diff --git a/paddle/fluid/operators/log_softmax_op.h b/paddle/fluid/operators/log_softmax_op.h
index b983ac54157d9d0679ac237ca94e742b38833864..c732ec5a2da0abcf608018dc0494f657ca2b4e59 100644
--- a/paddle/fluid/operators/log_softmax_op.h
+++ b/paddle/fluid/operators/log_softmax_op.h
@@ -29,16 +29,16 @@ static inline int CanonicalAxis(const int axis, const int rank) {
   return axis;
 }
 
-static inline int SizeToAxis(const int axis, const framework::DDim dims) {
-  int size = 1;
+static inline size_t SizeToAxis(const int axis, const framework::DDim dims) {
+  size_t size = 1;
   for (int i = 0; i < axis; i++) {
     size *= dims[i];
   }
   return size;
 }
 
-static inline int SizeFromAxis(const int axis, const framework::DDim dims) {
-  int size = 1;
+static inline size_t SizeFromAxis(const int axis, const framework::DDim dims) {
+  size_t size = 1;
   for (int i = axis; i < dims.size(); i++) {
     size *= dims[i];
   }
diff --git a/paddle/fluid/operators/softmax_with_cross_entropy_op.cu b/paddle/fluid/operators/softmax_with_cross_entropy_op.cu
index f86f02544dc980e7235aeaf3733d560b581ba6dc..cb4eeab56a6fd62959f2bb42632333bb707f85c7 100644
--- a/paddle/fluid/operators/softmax_with_cross_entropy_op.cu
+++ b/paddle/fluid/operators/softmax_with_cross_entropy_op.cu
@@ -22,27 +22,27 @@ using Tensor = framework::Tensor;
 namespace {
 template <typename T>
 __global__ void CrossEntropyGrad(T* logit_grad, const int64_t* labels,
-                                 const int n, const int d, const int remain,
-                                 const int ignore_index) {
-  CUDA_KERNEL_LOOP(index, n * remain) {
-    int idx_n = index / remain;
-    int idx_remain = index % remain;
-    int tmp = labels[index];
+                                 const int64_t n, const int64_t d,
+                                 const int64_t remain, const int ignore_index) {
+  CUDA_KERNEL_LOOP_TYPE(index, n * remain, int64_t) {
+    int64_t idx_n = index / remain;
+    int64_t idx_remain = index % remain;
+    int64_t tmp = labels[index];
     if (ignore_index != tmp) {
-      int idx = idx_n * d + tmp * remain + idx_remain;
+      int64_t idx = idx_n * d + tmp * remain + idx_remain;
       logit_grad[idx] -= static_cast<T>(1.);
     }
   }
 }
 
 template <typename T>
-__global__ void Scale(T* logit_grad, const T* loss_grad, const int num,
-                      const int d, const int remain, const int64_t* labels,
-                      const int ignore_index) {
-  CUDA_KERNEL_LOOP(index, num) {
-    int idx_n = index / d;
-    int idx_remain = index % remain;
-    int idx_lbl = idx_n * remain + idx_remain;
+__global__ void Scale(T* logit_grad, const T* loss_grad, const int64_t num,
+                      const int64_t d, const int64_t remain,
+                      const int64_t* labels, const int ignore_index) {
+  CUDA_KERNEL_LOOP_TYPE(index, num, int64_t) {
+    int64_t idx_n = index / d;
+    int64_t idx_remain = index % remain;
+    int64_t idx_lbl = idx_n * remain + idx_remain;
     if (labels[idx_lbl] == ignore_index) {
       logit_grad[index] = static_cast<T>(0.);
     } else {
@@ -54,13 +54,14 @@ __global__ void Scale(T* logit_grad, const T* loss_grad, const int num,
 template <typename T>
 __global__ void SoftCrossEntropyGradientKernel(T* logit_grad,
                                                const T* loss_grad,
-                                               const T* labels, const int n,
-                                               const int d, const int remain) {
-  int ids = blockIdx.x * blockDim.x + threadIdx.x;
+                                               const T* labels, const int64_t n,
+                                               const int64_t d,
+                                               const int64_t remain) {
+  int64_t ids = blockIdx.x * blockDim.x + threadIdx.x;
   if (ids < n * d) {
-    int idx_n = ids / d;
-    int idx_remain = ids % remain;
-    int idx_loss = idx_n * remain + idx_remain;
+    int64_t idx_n = ids / d;
+    int64_t idx_remain = ids % remain;
+    int64_t idx_loss = idx_n * remain + idx_remain;
     logit_grad[ids] = loss_grad[idx_loss] * (logit_grad[ids] - labels[ids]);
   }
 }
@@ -132,19 +133,19 @@ using BlockReduceTempStorage = typename BlockReduce<T, BlockDim>::TempStorage;
 // This kernel is used to calculate the max element of each row
 template <typename T, int BlockDim>
 static __global__ void RowReductionForMax(const T* logits_data, T* max_data,
-                                          int d, int axis_dim) {
+                                          int64_t d, int axis_dim) {
   __shared__ BlockReduceTempStorage<T, BlockDim> temp_storage;
 
