful github packages which help me make notes while listening to lectures. These would be 1. pix2tex (allows you to scan an equation and convert it to latex) 2. pix2text (allows you to scan an equation with words in it and converts it to latex and text) 3. Tesseract (not really a physics related package, but it does allow me to copy notes from transcripts easily) 4. Mathpix an app that performs all the above mentioned operations better than the packages above, but one which ain't free.

This is also a great aid to learing LaTex. I wonder if anyone has ever tried to make an OCR system that generates the appropriate LaTex from an picture of an equation?

Turns out the answer is yes:

https://github.com/lukas-blecher/LaTeX-OCR

LaTeX-OCR

Ok, using ChatGPT and Bard (the irony lol) I learned a bit more about GNNs:

GNNs are probabilistic and can be trained to learn representations in graph-structured data and handling complex relationships, while classical graph algorithms are specialized for specific graph analysis tasks and operate based on predefined rules/steps.

* Why is PyG it called "Geometric" and not "Topologic" ?

Properties like connectivity, neighborhoods, and even geodesic distances can all be considered topological features of a graph. These features remain unchanged under continuous deformations like stretching or bending, which is the defining characteristic of topological equivalence. In this sense, "PyTorch Topologic" might be a more accurate reflection of the library's focus on analyzing the intrinsic structure and connections within graphs.

However, the term "geometric" still has some merit in the context of PyG. While most GNN operations rely on topological principles, some do incorporate notions of Euclidean geometry, such as:

- Node embeddings: Many GNNs learn low-dimensional vectors for each node, which can be interpreted as points in a vector space, allowing geometric operations like distances and angles to be applied.

- Spectral GNNs: These models leverage the eigenvalues and eigenvectors of the graph Laplacian, which encodes information about the geometric structure and distances between nodes.

- Manifold learning: Certain types of graphs can be seen as low-dimensional representations of high-dimensional manifolds. Applying GNNs in this context involves learning geometric properties on the manifold itself.

Therefore, although topology plays a primary role in understanding and analyzing graphs, geometry can still be relevant in certain contexts and GNN operations.

* Real world applications:

- HuggingFace has a few models [0] around things like computational chemistry [1] or weather forecasting.

- PyGod [2] can be used for Outlier Detection (Anomaly Detection).

- Apparently ULTRA [3] can "infer" (in the knowledge graph sense), that Michael Jackson released some disco music :-p (see the paper).

- RGCN [4] can be used for knowledge graph link prediction (recovery of missing facts, i.e. subject-predicate-object triples) and entity classification (recovery of missing entity attributes).

- GreatX [5] tackles removing inherent noise, "Distribution Shift" and "Adversarial Attacks" (ex: noise purposely introduced to hide a node presence) from networks. Apparently this is a thing and the field is called "Graph Reliability" or "Reliable Deep Graph Learning". The author even has a bunch of "awesome" style lists of links! [6]

- Finally this repo has a nice explanation of how/why to run machine learning algorithms "outside of the DB":

"Pytorch Geometric (PyG) has a whole arsenal of neural network layers and techniques to approach machine learning on graphs (aka graph representation learning, graph machine learning, deep graph learning) and has been used in this repo [7] to learn link patterns, also known as link or edge predictions."

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0: https://huggingface.co/models?pipeline_tag=graph-ml&sort=tre...

1: https://github.com/Microsoft/Graphormer

2: https://github.com/pygod-team/pygod

3: https://github.com/DeepGraphLearning/ULTRA

4: https://huggingface.co/riship-nv/RGCN

5: https://github.com/EdisonLeeeee/GreatX

6: https://edisonleeeee.github.io/projects.html

7: https://github.com/Orbifold/pyg-link-prediction

Github Repo Here: https://github.com/microsoft/Graphormer

Autoregressive models like GPT-2 do fairly well in text generation. Is it possible to do the same for graph data? A transformer based model Graphormer has recently shown its effectiveness in graph representation learning. Is there any way I can train Graphormer or any other model to generate graphs from an initial graph context?