diff --git a/paddle/fluid/operators/matmul_op.cc b/paddle/fluid/operators/matmul_op.cc
index 73c2577caa81c72528442386b0e4b7cc2da8135c..e1a36fa41894d799e99967cadf1f185e777ca322 100644
--- a/paddle/fluid/operators/matmul_op.cc
+++ b/paddle/fluid/operators/matmul_op.cc
@@ -666,10 +666,6 @@ class MatMulOp : public framework::OperatorWithKernel {
       dim_out.resize(dim_out.size() - 1);
     }
 
-    if (dim_out.empty()) {
-      dim_out = {1};
-    }
-
     phi::DDim ddim_out = phi::make_ddim(dim_out);
 
     context->SetOutputDim("Out", ddim_out);
diff --git a/paddle/fluid/operators/matmul_v2_op.cc b/paddle/fluid/operators/matmul_v2_op.cc
index 4d46a87ccef220953e89a96e390550a917f79d01..7e61d1c9c814a6ce67ab6c5acc3e9dbc15a4dbc8 100644
--- a/paddle/fluid/operators/matmul_v2_op.cc
+++ b/paddle/fluid/operators/matmul_v2_op.cc
@@ -91,9 +91,6 @@ void MatMulV2Op::InferShape(framework::InferShapeContext* ctx) const {
   if (!y_broadcasted) {
     new_dims.push_back(N);
   }
-  if (x_broadcasted && y_broadcasted) {
-    new_dims.push_back(1);
-  }
 
   ctx->SetOutputDim("Out", phi::make_ddim(new_dims));
   ctx->ShareLoD("X", "Out");
diff --git a/paddle/fluid/operators/mkldnn/matmul_mkldnn_op.cc b/paddle/fluid/operators/mkldnn/matmul_mkldnn_op.cc
index ffd72b968123348dc8c79c534928a8515fa43289..9d35e40ec201e969e37b5c11d45656cf0bd6bb8e 100644
--- a/paddle/fluid/operators/mkldnn/matmul_mkldnn_op.cc
+++ b/paddle/fluid/operators/mkldnn/matmul_mkldnn_op.cc
@@ -334,8 +334,9 @@ void ExecuteMatMulV1(const ExecutionContext &ctx,
   matmul_p->execute(astream, matmul_args);
   astream.wait();
 
-  out->set_mem_desc(
-      dst_memory_p->get_desc().reshape(vectorize<int64_t>(out->dims())));
+  auto reshape_dims = out->dims().size() != 0 ? vectorize(out->dims())
+                                              : std::vector<int64_t>{1};
+  out->set_mem_desc(dst_memory_p->get_desc().reshape(reshape_dims));
 }
 
 template <typename T>
diff --git a/paddle/phi/backends/onednn/matmul_utils.h b/paddle/phi/backends/onednn/matmul_utils.h
index 70ed7e29c9637ce29829ae589d72168ef036c8ad..7248e64fe60b16b3a33ef0f8d01f5269ce48843a 100644
--- a/paddle/phi/backends/onednn/matmul_utils.h
+++ b/paddle/phi/backends/onednn/matmul_utils.h
@@ -146,8 +146,9 @@ inline void ExecuteMul(const OneDNNContext& dev_ctx,
   // This kernel is flattening dims so then we need to unflattened version
   // that should be set in out reshape require plain layout, but
   // MatmulV2MKLDNNHanlder enforces one so it should work
-  out->set_mem_desc(
-      dst_memory_p->get_desc().reshape(vectorize<int64_t>(out->dims())));
+  auto reshape_dims = out->dims().size() != 0 ? vectorize(out->dims())
+                                              : std::vector<int64_t>{1};
+  out->set_mem_desc(dst_memory_p->get_desc().reshape(reshape_dims));
 }
 
 template <typename T, typename T_out>
@@ -177,8 +178,9 @@ inline void ExecuteMatmul(const OneDNNContext& dev_ctx,
   matmul_p->execute(astream, matmul_args);
   astream.wait();
 
-  out->set_mem_desc(
-      dst_memory_p->get_desc().reshape(vectorize<int64_t>(out->dims())));
+  auto reshape_dims = out->dims().size() != 0 ? vectorize(out->dims())
+                                              : std::vector<int64_t>{1};
+  out->set_mem_desc(dst_memory_p->get_desc().reshape(reshape_dims));
 }
 