   // logits_data view as [n, axis_dim, remain]
   // max_data view as [n, 1, remain]
   // blockDim = n * remain, split blockIdx to idx_n and idx_remain
-  int remain = d / axis_dim;
-  int idx_n = blockIdx.x / remain;
-  int idx_remain = blockIdx.x % remain;
-  int beg_idx = idx_n * d + threadIdx.x * remain + idx_remain;
-  int end_idx = (idx_n + 1) * d;
+  int64_t remain = d / axis_dim;
+  int64_t idx_n = blockIdx.x / remain;
+  int64_t idx_remain = blockIdx.x % remain;
+  int64_t beg_idx = idx_n * d + threadIdx.x * remain + idx_remain;
+  int64_t end_idx = (idx_n + 1) * d;
 
-  int step = BlockDim * remain;
+  int64_t step = BlockDim * remain;
   T cur_max = logits_data[beg_idx];
   beg_idx += step;
   while (beg_idx < end_idx) {
@@ -162,21 +163,21 @@ static __global__ void RowReductionForMax(const T* logits_data, T* max_data,
 // Make sure that BlockDim <= axis_dim
 template <typename T, int BlockDim, bool CalculateLogSoftmax = false>
 static __global__ void RowReductionForDiffMaxSum(const T* logits_data,
-                                                 T* max_data, T* softmax, int d,
-                                                 int axis_dim) {
+                                                 T* max_data, T* softmax,
+                                                 int64_t d, int axis_dim) {
   __shared__ BlockReduceTempStorage<T, BlockDim> temp_storage;
 
   // logits, softmax data view as [n, axis_dim, remain]
   // max_data view as [n, 1, remain]
   // blockDim = n * remain, split blockIdx to idx_n and idx_remain
-  int remain = d / axis_dim;
-  int idx_n = blockIdx.x / remain;
-  int idx_remain = blockIdx.x % remain;
-  int beg_idx = idx_n * d + threadIdx.x * remain + idx_remain;
-  int end_idx = (idx_n + 1) * d;
+  int64_t remain = d / axis_dim;
+  int64_t idx_n = blockIdx.x / remain;
+  int64_t idx_remain = blockIdx.x % remain;
+  int64_t beg_idx = idx_n * d + threadIdx.x * remain + idx_remain;
+  int64_t end_idx = (idx_n + 1) * d;
 
   auto block_max = max_data[blockIdx.x];
-  int step = BlockDim * remain;
+  int64_t step = BlockDim * remain;
 
   // In numeric stable mode softmax_with_loss, we calc loss with
   // tmp_i_j = x_i_j - max_i - logDiffMaxSum_i, instead of
@@ -216,25 +217,25 @@ static __global__ void RowReductionForDiffMaxSum(const T* logits_data,
 // Make sure that BlockDim <= axis_dim
 template <typename T, int BlockDim>
 static __global__ void RowReductionForSoftmaxAndCrossEntropy(
-    const T* logits_data, const T* labels_data, T* loss_data, T* softmax, int d,
-    int axis_dim) {
+    const T* logits_data, const T* labels_data, T* loss_data, T* softmax,
+    int64_t d, int axis_dim) {
   __shared__ BlockReduceTempStorage<T, BlockDim> temp_storage;
 
