[mlir][linalg] Implement Conv2D using Winograd Conv2D algorithm

[Hsiangkai]

Define high level winograd operators and convert conv_2d_nhwc_fhwc into winograd operators. According to Winograd Conv2D algorithm, we need three transform operators for input, filter, and output transformation.

The formula of Winograd Conv2D algorithm is

Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A

filter transform: G x g x G^T
input transform: B^T x d x B
output transform: A^T x y x A

The implementation is based on the paper, Fast Algorithm for Convolutional Neural Networks. (https://arxiv.org/abs/1509.09308)

[llvmbot]

@llvm/pr-subscribers-mlir-linalg

@llvm/pr-subscribers-mlir

Author: Hsiangkai Wang (Hsiangkai)

Changes

Define high level winograd operators and convert conv_2d_nhwc_fhwc into winograd operators. According to Winograd Conv2D algorithm, we need three transform operators for input, filter, and output transformation.

The formula of Winograd Conv2D algorithm is

Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A

filter transform: G x g x G^T
input transform: B^T x d x B
output transform: A^T x y x A

The implementation is based on the paper, Fast Algorithm for Convolutional Neural Networks. (https://arxiv.org/abs/1509.09308)

---

Patch is 45.03 KiB, truncated to 20.00 KiB below, full version: https://github.com/llvm/llvm-project/pull/96176.diff

7 Files Affected:

• (modified) mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.td (+114)
• (modified) mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h (+4)
• (modified) mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp (+78)
• (modified) mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt (+1)
• (added) mlir/lib/Dialect/Linalg/Transforms/WinogradConv2D.cpp (+321)
• (added) mlir/test/Dialect/Linalg/winograd-conv2d.mlir (+248)
• (modified) mlir/test/lib/Dialect/Linalg/TestLinalgTransforms.cpp (+13)

diff --git a/mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.td b/mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.td
index 64c538367267d..de1097b6ac27b 100644
--- a/mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.td
+++ b/mlir/include/mlir/Dialect/Linalg/IR/LinalgOps.td
@@ -154,4 +154,118 @@ def Linalg_SoftmaxOp : Linalg_Op<"softmax",
   let hasVerifier = 1;
 }
 
