//+------------------------------------------------------------------+ //| opencl_program.cl | //| Copyright 2021, MetaQuotes Ltd. | //| https://www.mql5.com | //+------------------------------------------------------------------+ //--- by default some GPU doesn't support TYPEs //--- cl_khr_fp64 directive is used to enable work with TYPEs #pragma OPENCL EXTENSION cl_khr_fp64 : enable //+------------------------------------------------------------------+ //| Activation functions | //+------------------------------------------------------------------+ //| Linear activation function | //| Parameter 'value' Weighted sum of initial data | //| 'a' defines the angle of inclination of the line | //| 'b' - the vertical offset of the line | //+------------------------------------------------------------------+ TYPE LineActivation(TYPE value, TYPE a, TYPE b) { return (a * value + b); } //+------------------------------------------------------------------+ //| Sigmoid activation function | //| Parameter 'value' Weighted sum of initial data | //| 'a' stretches the range of values of the function | //| from '0' to 'a' | //| 'b' shifts the resulting value | //+------------------------------------------------------------------+ TYPE SigmoidActivation(TYPE value, TYPE a, TYPE b) { return (a / (1 + exp(-value)) - b); } //--- TYPE4 SigmoidActivation4(TYPE4 value, TYPE a, TYPE b) { return (a / (1 + exp(-value)) - b); } //+------------------------------------------------------------------+ //| Derivative of Sigmoid activation function | //| Parameter 'value' current point (result of feed forward). | //| 'a' stretches the range of values of the function from | //| '0' to 'a' | //| 'b' shifts the resulting value | //+------------------------------------------------------------------+ TYPE4 SigmoidDerivative(TYPE4 value, TYPE a, TYPE b) { if(a == 0) return (TYPE4)(0); //--- TYPE4 z = max(min((TYPE4)a, value + b), (TYPE4)(0)); return (z * (1 - z / a)); } //+------------------------------------------------------------------+ //| TANH activation function | //| Parameter 'value' Weighted sum of initial data | //+------------------------------------------------------------------+ TYPE TanhActivation(TYPE value) { return tanh(value); } //+------------------------------------------------------------------+ //| Derivative of TANH activation function | //| Parameter 'value' current point (result of feed forward). | //+------------------------------------------------------------------+ TYPE4 TanhDerivative(TYPE4 value) { return (1 - pow(value, 2)); } //+------------------------------------------------------------------+ //| LReLU activation function | //| Parameter 'value' current point (result of feed forward). | //| 'a' leak parameter | //+------------------------------------------------------------------+ TYPE LReLUActivation(TYPE value, TYPE a) { return (value > 0 ? value : a * value); } //+------------------------------------------------------------------+ //| Derivative of LReLU activation function | //| Parameter 'value' current point (result of feed forward). | //| 'a' leak parameter | //+------------------------------------------------------------------+ TYPE4 LReLUDerivative(TYPE4 value, TYPE a) { TYPE4 result = (TYPE4)((value.s0 > 0 ? 1 : a), (value.s1 > 0 ? 1 : a), (value.s2 > 0 ? 1 : a), (value.s3 > 0 ? 1 : a)); return (result); } //+------------------------------------------------------------------+ //| Swish activation function | //| Parameter 'value' Weighted sum of initial data | //| 'b' affects the nonlinearity of the function | //+------------------------------------------------------------------+ TYPE SwishActivation(TYPE value, TYPE b) { return value * SigmoidActivation(b * value, 1, 0); } //+------------------------------------------------------------------+ //| Derivative of Swish activation function | //| Parameter 'value' current point (result of feed forward). | //| 'value_input' Weighted sum of initial data | //| 'b' affects the nonlinearity of the function | //+------------------------------------------------------------------+ TYPE4 SwishDerivative(TYPE4 value, TYPE4 input_value, TYPE b) { //--- TYPE4 by = b * value; return (by + SigmoidActivation4(b * input_value, 1, 0) * (1 - by)); } //+------------------------------------------------------------------+ //| Transfer 4 elements of TYPE vector to TYPE4 | //| Parameter 'array' source array of data | //| 'start' first position to copy | //| 'step' step between elements to copy | //| 'size' Size of source array | //| 'shift' Shift in source array to the 1-st copied element | //+------------------------------------------------------------------+ TYPE4 ToVect4(__global TYPE *array, int start, int step, int size, int shift) { TYPE4 result = (TYPE4)(0, 0, 0, 0); step = max(1, step); int st = start * step + shift; if(st < size) { int k = (size - shift) % step; k = (size - shift - k) / step - start + (k > 0 ? 