   // logits, softmax, labels data view as [n, axis_dim, remain]
   // loss_data view as [n, 1, remain]
   // blockDim = n * remain, split blockIdx to idx_n and idx_remain
-  int remain = d / axis_dim;
-  int idx_n = blockIdx.x / remain;
-  int idx_remain = blockIdx.x % remain;
-  int beg_idx = idx_n * d + threadIdx.x * remain + idx_remain;
-  int end_idx = (idx_n + 1) * d;
+  int64_t remain = d / axis_dim;
+  int64_t idx_n = blockIdx.x / remain;
+  int64_t idx_remain = blockIdx.x % remain;
+  int64_t beg_idx = idx_n * d + threadIdx.x * remain + idx_remain;
+  int64_t end_idx = (idx_n + 1) * d;
 
   // log_diff_max_sum shares memory with loss
   auto block_log_diff_max_sum = loss_data[blockIdx.x];
   auto tmp = softmax[beg_idx] - block_log_diff_max_sum;
   softmax[beg_idx] = exp_on_device(tmp);
   auto loss = -labels_data[beg_idx] * tmp;
-  int step = BlockDim * remain;
+  int64_t step = BlockDim * remain;
   beg_idx += step;
   while (beg_idx < end_idx) {
     tmp = softmax[beg_idx] - block_log_diff_max_sum;
@@ -251,21 +252,22 @@ template <typename T>
 struct HardLabelSoftmaxWithCrossEntropyFunctor {
  public:
   HardLabelSoftmaxWithCrossEntropyFunctor(const int64_t* labels, T* loss,
-                                          T* log_softmax, int d, int axis_dim)
+                                          T* log_softmax, int64_t d,
+                                          int axis_dim)
       : labels_(labels),
         loss_(loss),
         log_softmax_(log_softmax),
         d_(d),
         axis_dim_(axis_dim) {}
 
-  __device__ void operator()(int idx) const {
+  __device__ void operator()(int64_t idx) const {
     // logits view as [n, axis_dim, remain], where d = axis_dim * remain
-    int remain = d_ / axis_dim_;
-    int idx_n = idx / d_;
-    int idx_axis = (idx % d_) / remain;
-    int idx_remain = idx % remain;
+    int64_t remain = d_ / axis_dim_;
+    int64_t idx_n = idx / d_;
+    int64_t idx_axis = (idx % d_) / remain;
+    int64_t idx_remain = idx % remain;
     // labels, loss view as [n, remain]
-    int idx_lbl = idx_n * remain + idx_remain;
+    int64_t idx_lbl = idx_n * remain + idx_remain;
     // It also would ignore labels not in range(class_num).
     if (idx_axis != labels_[idx_lbl]) {
       log_softmax_[idx] = exp_on_device(log_softmax_[idx]);
@@ -280,7 +282,7 @@ struct HardLabelSoftmaxWithCrossEntropyFunctor {
   const int64_t* labels_;
   T* loss_;
   T* log_softmax_;
-  int d_;
+  int64_t d_;
   int axis_dim_;
 };
 
@@ -289,7 +291,7 @@ struct HardLabelSoftmaxWithCrossEntropyFunctorWithIgnoreIdx {
  public:
   HardLabelSoftmaxWithCrossEntropyFunctorWithIgnoreIdx(const int64_t* labels,
                                                        T* loss, T* log_softmax,
-                                                       int d, int axis_dim,
+                                                       int64_t d, int axis_dim,
                                                        int ignore_idx)
       : labels_(labels),
         loss_(loss),
@@ -298,14 +300,14 @@ struct HardLabelSoftmaxWithCrossEntropyFunctorWithIgnoreIdx {
         axis_dim_(axis_dim),
         ignore_idx_(ignore_idx) {}
 