+def Linalg_WinogradFilterTransformOp : Linalg_Op<"winograd_filter_transform"> {
+  let summary = "Winograd filter transform operator";
+  let description = [{
+    Winograd Conv2D algorithm will convert linalg Conv2D operator into batched
+    matrix multiply. Before the matrix multiply, it will convert filter and
+    input into a format suitable for batched matrix multiply. After the matrix
+    multiply, it will convert output to the final result tensor.
+
+    The algorithm F(m x m, r x r) is
+
+    Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A
+
+    The size of output Y is m x m. The size of filter g is r x r. The size of
+    input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are
+    transformation matrices.
+
+    This operator is defined to represent the high level concept of filter
+    transformation (G x g x G^T) in the Winograd Conv2D algorithm.
+  }];
+
+  let arguments = (ins AnyRankedTensor:$filter,
+                       AnyRankedTensor:$output,
+                       I64Attr:$m,
+                       I64Attr:$r
+  );
+
+  let results = (outs AnyRankedTensor:$result);
+  let assemblyFormat = [{
+    attr-dict
+    `m` `(` $m `)`
+    `r` `(` $r `)`
+    `ins` `(` $filter `:` type($filter) `)`
+    `outs` `(` $output `:` type($output) `)`
+    `->` type($result)
+  }];
+  let hasVerifier = 1;
+}
+
+def Linalg_WinogradInputTransformOp : Linalg_Op<"winograd_input_transform"> {
+  let summary = "Winograd input transform operator";
+  let description = [{
+    Winograd Conv2D algorithm will convert linalg Conv2D operator into batched
+    matrix multiply. Before the matrix multiply, it will convert filter and
+    input into a format suitable for batched matrix multiply. After the matrix
+    multiply, it will convert output to the final result tensor.
+
+    The algorithm F(m x m, r x r) is
+
+    Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A
+
+    The size of output Y is m x m. The size of filter g is r x r. The size of
+    input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are
+    transformation matrices.
+
+    This operator is defined to represent the high level concept of input
+    transformation (B^T x d x B) in the Winograd Conv2D algorithm.
+  }];
+
+  let arguments = (ins AnyRankedTensor:$input,
+                       AnyRankedTensor:$output,
+                       I64Attr:$m,
+                       I64Attr:$r
+  );
+
+  let results = (outs AnyRankedTensor:$result);
+  let assemblyFormat = [{
+    attr-dict
+    `m` `(` $m `)`
+    `r` `(` $r `)`
+    `ins` `(` $input `:` type($input) `)`
+    `outs` `(` $output `:` type($output) `)`
+    `->` type($result)
+  }];
+  let hasVerifier = 1;
+}
+
+def Linalg_WinogradOutputTransformOp : Linalg_Op<"winograd_output_transform"> {
+  let summary = "Winograd output transform operator";
+  let description = [{
+    Winograd Conv2D algorithm will convert linalg Conv2D operator into batched
+    matrix multiply. Before the matrix multiply, it will convert filter and
+    input into a format suitable for batched matrix multiply. After the matrix
+    multiply, it will convert output to the final result tensor.
+
+    The algorithm F(m x m, r x r) is
+
+    Y = A^T x [(G x g x G^T) @ (B^T x d x B)] x A
+
+    The size of output Y is m x m. The size of filter g is r x r. The size of
+    input d is (m + r - 1) x (m + r - 1). A^T, A, G^T, G, B^T, and B are
+    transformation matrices.
+
+    This operator is defined to represent the high level concept of output
+    transformation (A^T x y x A) in the Winograd Conv2D algorithm.
+  }];
+
+  let arguments = (ins AnyRankedTensor:$value,
+                       AnyRankedTensor:$output,
+                       I64Attr:$m,
+                       I64Attr:$r
+  );
+
+  let results = (outs AnyRankedTensor:$result);
+  let assemblyFormat = [{
+    attr-dict
+    `m` `(` $m `)`
+    `r` `(` $r `)`
+    `ins` `(` $value `:` type($value) `)`
+    `outs` `(` $output `:` type($output) `)`
+    `->` type($result)
+  }];
+  let hasVerifier = 1;
+}
+
 #endif // LINALG_OPS
diff --git a/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h b/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
index 05e97befdec1f..835aeaf2ffed3 100644
--- a/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
+++ b/mlir/include/mlir/Dialect/Linalg/Transforms/Transforms.h
@@ -1692,6 +1692,10 @@ void populateTransposeMatmulPatterns(RewritePatternSet &patterns,
 void populateBlockPackMatmulPatterns(RewritePatternSet &patterns,
                                      const ControlBlockPackMatmulFn &controlFn);
 
+/// Patterns to apply Winograd Conv2D algorithm F(m x m, r x r).
+void populateWinogradConv2DPatterns(RewritePatternSet &patterns, int64_t m,
+                                    int64_t r);
+
 } // namespace linalg
 } // namespace mlir
 
diff --git a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
index 57d126603ebd7..7bf2a5bca037f 100644
--- a/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
+++ b/mlir/lib/Dialect/Linalg/IR/LinalgOps.cpp
@@ -2734,6 +2734,84 @@ FailureOr<SmallVector<Value>> SoftmaxOp::decomposeOperation(OpBuilder &b) {
   return SmallVector<Value>{result};
 }
 