1 : 0); switch(k) { case 0: break; case 1: result = (TYPE4)(array[st], 0, 0, 0); break; case 2: result = (TYPE4)(array[st], array[st + step], 0, 0); break; case 3: result = (TYPE4)(array[st], array[st + step], array[st + 2 * step], 0); break; default: result = (TYPE4)(array[st], array[st + step], array[st + 2 * step], array[st + 3 * step]); break; } } return result; } //+------------------------------------------------------------------+ //| Derivative of SoftMax activation function | //| Parameter 'outputs' vector of previous FF outputs data | //| 'gradients' vector of gradients | //| 'shift' shift to first position in vector | //| 'outputs_total' size of outputs vector | //+------------------------------------------------------------------+ TYPE4 SoftMaxDerivative(__global TYPE *outputs, __global TYPE *gradient, int shift, int outputs_total) { TYPE4 result = (TYPE4)0; for(int j = 0; j < outputs_total; j++) result += (TYPE4)(outputs[j] * gradient[j]) * ((TYPE4)(shift == j, (shift + 1) == j, (shift + 2) == j, (shift + 3) == j) - ToVect4(outputs, shift, 1, outputs_total, 0)); return result; } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ TYPE Max4(TYPE4 vect, TYPE value) { TYPE result = fmax(vect.s0, value); result = fmax(vect.s1, result); result = fmax(vect.s2, result); return(fmax(vect.s3, result)); } //+------------------------------------------------------------------+ //| Transfer TYPE4 to 4 elements of TYPE vector | //| Parameter 'array' target array of data | //| 'value' source TYPE4 vector | //| 'start' first position to copy in target array | //| 'step' step between elements in target array | //| 'size' Size of target array | //| 'shift' Shift in target array to the 1-st copied element | //+------------------------------------------------------------------+ void D4ToArray(__global TYPE *array, TYPE4 value, int start, int step, int size, int shift) { step = max(1, step); int st = start * step + shift; if(st < size) { int k = (size - shift) % step; k = (size - shift - k) / step - start + (k > 0 ? 1 : 0); switch(k) { case 3: array[st + 2 * step] = value.s2; case 2: array[st + step] = value.s1; case 1: array[st] = value.s0; break; default: array[st + 3 * step] = value.s3; array[st + 2 * step] = value.s2; array[st + step] = value.s1; array[st] = value.s0; break; } } return; } //+------------------------------------------------------------------+ //| Kernel Feed Forward of perceptron | //| Parameter 'inputs' vector of inputs data | //| 'weights' matrix of weights | //| 'sums' vector of multiploer inputs to weights | //| 'outputs' output data after activation function | //| 'inputs_total' size of inputs vector | //| 'activation' type of activation function | //| 'act_param_a' 1st parameter of activation function | //| 'act_param_b' 2nd parameter of activation function | //+------------------------------------------------------------------+ __kernel void PerceptronFeedForward(__global TYPE *inputs, __global TYPE *weights, __global TYPE *sums, __global TYPE *outputs, int inputs_total, int activation, TYPE act_param_a, TYPE act_param_b) { const int n = get_global_id(0); const int weights_total = get_global_size(0) * (inputs_total + 1); int shift = n * (inputs_total + 1); TYPE s = weights[shift + inputs_total]; for(int i = 0; i < inputs_total; i += 4) s += dot(ToVect4(inputs, i, 1, inputs_total, 0), ToVect4(weights, i, 1, weights_total, shift)); switch(activation) { case 0: outputs[n] = LineActivation(s, act_param_a, act_param_b); break; case 1: outputs[n] = SigmoidActivation(s, act_param_a, act_param_b); break; case 2: outputs[n] = TanhActivation(s); break; case 3: outputs[n] = LReLUActivation(s, act_param_a); break; case 4: outputs[n] = exp(s); break; case 5: sums[n] = s; outputs[n] = SwishActivation(s, act_param_a); break; default: outputs[n] = s; break; } } //+------------------------------------------------------------------+ //| Kernel of divide vector to constant value | //| Parameter 'inputs' vector of inputs data | //| 'outputs' vector of output data | //| 'inputs_total' size of inputs vector | //| 'const_value' constant value | //+------------------------------------------------------------------+ __kernel void Normalize(__global TYPE *inputs, __global TYPE *outputs, int inputs_total, TYPE const_value) { const int n = get_global_id(0); int shift = n * 4; TYPE4 