Make einsum_v2 support multi-operands (#42327)

* Extend python einsum interface to make einsum_v2 support multi-operands and switch it to default.

* add opt_einsum dependence

* add yaml and support eager model

* fix by code review

paddle/fluid/operators/einsum_op.cc

@@ -18,7 +18,7 @@
 #include "paddle/fluid/framework/op_registry.h"
 #include "paddle/fluid/framework/operator.h"
 #include "paddle/phi/core/ddim.h"
-#include "paddle/phi/kernels/impl/einsum_impl.h"
+#include "paddle/phi/infermeta/unary.h"
 
 namespace paddle {
 namespace operators {
@@ -85,7 +85,7 @@ class EinsumGradMaker : public framework::SingleGradOpMaker<T> {
 namespace ops = paddle::operators;
 
 DECLARE_INFER_SHAPE_FUNCTOR(einsum, EinsumInferShapeFunctor,
-                            PD_INFER_META(phi::EinsumInferShape));
+                            PD_INFER_META(phi::EinsumInferMeta));
 
 REGISTER_OPERATOR(einsum, ops::EinsumOp, ops::EinsumOpMaker,
                   EinsumInferShapeFunctor,

paddle/phi/infermeta/unary.cc

@@ -28,6 +28,7 @@ limitations under the License. */
 #include "paddle/phi/kernels/funcs/strided_slice.h"
 #include "paddle/phi/kernels/funcs/unfold_functor.h"
 #include "paddle/phi/kernels/funcs/unsqueeze.h"
+#include "paddle/phi/kernels/impl/einsum_impl.h"
 
 namespace phi {
 
@@ -398,6 +399,45 @@ void EighInferMeta(const MetaTensor& x,
   out_v->set_dims(input_dim);
 }
 
+void EinsumInferMeta(const std::vector<const MetaTensor*>& inputs,
+                     const std::string& equation,
+                     MetaTensor* out) {
+  // collect the following informations to prepare einsum.
+  LabelMap labelshape(0);
+  LabelMap labeltype(LabelType::Reduction);
+  std::vector<LabelMap> label2perms(inputs.size(), LabelMap(-1));
+  std::vector<char> all_labels;
+  std::vector<int> broadcast_dims;
+  std::vector<int> output_dims;
+  std::vector<std::vector<int>> ellipsis_dims(2);
+
+  std::vector<DDim> input_dims;
+  for (auto& i : inputs) {
+    input_dims.push_back(i->dims());
+  }
+  std::string right;
+  ParseEinsumEquation(equation,
+                      input_dims,
+                      &labelshape,
+                      &labeltype,
+                      &all_labels,
+                      &label2perms,
+                      &ellipsis_dims,
+                      &broadcast_dims,
+                      &output_dims,
+                      &right);
+
+  VLOG(3) << "Einsum Infershape: input dims:"
+          << paddle::string::join_strings(input_dims, "\n");
+  VLOG(3) << "Einsum Infershape: equation:" << equation;
+  VLOG(3) << "Einsum Infershape: all_labels:"
+          << paddle::string::join_strings(all_labels, ",");
+  VLOG(3) << "Einsum Infershape: output dims:"
+          << paddle::string::join_strings(output_dims, ",");
+  VLOG(3) << "Label Type is : " << label_to_string(all_labels, labeltype);
+  VLOG(3) << "Label Shape is : " << label_to_string(all_labels, labelshape);
+}
+
 void ExpandInferMeta(const MetaTensor& x,
                      const IntArray& shape,
                      MetaTensor* out) {

paddle/phi/infermeta/unary.h

@@ -80,6 +80,10 @@ void EighInferMeta(const MetaTensor& x,
                    MetaTensor* out_w,
                    MetaTensor* out_v);
 