+//===----------------------------------------------------------------------===//
+// WinogradFilterTransformOp
+//===----------------------------------------------------------------------===//
+
+LogicalResult WinogradFilterTransformOp::verify() {
+  auto filterType = cast<ShapedType>(getFilter().getType());
+  auto outputType = cast<ShapedType>(getOutput().getType());
+  auto filterElemType = filterType.getElementType();
+  auto outputElemType = outputType.getElementType();
+  if (filterElemType != outputElemType) {
+    return emitOpError() << "expected element type of input " << filterElemType
+                         << " to match element type of output "
+                         << outputElemType;
+  }
+
+  unsigned filterRank = filterType.getRank();
+  if (filterRank != 4)
+    return emitOpError() << "expected rank of input is 4";
+
+  unsigned outputRank = outputType.getRank();
+  if (outputRank != 6)
+    return emitOpError() << "expected rank of output is 6";
+
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
+// WinogradInputTransformOp
+//===----------------------------------------------------------------------===//
+
+LogicalResult WinogradInputTransformOp::verify() {
+  auto inputType = cast<ShapedType>(getInput().getType());
+  auto outputType = cast<ShapedType>(getOutput().getType());
+  auto inputElemType = inputType.getElementType();
+  auto outputElemType = outputType.getElementType();
+  if (inputElemType != outputElemType) {
+    return emitOpError() << "expected element type of input " << inputElemType
+                         << " to match element type of output "
+                         << outputElemType;
+  }
+
+  unsigned inputRank = inputType.getRank();
+  if (inputRank != 4)
+    return emitOpError() << "expected rank of input is 4";
+
+  unsigned outputRank = outputType.getRank();
+  if (outputRank != 6)
+    return emitOpError() << "expected rank of output is 6";
+
+  return success();
+}
+
+//===----------------------------------------------------------------------===//
+// WinogradOutputTransformOp
+//===----------------------------------------------------------------------===//
+
+LogicalResult WinogradOutputTransformOp::verify() {
+  auto valueType = cast<ShapedType>(getValue().getType());
+  auto outputType = cast<ShapedType>(getOutput().getType());
+  auto valueElemType = valueType.getElementType();
+  auto outputElemType = outputType.getElementType();
+  if (valueElemType != outputElemType) {
+    return emitOpError() << "expected element type of value " << valueElemType
+                         << " to match element type of output "
+                         << outputElemType;
+  }
+
+  unsigned valueRank = valueType.getRank();
+  if (valueRank != 6)
+    return emitOpError() << "expected rank of input is 6";
+
+  unsigned outputRank = outputType.getRank();
+  if (outputRank != 4)
+    return emitOpError() << "expected rank of output is 4";
+
+  return success();
+}
+
 //===----------------------------------------------------------------------===//
 // LinalgDialect
 //===----------------------------------------------------------------------===//
diff --git a/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt b/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
index 7e3dc56e0acdc..a7dcc29b5b9be 100644
--- a/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
+++ b/mlir/lib/Dialect/Linalg/Transforms/CMakeLists.txt
@@ -38,6 +38,7 @@ add_mlir_dialect_library(MLIRLinalgTransforms
   Transforms.cpp
   TransposeConv2D.cpp
   Vectorization.cpp
+  WinogradConv2D.cpp
 