 }  // namespace funcs
diff --git a/paddle/phi/infermeta/backward.cc b/paddle/phi/infermeta/backward.cc
index cb4912401722173ffab766f5d716a853ac70991b..2ea81ad52f7ee2d617779b79f9fde4f138632c49 100644
--- a/paddle/phi/infermeta/backward.cc
+++ b/paddle/phi/infermeta/backward.cc
@@ -822,11 +822,11 @@ void NllLossGradInferMeta(const MetaTensor& x,
   if (check) {
     auto batch_size = x_dims[0];
     if (x_dims.size() == 2) {
-      PADDLE_ENFORCE_EQ(dout_dims.size(),
-                        1,
-                        phi::errors::InvalidArgument(
-                            "The dimensions of Input(Out@Grad) must be 1"));
       if (reduction == "none") {
+        PADDLE_ENFORCE_EQ(dout_dims.size(),
+                          1,
+                          phi::errors::InvalidArgument(
+                              "The dimensions of Input(Out@Grad) must be 1"));
         PADDLE_ENFORCE_EQ(
             dout_dims[0],
             batch_size,
@@ -834,10 +834,10 @@ void NllLossGradInferMeta(const MetaTensor& x,
                 "The unreduced size ofInput(Out@Grad) must be the "
                 "same as batch_size."));
       } else {
-        PADDLE_ENFORCE_EQ(dout_dims[0],
-                          1,
+        PADDLE_ENFORCE_EQ(dout_dims.size(),
+                          0,
                           phi::errors::InvalidArgument(
-                              "The reduced size of Input(Out@Grad) must be 1"));
+                              "The dimensions of Input(Out@Grad) must be 0"));
       }
     } else if (x_dims.size() == 4) {
       if (reduction == "none") {
@@ -855,10 +855,10 @@ void NllLossGradInferMeta(const MetaTensor& x,
                               "The dimensions of Input(Out@Grad) must be match "
                               "to Input(Label) dimensions."));
       } else {
-        PADDLE_ENFORCE_EQ(dout_dims[0],
-                          1,
+        PADDLE_ENFORCE_EQ(dout_dims.size(),
+                          0,
                           phi::errors::InvalidArgument(
-                              "The reduced size of Input(Out@Grad) must be 1"));
+                              "The dimensions of Input(Out@Grad) must be 0"));
       }
     }
   }
diff --git a/paddle/phi/infermeta/binary.cc b/paddle/phi/infermeta/binary.cc
index dde953b5d9db140c08860ae80bafeb9aeaba24b5..87e10cb62524e1c8cdc9d09790d6f50e92185704 100644
--- a/paddle/phi/infermeta/binary.cc
+++ b/paddle/phi/infermeta/binary.cc
@@ -2057,9 +2057,6 @@ void MatmulInferMeta(const MetaTensor& x,
   if (!y_broadcasted) {
     new_dims.push_back(N);
   }
-  if (x_broadcasted && y_broadcasted) {
-    new_dims.push_back(1);
-  }
 
   auto ddim_out = phi::make_ddim(new_dims);
 
diff --git a/paddle/phi/infermeta/ternary.cc b/paddle/phi/infermeta/ternary.cc
index 95a9c9546746cae83758167336ddaf26dcb2b4ae..c4a28877651798ba7fd774b1d3e1845038a49f27 100644
--- a/paddle/phi/infermeta/ternary.cc
+++ b/paddle/phi/infermeta/ternary.cc
@@ -831,7 +831,7 @@ void NllLossRawInferMeta(const MetaTensor& input,
     if (reduction == "none") {
       out->set_dims({x_dims[0]});
     } else {
-      out->set_dims({1});
+      out->set_dims(phi::make_ddim({}));
     }
   } else if (x_dims.size() == 4) {
     PADDLE_ENFORCE_EQ(label_dims.size(),
@@ -854,10 +854,10 @@ void NllLossRawInferMeta(const MetaTensor& input,
     if (reduction == "none") {
       out->set_dims({x_dims[0], x_dims[2], x_dims[3]});
     } else {
-      out->set_dims({1});
+      out->set_dims(phi::make_ddim({}));
     }
   }
-  total_weight->set_dims({1});
+  total_weight->set_dims(phi::make_ddim({}));
   out->set_dtype(input.dtype());
   total_weight->set_dtype(input.dtype());
 }
diff --git a/paddle/phi/kernels/impl/matmul_kernel_impl.h b/paddle/phi/kernels/impl/matmul_kernel_impl.h
index 786d97e38b96ec472adc970a6b7bd99ab217ddbd..cac393d6360517f53dfe0549d1ac9a0de9ef383a 100644
--- a/paddle/phi/kernels/impl/matmul_kernel_impl.h
+++ b/paddle/phi/kernels/impl/matmul_kernel_impl.h
@@ -126,7 +126,7 @@ void MatMulFunctionImplWithBlas(
             M,
             N));
     VLOG(3) << "MatMul's case 1";
-    Out->Resize({1});
+    Out->Resize(phi::make_ddim({}));
     dev_ctx.template Alloc<T>(Out);
     blas.GEMM(CblasNoTrans,
               CblasTrans,
@@ -516,7 +516,7 @@ void MatMulFunctionImplWithCublasLt(
             N));
 
     // MatMul's case 0  =>  vector * vector
-    Out->Resize({1});
+    Out->Resize(phi::make_ddim({}));
     dev_ctx.template Alloc<T>(Out);
     VLOG(3) << "MatMul with blaslt case 1";
     blaslt::Run(dev_ctx,
diff --git a/paddle/phi/kernels/nll_loss_kernel.cc b/paddle/phi/kernels/nll_loss_kernel.cc
index c1a16f175c14b0b42e053df03af00573e7650187..b9278d152269ce0874e5d59866644439dd0cfb91 100644
--- a/paddle/phi/kernels/nll_loss_kernel.cc
+++ b/paddle/phi/kernels/nll_loss_kernel.cc
@@ -24,8 +24,7 @@ void NllLossKernel(const Context& dev_ctx,
                    const std::string& reduction,
                    DenseTensor* out) {
   DenseTensor total_weight;
-  total_weight.set_meta(
-      DenseTensorMeta(phi::CppTypeToDataType<T>::Type(), {1}));
+  total_weight.set_meta(DenseTensorMeta(phi::CppTypeToDataType<T>::Type(), {}));
   dev_ctx.template Alloc<T>(total_weight);
   NllLossRawKernel(dev_ctx,
                    input,
diff --git a/python/paddle/distribution/transform.py b/python/paddle/distribution/transform.py
index 53316911559e8707f5334245fa988c01925c25db..ec2bdb0ed19112799b2aec36c9ff7f9f3165aec2 100644
--- a/python/paddle/distribution/transform.py
+++ b/python/paddle/distribution/transform.py
@@ -856,8 +856,8 @@ class ReshapeTransform(Transform):
             #        [[[1., 1., 1.],
             #          [1., 1., 1.]]])
             print(reshape_transform.forward_log_det_jacobian(x))
-            # Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True,
-            #        [0.])
+            # Tensor(shape=[], dtype=float32, place=Place(gpu:0), stop_gradient=True,
+            #        0.)
     """
     _type = Type.BIJECTION
 
@@ -945,8 +945,7 @@ class ReshapeTransform(Transform):
         )
 
     def _forward_log_det_jacobian(self, x):
-        # TODO(zhouwei): should not set shape to [1], which is []
-        shape = x.shape[: x.dim() - len(self._in_event_shape)] or [1]
+        shape = x.shape[: x.dim() - len(self._in_event_shape)]
         return paddle.zeros(shape, dtype=x.dtype)
 
 
diff --git a/python/paddle/fluid/tests/unittests/test_matmul_op.py b/python/paddle/fluid/tests/unittests/test_matmul_op.py
index c7c870b3c46eb67f6c5635ec83a4acc01852754b..b5ac23f3e38add0f241e1d7b5d8eb82a1b6b03f7 100644
--- a/python/paddle/fluid/tests/unittests/test_matmul_op.py
+++ b/python/paddle/fluid/tests/unittests/test_matmul_op.py
@@ -77,12 +77,6 @@ def reference_matmul(X, Y, transpose_X=False, transpose_Y=False):
             Y = np.transpose(Y, tuple(dim))
 
     Out = np.matmul(X, Y)
-    if not Out.shape:
-        # We do not support 0-dimensional Tensors (scalars). So where
-        # np.matmul outputs a scalar, we must convert to a Tensor of
-        # shape (1, ) instead.
-        # Everywhere else, we are compatible with np.matmul.
-        Out = np.array([Out], dtype="float32")
     return Out
 
