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Torch-MLIR Shape Library Infrastructure

Overview

The Torch-MLIR project has an infrastructure for maintaining a library of shape functions for different Torch operators. These shape functions are fully executable specifications of the shape functions for each operator and can be authored and tested from Python for convenience. These are then brought into the compiler and can be manipulated / transformed for various purposes. Additionally, this effort is synergistic with upstream PyTorch efforts to maintain a library of shape functions.

The two main use cases are:

  • Shape refinement / shape inference. The torch-shape-refinement-pipeline pass pipeline orchestrates a series of passes that use the available shape information in the program to further refine the types in the program.

  • Error guard insertion for backends (Not Yet Implemented). The executable shape functions can include error guards / assertions that abort the program in case of invalid input (such as a matmul with a mismatching contracting dimension).

Architecture

Shape functions are defined as TorchScript-able Python functions in python/torch_mlir/dialects/torch/importer/jit_ir/build_tools/shape_lib_gen.py. The signatures of the shape functions are systematically derived from Torch JIT operator registry (mainly by replacing Tensor with List[int] in the operator signatures). Most shape functions are expected to reuse the upstream helper functions torch/jit/_shape_functions.py, and any new shape functions should be added there.

The build_tools/update_shape_lib.sh script invokes shape_lib_gen.py to generate an MLIR module containing the shape functions, which is currently embedded as a string literal in lib/Dialect/Torch/Transforms/ShapeLibrary.cpp.

The function StringRef mlir::torch::Torch::getShapeLibrary() is available for use inside the compiler any time that the shape library is needed.

Shape Refinement Pipeline Architecture

One of the main services that Torch-MLIR provides for backends is to normalize all Torch frontends into a common form which includes tensor shapes that are as precise as possible. This alleviates the need for backends to solve this problem themselves. This process of shape refinement is accomplished in Torch-MLIR through a pipeline of passes which uses the shape library combined with abstract interpretation of the shape functions to calculate shapes that are as precise as possible.

The pipeline works as follows:

  1. Shape calculations are reified. The torch-reify-shape-calculations reifies (i.e., materializes into the IR) the shape functions for each op with a shape function in the shape library. To do this, it wraps those ops in a torch.shape.calculate op, which has two regions: 1) a body with the op itself, and 2) the shape calculation, which calculates the shapes of the tensors yielded by the body.

  2. Simplifying the shape functions and propagating the shapes. After the shape functions are reified, we then attempt to "optimize hard enough" until the shapes yielded by the shape calculation regions become obvious in the IR. Those shapes are propagated through the IR, which usually reveals more opportunities for simplification.

    a. After reification, the shape functions are just a loose collection of functions, which are difficult to analyze. The first step is to inline them.

    b. After inlining, the torch-simplify-shape-calculations pass is used to simplify the shape calculations. This pass brings in a number of targeted canonicalization patterns and folds, along with a few specific patterns such as unrolling fixed-trip-count loops and abstractly interpreting list operations (an example is turning a series of "append" operations into a list literal). This pass also looks at the values yielded by the shape calculation regions, and if the resulting shape can be deduced by looking at the IR (for example, the shape is the list literal [1, 2, 3]), it will refine the types of the torch.shape.calculate op. This usually yields more opportunities for simplification. This process runs to a fixed-point.

  3. Dropping the shape calculations. Once all the types in the program have been refined as much as possible, the ops that were originally wrapped in torch.shape.calculate are unwrapped by the torch-drop-shape-calculations pass which drops the reified shape calculations, leaving behind the shape-refined program.

Inferring precise shape often is needed for correctness by backends. That said, requiring "optimizing hard enough" for correctness is usually considered quite brittle in a compiler flow. In this case, the saving grace is that we are only optimizing the shape functions, which are authored by compiler developers (not users), and thus there is some give-and-take in terms of understanding the optimizable constructs while authoring the shape functions, or improving the optimizations to enable easier authoring. Some brittleness is likely to escape to users, unfortunately, since there will always be situations where, for example, a statically shaped program allows the shape functions to be simplified to a greater extent than in a dynamically shaped program (for example, if the shape function checks "is this dimension of size 1"). We hope that this is minimal.

Adding to the shape library

See Adding a Shape Function for details on how to add a shpae function for an operator.

Rationale

Use of full operator signatures

The use of the full operator signature such as def aten〇add〇Tensor(self: List[int], other: List[int], alpha: float = 1) -> List[int]: for defining shape functions is somewhat verbose and repetitive, especially when there are multiple identical shape functions. Upstream uses a map with key-value pairs like "aten.add.Tensor": upstream_shape_helpers.broadcast, which is more compact and less repetitive in some ways (upstream also allows trailing arguments beyond those accepted by the shape function to be ignored, allowing further deduplication). The decision to do it the more verbose way in Torch-MLIR was based on the following goals:

  • To make the system very easy to debug and test.

  • To make the system maximally consistent between shape functions that are implemented with the upstream shape helpers and the ones that are manually written, which are still a fairly large and non-trivial set.

  • To make it as mechanical as possible to add a new shape function.