   ADDITIONAL_HEADER_DIRS
   ${MLIR_MAIN_INCLUDE_DIR}/mlir/Dialect/Linalg
diff --git a/mlir/lib/Dialect/Linalg/Transforms/WinogradConv2D.cpp b/mlir/lib/Dialect/Linalg/Transforms/WinogradConv2D.cpp
new file mode 100644
index 0000000000000..86e834d51f2fc
--- /dev/null
+++ b/mlir/lib/Dialect/Linalg/Transforms/WinogradConv2D.cpp
@@ -0,0 +1,321 @@
+//===- WinogradConv2D.cpp - Winograd Conv2D implementation ----------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+//
+// Implement Winograd Conv2D algorithm. The implementation is based on the
+// paper: Fast Algorithms for Convolutional Neural Networks
+// (https://arxiv.org/abs/1509.09308)
+//
+//===----------------------------------------------------------------------===//
+
+#include "mlir/Dialect/Linalg/IR/Linalg.h"
+#include "mlir/Dialect/Tensor/IR/Tensor.h"
+#include "mlir/Dialect/Tosa/Utils/ConversionUtils.h"
+#include "mlir/Transforms/GreedyPatternRewriteDriver.h"
+#include "llvm/Support/MathExtras.h"
+
+namespace mlir {
+namespace linalg {
+
+namespace {
+
+using TransformMapKeyTy = std::pair<int, int>;
+
+// We use F(m, r) to define the size of minimal filtering algorithms.
+// m is the output dimension and r is the filter dimension. We can get
+// the input dimension, alpha, from the formula, alpha = m + r - 1.
+//
+// For example, when m = 2 and r = 3, we know its input size is 4.
+// The Conv2D will operate on 4x4 input data with 3x3 filter and get
+// 2x2 output result.
+constexpr TransformMapKeyTy F_2_3{2, 3};
+constexpr TransformMapKeyTy F_4_3{4, 3};
+constexpr TransformMapKeyTy F_2_5{2, 5};
+
+Value collapse2DData(RewriterBase &rewriter, Location loc, Value data) {
+  auto type = cast<ShapedType>(data.getType());
+  auto elementType = type.getElementType();
+  auto shape = type.getShape();
+  auto collapseType = RankedTensorType::get(
+      {shape[0] * shape[1] * shape[2] * shape[3], shape[4], shape[5]},
+      elementType);
+  SmallVector<ReassociationIndices> reassociation = {{0, 1, 2, 3}, {4}, {5}};
+  return rewriter.create<tensor::CollapseShapeOp>(loc, collapseType, data,
+                                                  reassociation);
+}
+
+// This function generates linalg.batch_matmul to multiply input with filter.
+// linalg.batch_matmul only supports 3-dimension data sets. We can treat
+// tileH x tileW x H x W data as the 1-dimension data array. That is to convert
+// [tileH, tileW, H, W, N, C] to [tileH x tileW x H x W, N, C]. In this way, we
+// can convert 6-dimension input data to 3-dimension representation that is
+// suitable for linalg.batch_matmul.
+//
+// Batched matmul will do the matrix multiply with the reduction on channel.
+//
+// We get
+//
+// %collapsed_input = tensor.collapse_shape %input
+// %collapsed_filter = tensor.collapse_shape %filter
+// %ret = linalg.batch_matmul %collapsed_input, %collapsed_filter
+// %expanded_ret = tensor.expand_shape %ret
+//
+// After this function, we get return value with data layout
+// (tileH, tileW, H, W, N, F).
+Value matrixMultiply(RewriterBase &rewriter, Location loc,
+                     Value transformedFilter, Value transformedInput) {
+  auto collapseFilter = collapse2DData(rewriter, loc, transformedFilter);
+  auto collapseInput = collapse2DData(rewriter, loc, transformedInput);
+
+  // Batched matrix multiply
+  auto filterType = cast<ShapedType>(transformedFilter.getType());
+  auto filterShape = filterType.getShape();
+  auto inputType = cast<ShapedType>(transformedInput.getType());
+  auto inputElemType = inputType.getElementType();
+  auto inputShape = inputType.getShape();
+
+  auto matmulType = RankedTensorType::get(
+      {inputShape[0] * inputShape[1] * inputShape[2] * inputShape[3],