 
@@ -177,9 +171,6 @@ class API_TestMm(unittest.TestCase):
             with fluid.program_guard(fluid.Program()):
                 x = paddle.static.data(name="x", shape=[2], dtype="float64")
                 y = paddle.static.data(name='y', shape=[2], dtype='float64')
-                res = paddle.static.data(
-                    name="output", shape=[1], dtype="float64"
-                )
                 result = paddle.mm(x, y)
                 exe = fluid.Executor(fluid.CPUPlace())
                 data1 = np.random.rand(2)
@@ -187,9 +178,7 @@ class API_TestMm(unittest.TestCase):
                 np_res = exe.run(
                     feed={'x': data1, 'y': data2}, fetch_list=[result]
                 )
-                expected_result = np.matmul(
-                    data1.reshape(1, 2), data2.reshape(2, 1)
-                )
+                expected_result = np.matmul(data1, data2)
 
             np.testing.assert_allclose(
                 np_res,
diff --git a/python/paddle/fluid/tests/unittests/test_matmul_op_with_head.py b/python/paddle/fluid/tests/unittests/test_matmul_op_with_head.py
index 37ac37b6a99d9e5c78b35d221acc402eaa90e48b..475ede6fd05d7189848ca9bcfab11505e1e22d21 100644
--- a/python/paddle/fluid/tests/unittests/test_matmul_op_with_head.py
+++ b/python/paddle/fluid/tests/unittests/test_matmul_op_with_head.py
@@ -102,12 +102,6 @@ def reference_matmul_mul_head(
         Y = transpose_mat(Y)
 
     Out = matmul_head(X, Y, head_number)
-    if not Out.shape:
-        # We do not support 0-dimensional Tensors (scalars). So where
-        # np.matmul outputs a scalar, we must convert to a Tensor of
-        # shape (1, ) instead.
-        # Everywhere else, we are compatible with np.matmul.
-        Out = np.array([Out], dtype="float32")
     return Out
 
 
@@ -196,12 +190,6 @@ def reference_matmul_mul_head2(
         Y = transpose_mat(Y)
 
     Out = matmul_head2(X, Y, head_number)
-    if not Out.shape:
-        # We do not support 0-dimensional Tensors (scalars). So where
-        # np.matmul outputs a scalar, we must convert to a Tensor of
-        # shape (1, ) instead.
-        # Everywhere else, we are compatible with np.matmul.
-        Out = np.array([Out], dtype="float32")
     return Out
 
 
diff --git a/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py b/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py
index e0dcc3bfdd35ef896b4b0ea55402468abe7f1931..957b03549ef3e0093439c1107507ce3cfd3cb423 100644
--- a/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py
+++ b/python/paddle/fluid/tests/unittests/test_matmul_v2_op.py
@@ -45,12 +45,6 @@ def reference_matmul(X, Y, transpose_X=False, transpose_Y=False):
             Y = np.transpose(Y, tuple(dim))
 
     Out = np.matmul(X, Y)
-    if not Out.shape:
-        # We do not support 0-dimensional Tensors (scalars). So where
-        # np.matmul outputs a scalar, we must convert to a Tensor of
-        # shape (1, ) instead.
-        # Everywhere else, we are compatible with np.matmul.
-        Out = np.array([Out], dtype="float64")
     return Out
 
 
diff --git a/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py b/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py
index 76f0ce1791a7b9565e0d6708da9e4e3df877bb78..db8550831878331719b6cd4361b94095c8e80282 100644
--- a/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py
+++ b/python/paddle/fluid/tests/unittests/test_zero_dim_tensor.py
@@ -2571,6 +2571,33 @@ class TestSundryAPI(unittest.TestCase):
         self.assertEqual(out2.shape, [])
         self.assertEqual(out2, 2.5)
 
+    def test_matmul(self):
+        # 1) no transpose
+        x = paddle.randn([10])
+        x.stop_gradient = False
+        y = paddle.randn([10])
+        y.stop_gradient = False
+        out1 = paddle.matmul(x, y)
+        out1.retain_grads()
+        out1.backward()
+
+        self.assertEqual(out1.shape, [])
+        self.assertEqual(x.grad.shape, [10])
+        self.assertEqual(y.grad.shape, [10])
+
+        # 2) transpose x and y
+        x = paddle.randn([10])
+        x.stop_gradient = False
+        y = paddle.randn([10])
+        y.stop_gradient = False
+        out2 = paddle.matmul(x, y, True, True)
+        out2.retain_grads()
+        out2.backward()
+
+        self.assertEqual(out2.shape, [])
+        self.assertEqual(x.grad.shape, [10])
+        self.assertEqual(y.grad.shape, [10])
+
     def test_linalg_slogdet(self):
         # 2-D input
         x = paddle.randn([3, 3])
@@ -4872,6 +4899,40 @@ class TestSundryAPIStatic(unittest.TestCase):
         self.assertEqual(res[1].shape, ())
         self.assertEqual(res[1], 2.5)
 
