[FSDP][2/N] Add util for computing shared param LCA #94197
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🔗 Helpful Links🧪 See artifacts and rendered test results at hud.pytorch.org/pr/94197
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ghstack-source-id: d63f1ef Pull Request resolved: pytorch#94197
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**Overview** - This PR implements a utility function `get_shared_param_info_to_lca()` that returns a `Dict[SharedParamInfo, nn.Module]` mapping `SharedParamInfo` (representing a shared parameter) to its lowest common ancestor (LCA) module. - This function can be used as a subroutine for assigning shared parameters to their LCA modules during FSDP initialization (for the composable code path in the short term). **Details** The implementation follows a simple version of [Tarjan's offline LCA algorithm](https://en.wikipedia.org/wiki/Tarjan%27s_off-line_lowest_common_ancestors_algorithm) that is based on a union-find data structure. We can use this algorithm because the set of LCA queries is fixed a priori (i.e. this is offline). Each module represents a vertex in the module tree, where there is a directed edge from parent module to child module (i.e. `p` is a parent of `c` if `c` is returned from `p.children()`). The LCA module `lca` of two modules `a` and `b` is the lowest (i.e. greatest depth) module that includes both `a` and `b` in its subtree. For the unit test, here is a visualization of the module tree:  [ghstack-poisoned]
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ghstack-source-id: a3e61ab Pull Request resolved: pytorch#94197
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ghstack-source-id: a3e61ab Pull Request resolved: pytorch#94197
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fully_shard#94198 [FSDP][3/N] Add LCA logic tofully_shardOverview
get_shared_param_info_to_lca()that returns aDict[SharedParamInfo, nn.Module]mappingSharedParamInfo(representing a shared parameter) to its lowest common ancestor (LCA) module.Details
The implementation follows a simple version of Tarjan's offline LCA algorithm that is based on a union-find data structure. We can use this algorithm because the set of LCA queries is fixed a priori (i.e. this is offline).
Each module represents a vertex in the module tree, where there is a directed edge from parent module to child module (i.e.
pis a parent ofcifcis returned fromp.children()). The LCA modulelcaof two modulesaandbis the lowest (i.e. greatest depth) module that includes bothaandbin its subtree.For the unit test, here is a visualization of the module tree:
