Gradient of Softmaxgrad

theano/tensor/nnet/nnet.py

@@ -77,11 +77,16 @@ class SoftmaxWithBias(gof.Op):
         if b.shape[0] != x.shape[1]:
             raise ValueError('b must have same number of columns as x')
 
-        sm = numpy.zeros_like(x)
-        for i in xrange(sm.shape[0]):
-            row = x[i] + b
-            sm[i] = numpy.exp(row - numpy.max(row))
-            sm[i] *= 1.0 / numpy.sum(sm[i])
+        # sm = numpy.zeros_like(x)
+        # for i in xrange(sm.shape[0]):
+            # row = x[i] + b
+            # sm[i] = numpy.exp(row - numpy.max(row))
+            # sm[i] *= 1.0 / numpy.sum(sm[i])
+        # output_storage[0][0] = sm
+
+        x_plus_b = x + b[None, :]
+        e_x = numpy.exp(x_plus_b - x_plus_b.max(axis=1)[:, None])
+        sm = e_x / e_x.sum(axis=1)[:, None]
         output_storage[0][0] = sm
 
     def grad(self, inp, grads):
@@ -303,8 +308,17 @@ class SoftmaxGrad(gof.Op):
             dx[i] = dy_times_sm_i - sum(dy_times_sm_i) * sm[i]
         output_storage[0][0] = dx
 
-    def grad(self, *args):
-        raise NotImplementedError()
+    def grad(self, inp, grads):
+        dy, sm = inp
+        g, = grads
+        
+        tmp = g + tensor.neg(tensor.sum(g*sm, axis=1).dimshuffle((0, 'x')))
+        g_dy = tmp * sm
+        
+        tmp2 = tensor.sum(dy*sm, axis=1).dimshuffle((0, 'x'))
+        g_sm = tmp*dy - g *tmp2
+    
+        return g_dy, g_sm
 
     def infer_shape(self, node, shape):
         return [shape[1]]
@@ -573,9 +587,7 @@ def softmax_graph(c):
     return tensor.exp(c) / tensor.exp(c).sum(axis=-1, keepdims=True)
 
 def softmax(c):
-    if c.ndim == 1:
-        c = tensor.shape_padleft(c, n_ones=1)
-    return softmax_graph(c)    
+    return softmax_op(c)
 
 @opt.register_specialize('fast_compile_gpu')
 @gof.local_optimizer([softmax_op])
@@ -733,7 +745,7 @@ if 0:
                             rest.append(add_in)
                             # print 'maybe_ds =', maybe_ds
                             # if maybe_ds:
-                  #I will make a plot with the average over many realizations.            #    print 'maybe_ds.ndim =', maybe_ds.ndim, ', maybe_sm.ndim =', maybe_sm.ndim
+                            #    print 'maybe_ds.ndim =', maybe_ds.ndim, ', maybe_sm.ndim =', maybe_sm.ndim
                             continue
 
                         if maybe_sm is mul_inputs[0]:

theano/tensor/nnet/tests/test_nnet.py

@@ -1011,7 +1011,7 @@ class T_CrossentropyCategorical1Hot(utt.InferShapeTester):
             try:
                 g = theano.function([x, b, y], T.grad(expr, x), mode=mode)
             finally:
-                config.warn.sum_div_dimshuffle_bug = backup
+                config.warn.sum_div_dimshuffle_qbug = backup
 
             if verbose:
                 printing.debugprint(g)
@@ -1026,7 +1026,7 @@ class T_CrossentropyCategorical1Hot(utt.InferShapeTester):
                 theano.printing.debugprint(g)
                 raise
 
-    def test_scale_cost(self):
+    def test_scrossentropy_softmax_1hot_with_bias_dxcale_cost(self):
         # TODO: add the optimization in FAST_COMPILE?
         # In the mean time, run it as 'FAST_RUN' instead
         mode = theano.compile.mode.get_default_mode()
@@ -1071,25 +1071,25 @@ class T_CrossentropyCategorical1Hot(utt.InferShapeTester):
 