+    @prog_scope()
+    def test_matmul(self):
+        # 1) no transpose
+        x = paddle.randn([10])
+        x.stop_gradient = False
+        y = paddle.randn([10])
+        y.stop_gradient = False
+        out = paddle.matmul(x, y)
+        paddle.static.append_backward(out)
+
+        self.assertEqual(out.shape, ())
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out, x.grad_name, y.grad_name])
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, (10,))
+        self.assertEqual(res[2].shape, (10,))
+
+        # 2) transpose x and y
+        x = paddle.randn([10])
+        x.stop_gradient = False
+        y = paddle.randn([10])
+        y.stop_gradient = False
+        out = paddle.matmul(x, y, True, True)
+        paddle.static.append_backward(out)
+
+        self.assertEqual(out.shape, ())
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[out, x.grad_name, y.grad_name])
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, (10,))
+        self.assertEqual(res[2].shape, (10,))
+
     @prog_scope()
     def test_linalg_slogdet(self):
         # 2-D input
@@ -5994,6 +6055,31 @@ class TestLossAPI(unittest.TestCase):
         self.assertEqual(loss.shape, [])
         self.assertEqual(input.grad.shape, [3, 5])
 
+    def test_nll_loss(self):
+        input = paddle.rand([5, 3])
+        input.stop_gradient = False
+        log_softmax = paddle.nn.LogSoftmax(axis=1)
+        log_out = log_softmax(input)
+        label = paddle.randint(0, 3, [5], "int64")
+
+        loss = paddle.nn.functional.nll_loss(log_out, label)
+        loss.backward()
+
+        self.assertEqual(loss.shape, [])
+        self.assertEqual(input.grad.shape, [5, 3])
+
+        input = paddle.rand([5, 3, 2, 4])
+        input.stop_gradient = False
+        log_softmax = paddle.nn.LogSoftmax(axis=1)
+        log_out = log_softmax(input)
+        label = paddle.randint(0, 3, [5, 2, 4], "int64")
+
+        loss = paddle.nn.functional.nll_loss(log_out, label)
+        loss.backward()
+
+        self.assertEqual(loss.shape, [])
+        self.assertEqual(input.grad.shape, [5, 3, 2, 4])
+
 
 class TestLossAPIStatic(unittest.TestCase):
     def setUp(self):
@@ -6060,6 +6146,40 @@ class TestLossAPIStatic(unittest.TestCase):
         self.assertEqual(res[0].shape, ())
         self.assertEqual(res[1].shape, (3, 5))
 
+    @prog_scope()
+    def test_nll_loss(self):
+        input = paddle.rand([5, 3])
+        input.stop_gradient = False
+        log_softmax = paddle.nn.LogSoftmax(axis=1)
+        log_out = log_softmax(input)
+
+        label = paddle.randint(0, 3, shape=[5])
+        label.stop_gradient = False
+
+        loss = paddle.nn.functional.nll_loss(log_out, label)
+        paddle.static.append_backward(loss)
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[loss, input.grad_name])
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, (5, 3))
+
+        input = paddle.rand([5, 3, 2, 4])
+        input.stop_gradient = False
+        log_softmax = paddle.nn.LogSoftmax(axis=1)
+        log_out = log_softmax(input)
+
+        label = paddle.randint(0, 3, shape=[5, 2, 4])
+        label.stop_gradient = False
+
+        loss = paddle.nn.functional.nll_loss(log_out, label)
+        paddle.static.append_backward(loss)
+
+        prog = paddle.static.default_main_program()
+        res = self.exe.run(prog, fetch_list=[loss, input.grad_name])
+        self.assertEqual(res[0].shape, ())
+        self.assertEqual(res[1].shape, (5, 3, 2, 4))
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/python/paddle/tensor/linalg.py b/python/paddle/tensor/linalg.py
index db0805669a17c9d0e3857b503341a5f9a0668174..da77bee601824aab3d074d20ed20dea980e8ae73 100644
--- a/python/paddle/tensor/linalg.py
+++ b/python/paddle/tensor/linalg.py
@@ -27,6 +27,7 @@ from ..fluid.data_feeder import (
 from ..framework import LayerHelper, in_dynamic_mode
 from .creation import full
 from .manipulation import cast
+from .math import _get_reduce_axis
 
 __all__ = []
 
@@ -198,7 +199,7 @@ def matmul(x, y, transpose_x=False, transpose_y=False, name=None):
             y = paddle.rand([10])
             z = paddle.matmul(x, y)
             print(z.shape)
-            # (1,)
+            # ()
 