result = ToVect4(inputs, shift, 1, inputs_total, 0) / (TYPE4)(const_value); D4ToArray(outputs, result, shift, 1, inputs_total, 0); } //+------------------------------------------------------------------+ //| Kernel of calculation output gradients | //| Parameter 'target' vector of target data | //| 'outputs' vector of previous FF outputs data | //| 'gradients' vector of gradients | //| 'outputs_total' size of outputs vector | //+------------------------------------------------------------------+ __kernel void CalcOutputGradient(__global TYPE *target, __global TYPE *outputs, __global TYPE *gradients, int outputs_total) { const int n = get_global_id(0); TYPE4 result = ToVect4(target, n * 4, 1, outputs_total, 0) - ToVect4(outputs, n * 4, 1, outputs_total, 0); D4ToArray(gradients, result, n * 4, 1, outputs_total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void DeActivateGradient(__global TYPE *sums, __global TYPE *outputs, __global TYPE *gradients, int outputs_total, int activation, TYPE act_param_a, TYPE act_param_b) { const int n = get_global_id(0); int shift = n * 4; TYPE4 grad = ToVect4(gradients, shift, 1, outputs_total, 0); TYPE4 out = ToVect4(outputs, shift, 1, outputs_total, 0); TYPE4 s = ToVect4(sums, shift, 1, outputs_total, 0); switch(activation) { case 0: grad = grad * act_param_a; break; case 1: grad = grad * SigmoidDerivative(out, act_param_a, act_param_b); break; case 2: grad = grad * TanhDerivative(out); break; case 3: grad = grad * LReLUDerivative(out, act_param_a); break; case 4: grad = SoftMaxDerivative(outputs, sums, shift, outputs_total); break; case 5: grad = grad * SwishDerivative(out, s, act_param_a); break; default: break; } D4ToArray(gradients, grad, shift, 1, outputs_total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void CalcHiddenGradient(__global TYPE *gradient_inputs, __global TYPE *weights, __global TYPE *gradients, int outputs_total) { const int n = get_global_id(0); const int inputs_total = get_global_size(0); int weights_total = (inputs_total + 1) * outputs_total; //--- TYPE grad = 0; for(int o = 0; o < outputs_total; o += 4) grad += dot(ToVect4(gradients, o, 1, outputs_total, 0), ToVect4(weights, o, (inputs_total + 1), weights_total, n)); gradient_inputs[n] = grad; } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void CalcDeltaWeights(__global TYPE *inputs, __global TYPE *delta_weights, __global TYPE *gradients) { const int n = get_global_id(0); const int outputs_total = get_global_size(0); const int i = get_global_id(1); const int inputs_total = get_global_size(1); //--- TYPE grad = gradients[n]; int shift = n * (inputs_total + 1); delta_weights[shift + i] = inputs[i] * grad + delta_weights[shift + i]; if(i == 0) delta_weights[shift + inputs_total] += grad; } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void SGDUpdate(__global TYPE *delta_weights, __global TYPE *weights, int total, int batch_size, TYPE learningRate, TYPE Lambda1, TYPE Lambda2 ) { int start = 4 * get_global_id(0); TYPE4 delta4 = ToVect4(delta_weights, start, 1, total, 0); TYPE4 weights4 = ToVect4(weights, start, 1, total, 0); TYPE lr = learningRate / ((TYPE)batch_size); weights4 -= (TYPE4)(Lambda1) + Lambda2 * weights4; weights4 += (TYPE4)(lr) * delta4; D4ToArray(weights, weights4, start, 1, total, 0); D4ToArray(delta_weights, (TYPE4)(0), start, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void MomentumUpdate(__global TYPE *delta_weights, __global TYPE *weights, __global TYPE *momentum, int total, int batch_size, TYPE learningRate, TYPE beta, TYPE Lambda1, TYPE Lambda2) { int start = 4 * get_global_id(0); //--- TYPE4 delta4 = ToVect4(delta_weights, start, 1, total, 0) / ((TYPE4)(batch_size)); TYPE4 weights4 = ToVect4(weights, start, 1, total, 0); TYPE4 momentum4 = ToVect4(momentum, start, 1, total, 0); weights4 -= (TYPE4)(Lambda1) + Lambda2 * weights4; momentum4 = (TYPE4)(learningRate) * delta4 + (TYPE4)(beta) * momentum4; weights4 += momentum4; D4ToArray(weights, weights4, start, 1, total, 0); D4ToArray(momentum, momentum4, start, 1, total, 0); D4ToArray(delta_weights, (TYPE4)(0), start, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void AdaGradUpdate(__global TYPE *delta_weights, __global TYPE *weights, __global TYPE *momentum, int total, int batch_size, TYPE learningRate, TYPE Lambda1, TYPE Lambda2) { int start = 4 * get_global_id(0); //--- TYPE4 delta4 = ToVect4(delta_weights, start, 1, total, 0) / ((TYPE4)(batch_size)); TYPE4 weights4 = ToVect4(weights, start, 1, total, 0); TYPE4 momentum4 = ToVect4(momentum, start, 1, total, 0); //--- weights4 -= (TYPE4)(Lambda1) + Lambda2 * weights4; TYPE4 G = momentum4 + pow(delta4, 