Moving files from MTGCardDetector repo

Edmond Yoo

2018-09-16 0dab894a5be9f7d10d85e89dea91d02c71bae84d

 src/convolutional_kernels.cu

@@ -2,6 +2,10 @@
#include "curand.h"
#include "cublas_v2.h"

#ifdef CUDNN
#pragma comment(lib, "cudnn.lib")  
#endif

extern "C" {
#include "convolutional_layer.h"
#include "batchnorm_layer.h"
@@ -17,7 +21,7 @@
{
    int i = (blockIdx.x + blockIdx.y*gridDim.x) * blockDim.x + threadIdx.x;
    if (i >= n) return;
    binary[i] = (x[i] > 0) ? 1 : -1;
    binary[i] = (x[i] >= 0) ? 1 : -1;
}

void binarize_gpu(float *x, int n, float *binary)
@@ -33,7 +37,7 @@
    int i = 0;
    float mean = 0;
    for(i = 0; i < n; ++i){
        mean += abs(input[i*size + s]);
        mean += fabs(input[i*size + s]);
    }
    mean = mean / n;
    for(i = 0; i < n; ++i){
@@ -48,58 +52,177 @@
}


__global__ void binarize_filters_kernel(float *filters, int n, int size, float *binary)
__global__ void binarize_weights_kernel(float *weights, int n, int size, float *binary)
{
    int f = (blockIdx.x + blockIdx.y*gridDim.x) * blockDim.x + threadIdx.x;
    if (f >= n) return;
    int i = 0;
    float mean = 0;
    for(i = 0; i < size; ++i){
        mean += abs(filters[f*size + i]);
        mean += fabs(weights[f*size + i]);
    }
    mean = mean / size;
    for(i = 0; i < size; ++i){
        binary[f*size + i] = (filters[f*size + i] > 0) ? mean : -mean;
        binary[f*size + i] = (weights[f*size + i] > 0) ? mean : -mean;
        //binary[f*size + i] = weights[f*size + i];
    }
}

void binarize_filters_gpu(float *filters, int n, int size, float *binary)
void binarize_weights_gpu(float *weights, int n, int size, float *binary)
{
    binarize_filters_kernel<<<cuda_gridsize(n), BLOCK>>>(filters, n, size, binary);
    binarize_weights_kernel<<<cuda_gridsize(n), BLOCK>>>(weights, n, size, binary);
    check_error(cudaPeekAtLastError());
}

__global__ void cuda_f32_to_f16(float* input_f32, size_t size, half *output_f16)
{
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) output_f16[idx] = __float2half(input_f32[idx]);
    //if (idx < size) *((unsigned short *)output_f16 + idx) = __float2half(input_f32[idx]);
}

void cuda_convert_f32_to_f16(float* input_f32, size_t size, float *output_f16) {
    cuda_f32_to_f16 <<< size / BLOCK + 1, BLOCK, 0, get_cuda_stream() >>> (input_f32, size, (half *)output_f16);
}

__global__ void cuda_f16_to_f32(half* input_f16, size_t size, float *output_f32)
{
    int idx = blockIdx.x * blockDim.x + threadIdx.x;
    if (idx < size) output_f32[idx] = __half2float(input_f16[idx]);
    //if (idx < size) output_f32[idx] = __half2float(*((unsigned short *)input_f16 + idx));
}

void cuda_convert_f16_to_f32(float* input_f16, size_t size, float *output_f32) {
    cuda_f16_to_f32 <<< size / BLOCK + 1, BLOCK, 0, get_cuda_stream() >>> ((half *)input_f16, size, output_f32);
}

half *cuda_make_f16_from_f32_array(float *src, size_t n)
{
    half *dst16;
    size_t size = sizeof(half)*n;
    check_error(cudaMalloc((void **)&dst16, size));
    if (src) {
        cuda_convert_f32_to_f16(src, n, (float *)dst16);
    }
    if (!dst16) error("Cuda malloc failed\n");
    return dst16;
}

void forward_convolutional_layer_gpu(convolutional_layer l, network_state state)
{
    int i;
    int m = l.n;
    int k = l.size*l.size*l.c;
    int n = convolutional_out_height(l)*
        convolutional_out_width(l);

    fill_ongpu(l.outputs*l.batch, 0, l.output_gpu, 1);
    if(l.binary){
        binarize_filters_gpu(l.filters_gpu, l.n, l.c*l.size*l.size, l.binary_filters_gpu);
        binarize_weights_gpu(l.weights_gpu, l.n, l.c*l.size*l.size, l.binary_weights_gpu);
        swap_binary(&l);
    }

    if(l.xnor){
        binarize_filters_gpu(l.filters_gpu, l.n, l.c*l.size*l.size, l.binary_filters_gpu);
        binarize_weights_gpu(l.weights_gpu, l.n, l.c*l.size*l.size, l.binary_weights_gpu);
        swap_binary(&l);
        for(i = 0; i < l.batch; ++i){
            binarize_input_gpu(state.input + i*l.inputs, l.c, l.h*l.w, l.binary_input_gpu + i*l.inputs);
        }
        binarize_gpu(state.input, l.c*l.h*l.w*l.batch, l.binary_input_gpu);
        state.input = l.binary_input_gpu;
    }

#ifdef CUDNN
    float one = 1;
    float one = 1;    // alpha[0], beta[0] is float for HALF and FLOAT
    float alpha = 1, beta = 0; 

#ifdef CUDNN_HALF
    // Note: For improved performance it is advised to use beta[0] = 0.0. 
    // For Tensor Core: cudnnSetConvolutionMathType() where cudnnMathType_t mathType = CUDNN_TENSOR_OP_MATH;
    // 1. or CUDNN_CONVOLUTION_FWD_ALGO_IMPLICIT_PRECOMP_GEMM and use CUDNN_DATA_HALF
    // 2. or CUDNN_CONVOLUTION_FWD_ALGO_WINOGRAD_NONFUSED
    // More: http://docs.nvidia.com/deeplearning/sdk/cudnn-developer-guide/index.html#tensor_ops

    const size_t input16_size = l.batch*l.c*l.w*l.h;
    const size_t output16_size = l.batch*l.out_c*l.out_h*l.out_w;

    if (*state.net.max_input16_size < input16_size) {
        //printf("\n input16_size: cur = %zu \t max = %zu \n", input16_size, *state.net.max_input16_size);
        *state.net.max_input16_size = input16_size;
        if (*state.net.input16_gpu) cuda_free(*state.net.input16_gpu);
        *state.net.input16_gpu = (float *)cuda_make_f16_from_f32_array(NULL, *state.net.max_input16_size);
    }
    float *input16 = *state.net.input16_gpu;

    if (*state.net.max_output16_size < output16_size) {
        *state.net.max_output16_size = output16_size;
        if (*state.net.output16_gpu) cuda_free(*state.net.output16_gpu);
        *state.net.output16_gpu = (float *)cuda_make_f16_from_f32_array(NULL, *state.net.max_output16_size);
    }
    float *output16 = *state.net.output16_gpu;

    cuda_convert_f32_to_f16(state.input, input16_size, input16);

    //fill_ongpu(output16_size / 2, 0, (float *)output16, 1);
    cudnnConvolutionForward(cudnn_handle(),
        &alpha,
        l.srcTensorDesc,
        input16,
        l.weightDesc,
        l.weights_gpu16,
        l.convDesc,
        l.fw_algo,
        state.workspace,
        l.workspace_size,
        &beta,
        l.dstTensorDesc,
        output16);
    

    if (l.batch_normalize) 
    {        
        if (state.train) // Training
        {
            copy_ongpu(l.outputs*l.batch / 2, output16, 1, l.x_gpu, 1);
            //cudaMemcpyAsync(l.x_gpu, output16, l.outputs*l.batch*sizeof(half), cudaMemcpyDefault, get_cuda_stream());
            float one = 1;
            float zero = 0;
            // Batch-normalization can still take FP16 inputs and outputs, saving half the bandwidth
            // compared to FP32, it’s just that the statistics and value adjustment should be done in FP32.
            cudnnBatchNormalizationForwardTraining(cudnn_handle(),
                CUDNN_BATCHNORM_SPATIAL,
                &one,
                &zero,
                l.normDstTensorDescF16,
                l.x_gpu,            // input
                l.normDstTensorDescF16,
                output16,            // output
                l.normTensorDesc,
                l.scales_gpu,
                l.biases_gpu,
                .01,
                l.rolling_mean_gpu,        // output (should be FP32)
                l.rolling_variance_gpu,    // output (should be FP32)
                .00001,
                l.mean_gpu,            // output (should be FP32)
                l.variance_gpu);    // output (should be FP32)

            cuda_convert_f16_to_f32(output16, output16_size, l.output_gpu);
            //forward_batchnorm_layer_gpu(l, state);
        }
        else // Detection
        {
            cuda_convert_f16_to_f32(output16, output16_size, l.output_gpu);
            normalize_gpu(l.output_gpu, l.rolling_mean_gpu, l.rolling_variance_gpu, l.batch, l.out_c, l.out_h*l.out_w);
            scale_bias_gpu(l.output_gpu, l.scales_gpu, l.batch, l.out_c, l.out_h*l.out_w);
            add_bias_gpu(l.output_gpu, l.biases_gpu, l.batch, l.out_c, l.out_w*l.out_h);
        }
    }
    else // BIAS only
    {
        cuda_convert_f16_to_f32(output16, output16_size, l.output_gpu);
        add_bias_gpu(l.output_gpu, l.biases_gpu, l.batch, l.n, l.out_w*l.out_h);
    }    

#else

    cudnnConvolutionForward(cudnn_handle(),
                &one,
                l.srcTensorDesc,
                state.input,
                l.filterDesc,
                l.filters_gpu,
                l.weightDesc,
                l.weights_gpu,
                l.convDesc,
                l.fw_algo,
                state.workspace,
@@ -107,46 +230,168 @@
                &one,
                l.dstTensorDesc,
                l.output_gpu);
#endif    // CUDNN_HALF


#else
    int i;
    int m = l.n;
    int k = l.size*l.size*l.c;
    int n = l.out_w*l.out_h;
    for(i = 0; i < l.batch; ++i){
        im2col_ongpu(state.input + i*l.c*l.h*l.w, l.c,  l.h,  l.w,  l.size,  l.stride, l.pad, state.workspace);
        float * a = l.filters_gpu;
        float * a = l.weights_gpu;
        float * b = state.workspace;
        float * c = l.output_gpu;
        gemm_ongpu(0,0,m,n,k,1.,a,k,b,n,1.,c+i*m*n,n);
    }
#endif

#ifndef CUDNN_HALF
    if (l.batch_normalize) {
        forward_batchnorm_layer_gpu(l, state);
    }
    add_bias_gpu(l.output_gpu, l.biases_gpu, l.batch, l.n, n);
    else {
        add_bias_gpu(l.output_gpu, l.biases_gpu, l.batch, l.n, l.out_w*l.out_h);
    }
#endif // no CUDNN_HALF

    activate_array_ongpu(l.output_gpu, m*n*l.batch, l.activation);
    activate_array_ongpu(l.output_gpu, l.outputs*l.batch, l.activation);
    //if(l.dot > 0) dot_error_gpu(l);
    if(l.binary || l.xnor) swap_binary(&l);
    //cudaDeviceSynchronize();    // for correct profiling of performance
}

void backward_convolutional_layer_gpu(convolutional_layer l, network_state state)
{
    int m = l.n;
    int n = l.size*l.size*l.c;
    int k = convolutional_out_height(l)*
        convolutional_out_width(l);
    gradient_array_ongpu(l.output_gpu, l.outputs*l.batch, l.activation, l.delta_gpu);

    gradient_array_ongpu(l.output_gpu, m*k*l.batch, l.activation, l.delta_gpu);
    backward_bias_gpu(l.bias_updates_gpu, l.delta_gpu, l.batch, l.n, l.out_w*l.out_h);

    backward_bias_gpu(l.bias_updates_gpu, l.delta_gpu, l.batch, l.n, k);

#ifndef CUDNN_HALF
    if(l.batch_normalize){
        backward_batchnorm_layer_gpu(l, state);
    } else {
        //backward_bias_gpu(l.bias_updates_gpu, l.delta_gpu, l.batch, l.n, l.out_w*l.out_h);
    }
#endif // no CUDNN_HALF
    float *original_input = state.input;

    if(l.xnor) state.input = l.binary_input_gpu;
#ifdef CUDNN
    float one = 1;
    float alpha = 1, beta = 0;

#ifdef CUDNN_HALF
        
    const size_t input16_size = l.batch*l.c*l.w*l.h;
    const size_t delta16_size = l.batch*l.n*l.out_w*l.out_h;
    
    if (*state.net.max_input16_size < input16_size) {        
        *state.net.max_input16_size = input16_size;
        if(*state.net.input16_gpu) cuda_free(*state.net.input16_gpu);
        *state.net.input16_gpu = (float *)cuda_make_f16_from_f32_array(NULL, *state.net.max_input16_size);
    }
    float *input16 = *state.net.input16_gpu;

    if (*state.net.max_output16_size < delta16_size) {
        *state.net.max_output16_size = delta16_size;
        if(*state.net.output16_gpu) cuda_free(*state.net.output16_gpu);
        *state.net.output16_gpu = (float *)cuda_make_f16_from_f32_array(NULL, *state.net.max_output16_size);
    }
    float *delta16 = *state.net.output16_gpu;

    cuda_convert_f32_to_f16(state.input, input16_size, input16);
    cuda_convert_f32_to_f16(l.delta_gpu, delta16_size, delta16);

    if (l.batch_normalize) {
        //if (!state.train) {
        //    l.mean_gpu = l.rolling_mean_gpu;
        //    l.variance_gpu = l.rolling_variance_gpu;
        //}
        float one = 1;
        float zero = 0;
        cudnnBatchNormalizationBackward(cudnn_handle(),
            CUDNN_BATCHNORM_SPATIAL,
            &one,
            &zero,
            &one,
            &one,
            l.normDstTensorDescF16,
            l.x_gpu,                // input
            l.normDstTensorDescF16,
            delta16,                // input
            l.normDstTensorDescF16,
            l.x_norm_gpu,            // output
            l.normTensorDesc,
            l.scales_gpu,            // output (should be FP32)
            l.scale_updates_gpu,    // output (should be FP32)
            l.bias_updates_gpu,        // output (should be FP32)
            .00001,
            l.mean_gpu,                // input (should be FP32)
            l.variance_gpu);        // input (should be FP32)
        copy_ongpu(l.outputs*l.batch / 2, l.x_norm_gpu, 1, delta16, 1);
        //cudaMemcpyAsync(delta16, l.x_norm_gpu, l.outputs*l.batch * sizeof(half), cudaMemcpyDefault, get_cuda_stream());
    }
    else
    {
        //backward_bias_gpu(l.bias_updates_gpu, l.delta_gpu, l.batch, l.n, l.out_w*l.out_h);
    }

    // convert input: state.input (x), l.delta_gpu (y) from fp32 to fp16
    // get output: l.weight_updates_gpu (dw) and convert it to fp32 (ONLY if it is fp16)

    // calculate conv weight updates
    // Already: l.weight_updates_gpu = (l.weight_updates_gpu - l.weight*decay*batch*subdivision)*momentum
    //   so we should copy f32 to f16, or compute: f16=(w_up - w*d*b*s)*m
    cuda_convert_f32_to_f16(l.weight_updates_gpu, l.c*l.n*l.size*l.size, l.weight_updates_gpu16);

    cudnnConvolutionBackwardFilter(cudnn_handle(),
        &one,
        l.srcTensorDesc,
        input16, //state.input,
        l.ddstTensorDesc,
        delta16, //l.delta_gpu,
        l.convDesc,
        l.bf_algo,
        state.workspace,
        l.workspace_size,
        &one,
        l.dweightDesc,
        l.weight_updates_gpu16);    // l.weight_updates_gpu);

    cuda_convert_f16_to_f32(l.weight_updates_gpu16, l.c*l.n*l.size*l.size, l.weight_updates_gpu);

    if (state.delta) {
        if (l.binary || l.xnor) swap_binary(&l);

        // http://docs.nvidia.com/deeplearning/sdk/cudnn-developer-guide/index.html#cudnnConvolutionBackwardData
        // calculate delta for the next layer
        // convert input: l.weights_gpu (w), l.delta_gpu (dy) from fp32 to fp16
        // get output: state.delta (dx) and convert it to fp32 (ONLY if it is fp16)    
        cudnnConvolutionBackwardData(cudnn_handle(),
            &alpha,
            l.weightDesc,
            l.weights_gpu16, //l.weights_gpu,
            l.ddstTensorDesc,
            delta16, //l.delta_gpu,
            l.convDesc,
            l.bd_algo,
            state.workspace,
            l.workspace_size,
            &beta,
            l.dsrcTensorDesc,
            input16);    // state.delta);

        cuda_convert_f16_to_f32(input16, input16_size, state.delta);

        if (l.binary || l.xnor) swap_binary(&l);
        if (l.xnor) gradient_array_ongpu(original_input, l.batch*l.c*l.h*l.w, HARDTAN, state.delta);
    }
#else    // CUDNN_HALF

    // calculate conv weight updates
    // if used: beta=1 then loss decreases faster
    cudnnConvolutionBackwardFilter(cudnn_handle(),
            &one,
            l.srcTensorDesc,
@@ -158,15 +403,17 @@
            state.workspace,
            l.workspace_size,
            &one,
            l.dfilterDesc,
            l.filter_updates_gpu);
            l.dweightDesc,
            l.weight_updates_gpu);

    if(state.delta){
        if(l.binary || l.xnor) swap_binary(&l);
        // http://docs.nvidia.com/deeplearning/sdk/cudnn-developer-guide/index.html#cudnnConvolutionBackwardData
        // calculate delta for the next layer
        cudnnConvolutionBackwardData(cudnn_handle(),
                &one,
                l.filterDesc,
                l.filters_gpu,
                l.weightDesc,
                l.weights_gpu,
                l.ddstTensorDesc,
                l.delta_gpu,
                l.convDesc,
@@ -180,19 +427,25 @@
        if(l.xnor) gradient_array_ongpu(original_input, l.batch*l.c*l.h*l.w, HARDTAN, state.delta);
    }

#else
#endif    // CUDNN_HALF

#else    // CUDNN
    int m = l.n;
    int n = l.size*l.size*l.c;
    int k = l.out_w*l.out_h;

    int i;
    for(i = 0; i < l.batch; ++i){
        float * a = l.delta_gpu;
        float * b = state.workspace;
        float * c = l.filter_updates_gpu;
        float * c = l.weight_updates_gpu;

        im2col_ongpu(state.input + i*l.c*l.h*l.w, l.c,  l.h,  l.w,  l.size,  l.stride, l.pad, state.workspace);
        gemm_ongpu(0,1,m,n,k,1,a + i*m*k,k,b,k,1,c,n);

        if(state.delta){
            if(l.binary || l.xnor) swap_binary(&l);
            float * a = l.filters_gpu;
            float * a = l.weights_gpu;
            float * b = l.delta_gpu;
            float * c = state.workspace;

@@ -210,43 +463,77 @@

void pull_convolutional_layer(convolutional_layer layer)
{
    cuda_pull_array(layer.filters_gpu, layer.filters, layer.c*layer.n*layer.size*layer.size);
    cuda_pull_array(layer.weights_gpu, layer.weights, layer.c*layer.n*layer.size*layer.size);
    cuda_pull_array(layer.biases_gpu, layer.biases, layer.n);
    cuda_pull_array(layer.filter_updates_gpu, layer.filter_updates, layer.c*layer.n*layer.size*layer.size);
    cuda_pull_array(layer.weight_updates_gpu, layer.weight_updates, layer.c*layer.n*layer.size*layer.size);
    cuda_pull_array(layer.bias_updates_gpu, layer.bias_updates, layer.n);
    if (layer.batch_normalize){
        cuda_pull_array(layer.scales_gpu, layer.scales, layer.n);
        cuda_pull_array(layer.rolling_mean_gpu, layer.rolling_mean, layer.n);
        cuda_pull_array(layer.rolling_variance_gpu, layer.rolling_variance, layer.n);
    }
    if (layer.adam){
        cuda_pull_array(layer.m_gpu, layer.m, layer.c*layer.n*layer.size*layer.size);
        cuda_pull_array(layer.v_gpu, layer.v, layer.c*layer.n*layer.size*layer.size);
    }
}

void push_convolutional_layer(convolutional_layer layer)
{
    cuda_push_array(layer.filters_gpu, layer.filters, layer.c*layer.n*layer.size*layer.size);
    cuda_push_array(layer.weights_gpu, layer.weights, layer.c*layer.n*layer.size*layer.size);
#ifdef CUDNN_HALF
    cuda_convert_f32_to_f16(layer.weights_gpu, layer.c*layer.n*layer.size*layer.size, layer.weights_gpu16);
#endif
    cuda_push_array(layer.biases_gpu, layer.biases, layer.n);
    cuda_push_array(layer.filter_updates_gpu, layer.filter_updates, layer.c*layer.n*layer.size*layer.size);
    cuda_push_array(layer.weight_updates_gpu, layer.weight_updates, layer.c*layer.n*layer.size*layer.size);
    cuda_push_array(layer.bias_updates_gpu, layer.bias_updates, layer.n);
    if (layer.batch_normalize){
        cuda_push_array(layer.scales_gpu, layer.scales, layer.n);
        cuda_push_array(layer.rolling_mean_gpu, layer.rolling_mean, layer.n);
        cuda_push_array(layer.rolling_variance_gpu, layer.rolling_variance, layer.n);
    }
    if (layer.adam){
        cuda_push_array(layer.m_gpu, layer.m, layer.c*layer.n*layer.size*layer.size);
        cuda_push_array(layer.v_gpu, layer.v, layer.c*layer.n*layer.size*layer.size);
    }
}

void update_convolutional_layer_gpu(convolutional_layer layer, int batch, float learning_rate, float momentum, float decay)
{
    int size = layer.size*layer.size*layer.c*layer.n;

    axpy_ongpu(layer.n, learning_rate/batch, layer.bias_updates_gpu, 1, layer.biases_gpu, 1);
    scal_ongpu(layer.n, momentum, layer.bias_updates_gpu, 1);

    axpy_ongpu(layer.n, learning_rate/batch, layer.scale_updates_gpu, 1, layer.scales_gpu, 1);
    scal_ongpu(layer.n, momentum, layer.scale_updates_gpu, 1);
    if(layer.scales_gpu){
        axpy_ongpu(layer.n, learning_rate/batch, layer.scale_updates_gpu, 1, layer.scales_gpu, 1);
        scal_ongpu(layer.n, momentum, layer.scale_updates_gpu, 1);
    }

    axpy_ongpu(size, -decay*batch, layer.filters_gpu, 1, layer.filter_updates_gpu, 1);
    axpy_ongpu(size, learning_rate/batch, layer.filter_updates_gpu, 1, layer.filters_gpu, 1);
    scal_ongpu(size, momentum, layer.filter_updates_gpu, 1);
    if(layer.adam){
        scal_ongpu(size, layer.B1, layer.m_gpu, 1);
        scal_ongpu(size, layer.B2, layer.v_gpu, 1);

        axpy_ongpu(size, -decay*batch, layer.weights_gpu, 1, layer.weight_updates_gpu, 1);

        axpy_ongpu(size, -(1-layer.B1), layer.weight_updates_gpu, 1, layer.m_gpu, 1);
        mul_ongpu(size, layer.weight_updates_gpu, 1, layer.weight_updates_gpu, 1);
        axpy_ongpu(size, (1-layer.B2), layer.weight_updates_gpu, 1, layer.v_gpu, 1);

        adam_gpu(size, layer.weights_gpu, layer.m_gpu, layer.v_gpu, layer.B1, layer.B2, learning_rate/batch, layer.eps, layer.t+1);
        fill_ongpu(size, 0, layer.weight_updates_gpu, 1);
    }else{
        // update weights:
        // weights_gpu = weights_gpu*(1 - decay*lr) + weight_updates_gpu*lr / (batch*subdivision) =
        //  weights_gpu*(1 - 0.0005*0.001) + weight_updates_gpu*0.001/(64*8) = 
        //  weights_gpu * 0.999 999 5 + weight_updates_gpu * 0.000 001 953125
        // 
        // weight_updates_gpu = (weight_updates_gpu - weights_gpu*decay*batch*subdivision)*momentum = 
        //  (weight_updates_gpu - weights_gpu * 0.0005 * 64 * 8) * 0.9 = 
        //  weight_updates_gpu*0.9 - weights_gpu*0.2304
        axpy_ongpu(size, -decay*batch, layer.weights_gpu, 1, layer.weight_updates_gpu, 1);
        axpy_ongpu(size, learning_rate/batch, layer.weight_updates_gpu, 1, layer.weights_gpu, 1);
        scal_ongpu(size, momentum, layer.weight_updates_gpu, 1);
    }
}