+void EinsumInferMeta(const std::vector<const MetaTensor*>& inputs,
+                     const std::string& equation,
+                     MetaTensor* out);
+
 void ExpandInferMeta(const MetaTensor& x,
                      const IntArray& shape,
                      MetaTensor* out);

paddle/phi/kernels/impl/einsum_impl.h

@@ -13,7 +13,6 @@
 // limitations under the License.
 #pragma once
 
-#include "paddle/fluid/framework/infershape_utils.h"
 #include "paddle/phi/core/dense_tensor.h"
 #include "paddle/phi/kernels/matmul_kernel.h"
 #include "paddle/phi/kernels/reduce_sum_kernel.h"
@@ -21,6 +20,7 @@
 #include "paddle/utils/string/string_helper.h"
 
 namespace phi {
+
 // check the validation of the Einsum equation.
 // 1. the label must between 'a' - 'z'.
 // 2. the dim of the same label must be same.
@@ -302,45 +302,6 @@ inline static void ParseEinsumEquation(
   }
 }
 
-inline void EinsumInferShape(const std::vector<const MetaTensor*>& inputs,
-                             const std::string& equation,
-                             MetaTensor* out) {
-  // collect the following informations to prepare einsum.
-  LabelMap labelshape(0);
-  LabelMap labeltype(LabelType::Reduction);
-  std::vector<LabelMap> label2perms(inputs.size(), LabelMap(-1));
-  std::vector<char> all_labels;
-  std::vector<int> broadcast_dims;
-  std::vector<int> output_dims;
-  std::vector<std::vector<int>> ellipsis_dims(2);
-
-  std::vector<DDim> input_dims;
-  for (auto& i : inputs) {
-    input_dims.push_back(i->dims());
-  }
-  std::string right;
-  ParseEinsumEquation(equation,
-                      input_dims,
-                      &labelshape,
-                      &labeltype,
-                      &all_labels,
-                      &label2perms,
-                      &ellipsis_dims,
-                      &broadcast_dims,
-                      &output_dims,
-                      &right);
-
-  VLOG(3) << "Einsum Infershape: input dims:"
-          << paddle::string::join_strings(input_dims, "\n");
-  VLOG(3) << "Einsum Infershape: equation:" << equation;
-  VLOG(3) << "Einsum Infershape: all_labels:"
-          << paddle::string::join_strings(all_labels, ",");
-  VLOG(3) << "Einsum Infershape: output dims:"
-          << paddle::string::join_strings(output_dims, ",");
-  VLOG(3) << "Label Type is : " << label_to_string(all_labels, labeltype);
-  VLOG(3) << "Label Shape is : " << label_to_string(all_labels, labelshape);
-}
-
 template <typename T>
 std::vector<T> GetLabelIndexByType(const std::vector<char>& all_labels,
                                    const LabelMap& type,
@@ -394,6 +355,13 @@ DenseTensor PerformReduction(const Context& dev_ctx,
   return Sum<T, Context>(dev_ctx, tensor, indices, tensor.dtype(), true);
 }
 
+inline bool is_no_need_transpose(const std::vector<int>& axis) {
+  for (size_t i = 0; i < axis.size(); ++i) {
+    if (i != static_cast<size_t>(axis[i])) return false;
+  }
+  return true;
+}
+
 template <typename T, typename Context>
 DenseTensor PerformTranspose(const Context& dev_ctx,
                              const DenseTensor& tensor,
@@ -401,12 +369,6 @@ DenseTensor PerformTranspose(const Context& dev_ctx,
                              const std::vector<char>& all_labels,
                              const std::vector<int>& ellipsis,
                              const LabelMap& label2type) {
-  auto is_no_need_transpose = [](std::vector<int>& axis) {
-    for (size_t i = 0; i < axis.size(); ++i) {
-      if (i != size_t(axis[i])) return false;
-    }
-    return true;
-  };
   auto axis = GetLabelIndexByType<int>(
       all_labels, label2type, label2perm, ellipsis, LabelType::ALL_TYPE);
   VLOG(5) << "PerformTranspose: " << paddle::string::join_strings(axis, ",");
@@ -496,9 +458,9 @@ void TransposeToOutput(const Context& dev_ctx,
       axis.push_back(it - all_labels.begin() + offset);
     }
   }
+  if (is_no_need_transpose(axis)) return output->ShareBufferWith(to_trans);
   VLOG(5) << "call TransposeToOutput: with axis: "
           << paddle::string::join_strings(axis, ",");
-  if (axis.size() == 0) return output->ShareBufferWith(to_trans);
   return TransposeKernel<T, Context>(dev_ctx, to_trans, axis, output);
 }
 