2); weights4 += learningRate / sqrt(G + 1.0e-10); D4ToArray(weights, weights4, start, 1, total, 0); D4ToArray(momentum, momentum4, start, 1, total, 0); D4ToArray(delta_weights, (TYPE4)(0), start, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void RMSPropUpdate(__global TYPE *delta_weights, __global TYPE *weights, __global TYPE *momentum, int total, int batch_size, TYPE learningRate, TYPE beta, TYPE Lambda1, TYPE Lambda2) { int start = 4 * get_global_id(0); //--- TYPE4 delta4 = ToVect4(delta_weights, start, 1, total, 0) / ((TYPE4)(batch_size)); TYPE4 weights4 = ToVect4(weights, start, 1, total, 0); TYPE4 momentum4 = ToVect4(momentum, start, 1, total, 0); //--- weights4 -= (TYPE4)(Lambda1) + Lambda2 * weights4; TYPE4 G = beta * momentum4 + (1 - beta) * pow(delta4, 2); weights4 += learningRate / (sqrt(G) + 1.0e-10) * delta4; D4ToArray(weights, weights4, start, 1, total, 0); D4ToArray(momentum, momentum4, start, 1, total, 0); D4ToArray(delta_weights, (TYPE4)(0), start, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void AdaDeltaUpdate(__global TYPE *delta_weights, __global TYPE *weights, __global TYPE *momentumW, __global TYPE *momentumG, int total, int batch_size, TYPE beta1, TYPE beta2, TYPE Lambda1, TYPE Lambda2) { int start = 4 * get_global_id(0); //--- TYPE4 delta4 = ToVect4(delta_weights, start, 1, total, 0) / ((TYPE4)(batch_size)); TYPE4 weights4 = ToVect4(weights, start, 1, total, 0); TYPE4 momentumW4 = ToVect4(momentumW, start, 1, total, 0); TYPE4 momentumG4 = ToVect4(momentumG, start, 1, total, 0); //--- weights4 -= (TYPE4)(Lambda1) + Lambda2 * weights4; TYPE4 W = beta1 * momentumW4 + (1 - beta1) * pow(weights4, 2); TYPE4 G = beta2 * momentumG4 + (1 - beta2) * pow(delta4, 2); weights4 += sqrt(W) / (sqrt(G) + 1.0e-10) * delta4; D4ToArray(weights, weights4, start, 1, total, 0); D4ToArray(momentumW, momentumW4, start, 1, total, 0); D4ToArray(momentumG, momentumG4, start, 1, total, 0); D4ToArray(delta_weights, (TYPE4)(0), start, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void AdamUpdate(__global TYPE *delta_weights, __global TYPE *weights, __global TYPE *momentumM, __global TYPE *momentumV, int total, int batch_size, TYPE learningRate, TYPE beta1, TYPE beta2, TYPE Lambda1, TYPE Lambda2) { int start = 4 * get_global_id(0); //--- TYPE4 delta4 = ToVect4(delta_weights, start, 1, total, 0) / ((TYPE4)(batch_size)); TYPE4 weights4 = ToVect4(weights, start, 1, total, 0); TYPE4 momentumM4 = ToVect4(momentumM, start, 1, total, 0); TYPE4 momentumV4 = ToVect4(momentumV, start, 1, total, 0); //--- TYPE4 M = beta1 * momentumM4 + (1 - beta1) * delta4; TYPE4 V = beta2 * momentumV4 + (1 - beta2) * pow(delta4, 2); TYPE4 m = M / (1 - beta1); TYPE4 v = V / (1 - beta2); weights4 -= (TYPE4)(Lambda1) + Lambda2 * weights4; weights4 += learningRate * m / (sqrt(v) + 1.0e-10); D4ToArray(weights, weights4, start, 1, total, 0); D4ToArray(momentumM, momentumM4, start, 1, total, 0); D4ToArray(momentumV, momentumV4, start, 1, total, 0); D4ToArray(delta_weights, (TYPE4)(0), start, 1, total, 0); } //+------------------------------------------------------------------+ //| Кернел прямого прохода сверточного слоя | //| Параметры 'inputs' вектор исхрордных данных | //| 'weights' матрица весов | //| 'sums' вектор взвешенных сумм перед функцией активации | //| 'outputs' вектор результатов | //| 'inputs_total' размер вектора исходных данных | //| 'window' размер окна анализа исходных данных | //| 'step' шаг перемещениия окна | //| 'window_out' количество фильтров | //| 'activation' тип функции активации | //| 'act_param_a' 1-й параметр функции активации | //| 'act_param_b' 2-ой параметр функции активации | //+------------------------------------------------------------------+ __kernel void ConvolutionFeedForward(__global TYPE *inputs, __global TYPE *weights, __global TYPE *sums, __global TYPE *outputs, int inputs_total, int window, int step, int window_out, int activation, TYPE act_param_a, TYPE act_param_b, int transposed_out) { const int n = get_global_id(0); const int neurons = get_global_size(0); const int weights_total = (window + 1) * window_out; int shift = n * step; for(int w = 0; w < window_out; w++) { int out = (transposed_out == 1 ? w + n * window_out : w * neurons + n); int shift_weights = w * (window + 1) ; if((shift_weights + window) >= weights_total) break; TYPE s = weights[shift_weights + window]; for(int i = 0; i < window; i += 4) s += dot(ToVect4(inputs, i, 1, inputs_total, shift), ToVect4(weights, i, 1, weights_total, shift_weights)); switch(activation) { case 0: outputs[out] = LineActivation(s, act_param_a, act_param_b); break; case 1: outputs[out] = SigmoidActivation(s, act_param_a, act_param_b); break; case 2: outputs[out] = TanhActivation(s); break; case 3: outputs[out] = LReLUActivation(s, act_param_a); break; case 4: outputs[out] = exp(s); break; case 5: sums[out] = s; outputs[out] = SwishActivation(s, act_param_a); break; default: outputs[out] = s; break; } } } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void ConvolutionCalcHiddenGradient(__global TYPE *gradient_inputs, __global TYPE *weights, __global TYPE *gradients, int outputs_total, int window, int step, int window_out, int neurons, int transposed_out) { const int n = get_global_id(0); const int inputs_total = get_global_size(0); int weights_total = (window + 1) * window_out; //--- TYPE grad = 0; int start = n - window + step; start = max((start - start % step) / step, 0); int stop = min((n - n % step) / step + 1, neurons); for(int w = 0; w < window_out; w++) { int shift_w = w * (window + 1); if((shift_w + window) > weights_total) break; for(int o = start; o < stop; o ++) { int shift_wl = (stop - o - 1) * step + n % step + shift_w; int shift_gl = (transposed_out == 1 ? w + o * window_out : w * neurons + o); grad += gradients[shift_gl] * weights[shift_wl]; } } gradient_inputs[n] = grad; } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void ConcolutionCalcDeltaWeights(__global TYPE *inputs, __global TYPE *delta_weights, __global TYPE *gradients, int inputs_total, int step, int neurons, int transposed_out) { const int inp_w = get_global_id(0); const int w = get_global_id(1); const int window = get_global_size(0) - 1; const int window_out = get_global_size(1); // int weights_total = (window + 1) * window_out; //--- int shift_delt = w * (window + 1) + inp_w; TYPE value = 0; if(inp_w == window) { for(int n = 0; n < neurons; n ++) value += gradients[transposed_out == 1 ? w + n*window_out : w * neurons + n]; } else for(int n = 0; n < neurons; n ++) { int shift_inp = n * step + inp_w; if(shift_inp >= inputs_total) break; value += inputs[shift_inp] * gradients[transposed_out == 1 ? w + n*window_out : w * neurons + n]; } delta_weights[shift_delt] += value; } //+------------------------------------------------------------------+ //| Кернел прямого прохода подвыборочного слоя | //| Параметры 'inputs' вектор исхрордных данных | //| 'outputs' вектор результатов | //| 'inputs_total' размер вектора исходных данных | //| 'input_neurons' размер вектора 1-го фильтра исх.данных | //| 'window' размер окна анализа исходных данных | //| 'step' шаг перемещениия окна | //| 'window_out' количество фильтров | //| 'activation' тип функции активации | //+------------------------------------------------------------------+ __kernel void ProofFeedForward(__global TYPE *inputs, __global TYPE *outputs, int inputs_total, int input_neurons, int window, int step, int window_out, int activation) { const int n = get_global_id(0); const int neurons = get_global_size(0); int shift = n * step; for(int w = 0; w < window_out; w++) { int out = w * neurons + n; int shift_inp = w * input_neurons; TYPE s = 0; TYPE k = 1.0 / (TYPE)window; TYPE4 k4 = (TYPE4)(k); for(int i = 0; i < window; i += 4) switch(activation) { case 6: s += dot(ToVect4(inputs, i, 1, min(shift_inp + input_neurons, inputs_total), shift_inp + shift), k4); break; case 7: s = Max4(ToVect4(inputs, i, 1, min(shift_inp + input_neurons, inputs_total), shift_inp + shift), s); break; default: break; } outputs[out] = s; } } //+------------------------------------------------------------------+ //| Кернел обратного прохода подвыборочного слоя | //| Параметры 'inputs' вектор исхрордных данных | //| 'gradient_inputs'вектор градиентов предшествующего слоя| //| 'outputs' вектор результатов | //| 'gradients' вектор градиентов текущего слоя | //| 'inputs_total' размер вектора исходных данных | //| 'outputs_total' размер вектора результатов | //| 'window' размер окна анализа исходных данных | //| 'step' шаг перемещениия окна | //| 'window_out' количество фильтров | //| 'neurons' размер вектора 1-го фильтра результатов | //| 'activation' тип функции активации | //+------------------------------------------------------------------+ __kernel void ProofCalcHiddenGradient(__global TYPE *inputs, __global TYPE *gradient_inputs, __global TYPE *outputs, __global TYPE *gradients, int inputs_total, int outputs_total, int window, int step, int window_out, int neurons, int activation) { const int n = get_global_id(0); const int input_neurons = get_global_size(0); //--- int start = n - window + step; start = max((start - start % step) / step, 0); int stop = min((n - n % step) / step + 1, neurons); for(int w = 0; w < window_out; w++) { TYPE grad = 0; int