         # Cases to test
         expressions = [
-                a * T.sum(-T.log(softmax_graph(x)[T.arange(y.shape[0]), y])),
-                -a * T.sum(T.log(softmax_graph(x)[T.arange(y.shape[0]), y])),
-                a * (-T.sum(T.log(softmax_graph(x)[T.arange(y.shape[0]), y]))),
-                a * T.sum(T.log(softmax_graph(x)[T.arange(y.shape[0]), y])),
-
-                a * T.sum(-T.log(softmax_graph(x))[T.arange(y.shape[0]), y]),
-                -a * T.sum(T.log(softmax_graph(x))[T.arange(y.shape[0]), y]),
-                a * (-T.sum(T.log(softmax_graph(x))[T.arange(y.shape[0]), y])),
-                a * T.sum(T.log(softmax_graph(x))[T.arange(y.shape[0]), y]),
-
-                a * T.mean(-T.log(softmax_graph(x)[T.arange(y.shape[0]), y])),
-                -a * T.mean(T.log(softmax_graph(x)[T.arange(y.shape[0]), y])),
-                a * (-T.mean(T.log(softmax_graph(x)[T.arange(y.shape[0]), y]))),
-                a * T.mean(T.log(softmax_graph(x)[T.arange(y.shape[0]), y])),
-
-                a * T.mean(-T.log(softmax_graph(x))[T.arange(y.shape[0]), y]),
-                -a * T.mean(T.log(softmax_graph(x))[T.arange(y.shape[0]), y]),
-                a * (-T.mean(T.log(softmax_graph(x))[T.arange(y.shape[0]), y])),
-                a * T.mean(T.log(softmax_graph(x))[T.arange(y.shape[0]), y]),
+                a * T.sum(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
+                -a * T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y])),
+                a * (-T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y]))),
+                a * T.sum(T.log(softmax(x)[T.arange(y.shape[0]), y])),
+
+                a * T.sum(-T.log(softmax(x))[T.arange(y.shape[0]), y]),
+                -a * T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y]),
+                a * (-T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y])),
+                a * T.sum(T.log(softmax(x))[T.arange(y.shape[0]), y]),
+
+                a * T.mean(-T.log(softmax(x)[T.arange(y.shape[0]), y])),
+                -a * T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y])),
+                a * (-T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y]))),
+                a * T.mean(T.log(softmax(x)[T.arange(y.shape[0]), y])),
+
+                a * T.mean(-T.log(softmax(x))[T.arange(y.shape[0]), y]),
+                -a * T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y]),
+                a * (-T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y])),
+                a * T.mean(T.log(softmax(x))[T.arange(y.shape[0]), y]),
                 ]
 
         for expr in expressions:
@@ -1130,7 +1130,7 @@ def test_argmax_pushdown():
 
     # test that the max_and_argmax is pushed down if the max is not used
     out = tensor.max_and_argmax(
-            softmax_graph(tensor.exp(tensor.tanh(sigmoid(x)))),
+            softmax(tensor.exp(tensor.tanh(sigmoid(x)))),
             axis=-1)[1]
     fgraph = gof.FunctionGraph(
             [x],
@@ -1147,7 +1147,7 @@ def test_argmax_pushdown():
     x = tensor.matrix()
     # test that the max_and_argmax is not pushed down if the max is used
     out = tensor.max_and_argmax(
-            softmax_graph(tensor.exp(tensor.tanh(sigmoid(x)))),
+            softmax(tensor.exp(tensor.tanh(sigmoid(x)))),
             axis=-1)[0]
     fgraph = gof.FunctionGraph(
             [x],
@@ -1236,7 +1236,7 @@ def test_asymptotic_32():
             x2 = tensor.dvector()
         y = tensor.lvector()
 
-        c = categorical_crossentropy(softmax_graph(x + x2), y)
+        c = categorical_crossentropy(softmax(x + x2), y)
         f = theano.function([x, y, x2], [c.sum(),
                             tensor.grad(c.sum(), x)], mode='FAST_RUN')
         if 0:
@@ -1374,15 +1374,26 @@ class Test_softmax_opt:
     # REPEAT 3 CASES in presence of log(softmax) with the advanced indexing
     # etc.
 
+
 def test_softmax_graph():
     rng = numpy.random.RandomState(utt.fetch_seed())
     x = theano.shared(rng.normal(size=(3, 4)))
+
     def f(inputs):
         y = softmax_graph(x)
-        z = (y**2).mean()
-        return theano.grad(z, x, known_grads={y: inputs})
+        return theano.grad(None, x, known_grads={y: inputs})
 
-    utt.verify_grad(f, [numpy.random.rand(3, 4)])
+    utt.verify_grad(f, [rng.rand(3, 4)])
+
+
+def test_grad_softmax_grad():
+    rng = numpy.random.RandomState(utt.fetch_seed())
+    x = theano.shared(rng.normal(size=(3, 4)))
+
+    def f(inputs):
+        y = softmax_op(x)
+        return theano.grad(None, x, known_grads={y: inputs})
+    utt.verify_grad(f, [rng.rand(3, 4)])
 
 
 def test_stabilize_log_softmax():
@@ -1390,7 +1401,7 @@ def test_stabilize_log_softmax():
     mode = mode.including('local_log_softmax', 'specialize')
 
     x = matrix()
-    y = theano.tensor.nnet.softmax_graph(x)
+    y = softmax(x)
     z = theano.tensor.log(y)
 
     f = theano.function([x], z, mode=mode)