python/paddle/fluid/tests/unittests/test_einsum_v2.py

+#   Copyright (c) 2021 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import numpy as np
+import contextlib
+import unittest
+import paddle
+from paddle.fluid import core
+
+import os
+os.environ['FLAGS_new_einsum'] = "1"
+
+
+def error_trans(func, *args, **kargs):
+    """ 
+    transport C++ exception into Python exception. 
+    because einsum_v2 raise different exception with einsum_v1.
+    """
+    try:
+        out = func(*args, **kargs)
+    except ValueError as e:
+        if "Same label have different shapes" in str(e):
+            raise AssertionError("Invalid operands: label i "
+                                 "corresponds to non-broadcastable dimensions.")
+
+
+class TestErrors(unittest.TestCase):
+    def setUp(self):
+        pass
+
+    def test_diagonalize_errors(self):
+        a = np.arange(4 * 3 * 4 * 4).reshape(4, 3, 4, 4).astype('float')
+        a = paddle.to_tensor(a)
+        with self.assertRaisesRegex(AssertionError,
+                                    ('Duplicate labels are not supported.')):
+            paddle.einsum('...ii->...i', a)
+        with self.assertRaisesRegex(AssertionError,
+                                    ('Duplicate labels are not supported.')):
+            paddle.einsum('i...i', a)
+        with self.assertRaisesRegex(AssertionError,
+                                    ('Duplicate labels are not supported.')):
+            paddle.einsum('i...i->i...', a)
+
+    def test_param_errors(self):
+        a = np.arange(4 * 3 * 4 * 4).reshape(4, 3, 4, 4).astype('float')
+        a = paddle.to_tensor(a)
+        with self.assertRaisesRegex(
+                AssertionError,
+            ("Required at least one operand in Einsum API, but received 0 ")):
+            paddle.einsum('ijk')
+        with self.assertRaisesRegex(AssertionError, (
+                'Invalid equation: multiple `->` were found.')):
+            paddle.einsum('i -> j -> k', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: the number of operands is 2, "
+                "but found 3 segments in the label equation.")):
+            paddle.einsum('i,j,k', a, a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: the number of operands is 2, "
+                "but found 1 segments in the label equation.")):
+            paddle.einsum('ij -> k', a, a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: the number of operands is 1, "
+                "but found 2 segments in the label equation.")):
+            paddle.einsum('i, -> k', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: the label string '' misses dimensions.")):
+            paddle.einsum('->', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: the label string 'i' misses dimensions.")):
+            paddle.einsum('i', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: _ is not a valid label, "
+                "which should be letters.")):
+            paddle.einsum('i_', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: `.` is found outside of an ellipsis.")):
+            paddle.einsum('i..j', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: `.` is found outside of an ellipsis.")):
+            paddle.einsum('...k...', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: missing ellipsis in output labels.")):
+            paddle.einsum('i...->i', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid equation: duplicate output labels are found.")):
+            paddle.einsum('i...->i...i', a)
+        with self.assertRaisesRegex(AssertionError, (
+                "Invalid operands: label i "
+                "corresponds to non-broadcastable dimensions.")):
+            error_trans(paddle.einsum, 'ij...,ji...', a, a)
+
+
+class TestEinsum(unittest.TestCase):
+    @classmethod
+    def setUpClass(cls):
+        np.random.seed(12345)
+
+        cls.TEST_SAMPLES = {
+            "a": np.random.rand(1, 1),
+            "b": np.random.rand(1),
+            "x": np.random.rand(5),
+            "y": np.random.rand(7),
+            "A": np.random.rand(4, 5),
+            "B": np.random.rand(2, 5),
+            "C": np.random.rand(3, 7),