shift_inp = w * input_neurons + n; if(shift_inp >= inputs_total) break; TYPE inp = inputs[shift_inp]; for(int o = start; o < stop; o ++) { int shift_g = w * neurons + o; if(shift_g >= outputs_total) break; switch(activation) { case 6: grad += gradients[shift_g] / (TYPE)window; break; case 7: grad += (outputs[shift_g] == inp ? gradients[shift_g] : 0); break; default: break; } } gradient_inputs[shift_inp] = grad; } } //+------------------------------------------------------------------+ //| Кернел прямого прохода LSTM блока | //| Параметры 'forgetgate' врата забвения | //| 'inputgate' входные врата | //| 'outputgate' врата результатов | //| 'newcontent' новый контент | //| 'memory' поток памяти | //| 'hiddenstate' поток скрытого состояния | //| 'outputs_total' количество элементов в потоке данных | //+------------------------------------------------------------------+ __kernel void LSTMFeedForward(__global TYPE *forgetgate, __global TYPE *inputgate, __global TYPE *outputgate, __global TYPE *newcontent, __global TYPE *memory, __global TYPE *hiddenstate, int outputs_total) { const int n = get_global_id(0); const int shift = n * 4; TYPE4 fg = ToVect4(forgetgate, shift, 1, outputs_total, 0); TYPE4 ig = ToVect4(inputgate, shift, 1, outputs_total, 0); TYPE4 og = ToVect4(outputgate, shift, 1, outputs_total, 0); TYPE4 nc = ToVect4(newcontent, shift, 1, outputs_total, 0); TYPE4 mem = ToVect4(memory, shift, 1, outputs_total, 0); //--- TYPE4 temp = mem * fg; temp += ig * nc; D4ToArray(memory, temp, shift, 1, outputs_total, 0); temp = tanh(temp) * og; D4ToArray(hiddenstate, temp, shift, 1, outputs_total, 0); } //+------------------------------------------------------------------+ //| Кернел обратного прохода LSTM блока | //| Параметры 'outputs' вектор результатов | //| 'gradients' вектор градиентов текущего слоя | //| 'inputgate' входные врата | //| 'outputgate' врата результатов | //| 'newcontent' новый контент | //| 'memory' поток памяти | //| 'fg_gradients' градиент врат забвениия | //| 'ig_gradients' градиент входных врат | //| 'og_gradients' градиент врат результатов | //| 'nc_gradients' градиент нового контента | //| 'outputs_total' размер вектора результатов | //+------------------------------------------------------------------+ __kernel void LSTMCalcHiddenGradient(__global TYPE *outputs, __global TYPE *gradients, __global TYPE *inputgate, __global TYPE *outputgate, __global TYPE *newcontent, __global TYPE *memory, __global TYPE *fg_gradients, __global TYPE *ig_gradients, __global TYPE *og_gradients, __global TYPE *nc_gradients, int outputs_total) { const int n = get_global_id(0); int shift = n * 4; //--- TYPE4 out = ToVect4(outputs, shift, 1, outputs_total, 0); TYPE4 grad = ToVect4(gradients, shift, 1, outputs_total, 0); TYPE4 ig = ToVect4(inputgate, shift, 1, outputs_total, 0); TYPE4 og = ToVect4(outputgate, shift, 1, outputs_total, 0); TYPE4 nc = ToVect4(newcontent, shift, 1, outputs_total, 0); TYPE4 mem = ToVect4(memory, shift, 1, outputs_total, 0); //--- TYPE4 m = out / (og + 1.0e-8); //--- OutputGate градиент TYPE4 temp = grad * m; D4ToArray(og_gradients, temp, shift, 1, outputs_total, 0); //--- Градиент памяти cкорректируем на производную TANH grad = grad * og * (1 - pow(m, 2)); //--- InputGate градиент temp = grad * nc; D4ToArray(ig_gradients, temp, shift, 1, outputs_total, 0); //--- NewContent градиент temp = grad * ig; D4ToArray(nc_gradients, temp, shift, 1, outputs_total, 0); //--- ForgetGates градиент temp = grad * mem; D4ToArray(fg_gradients, temp, shift, 1, outputs_total, 0); } //+------------------------------------------------------------------+ //| Кернел рассчтёта коэффициентов зависимостей блока Self-Attention | //| Параметры 'querys' тензор запросов | //| 'keys' тензор ключей | //| 'values' тензор значений | //| 'scores' матрица коэффициентов зависимостей | //| 'inputs' тензор исходных данных | //| 'outputs' тензор результатов | //| 'window' размер окна анализа исходных данных | //| 'key_size' размер вектора ключей одного элемента | //+------------------------------------------------------------------+ __kernel void AttentionFeedForward(__global TYPE *querys, __global TYPE *keys, __global TYPE *scores, __global TYPE *values, __global TYPE *outputs, int window, int key_size, int mask) { const int q = get_global_id(0); const int units = get_global_size(0); const int h = get_global_id(1); const int heads = get_global_size(1); int shift_query = key_size * (q * heads + h); int shift_scores = units * (q * heads + h); TYPE summ = 0; for(int s = 0; s < units; s++) { TYPE score = 0; if(mask > 0 && s > q) { scores[shift_scores + s] = score; continue; } int