-  __device__ void operator()(int idx) const {
+  __device__ void operator()(int64_t idx) const {
     // logits view as [n, axis_dim, remain], where d = axis_dim * remain
-    int remain = d_ / axis_dim_;
-    int idx_n = idx / d_;
-    int idx_axis = (idx % d_) / remain;
-    int idx_remain = idx % remain;
+    int64_t remain = d_ / axis_dim_;
+    int64_t idx_n = idx / d_;
+    int64_t idx_axis = (idx % d_) / remain;
+    int64_t idx_remain = idx % remain;
     // labels, loss view as [n, remain]
-    int idx_lbl = idx_n * remain + idx_remain;
+    int64_t idx_lbl = idx_n * remain + idx_remain;
     if (idx_axis != labels_[idx_lbl] || idx_axis == ignore_idx_) {
       log_softmax_[idx] = exp_on_device(log_softmax_[idx]);
     } else {
@@ -319,7 +321,7 @@ struct HardLabelSoftmaxWithCrossEntropyFunctorWithIgnoreIdx {
   const int64_t* labels_;
   T* loss_;
   T* log_softmax_;
-  int d_;
+  int64_t d_;
   int axis_dim_;
   int ignore_idx_;
 };
@@ -327,13 +329,13 @@ struct HardLabelSoftmaxWithCrossEntropyFunctorWithIgnoreIdx {
 template <typename T>
 static void HardLabelSoftmaxWithCrossEntropy(
     const platform::CUDADeviceContext& ctx, const T* logits_data,
-    const int64_t* labels_data, T* loss_data, T* softmax_data, int n, int d,
-    int axis_dim, int ignore_idx) {
+    const int64_t* labels_data, T* loss_data, T* softmax_data, int64_t n,
+    int64_t d, int axis_dim, int ignore_idx) {
   constexpr int kMaxBlockDim = 512;
-  int block_dim = axis_dim >= kMaxBlockDim
-                      ? kMaxBlockDim
-                      : (1 << static_cast<int>(std::log2(axis_dim)));
-  int grid_dim = n * d / axis_dim;
+  int64_t block_dim = axis_dim >= kMaxBlockDim
+                          ? kMaxBlockDim
+                          : (1 << static_cast<int>(std::log2(axis_dim)));
+  int64_t grid_dim = n * d / axis_dim;
   auto stream = ctx.stream();
 
 #define CALL_HARD_LABEL_SOFTMAX_WITH_CROSS_ENTROPY_FUSED_KERNEL(BlockDim)  \
@@ -372,16 +374,14 @@ static void HardLabelSoftmaxWithCrossEntropy(
 }
 
 template <typename T>
-static void SoftmaxWithCrossEntropyFusedKernel(const T* logits_data,
-                                               const T* labels_data,
-                                               T* softmax_data, T* loss_data,
-                                               int n, int d, int axis_dim,
-                                               cudaStream_t stream) {
+static void SoftmaxWithCrossEntropyFusedKernel(
+    const T* logits_data, const T* labels_data, T* softmax_data, T* loss_data,
+    int64_t n, int64_t d, int axis_dim, cudaStream_t stream) {
   constexpr int kMaxBlockDim = 512;
-  int block_dim = axis_dim >= kMaxBlockDim
-                      ? kMaxBlockDim
-                      : (1 << static_cast<int>(std::log2(axis_dim)));
-  int grid_dim = n * d / axis_dim;
+  int64_t block_dim = axis_dim >= kMaxBlockDim
+                          ? kMaxBlockDim
+                          : (1 << static_cast<int>(std::log2(axis_dim)));
+  int64_t grid_dim = n * d / axis_dim;
 
 #define CALL_SOFTMAX_WITH_CROSS_ENTROPY_FUSED_KERNEL(BlockDim)                 \
   case BlockDim:                                                               \
@@ -430,8 +430,8 @@ class SoftmaxWithCrossEntropyCUDAKernel : public framework::OpKernel<T> {
     const int axis = CanonicalAxis(context.Attr<int>("axis"), rank);
     int axis_dim = logits->dims()[axis];
 
-    const int n = SizeToAxis(axis, logits->dims());
-    const int d = SizeFromAxis(axis, logits->dims());
+    const int64_t n = SizeToAxis(axis, logits->dims());
+    const int64_t d = SizeFromAxis(axis, logits->dims());
 
     auto* softmax_data = softmax->mutable_data<T>(context.GetPlace());
     auto* loss_data = loss->mutable_data<T>(context.GetPlace());
@@ -500,24 +500,24 @@ class SoftmaxWithCrossEntropyGradCUDAKernel : public framework::OpKernel<T> {
     const int axis = CanonicalAxis(context.Attr<int>("axis"), rank);
     int axis_dim = logit_grad->dims()[axis];
 