+            "D": np.random.rand(3, 4, 5),
+            "E": np.random.rand(3, 5, 2),
+            "F": np.random.rand(2, 4, 5, 3),
+            "G": np.random.rand(4, 2, 5),
+            "H": np.random.rand(3, 2, 4),
+            "I": np.random.rand(2, 2),
+            "J": np.random.rand(1, 3, 5),
+            "K": np.random.rand(1, 2, 3, 4),
+        }
+
+    def _get_place(self, force_to_use_cpu=False):
+        if force_to_use_cpu:
+            return core.CPUPlace()
+        else:
+            if core.is_compiled_with_cuda():
+                return core.CUDAPlace(0)
+            return core.CPUPlace()
+
+    def check_output_equal(self, actual, expect, rtol=1.e-5, atol=1.e-8):
+        error_msg = 'Output has diff at place:{}. \nExpect: {} \nBut Got: {} in class {}'
+        self.assertTrue(
+            np.allclose(
+                actual, expect, rtol=rtol, atol=atol),
+            error_msg.format(paddle.get_device(), expect, actual,
+                             self.__class__.__name__))
+
+    def setUp(self):
+        self.sample = {"paradigm": "i->", "data": ["x"]}
+
+    def test_forward(self):
+        operands = [
+            TestEinsum.TEST_SAMPLES[operand] for operand in self.sample["data"]
+        ]
+        expected_result = np.einsum(self.sample["paradigm"], *operands)
+        equation = self.sample["paradigm"]
+
+        with paddle.fluid.dygraph.guard(
+                self._get_place(force_to_use_cpu=False)):
+            pd_operands = [paddle.to_tensor(operand) for operand in operands]
+            result = paddle.einsum(equation, *pd_operands)
+            self.check_output_equal(result.numpy(), expected_result)
+
+        with paddle.fluid.dygraph.guard(self._get_place(force_to_use_cpu=True)):
+            pd_operands = [paddle.to_tensor(operand) for operand in operands]
+            result = paddle.einsum(equation, *pd_operands)
+            self.check_output_equal(result.numpy(), expected_result)
+
+
+class TestEinsumVectorDot(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "i,i->", "data": ["x", "x"]}
+
+
+class TestEinsumVectorMul(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "i,i->i", "data": ["x", "x"]}
+
+
+class TestEinsumVectorOuter(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "i,j->ij", "data": ["x", "y"]}
+
+
+class TestEinsumMatrixTranspose(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij->ji", "data": ["A"]}
+
+
+class TestEinsumMatrixRowSum(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij->j", "data": ["A"]}
+
+
+class TestEinsumMatrixColSum(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij->i", "data": ["A"]}
+
+
+class TestEinsumMatrixEleMul(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij,ij->ij", "data": ["A", "A"]}
+
+
+class TestEinsumDegenerateMatrixVecMul(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij,j", "data": ["a", "b"]}
+
+
+class TestEinsumMatrixVecMul(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij,j->i", "data": ["A", "x"]}
+
+
+class TestEinsumMatrixMul(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij,kj->ik", "data": ["A", "B"]}
+
+
+class TestEinsumMatrixOuter(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij,kl->ijkl", "data": ["A", "C"]}
+
+
+class TestEinsumTensorBMM(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "bij,bjk->bik", "data": ["D", "E"]}
+
+
+class TestEinsumTensorContract1(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijk,jk->i", "data": ["D", "A"]}
+
+
+class TestEinsumTensorContract2(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijk,lk->ijl", "data": ["D", "B"]}
+
+
+class TestEinsumTensorContract3(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "abcd,dfg->abcfg", "data": ["F", "D"]}
+
+
+class TestEinsumTensorContract4(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijk,jk->ik", "data": ["D", "A"]}
+
+
+class TestEinsumTensorContract5(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijk,jk->ij", "data": ["D", "A"]}
+
+
+class TestEinsumTensorContract6(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ik, ijk->j", "data": ["A", "G"]}
+
+
