diff --git a/examples/autograd/mlp.py b/examples/autograd/mlp.py
index e90ff1d7df..dfc67b3c79 100755
--- a/examples/autograd/mlp.py
+++ b/examples/autograd/mlp.py
@@ -84,7 +84,7 @@ def to_categorical(y, num_classes):
         x = autograd.relu(x)
         x = autograd.matmul(x, w1)
         x = autograd.add_bias(x, b1)
-        x = autograd.soft_max(x)
+        x = autograd.softmax(x)
         loss = autograd.cross_entropy(x, target)
         for p, gp in autograd.backward(loss):
             sgd.apply(0, gp, p, '')
diff --git a/python/singa/autograd.py b/python/singa/autograd.py
index 11ad644bb5..e1557ca9e2 100755
--- a/python/singa/autograd.py
+++ b/python/singa/autograd.py
@@ -448,7 +448,7 @@ def backward(self, dy):
             return singa.DefaultTranspose(dx)
 
 
-def soft_max(x, axis=0):
+def softmax(x, axis=0):
     return SoftMax(axis)(x)[0]
 
 
@@ -540,7 +540,7 @@ def backward(self, dy=1.0):
             pass  # TODO, broadcast elementwise multiply seems not support
 
 
-def mean_square_error(x, t):
+def mse_loss(x, t):
     return MeanSquareError()(x, t)[0]
 
 
@@ -1076,7 +1076,8 @@ def backward(self, dy):
         return dx1, dx2
 
 
-def elemmatmul(x, y):
+def mul(x, y):
+    # do pointwise multiplication
     return ElemMatmul()(x, y)[0]
 
 
@@ -1088,7 +1089,7 @@ def add_all(*xs):
     return
 
 
-class RNN(Layer):
+class RNN_Base(Layer):
 
     def __init__(self):
         raise NotImplementedError
@@ -1100,7 +1101,7 @@ def step_forward(self):
         raise NotImplementedError
 
 
-class Vanilla_RNN(RNN):
+class RNN(RNN_Base):
 
     def __init__(self, input_size, hidden_size, num_layers=1, nonlinearity='tanh', bias=True, batch_first=False, dropout=0, bidirectional=False):
         self.nonlinearity = nonlinearity
@@ -1119,7 +1120,10 @@ def __init__(self, input_size, hidden_size, num_layers=1, nonlinearity='tanh', b
 
         self.params = (self.Wx, self.Wh, self.b)
 
-    def __call__(self, h0, *xs):
+    def __call__(self, xs, h0):
+        # xs: a tuple or list of input tensors
+        if not isinstance(xs, tuple):
+            xs = tuple(xs)
         inputs = xs + (h0,)
         self.device_check(*inputs)
         #self.device_check(inputs[0], *self.params)
@@ -1148,7 +1152,7 @@ def step_forward(self, x, h, Wx, Wh, b):
         return y
 
 
-class LSTM(RNN):
+class LSTM(RNN_Base):
 
     def __init__(self, input_size, hidden_size, nonlinearity='tanh', num_layers=1, bias=True, batch_first=False, dropout=0, bidirectional=False):
         self.nonlinearity = nonlinearity
@@ -1183,8 +1187,11 @@ def __init__(self, input_size, hidden_size, nonlinearity='tanh', num_layers=1, b
 
         self.params = self.Wx + self.Wh + self.Bx + self.Bh
 
-    def __call__(self, h0, c0, *xs):
-        inputs = xs + (h0, c0)
+    def __call__(self, xs, (h0, c0)):
+        # xs: a tuple or list of input tensors
+        if not isinstance(xs, list):
+            xs = list(xs)
+        inputs = xs + list((h0, c0))
         self.device_check(*inputs)
         #self.device_check(inputs[0], *self.params)
         self.device_check(inputs[0], *(self.Wx + self.Wh + self.Bx + self.Bh))
@@ -1229,10 +1236,10 @@ def step_forward(self, x, h, c, Wx, Wh, Bx, Bh):
         g = add(y1, y2)
         g = tanh(g)
 
-        cout1 = elemmatmul(f, c)
-        cout2 = elemmatmul(i, g)
+        cout1 = mul(f, c)
+        cout2 = mul(i, g)
         cout = add(cout1, cout2)
 
         hout = tanh(cout)
-        hout = elemmatmul(o, hout)
+        hout = mul(o, hout)
         return hout, cout
diff --git a/test/python/test_operation.py b/test/python/test_operation.py
index 9fb6a57c06..1df89498bf 100755
--- a/test/python/test_operation.py
+++ b/test/python/test_operation.py
@@ -141,9 +141,9 @@ def test_batchnorm2d_gpu(self):
     def test_vanillaRNN_gpu_tiny_ops_shape_check(self):
         # gradients shape check.
         inputs, target, h0 = prepare_inputs_targets_for_rnn_test()
-        rnn = autograd.Vanilla_RNN(3, 2)
+        rnn = autograd.RNN(3, 2)
 
-        hs, _ = rnn(h0, *inputs)
+        hs, _ = rnn(inputs, h0)
 
         loss = autograd.softmax_cross_entropy(hs[0], target[0])
         for i in range(1, len(hs)):
@@ -162,7 +162,7 @@ def test_LSTM_gpu_tiny_ops_shape_check(self):
 
         rnn = autograd.LSTM(3, 2)
 
-        hs, _, _ = rnn(h0, c0, *inputs)
+        hs, _, _ = rnn(inputs, (h0, c0))
         loss = autograd.softmax_cross_entropy(hs[0], target[0])
 
         for i in range(1, len(hs)):
@@ -206,10 +206,10 @@ def gradients_check(self, func, param, autograds, h=0.0005, df=1):
     def test_numerical_gradients_check_for_vallina_rnn(self):
         inputs, target, h0 = prepare_inputs_targets_for_rnn_test()
 
-        rnn = autograd.Vanilla_RNN(3, 2)
+        rnn = autograd.RNN(3, 2)
 
         def valinna_rnn_forward():
-            hs, _ = rnn(h0, *inputs)
+            hs, _ = rnn(inputs, h0)
 
             loss = autograd.softmax_cross_entropy(hs[0], target[0])
             for i in range(1, len(hs)):
@@ -234,7 +234,7 @@ def test_numerical_gradients_check_for_lstm(self):
         rnn = autograd.LSTM(3, 2)
 
         def lstm_forward():
-            hs, _, _ = rnn(h0, c0, *inputs)
+            hs, _, _ = rnn(inputs, (h0, c0))
 
             loss = autograd.softmax_cross_entropy(hs[0], target[0])
             for i in range(1, len(hs)):
@@ -258,7 +258,7 @@ def test_MeanSquareError(self):
         x.to_device(gpu_dev)
         t.to_device(gpu_dev)
 
-        loss= autograd.mean_square_error(x,t)
+        loss= autograd.mse_loss(x,t)
         dx=loss.creator.backward()[0]
 
         loss_np=tensor.to_numpy(loss)