+       inputShape[4], filterShape[5]},
+      inputElemType);
+  Value init = rewriter.create<tensor::EmptyOp>(loc, matmulType.getShape(),
+                                                inputElemType);
+
+  auto matmulOp = rewriter.create<linalg::BatchMatmulOp>(
+      loc, matmulType, ValueRange({collapseInput, collapseFilter}),
+      ValueRange{init});
+
+  // Expand matmul result
+  SmallVector<ReassociationIndices> reassociation = {{0, 1, 2, 3}, {4}, {5}};
+  auto expandType =
+      RankedTensorType::get({inputShape[0], inputShape[1], inputShape[2],
+                             inputShape[3], inputShape[4], filterShape[5]},
+                            inputElemType);
+  auto expandOutput = rewriter.create<tensor::ExpandShapeOp>(
+      loc, expandType, matmulOp.getResult(0), reassociation);
+  return expandOutput;
+}
+
+Value insertToAlignedTensor(RewriterBase &rewriter, Location loc, Value value,
+                            RankedTensorType alignedType) {
+  Value alignedInput = rewriter.create<tensor::EmptyOp>(
+      loc, alignedType.getShape(), alignedType.getElementType());
+
+  auto zeroIndex = rewriter.getIndexAttr(0);
+  auto oneIndex = rewriter.getIndexAttr(1);
+  SmallVector<OpFoldResult, 4> offsets(4, zeroIndex);
+  SmallVector<OpFoldResult, 4> strides(4, oneIndex);
+
+  auto valueType = cast<ShapedType>(value.getType());
+  auto valueShape = valueType.getShape();
+  SmallVector<OpFoldResult, 4> sizes;
+  sizes.emplace_back(rewriter.getIndexAttr(valueShape[0]));
+  sizes.emplace_back(rewriter.getIndexAttr(valueShape[1]));
+  sizes.emplace_back(rewriter.getIndexAttr(valueShape[2]));
+  sizes.emplace_back(rewriter.getIndexAttr(valueShape[3]));
+
+  return rewriter.create<tensor::InsertSliceOp>(loc, value, alignedInput,
+                                                offsets, sizes, strides);
+}
+
+Value extractFromAlignedTensor(RewriterBase &rewriter, Location loc,
+                               Value value, RankedTensorType extractedType) {
+  auto zeroIndex = rewriter.getIndexAttr(0);
+  auto oneIndex = rewriter.getIndexAttr(1);
+  SmallVector<OpFoldResult, 4> offsets(4, zeroIndex);
+  SmallVector<OpFoldResult, 4> strides(4, oneIndex);
+
+  auto extractedShape = extractedType.getShape();
+  SmallVector<OpFoldResult, 4> sizes;
+  sizes.emplace_back(rewriter.getIndexAttr(extractedShape[0]));
+  sizes.emplace_back(rewriter.getIndexAttr(extractedShape[1]));
+  sizes.emplace_back(rewriter.getIndexAttr(extractedShape[2]));
+  sizes.emplace_back(rewriter.getIndexAttr(extractedShape[3]));
+
+  return rewriter.create<tensor::ExtractSliceOp>(loc, extractedType, value,
+                                                 offsets, sizes, strides);
+}
+
+bool hasAllOneValues(DenseIntElementsAttr attr) {
+  return llvm::all_of(
+      attr, [](const APInt &element) { return element.getSExtValue() == 1; });
+}
+
+FailureOr<Operation *> winogradConv2DHelper(RewriterBase &rewriter,
+                                            linalg::Conv2DNhwcFhwcOp convOp,
+                                            int64_t m, int64_t r) {
+  Value input = convOp.getInputs()[0];
+  Value filter = convOp.getInputs()[1];
+  Value output = convOp.getOutputs()[0];
+  auto inputType = cast<ShapedType>(input.getType());
+  auto filterType = cast<ShapedType>(filter.getType());
+  auto outputType = cast<ShapedType>(output.getType());
+
+  if (!inputType.hasStaticShape())
+    return rewriter.notifyMatchFailure(convOp,
+                                       "expected a static shape for the input");
+
+  if (!filterType.hasStaticShape())
+    return rewriter.notifyMatchFailure(
+        convOp, "expected a static shape for the filter");
+