shift_key = key_size * (s * heads + h); for(int k = 0; k < key_size; k ++) score += querys[shift_query + k] * keys[shift_key + k]; score = exp(score / sqrt((TYPE)key_size)); summ += score; scores[shift_scores + s] = score; } for(int s = 0; s < units; s++) scores[shift_scores + s] /= summ; //--- shift_query = window * (q * heads + h); for(int i = 0; i < window; i++) { TYPE query = 0; for(int v = 0; v < units; v++) query += values[window * (v * heads + h) + i] * scores[shift_scores + v]; outputs[shift_query + i] = query; } } //+------------------------------------------------------------------+ //| Кернел распеределения градиента внутри блока Self-Attention | //| до уровня матрицы коэффициентов зависимости Score | //| Параметры 'values' тензор значений | //| 'values_grad' тензор градиентов на уровне значений | //| 'scores' матрица коэффициентов зависимостей | //| 'scores_grad' матрица градиентов коэф. зависимостей | //| 'outputs' тензор результатов | //| 'outputs_grad' тензор градиентов на уровне результатов | //| 'window' размер окна анализа исходных данных | //+------------------------------------------------------------------+ __kernel void AttentionCalcScoreGradient(__global TYPE *scores, __global TYPE *scores_grad, __global TYPE *values, __global TYPE *values_grad, __global TYPE *outputs_grad, __global TYPE *scores_temp, int window) { const int q = get_global_id(0); const int units = get_global_size(0); const int h = get_global_id(1); const int heads = get_global_size(1); int shift_value = window * (q * heads + h); int shift_score = units * (q * heads + h); //--- Распределение градиента на Values for(int i = 0; i < window; i ++) { TYPE grad = 0; for(int g = 0; g < units; g++) grad += scores[units * (g * heads + h) + q] * outputs_grad[window * (g * heads + h) + i]; values_grad[shift_value + i] = grad; } //--- Распределение градиента на Score for(int k = 0; k < units; k++) { TYPE grad = 0; for(int i = 0; i < window; i++) grad += outputs_grad[shift_value + i] * values[window * (k * heads + h) + i]; scores_temp[shift_score + k] = grad; } //--- Корректируем на производную Softmax for(int k = 0; k < units; k++) { TYPE grad = 0; TYPE score = scores[shift_score + k]; for(int i = 0; i < units; i++) grad += scores[shift_score + i] * ((int)(i == k) - score) * scores_temp[shift_score + i]; scores_grad[shift_score + k] = grad; } } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void AttentionCalcHiddenGradient(__global TYPE *querys, __global TYPE *querys_grad, __global TYPE *keys, __global TYPE *keys_grad, __global TYPE *scores_grad, int key_size) { const int q = get_global_id(0); const int units = get_global_size(0); const int h = get_global_id(1); const int heads = get_global_size(1); int shift_query = key_size * (q * heads + h); int shift_score = units * (q * heads + h); //--- Распределение градиента на Querys и Keys const TYPE k = 1 / sqrt((TYPE)key_size); //--- for(int i = 0; i < key_size; i++) { TYPE grad_q = 0; TYPE grad_k = 0; for(int s = 0; s < units; s++) { grad_q += keys[key_size * (s * heads + h) + i] * scores_grad[shift_score + s]; grad_k += querys[key_size * (s * heads + h) + i] * scores_grad[units * (s * heads + h) + q]; } querys_grad[shift_query + i] = grad_q * k; keys_grad[shift_query + i] = grad_k * k; } } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void GPTFeedForward(__global TYPE *querys, __global TYPE *keys, __global TYPE *scores, __global TYPE *values, __global TYPE *outputs, int key_size, int units) { const int h = get_global_id(0); const int heads = get_global_size(0); int shift_query = key_size * h; int shift_scores = units * h; TYPE summ = 0; for(int s = 0; s < units; s++) { TYPE score = 0; int shift_key = key_size * (s * heads + h); for(int k = 0; k < key_size; k ++) score += querys[shift_query + k] * keys[shift_key + k]; score = exp(score / sqrt((TYPE)key_size)); summ += score; scores[shift_scores + s] = score; } for(int s = 0; s < units; s++) scores[shift_scores + s] /= summ; //--- shift_query = key_size * h; for(int i = 0; i < key_size; i++) { TYPE query = 0; for(int v = 0; v < units; v++) query += values[key_size * (v * heads + h) + i] * scores[shift_scores + v]; outputs[shift_query + i] = query; } } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void GPTCalcScoreGradient(__global TYPE *scores, __global TYPE *scores_grad, __global TYPE *values, __global TYPE *values_grad, __global TYPE *outputs_grad, __global TYPE *scores_temp, int window, int units, int current) { const int h = get_global_id(0); const int heads = get_global_size(0); int shift_value = window * (2 * heads + h); int shift_score = units * h; //--- Распределение