diff --git a/paddle/fluid/operators/batch_norm_op.cc b/paddle/fluid/operators/batch_norm_op.cc
index cec3368a51867c3497b38a5271e9856861544232..ccf5aa6a62268be87d97661989aec31f822e2218 100644
--- a/paddle/fluid/operators/batch_norm_op.cc
+++ b/paddle/fluid/operators/batch_norm_op.cc
@@ -164,6 +164,9 @@ void BatchNormOp::InferShape(framework::InferShapeContext *ctx) const {
   ctx->SetOutputDim("SavedMean", {C});
   ctx->SetOutputDim("SavedVariance", {C});
   ctx->ShareLoD("X", "Y");
+  if (ctx->HasInput("ReserveSpace")) {
+    ctx->SetOutputDim("ReserveSpace", {-1});
+  }
 }
 
 framework::OpKernelType BatchNormOp::GetExpectedKernelType(
diff --git a/paddle/fluid/operators/common_infer_shape_functions.cc b/paddle/fluid/operators/common_infer_shape_functions.cc
index 9dce94d16b4db917f46931d57c9ccf768a3ffee8..b256d94a5a894f6cf126c7821da356b5341ab839 100644
--- a/paddle/fluid/operators/common_infer_shape_functions.cc
+++ b/paddle/fluid/operators/common_infer_shape_functions.cc
@@ -40,12 +40,13 @@ inline void GetBroadcastDimsArrays(const framework::DDim &x_dims,
       platform::errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    platform::errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      platform::errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
   if (x_dims.size() > y_dims.size()) {
     std::fill(y_dims_array, y_dims_array + axis, 1);
     if (axis + y_dims.size() < max_dim) {
diff --git a/paddle/fluid/operators/elementwise/elementwise_npu.h b/paddle/fluid/operators/elementwise/elementwise_npu.h
index 45e5a548f91ede3c5800d4544b42c6756d7aeb26..b7e85c45f4c7ccba142f91be763d129686d40502 100644
--- a/paddle/fluid/operators/elementwise/elementwise_npu.h
+++ b/paddle/fluid/operators/elementwise/elementwise_npu.h
@@ -123,12 +123,13 @@ void NpuElementWiseOpBroadcast(const platform::NPUDeviceContext& dev_ctx,
       platform::errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    platform::errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      platform::errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
 
   for (int i = 0; i < x_dims.size(); ++i) {
     dst_dims_vec[i + x_axis] =
diff --git a/paddle/phi/infermeta/multiary.cc b/paddle/phi/infermeta/multiary.cc
index c90c3a54de06f67d9bbf7a424fae5ea6db99ce34..b9e84c2df57141108fd619162cf87ad71e89ef59 100644
--- a/paddle/phi/infermeta/multiary.cc
+++ b/paddle/phi/infermeta/multiary.cc
@@ -640,6 +640,9 @@ void BatchNormInferMeta(const MetaTensor& x,
   if (saved_variance) {
     saved_variance->set_dims({C});
   }
+  if (reserve_space) {
+    reserve_space->set_dims({-1});
+  }
   y->share_lod(x);
   y->set_dtype(x.dtype());
 }
diff --git a/paddle/phi/kernels/funcs/common_shape.h b/paddle/phi/kernels/funcs/common_shape.h
index 01b06120965fc910c3856d9241d753c8bb1cd87a..f7524320e8807fec9a6567c020638ce5a64141cd 100644
--- a/paddle/phi/kernels/funcs/common_shape.h
+++ b/paddle/phi/kernels/funcs/common_shape.h
@@ -45,12 +45,13 @@ inline void GetBroadcastDimsArrays(const DDim &x_dims,
       phi::errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    phi::errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      phi::errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
   if (x_dims.size() > y_dims.size()) {
     std::fill(y_dims_array, y_dims_array + axis, 1);
     if (axis + y_dims.size() < max_dim) {
diff --git a/paddle/phi/kernels/funcs/elementwise_base.h b/paddle/phi/kernels/funcs/elementwise_base.h
index 29da61741385302ad943c25c6bf12ec77327c9b7..a1b0a70956931d41c7ce14a33d8c026003e69ed6 100644
--- a/paddle/phi/kernels/funcs/elementwise_base.h
+++ b/paddle/phi/kernels/funcs/elementwise_base.h
@@ -326,12 +326,13 @@ void CommonElementwiseBroadcastForward(const CPUContext &dev_ctx,
       phi::errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    phi::errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      phi::errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
   std::vector<int> x_dims_array(max_dim);
   std::vector<int> y_dims_array(max_dim);
   std::vector<int> out_dims_array(max_dim);
@@ -394,12 +395,13 @@ void ElementwiseCompute(const CPUContext &dev_ctx,
       errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
 
   int pre, n, post, is_run_common_broadcast, axis_trim = 0;
   if (is_xsize_larger) {
diff --git a/paddle/phi/kernels/funcs/elementwise_grad_base.h b/paddle/phi/kernels/funcs/elementwise_grad_base.h
index f8007319d697ce12d6087993e41806760f1a5606..c55ce6a89ae1c46bc36e78d3d8b076baee3d599d 100644
--- a/paddle/phi/kernels/funcs/elementwise_grad_base.h
+++ b/paddle/phi/kernels/funcs/elementwise_grad_base.h
@@ -287,12 +287,13 @@ void ElemwiseGradComputeWithBroadcast(const CPUContext &ctx,
       errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
 
   int pre, n, post, is_run_common_broadcast, axis_trim = 0;
   if (is_xsize_larger) {
@@ -1725,12 +1726,13 @@ void ElemwiseGradComputeWithBroadcast(const GPUContext &ctx,
       errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
 
   int pre, n, post, is_run_common_broadcast, axis_trim = 0;
   if (is_xsize_larger) {
diff --git a/paddle/phi/kernels/xpu/elementwise.h b/paddle/phi/kernels/xpu/elementwise.h
index dfaaae59bb3cef6a853c819179eb872092c2ecfc..46bac6ce299147550e56f1e025feceb2534095fc 100644
--- a/paddle/phi/kernels/xpu/elementwise.h
+++ b/paddle/phi/kernels/xpu/elementwise.h
@@ -51,12 +51,13 @@ void XPUElementwise(const XPUContext& dev_ctx,
       errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
   std::vector<int> x_dims_vec(max_dim, 1);
   std::vector<int> y_dims_vec(max_dim, 1);
   if (x_dims.size() == max_dim) {
@@ -121,12 +122,13 @@ void XPUElementwiseGrad(const XPUContext& dev_ctx,
       errors::InvalidArgument(
           "Axis should be great than or equal to 0, but received axis is %d.",
           axis));
-  PADDLE_ENFORCE_LE(axis,
-                    max_dim,
-                    errors::InvalidArgument(
-                        "Axis should be less than %d, but received axis is %d.",
-                        max_dim,
-                        axis));
+  PADDLE_ENFORCE_LE(
+      axis,
+      max_dim,
+      errors::InvalidArgument(
+          "Axis should be less than or equal to %d, but received axis is %d.",
+          max_dim,
+          axis));
   std::vector<int> x_dims_vec(max_dim, 1);
   std::vector<int> y_dims_vec(max_dim, 1);
   if (x_dims.size() == max_dim) {