             # matrix * vector
             x = paddle.rand([10, 5])
@@ -459,12 +460,7 @@ def norm(x, p='fro', axis=None, keepdim=False, name=None):
             reduce_out = helper.create_variable_for_type_inference(
                 dtype=helper.input_dtype()
             )
-
-            reduce_all = (
-                True if axis is None or axis == [] or asvector else False
-            )
-            axis = axis if axis is not None and axis != [] else [0]
-
+            reduce_all, axis = _get_reduce_axis(axis, x)
             reduce_type = (
                 'reduce_max' if porder == np.float64('inf') else 'reduce_min'
             )
@@ -516,6 +512,7 @@ def norm(x, p='fro', axis=None, keepdim=False, name=None):
         sum_out = block.create_variable_for_type_inference(
             dtype=block.input_dtype()
         )
+        reduce_all, axis = _get_reduce_axis(axis, x)
         block.append_op(
             type='reduce_sum',
             inputs={'X': pow_out},
@@ -523,7 +520,7 @@ def norm(x, p='fro', axis=None, keepdim=False, name=None):
             attrs={
                 'dim': axis,
                 'keep_dim': keepdim,
-                'reduce_all': True if axis is None else False,
+                'reduce_all': reduce_all,
             },
         )
         block.append_op(
@@ -834,8 +831,6 @@ def cond(x, p=None, name=None):
             if porder == -1 or porder == -np.inf:
                 return _C_ops.min(sum_out, [-1], False)
         else:
-            reduce_all = True if axis is None or axis == [] else False
-            axis = axis if axis is not None and axis != [] else [0]
             block = LayerHelper('norm', **locals())
             abs_out = block.create_variable_for_type_inference(
                 dtype=block.input_dtype()
@@ -849,6 +844,8 @@ def cond(x, p=None, name=None):
             block.append_op(
                 type='abs', inputs={'X': input}, outputs={'Out': abs_out}
             )
+
+            reduce_all, axis = _get_reduce_axis(axis, x)
             block.append_op(
                 type='reduce_sum',
                 inputs={'X': abs_out},
@@ -894,7 +891,6 @@ def cond(x, p=None, name=None):
             sum_out_2 = _C_ops.sum(sum_out_1, axis, None, False)
             return _C_ops.pow(sum_out_2, float(1.0 / porder))
         else:
-            reduce_all = True if axis is None or axis == [] else False
             block = LayerHelper('norm', **locals())
             pow_out = block.create_variable_for_type_inference(
                 dtype=block.input_dtype()
@@ -914,6 +910,8 @@ def cond(x, p=None, name=None):
                 outputs={'Out': pow_out},
                 attrs={'factor': porder},
             )
+
+            reduce_all, axis = _get_reduce_axis(axis, x)
             block.append_op(
                 type='reduce_sum',
                 inputs={'X': pow_out},
@@ -960,7 +958,7 @@ def cond(x, p=None, name=None):
             if porder == -2:
                 return _C_ops.divide(min_out, max_out)
         else:
-            reduce_all = True if axis is None or axis == [] else False
+            reduce_all, axis = _get_reduce_axis(axis, x)
             block = LayerHelper('norm', **locals())
             out = block.create_variable_for_type_inference(
                 dtype=block.input_dtype()
diff --git a/test/autograd/test_autograd_dynamic.py b/test/autograd/test_autograd_dynamic.py
index 2e6033a6ee937c792cf14ba1f9c4b8a64eb1ce60..cd3e54a814d5cb2c7cae09c41f541c94ffd065cf 100644
--- a/test/autograd/test_autograd_dynamic.py
+++ b/test/autograd/test_autograd_dynamic.py
@@ -90,25 +90,16 @@ class TestJacobianNoBatch(unittest.TestCase):
         )
         self._actual = paddle.autograd.jacobian(ys, xs, batch_axis=None)
         if isinstance(self._actual, (tuple, list)):
-            self._actual = paddle.concat([x[:] for x in self._actual], axis=1)
+            self._actual = paddle.concat([x[:] for x in self._actual], axis=0)
         self._expected = self._get_expected()
 