+class TestEinsumTensorContract7(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijk, ik->jk", "data": ["G", "A"]}
+
+
+class TestEinsumEllipsis1(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "i...->...", "data": ["G"]}
+
+
+class TestEinsumEllipsis2(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ij,...i->j...", "data": ["A", "H"]}
+
+
+class TestEinsumEllipsis3(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "k...,jk", "data": ["F", "I"]}
+
+
+class TestEinsumTestEinsumBilinear(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "bn,anm,bm->ba", "data": ["B", "E", "I"]}
+
+
+class TestEinsumTestEinsumOthers1(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijkl, lmn->kmn", "data": ["F", "H"]}
+
+
+class TestEinsumTestEinsumOthers2(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "ijkl, lmn->ijn", "data": ["F", "H"]}
+
+
+class TestEinsumBatch1(TestEinsum):
+    def setUp(self):
+        self.sample = {"paradigm": "blq,bhlk->bhlqk", "data": ["J", "K"]}
+
+
+class TestNumpyTests(unittest.TestCase):
+    def setUp(self):
+        pass
+
+    def _get_place(self, force_to_use_cpu=False):
+        if force_to_use_cpu:
+            return core.CPUPlace()
+        else:
+            if core.is_compiled_with_cuda():
+                return core.CUDAPlace(0)
+            return core.CPUPlace()
+
+    def check_output_equal(self, actual, expect, rtol=1.e-5, atol=1.e-8):
+        error_msg = 'Output has diff at place:{}. \nExpect: {} \nBut Got: {} in class {}'
+        self.assertTrue(
+            np.allclose(
+                actual, expect, rtol=rtol, atol=atol),
+            error_msg.format(paddle.get_device(), expect, actual,
+                             self.__class__.__name__))
+
+    def check_output(self, eqn, *ops):
+        expect = np.einsum(eqn, *ops)
+        with paddle.fluid.dygraph.guard(
+                self._get_place(force_to_use_cpu=False)):
+            pd_operands = [paddle.to_tensor(op) for op in ops]
+            actual = paddle.einsum(eqn, *pd_operands)
+            self.check_output_equal(actual.numpy(), expect)
+
+    def test_sums(self):
+        for n in range(1, 17):
+            a = np.arange(n).astype('float')
+            self.check_output("i->", a)
+
+        for n in range(1, 17):
+            a = np.arange(2 * 3 * n).reshape(2, 3, n).astype('float')
+            self.check_output("...i->...", a)
+
+        for n in range(1, 17):
+            a = np.arange(2 * n).reshape(2, n).astype('float')
+            self.check_output("i...->...", a)
+
+        for n in range(1, 17):
+            a = np.arange(2 * 3 * n).reshape(2, 3, n).astype('float')
+            self.check_output("i...->...", a)
+
+        for n in range(1, 17):
+            a = np.arange(3 * n).reshape(3, n).astype('float')
+            b = np.arange(2 * 3 * n).reshape(2, 3, n).astype('float')
+            self.check_output("..., ...", a, b)
+
+        for n in range(1, 17):
+            a = np.arange(2 * 3 * n).reshape(2, 3, n).astype('float')
+            b = np.arange(n).astype('float')
+            self.check_output("...i, ...i", a, b)
+
+        for n in range(1, 11):
+            a = np.arange(n * 3 * 2).reshape(n, 3, 2).astype('float')
+            b = np.arange(n).astype('float')
+            self.check_output("i..., i...", a, b)
+
+        for n in range(1, 17):
+            a = (np.arange(3) + 1).astype('float')
+            b = (np.arange(n) + 1).astype('float')
+            self.check_output("i,j", a, b)
+
+        for n in range(1, 17):
+            a = np.arange(4 * n).reshape(4, n).astype('float')
+            b = np.arange(n).astype('float')
+            self.check_output("ij, j", a, b)
+
+        for n in range(1, 17):
+            a = np.arange(4 * n).reshape(4, n).astype('float')
+            b = np.arange(n).astype('float')
+            self.check_output("ji,j", a.T, b.T)
+
+        for n in range(1, 17):
+            a = np.arange(4 * n).reshape(4, n).astype('float')
+            b = np.arange(n * 6).reshape(n, 6).astype('float')
+            self.check_output("ij,jk", a, b)
+
+        a = np.arange(12).reshape(3, 4).astype('float')
+        b = np.arange(20).reshape(4, 5).astype('float')
