代码 RNN

    import copy, numpy as np      np.random.seed(0)      # compute sigmoid nonlinearity      def sigmoid(x):          output = 1/(1+np.exp(-x))          return output      # convert output of sigmoid function to its derivative      def sigmoid_output_to_derivative(output):          return output*(1-output)      # training dataset generation      int2binary = {}      binary_dim = 8      largest_number = pow(2,binary_dim)      binary = np.unpackbits(          np.array([range(largest_number)],dtype=np.uint8).T,axis=1)      for i in range(largest_number):          int2binary[i] = binary[i]      # input variables      alpha = 0.1      input_dim = 2      hidden_dim = 16      output_dim = 1      # initialize neural network weights      synapse_0 = 2*np.random.random((input_dim,hidden_dim)) - 1      synapse_1 = 2*np.random.random((hidden_dim,output_dim)) - 1      synapse_h = 2*np.random.random((hidden_dim,hidden_dim)) - 1      synapse_0_update = np.zeros_like(synapse_0)      synapse_1_update = np.zeros_like(synapse_1)      synapse_h_update = np.zeros_like(synapse_h)      # training logic      for j in range(10000):          # generate a simple addition problem (a + b = c)          a_int = np.random.randint(largest_number/2) # int version          a = int2binary[a_int] # binary encoding          b_int = np.random.randint(largest_number/2) # int version          b = int2binary[b_int] # binary encoding          # true answer          c_int = a_int + b_int          c = int2binary[c_int]          # where we'll store our best guess (binary encoded)          d = np.zeros_like(c)          overallError = 0          layer_2_deltas = list()          layer_1_values = list()          layer_1_values.append(np.zeros(hidden_dim))          # moving along the positions in the binary encoding          for position in range(binary_dim):              # generate input and output              X = np.array([[a[binary_dim - position - 1],b[binary_dim - position - 1]]])              y = np.array([[c[binary_dim - position - 1]]]).T              # hidden layer (input ~+ prev_hidden)              layer_1 = sigmoid(np.dot(X,synapse_0) + np.dot(layer_1_values[-1],synapse_h))              # output layer (new binary representation)              layer_2 = sigmoid(np.dot(layer_1,synapse_1))              # did we miss?... if so by how much?              layer_2_error = y - layer_2              layer_2_deltas.append((layer_2_error)*sigmoid_output_to_derivative(layer_2))              overallError += np.abs(layer_2_error[0])              # decode estimate so we can print it out              d[binary_dim - position - 1] = np.round(layer_2[0][0])              # store hidden layer so we can use it in the next timestep              layer_1_values.append(copy.deepcopy(layer_1))          future_layer_1_delta = np.zeros(hidden_dim)          for position in range(binary_dim):              X = np.array([[a[position],b[position]]])              layer_1 = layer_1_values[-position-1]              prev_layer_1 = layer_1_values[-position-2]              # error at output layer              layer_2_delta = layer_2_deltas[-position-1]              # error at hidden layer              layer_1_delta = (future_layer_1_delta.dot(synapse_h.T) + \                  layer_2_delta.dot(synapse_1.T)) * sigmoid_output_to_derivative(layer_1)              # let's update all our weights so we can try again              synapse_1_update += np.atleast_2d(layer_1).T.dot(layer_2_delta)              synapse_h_update += np.atleast_2d(prev_layer_1).T.dot(layer_1_delta)              synapse_0_update += X.T.dot(layer_1_delta)              future_layer_1_delta = layer_1_delta          synapse_0 += synapse_0_update * alpha          synapse_1 += synapse_1_update * alpha          synapse_h += synapse_h_update * alpha              synapse_0_update *= 0          synapse_1_update *= 0          synapse_h_update *= 0          # print out progress          if(j % 1000 == 0):              print "Error:" + str(overallError)              print "Pred:" + str(d)              print "True:" + str(c)              out = 0              for index,x in enumerate(reversed(d)):                  out += x*pow(2,index)              print str(a_int) + " + " + str(b_int) + " = " + str(out)              print "------------"  

输出

Error:[ 3.45638663]Pred:[0 0 0 0 0 0 0 1]True:[0 1 0 0 0 1 0 1]9 + 60 = 1------------Error:[ 3.63389116]Pred:[1 1 1 1 1 1 1 1]True:[0 0 1 1 1 1 1 1]28 + 35 = 255------------Error:[ 3.91366595]Pred:[0 1 0 0 1 0 0 0]True:[1 0 1 0 0 0 0 0]116 + 44 = 72------------Error:[ 3.72191702]Pred:[1 1 0 1 1 1 1 1]True:[0 1 0 0 1 1 0 1]4 + 73 = 223------------Error:[ 3.5852713]Pred:[0 0 0 0 1 0 0 0]True:[0 1 0 1 0 0 1 0]71 + 11 = 8------------Error:[ 2.53352328]Pred:[1 0 1 0 0 0 1 0]True:[1 1 0 0 0 0 1 0]81 + 113 = 162------------Error:[ 0.57691441]Pred:[0 1 0 1 0 0 0 1]True:[0 1 0 1 0 0 0 1]81 + 0 = 81------------Error:[ 1.42589952]Pred:[1 0 0 0 0 0 0 1]True:[1 0 0 0 0 0 0 1]4 + 125 = 129------------Error:[ 0.47477457]Pred:[0 0 1 1 1 0 0 0]True:[0 0 1 1 1 0 0 0]39 + 17 = 56------------Error:[ 0.21595037]Pred:[0 0 0 0 1 1 1 0]True:[0 0 0 0 1 1 1 0]11 + 3 = 14------------