-        Index = collections.namedtuple('Index', ('type', 'value'))
-        indexes = (
-            Index('all', (slice(0, None, None), slice(0, None, None))),
-            Index('row', (0, slice(0, None, None))),
-            Index('col', (slice(0, None, None), 0)),
-            Index('multi-row', (slice(0, 2, 1), slice(0, None, None))),
+        self.assertEqual(self._actual.numpy().dtype, self._expected.dtype)
+        np.testing.assert_allclose(
+            self._actual.flatten(),
+            self._expected.flatten(),
+            rtol=self._rtol,
+            atol=self._atol,
         )
-        self.assertEqual(self._actual[:].numpy().dtype, self._expected.dtype)
-        for index in indexes:
-            np.testing.assert_allclose(
-                self._actual.__getitem__(index.value),
-                self._expected.__getitem__(index.value),
-                rtol=self._rtol,
-                atol=self._atol,
-                err_msg=f'Testcase {index.type} index not passed, value is {index.value}',
-            )
 
     def test_jacobian_attribute_operator(self):
         xs = (
@@ -121,25 +112,16 @@ class TestJacobianNoBatch(unittest.TestCase):
         )
         self._actual = paddle.autograd.jacobian(ys, xs, batch_axis=None)
         if isinstance(self._actual, (tuple, list)):
-            self._actual = paddle.concat([x[:] for x in self._actual], axis=1)
+            self._actual = paddle.concat([x[:] for x in self._actual], axis=0)
         self._expected = self._get_expected()
 
-        Index = collections.namedtuple('Index', ('type', 'value'))
-        indexes = (
-            Index('all', (slice(0, None, None), slice(0, None, None))),
-            Index('row', (0, slice(0, None, None))),
-            Index('col', (slice(0, None, None), 0)),
-            Index('multi-row', (slice(0, 2, 1), slice(0, None, None))),
-        )
         self.assertEqual(self._actual.numpy().dtype, self._expected.dtype)
-        for index in indexes:
-            np.testing.assert_allclose(
-                self._actual.__getitem__(index.value),
-                self._expected.__getitem__(index.value),
-                rtol=self._rtol,
-                atol=self._atol,
-                err_msg=f'Testcase {index.type} index not passed, value is {index.value}',
-            )
+        np.testing.assert_allclose(
+            self._actual.flatten(),
+            self._expected.flatten(),
+            rtol=self._rtol,
+            atol=self._atol,
+        )
 
     def _get_expected(self):
         xs = (
diff --git a/test/autograd/utils.py b/test/autograd/utils.py
index de1db9f2a19f58c0164edb92f67e00bcc49d582e..74f14c38b2a59e7a33b4c6d4162540047fb92340 100644
--- a/test/autograd/utils.py
+++ b/test/autograd/utils.py
@@ -398,6 +398,7 @@ def _np_concat_matrix_sequence(src, src_format=MatrixFormat.NM):
         return src
     if not isinstance(src[0], typing.Sequence):
         src = [src]
+
     return concat_row(tuple(concat_col(xs) for xs in src))
 
 
diff --git a/test/distribution/test_distribution_transform.py b/test/distribution/test_distribution_transform.py
index 640391b472d7a8480767c9d0af594c42e65f0dac..38ea037a65d9c1f29b5c52b2b0b0156eab41bab5 100644
--- a/test/distribution/test_distribution_transform.py
+++ b/test/distribution/test_distribution_transform.py
@@ -1029,8 +1029,8 @@ class TestReshapeTransform(unittest.TestCase):
 
         self.assertEqual(out.shape, [1, 1])
         self.assertEqual(reshape.inverse(out).shape, [])
-        # self.assertEqual(reshape.forward_log_det_jacobian(x).shape, [])
-        # self.assertEqual(reshape.inverse_log_det_jacobian(out).shape, [])
+        self.assertEqual(reshape.forward_log_det_jacobian(x).shape, [])
+        self.assertEqual(reshape.inverse_log_det_jacobian(out).shape, [])
         self.assertEqual(reshape.forward_shape(x.shape), (1, 1))
         self.assertEqual(reshape.inverse_shape(out.shape), ())
 
diff --git a/test/mkldnn/test_matmul_v2_mkldnn_op.py b/test/mkldnn/test_matmul_v2_mkldnn_op.py
index 958a8cca21e511d8ecdbacdc2958268bd89ee20f..a7c7fcfad46028c69d330d3665fc1f4796e656b5 100644
--- a/test/mkldnn/test_matmul_v2_mkldnn_op.py
+++ b/test/mkldnn/test_matmul_v2_mkldnn_op.py
@@ -46,7 +46,7 @@ def reference_matmul(X, Y, transpose_x=False, transpose_y=False):
             dim[-1], dim[len(Y.shape) - 2] = dim[len(Y.shape) - 2], dim[-1]
             Y = np.transpose(Y, tuple(dim))
 