+        c = np.arange(30).reshape(5, 6).astype('float')
+        self.check_output("ij,jk,kl", a, b, c)
+
+        a = np.arange(60).reshape(3, 4, 5).astype('float')
+        b = np.arange(24).reshape(4, 3, 2).astype('float')
+        self.check_output("ijk, jil -> kl", a, b)
+
+        for n in range(1, 25):
+            a = np.arange(n).astype('float')
+            self.check_output("...,...", a, a)
+            self.check_output("i,i", a, a)
+
+        # TODO(@xiongkun): explict broadcast in EinsumOp is not supported, it's not recommend to use einsum like this.
+        #p = np.ones((10, 2)).astype('float')
+        #q = np.ones((1, 2)).astype('float')
+        #self.check_output('ij,ij->j', p, q)
+
+        # TODO(@xiongkun): explict-label-broadcast in EinsumOp is not supported, it's not recommend to use einsum like this.
+        #x = np.array([2., 3.]).astype('float')
+        #y = np.array([4.]).astype('float')
+        #self.check_output("i, i", x, y)
+
+        # TODO(@xiongkun): explict-label-broadcast in EinsumOp is not supported, it's not recommend to use einsum like this.
+        #p = np.ones((1, 5)) / 2
+        #q = np.ones((5, 5)) / 2
+        #self.check_output("...ij,...jk->...ik", p, p)
+        #self.check_output("...ij,...jk->...ik", p, q)
+
+        x = np.eye(2).astype('float')
+        y = np.ones(2).astype('float')
+        self.check_output("ji,i->", x, y)
+        self.check_output("i,ij->", y, x)
+        self.check_output("ij,i->", x, y)
+
+    def test_large_nops(self):
+        pass
+        # TODO(@xiongkun): explict broadcast in EinsumOp is not supported, it's not recommend to use einsum like this.
+        #a = np.arange(4 * 3 * 1 * 4).reshape(4, 3, 1, 4).astype('float')
+        #self.check_output('a...b,b...c,c...d', a, a, a)
+        #self.check_output('a...b,b...c,c...a', a, a, a)
+        #self.check_output('a...b,b...c,c...a', a, a, a)
+        #self.check_output('...ab,...ba,...ab,...ab', a, a, a, a)
+
+    def test_static_graph(self):
+        paddle.enable_static()
+        fluid = paddle.fluid
+        if fluid.core.is_compiled_with_cuda():
+            self.place = fluid.CUDAPlace(0)
+        else:
+            self.place = fluid.CPUPlace()
+        main = fluid.Program()
+        startup = fluid.Program()
+        with fluid.program_guard(main, startup):
+            a = paddle.static.data(
+                name='a', shape=[3, None, None, None], dtype='float')
+            b = paddle.static.data(
+                name='b', shape=[2, None, None, None], dtype='float')
+            c = paddle.static.data(
+                name='c', shape=[None, None, 2, None], dtype='float')
+            d = paddle.static.data(
+                name='d', shape=[None, None, 5], dtype='float')
+            e = paddle.static.data(
+                name='e', shape=[None, 2, None], dtype='float')
+
+            outs = []
+            outs.append(paddle.einsum("ibnd,jbnd->bnij", a, b))
+            outs.append(paddle.einsum('...ik, ...j', c, d))
+            outs.append(paddle.einsum('...kj, ...ik', d, e))
+            outs.append(paddle.einsum('ijk..., ikj', c, e))
+            outs.append(paddle.einsum('ijk..., ikj->...ij', c, e))
+        exe = fluid.Executor(self.place)
+        exe.run(startup)
+        a = np.arange(72).reshape(3, 2, 3, 4).astype('float')
+        b = np.arange(48).reshape(2, 2, 3, 4).astype('float')
+        c = np.arange(48).reshape(2, 3, 2, 4).astype('float')
+        d = np.arange(30).reshape(2, 3, 5).astype('float')
+        e = np.arange(12).reshape(2, 2, 3).astype('float')
+        feeds = {'a': a, 'b': b, 'c': c, 'd': d, 'e': e}
+        actual = exe.run(main, feed=feeds, fetch_list=[outs])
+        expect = []
+        expect.append(np.einsum("ibnd,jbnd->bnij", a, b))
+        expect.append(np.einsum('...ik, ...j', c, d))
+        expect.append(np.einsum('...kj, ...ik', d, e))
+        expect.append(np.einsum('ijk..., ikj', c, e))
+        expect.append(np.einsum('ijk..., ikj->...ij', c, e))
+        for a, e in zip(actual, expect):
+            self.check_output_equal(a, e)
+
+
+if __name__ == "__main__":
+    u

