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This is probably a good start https://en.wikipedia.org/wiki/Graphical_model

It's traditionally fairly challenging to implement a relatively straightforward graphical model, but automatic differentiation changed that. Some people are working on getting the best of graphical models and black box models (like neural networks), which is where things like this come in.

Because it's jax, you get autograd and gpu/tpu acceleration for free, which further lets you stick these things in with other models, including black box models like NNs.

An example application is in sentence part of speech tagging (noun, adjective, etc). You could model each word's part of speech as a separate prediction, but you know that "noun-verb-noun" is more common than "noun-noun-noun" so you know your predictions should influence each other. Stuff like this makes that easier.

edit:

The authors of this library also put a paper on arxiv describing it https://arxiv.org/pdf/2308.03291.pdf The abstract gives a good sense of what they're going after:

> The development of deep learning software libraries enabled significant progress in the field by allowing users to focus on modeling, while letting the library to take care of the tedious and time-consuming task of optimizing execution for modern hardware accelerators. However, this has benefited only particular types of deep learning models, such as Transformers, whose primitives map easily to the vectorized computation. The models that explicitly account for structured objects, such as trees and segmentations, did not benefit equally because they require custom algorithms that are difficult to implement in a vectorized form. SynJax directly addresses this problem by providing an efficient vectorized implementation of inference algorithms for structured distributions covering alignment, tagging, segmentation, constituency trees and spanning trees.

> With SynJax we can build large-scale differentiable models that explicitly model structure in the data. The code is available at https://github.com/deepmind/synjax.



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