-    Out = np.atleast_1d(np.matmul(X, Y))
+    Out = np.matmul(X, Y)
     return Out
 
 
diff --git a/test/xpu/test_matmul_op_xpu.py b/test/xpu/test_matmul_op_xpu.py
index 07cea1b943c91c4e7c59d639f572e6df47ba42b4..fb30c2ecbe87931bd15f2305f638d7335201c571 100644
--- a/test/xpu/test_matmul_op_xpu.py
+++ b/test/xpu/test_matmul_op_xpu.py
@@ -56,12 +56,6 @@ def reference_matmul(X, Y, transpose_X=False, transpose_Y=False):
         y_dims = Y.shape
         Y = Y.reshape((y_dims[0] * y_dims[1], y_dims[2]))
     Out = np.matmul(X, Y)
-    if not Out.shape:
-        # We do not support 0-dimensional Tensors (scalars). So where
-        # np.matmul outputs a scalar, we must convert to a Tensor of
-        # shape (1, ) instead.
-        # Everywhere else, we are compatible with np.matmul.
-        Out = np.array([Out], dtype="float32")
     return Out
 
 
@@ -141,9 +135,6 @@ class XPUTestMatmulOpErr(XPUOpTestWrapper):
             with fluid.program_guard(fluid.Program()):
                 x = paddle.static.data(name="x", shape=[2], dtype=self.in_type)
                 y = paddle.static.data(name='y', shape=[2], dtype=self.in_type)
-                res = paddle.static.data(
-                    name="output", shape=[1], dtype=self.in_type
-                )
                 result = paddle.mm(x, y)
                 exe = fluid.Executor(fluid.XPUPlace(0))
                 data1 = np.random.rand(2).astype(self.in_type)
@@ -151,9 +142,7 @@ class XPUTestMatmulOpErr(XPUOpTestWrapper):
                 np_res = exe.run(
                     feed={'x': data1, 'y': data2}, fetch_list=[result]
                 )
-                expected_result = np.matmul(
-                    data1.reshape(1, 2), data2.reshape(2, 1)
-                )
+                expected_result = np.matmul(data1, data2)
 
                 np.testing.assert_allclose(np_res, expected_result, atol=1e-3)
 
diff --git a/test/xpu/test_matmul_v2_op_xpu.py b/test/xpu/test_matmul_v2_op_xpu.py
index eb10d1462e46618e94c74b60533f6cd7629d5f1e..76909c5fd83253c500c9c20bd7c1379b0be71bfc 100644
--- a/test/xpu/test_matmul_v2_op_xpu.py
+++ b/test/xpu/test_matmul_v2_op_xpu.py
@@ -46,12 +46,6 @@ def reference_matmul(X, Y, transpose_X=False, transpose_Y=False):
             dim[-1], dim[len(Y.shape) - 2] = dim[len(Y.shape) - 2], dim[-1]
             Y = np.transpose(Y, tuple(dim))
     Out = np.matmul(X, Y)
-    if not Out.shape:
-        # We do not support 0-dimensional Tensors (scalars). So where
-        # np.matmul outputs a scalar, we must convert to a Tensor of
-        # shape (1, ) instead.
-        # Everywhere else, we are compatible with np.matmul.
-        Out = np.array([Out], dtype="float64")
     return Out
 
 
diff --git a/test/xpu/test_zero_dim_tensor_xpu.py b/test/xpu/test_zero_dim_tensor_xpu.py
index 7591b3a402f5cc6b7b76e28232fde5e188430de8..a836e2e7fb58ed656dab5701bbab694c55732f09 100644
--- a/test/xpu/test_zero_dim_tensor_xpu.py
+++ b/test/xpu/test_zero_dim_tensor_xpu.py
@@ -2256,6 +2256,33 @@ class TestSundryAPI(unittest.TestCase):
         self.assertEqual(out2.shape, [])
         self.assertEqual(out2, 2.5)
 
+    def test_matmul(self):
+        # 1) no transpose
+        x = paddle.randn([10])
+        x.stop_gradient = False
+        y = paddle.randn([10])
+        y.stop_gradient = False
+        out1 = paddle.matmul(x, y)
+        out1.retain_grads()
+        out1.backward()
+
+        self.assertEqual(out1.shape, [])
+        self.assertEqual(x.grad.shape, [10])
+        self.assertEqual(y.grad.shape, [10])
+
+        # 2) transpose x and y
+        x = paddle.randn([10])
+        x.stop_gradient = False
+        y = paddle.randn([10])
+        y.stop_gradient = False
+        out2 = paddle.matmul(x, y, True, True)
+        out2.retain_grads()
+        out2.backward()
+
+        self.assertEqual(out2.shape, [])
+        self.assertEqual(x.grad.shape, [10])
+        self.assertEqual(y.grad.shape, [10])
+
     def test_linalg_slogdet(self):
         # 2-D input
         x = paddle.randn([3, 3])