градиента на Values for(int i = 0; i < window; i ++) values_grad[shift_value + i] = scores[units * h + current] * outputs_grad[window * h + i]; //--- Распределение градиента на Score for(int k = 0; k < units; k++) { TYPE grad = 0; for(int i = 0; i < window; i++) grad += outputs_grad[shift_value + i] * values[window * (k * heads + h) + i]; scores_temp[shift_score + k] = grad; } //--- Корректируем на производную Softmax for(int k = 0; k < units; k++) { TYPE grad = 0; TYPE score = scores[shift_score + k]; for(int i = 0; i < units; i++) grad += scores[shift_score + i] * ((int)(i == k) - score) * scores_temp[shift_score + i]; scores_grad[shift_score + k] = grad; } } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void GPTCalcHiddenGradient(__global TYPE *querys, __global TYPE *querys_grad, __global TYPE *keys, __global TYPE *scores_grad, int key_size, int units, int current) { const int h = get_global_id(0); const int heads = get_global_size(0); int shift_query = key_size * h; int shift_key = key_size * (heads + h); int shift_score = units * h; //--- Распределение градиента на Querys и Keys const TYPE k = 1 / sqrt((TYPE)key_size); //--- for(int i = 0; i < key_size; i++) { TYPE grad_q = 0; TYPE grad_k = 0; for(int s = 0; s < units; s++) { grad_q += keys[key_size * (s * heads + h) + i] * scores_grad[shift_score + s]; if(s == current) grad_k += querys[key_size * h + i] * scores_grad[units * h + current]; } querys_grad[shift_query + i] = grad_q * k; querys_grad[shift_key + i] = grad_k * k; } } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void BatchNormFeedForward(__global TYPE *inputs, __global TYPE *options, __global TYPE *weights, __global TYPE *output, int batch, int total) { int n = get_global_id(0); if(batch <= 1) { D4ToArray(output, ToVect4(inputs, n * 4, 1, total, 0), n * 4, 1, total, 0); return; } int shift = n * 4; int shift_options = n * 3 * 4; int shift_weights = n * 2 * 4; //--- TYPE4 inp = ToVect4(inputs, shift, 1, total, 0); TYPE4 mean = ToVect4(options, shift, 3, total * 3, 0) * ((TYPE)batch - 1.0) + inp ; if(options[shift_options ] > 0 && options[shift_options + 1] > 0) mean /= (TYPE4)batch; TYPE4 delt = inp - mean; TYPE4 variance = ToVect4(options, shift, 3, total * 3, 1) * ((TYPE)batch - 1.0) + pow(delt, 2); if(options[shift_options + 1] > 0) variance /= (TYPE4)batch; TYPE4 nx = delt / sqrt(variance + 1e-6); //--- if(weights[shift_weights] == 0) D4ToArray(weights, (TYPE4)1.0, shift, 2, total * 2, 0); //--- TYPE4 res = ToVect4(weights, shift, 2, total * 2, 0) * nx + ToVect4(weights, shift, 2, total * 2, 1); //--- D4ToArray(options, mean, shift, 3, total * 3, 0); D4ToArray(options, variance, shift, 3, total * 3, 1); D4ToArray(options, nx, shift, 3, total * 3, 2); D4ToArray(output, res, shift, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void BatchNormCalcHiddenGradient(__global TYPE *options, __global TYPE *gradient, __global TYPE *inputs, __global TYPE *gradient_inputs, __global TYPE *weights, int batch, int total ) { int n = get_global_id(0); int shift = n * 4; if(batch <= 1) { D4ToArray(gradient_inputs, ToVect4(gradient, shift, 1, total, 0), shift, 1, total, 0); return; } //--- TYPE4 inp = ToVect4(inputs, shift, 1, total, 0); TYPE4 gnx = ToVect4(gradient, shift, 1, total, 0) * ToVect4(weights, shift, 2, total * 2, 0); TYPE4 temp = 1 / sqrt(ToVect4(options, shift, 3, total * 3, 1) + 1e-6); TYPE4 delt = inp - ToVect4(options, shift, 3, total * 3, 0); TYPE4 gvar = delt / (-2 * pow(ToVect4(options, shift, 3, total * 3, 1) + 1.0e-6, 3.0 / 2.0)) * gnx; TYPE4 gmu = (-temp) * gnx - gvar * 2 * delt / (TYPE4)batch; TYPE4 gx = temp * gnx + gmu / (TYPE4)batch + gvar * 2 * delt / (TYPE4)batch; //--- D4ToArray(gradient_inputs, gx, shift, 1, total, 0); } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void BatchNormCalcDeltaWeights(__global TYPE *options, __global TYPE *delta_weights, __global TYPE *gradients) { const int n = get_global_id(0); int shift_options = n * 3; int shift_weights = n * 2; //--- TYPE grad = gradients[n]; delta_weights[shift_weights] += grad * options[shift_options + 2]; delta_weights[shift_weights + 1] += grad; } //+------------------------------------------------------------------+ //| | //+------------------------------------------------------------------+ __kernel void MaskMult(__global TYPE *inputs, __global TYPE *mask, __global TYPE *outputs, int outputs_total) { const int n = get_global_id(0) * 4; //--- TYPE4 out = ToVect4(inputs, n, 1, outputs_total, 0) * ToVect4(mask, n, 1, outputs_total, 0); D4ToArray(outputs, out, n, 1, outputs_total, 0); } //+------------------------------------------------------------------+