-    const int n = SizeToAxis(axis, logit_grad->dims());
-    const int d = SizeFromAxis(axis, logit_grad->dims());
-    const int remain = d / axis_dim;
+    const int64_t n = SizeToAxis(axis, logit_grad->dims());
+    const int64_t d = SizeFromAxis(axis, logit_grad->dims());
+    const int64_t remain = d / axis_dim;
 
     int block = 512;
     auto stream = context.cuda_device_context().stream();
     auto ignore_index = context.Attr<int>("ignore_index");
     if (context.Attr<bool>("soft_label")) {
-      int grid = (n * d + block - 1) / block;
+      int64_t grid = (n * d + block - 1) / block;
       const T* label_data = labels->data<T>();
       SoftCrossEntropyGradientKernel<T><<<grid, block, 0, stream>>>(
           logit_grad_data, loss_grad_data, label_data, n, d, remain);
     } else {
-      int grid = (n * remain + block - 1) / block;
+      int64_t grid = (n * remain + block - 1) / block;
       const int64_t* label_data = labels->data<int64_t>();
       CrossEntropyGrad<T><<<grid, block, 0, stream>>>(
           logit_grad_data, label_data, n, d, remain, ignore_index);
-      int num = n * d;
+      int64_t num = n * d;
       grid = (num + block - 1) / block;
       Scale<T><<<grid, block, 0, stream>>>(logit_grad_data, loss_grad_data, num,
                                            d, remain, label_data, ignore_index);
diff --git a/paddle/fluid/platform/cuda_helper.h b/paddle/fluid/platform/cuda_helper.h
index ef0e3a72d1a67302edefe2e8ddc594e23286da9e..006062848e080eedcafc1bbf35ccd789bb57ce37 100644
--- a/paddle/fluid/platform/cuda_helper.h
+++ b/paddle/fluid/platform/cuda_helper.h
@@ -75,11 +75,14 @@ namespace platform {
  *    }
  *
 */
-#define CUDA_KERNEL_LOOP(i, num)                             \
+
+#define CUDA_KERNEL_LOOP_TYPE(i, num, index_type)            \
   int64_t __index__ = blockIdx.x * blockDim.x + threadIdx.x; \
-  for (int i = __index__; __index__ < (num);                 \
+  for (index_type i = __index__; __index__ < (num);          \
        __index__ += blockDim.x * gridDim.x, i = __index__)
 
+#define CUDA_KERNEL_LOOP(i, num) CUDA_KERNEL_LOOP_TYPE(i, num, int)
+
 class CublasHandleHolder {
  public:
 #ifdef PADDLE_WITH_HIP
diff --git a/paddle/fluid/platform/for_range.h b/paddle/fluid/platform/for_range.h
index 1869f3e2f78440375e551e5a98f8e4b357f19ec7..22d187b25902fd9dc96b3ebe1e6c5bd6c2bb3a44 100644
--- a/paddle/fluid/platform/for_range.h
+++ b/paddle/fluid/platform/for_range.h
@@ -48,7 +48,7 @@ __global__ static void ForRangeElemwiseOpGridIsOne(Function func) {
 }
 
 template <typename Function>
-__global__ static void ForRangeElemwiseOp(Function func, int limit) {
+__global__ static void ForRangeElemwiseOp(Function func, size_t limit) {
   size_t idx = static_cast<size_t>(blockIdx.x * blockDim.x + threadIdx.x);
   if (idx < limit) {
     func(idx);
@@ -58,13 +58,13 @@ __global__ static void ForRangeElemwiseOp(Function func, int limit) {
 template <>
 struct ForRange<CUDADeviceContext> {
   ForRange(const CUDADeviceContext& dev_ctx, size_t limit)
-      : dev_ctx_(dev_ctx), limit_(static_cast<int>(limit)) {}
+      : dev_ctx_(dev_ctx), limit_(static_cast<size_t>(limit)) {}
 
   template <typename Function>
   inline void operator()(Function func) const {
     constexpr int num_threads = 1024;
-    int block_size = limit_ <= num_threads ? limit_ : num_threads;
-    int grid_size = (limit_ + num_threads - 1) / num_threads;
+    size_t block_size = limit_ <= num_threads ? limit_ : num_threads;
+    size_t grid_size = (limit_ + num_threads - 1) / num_threads;
 
     if (grid_size == 1) {
       ForRangeElemwiseOpGridIsOne<<<1, block_size, 0, dev_ctx_.stream()>>>(
@@ -76,7 +76,7 @@ struct ForRange<CUDADeviceContext> {
   }
 
   const CUDADeviceContext& dev_ctx_;
-  int limit_;
+  size_t limit_;
 };
 
 #endif