python/paddle/tensor/einsum.py

@@ -24,6 +24,10 @@ from ..fluid.framework import _in_legacy_dygraph
 from paddle import _C_ops
 from ..fluid.data_feeder import check_variable_and_dtype, check_type, check_dtype
 from ..fluid.layer_helper import LayerHelper
+from ..fluid.framework import _non_static_mode, in_dygraph_mode, _in_legacy_dygraph
+import collections
+import string
+import opt_einsum
 
 from paddle.common_ops_import import dygraph_only
 
@@ -664,7 +668,138 @@ def plan_einsum(operands, g_view, g_shape, g_supports, g_count, n_bcast):
     return plan
 
 
+def preprocess(equation, *operands):
+    """
+    check equation / raise error, default right labels generation
+    """
+    equation = equation.replace(" ", "")
+    nop = len(operands)
+    assert nop > 0, "Required at least one operand in Einsum API, but received %s " % nop
+
+    # Part the equation to left hand side and right hand side
+    lhs, *rhs = equation.lower().split('->')
+    assert len(rhs) < 2, "Invalid equation: multiple `->` were found."
+
+    labels = parse_labels(lhs, operands)
+    # Note, we distinguish between 'ij->' and 'ij' by setting rhs to '' and None
+    rhs = rhs[0] if rhs else None
+    if rhs is None:
+        rhs = rhs_inference(lhs)
+
+    assert len(lhs.split(',')) == len(operands), (
+        f"Invalid equation: the number of operands is {len(operands)}, "
+        f"but found {len(lhs.split(','))} segments in the label equation.")
+
+    assert not ('...' in lhs and '...' not in rhs
+                ), f'Invalid equation: missing ellipsis in output labels.'
+
+    assert not (len(list(filter(has_duplicated_labels, lhs.split(',')))) > 0
+                ), f'Duplicate labels are not supported.'
+
+    assert not has_duplicated_labels(
+        rhs), f'Invalid equation: duplicate output labels are found.'
+
+    return lhs, rhs, labels
+
+
+def parse_fake_shape(equation, operands, labels):
+    """ 
+    this shape is just used for operands planning. may differ with the original shape.
+    for example: 
+    ... is replaced by 1
+    -1  is replaced by 1
+    Results
+    -------
+    list of shape
+    """
+    shaped = collections.namedtuple('shaped', ['shape'])
+
+    def fake_shape(label, op):
+        assert len(op.shape) == len(
+            label
+        ), "length of shape and length of label must be the same, but received %d != %d" % (
+            len(op.shape), len(label))
+        fakes = [s for i, (l, s) in enumerate(zip(label, op.shape)) if l != '.']
+        fakes = list(map(abs, fakes))  # make -1 -> 1
+        if '.' in label:
+            fakes.insert(label.index('.'), 1)
+        return shaped(fakes)
+
+    out = list(map(fake_shape, labels, operands))
+    return out
+
+
+def rhs_inference(lhs):
+    def is_free(key):
+        return cnt.get(key) == 1 and key not in ['.', ',']
+
+    cnt = collections.Counter(lhs)
+    rhs = "..." if '...' in lhs else ""
+    rhs = rhs + "".join(filter(is_free, sorted(cnt.elements())))
+    return rhs
+
+
+def gen_equation_for_opteinsum(lhs, rhs):
+    """ 
+    1. gen rhs if rhs is None
+    2. '...' -> 'A'
+    """
+
+    def get_used_label(counter):
