The post-grad FX passes in Inductor run after AOTAutograd has functionalized and normalized the input program into separate forward/backward graphs. As such, they generally can assume that the graph in question is functionalized, except for some mutations to inputs at the end of the graph. At the end of post-grad passes, there are special passes that reintroduce mutation into the graph before going into the rest of Inductor lowering which is generally aware of passes. The post-grad FX passes are varied but are typically domain specific passes making local changes to specific parts of the graph.

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