+  if (!hasAllOneValues(convOp.getDilations()))
+    return rewriter.notifyMatchFailure(convOp,
+                                       "expected all ones for dilations");
+
+  if (!hasAllOneValues(convOp.getStrides()))
+    return rewriter.notifyMatchFailure(convOp, "expected all ones for strides");
+
+  auto filterShape = filterType.getShape();
+  int64_t filterF = filterShape[0];
+  int64_t filterH = filterShape[1];
+  int64_t filterW = filterShape[2];
+  int64_t filterC = filterShape[3];
+  auto inputShape = inputType.getShape();
+  int64_t inputN = inputShape[0];
+  int64_t inputH = inputShape[1];
+  int64_t inputW = inputShape[2];
+  int64_t inputC = inputShape[3];
+  auto outputShape = outputType.getShape();
+  int64_t outputN = outputShape[0];
+  int64_t outputH = outputShape[1];
+  int64_t outputW = outputShape[2];
+  int64_t outputF = outputShape[3];
+
+  // Only support F(m x m, r x r), F(m x 1, r x 1) or F(1 x m, 1 x r)
+  bool isSupportedFilter = false;
+  if (filterH == filterW && filterH == r)
+    isSupportedFilter = true;
+  if (filterH == r && filterW == 1)
+    isSupportedFilter = true;
+  if (filterH == 1 && filterW == r)
+    isSupportedFilter = true;
+
+  if (!isSupportedFilter)
+    return rewriter.notifyMatchFailure(
+        convOp, "only support filter (r x r), (r x 1) or (1 x r)");
+
+  // Currently, we support (m, r) = (2, 3) or (4, 3) or (2, 5)
+  static const llvm::SmallVector<TransformMapKeyTy, 3> validConfigs = {
+      F_2_3, F_4_3, F_2_5};
+
+  TransformMapKeyTy key = {m, r};
+  auto it = std::find(validConfigs.begin(), validConfigs.end(), key);
+  // If we cannot find the constant transformation matrix, it means we do
+  // not support this configuration yet.
+  if (it == validConfigs.end())
+    return failure();
+
+  // All the criterias are satisfied. We can do Winograd Conv2D.
+  Location loc = convOp.getLoc();
+
+  // For F(m x 1, r x 1), we only need to do left side transform.
+  bool leftTransform = filterH != 1;
+  // For F(1 x m, 1 x r), we only need to do right side transform.
+  bool rightTransform = filterW != 1;
+  int64_t heightM = leftTransform ? m : 1;
+  int64_t widthM = rightTransform ? m : 1;
+  int64_t heightR = leftTransform ? r : 1;
+  int64_t widthR = rightTransform ? r : 1;
+
+  // --- Create operator for filter transform ---
+  Type elementType = filterType.getElementType();
+  int64_t alphaH = heightM + heightR - 1;
+  int64_t alphaW = widthM + widthR - 1;
+  int64_t tileH = llvm::divideCeilSigned(outputH, heightM);
+  int64_t tileW = llvm::divideCeilSigned(outputW, widthM);
+  auto retType = RankedTensorType::get(
+      {tileH, tileW, alphaH, alphaW, filterC, filterF}, elementType);
+  Value retValue =
+      rewriter.create<tensor::EmptyOp>(loc, retType.getShape(), elementType);
+  auto transformedFilter = rewriter.create<linalg::WinogradFilterTransformOp>(
+      loc, retType, filter, retValue, m, r);
+
+  // --- Create operator for input transform ---
+
+  // When input size - (r - 1) is not aligned with output tile size, we need to
+  // pad the input data to create the full tiles as tiling.
+  int64_t alignedInputH = tileH * heightM + (heightR - 1);
+  int64_t alignedInputW = tileW * widthM + (widthR - 1);
+  if (alignedInputH != inputH || alignedInputW != inputW) {
+    auto alignedInputType = RankedTensorType::get(
+        {inputN, alignedInputH, alignedInputW, inputC}, elementType);
+    input = insertToAlignedTensor(rewriter, loc, input, alignedInputType);
+  }
+
+  retType = RankedTensorType::get(
+      {tileH, tileW, alphaH, alphaW, inputN, inputC}, elementType);
+  retValue =
+ ...
[truncated]

[Hsiangkai]

Sorry, I am still figuring out how to create stack PRs.