+        used = set(counter.elements())
+        for c in string.ascii_lowercase:
+            if c not in used: return c
+        raise ValueError(
+            "You have used all `a` - `z`, there can't find a unused for einsum optimization"
+        )
+
+    cnt = collections.Counter(lhs)
+    broadcast_label = get_used_label(cnt)
+    if rhs is None:
+        rhs = rhs_inference(lhs)
+    lhs = lhs.replace("...", broadcast_label)
+    rhs = rhs.replace("...", broadcast_label)
+    return lhs + "->" + rhs, broadcast_label
+
+
 def einsum_v2(equation, *operands):
+    """ 
+    einsum v2 implementation.
+    1. Implement C++ EinsumOp.
+    2. V2 create the EinsumOp to calculate, so just a little verifty work in python.
+    3. V2 use opt_einsum.contract_path to optimize the multivariable einsum.
+    """
+    n_op = len(operands)
+    lhs, rhs, labels = preprocess(equation, *operands)
+
+    if n_op <= 2:
+        return gen_einsum_op(lhs + '->' + rhs, *operands)
+
+    shapes = parse_fake_shape(lhs, operands, labels)
+    opt_equation, broadcast_label = gen_equation_for_opteinsum(lhs, rhs)
+    _, cons = opt_einsum.contract_path(opt_equation, *shapes, einsum_call=True)
+    var_list = list(operands)
+    for path in cons:
+        (a, b), _, eq, *__ = path
+        assert a > b, "Assume the first var_idx is smaller than the second_idx. opt_einsum can guarantee it."
+        var_s = [var_list.pop(a), var_list.pop(b)]
+        eq = eq.replace(broadcast_label, "...")
+        var_list.append(gen_einsum_op(eq, *var_s))
+    assert len(
+        var_list
+    ) == 1, "There must be one elements in list, but received %d." % len(
+        var_list)
+    return var_list[0]
+
+
+def gen_einsum_op(equation, *operands):
+    """ 
+    EinsumOp Python Interface: 
+    """
+    assert len(operands) <= 2, "Only support two operands in EinsumOp."
+    if in_dygraph_mode():
+        return _C_ops.final_state_einsum(operands, equation)
+
     if _in_legacy_dygraph():
         # dygraph
         return _C_ops.einsum(operands, 'equation', equation)

python/paddle/utils/code_gen/api.yaml

@@ -561,6 +561,16 @@
     func : eigh
   backward : eigh_grad
 
+- api : einsum
+  args : (Tensor[] x, str equation)
+  output : Tensor
+  infer_meta :
+    func : EinsumInferMeta
+    param : [x, equation]
+  kernel :
+    func : einsum
+  backward : einsum_grad
+
 - api : elementwise_pow
   args : (Tensor x, Tensor y)
   output : Tensor(out)

python/paddle/utils/code_gen/backward.yaml

@@ -475,6 +475,16 @@
   data_transform:
     skip_transform : out_w, out_w_grad
 
+- backward_api : einsum_grad
+  forward : einsum (Tensor[] x, str equation) -> Tensor(out)
+  args : (Tensor[] x, Tensor out_grad, str equation)
+  output : Tensor[](x_grad){x.size()}
+  infer_meta :
+    func : UnchangedMultiInferMeta
+    param : [x]
+  kernel :
+    func : einsum_grad
+
 - backward_api : elementwise_pow_grad
   forward : elementwise_pow(Tensor x, Tensor y) -> Tensor(out)
   args : (Tensor x, Tensor y, Tensor out_grad, int axis=-1)

python/requirements.txt

@@ -6,3 +6,4 @@ six
 decorator
 astor
 paddle_bfloat==0.1.2
+opt_einsum==3.3.0