A few clarifications in the comments

theano/tensor/opt.py

@@ -3008,8 +3008,8 @@ def local_elemwise_fusion_op(OP, max_input_fct=lambda node: 1024):
         if not isinstance(node.op, OP):
             return False
         inputs=[]#inputs of the new Elemwise op.
-        s_inputs = []#inputs of the new scalar op.
-        s_g=[]#graph of scalar, what will by done in the inner loop.
+        s_inputs = []#inputs of the new scalar op used by the Composite.
+        s_g=[] # Inputs of the new scalar op that represents the current node.
 
         # There is a hard limit of 256 bytes for the formal argument list to a
         # GPU kernel function.
@@ -3025,7 +3025,10 @@ def local_elemwise_fusion_op(OP, max_input_fct=lambda node: 1024):
         for i in node.inputs:
             do_fusion = False
             catch = False
-            tmp_input=[]#used to remove duplicate input.
+            # Will store inputs of the fused node that are not currently inputs
+            # of the node we want to create (to avoid duplicating inputs).
+            tmp_input=[]
+            # Same as tmp_input, but for scalars.
             tmp_scalar=[]
 
             # We should not check the number of inputs here
@@ -3061,11 +3064,16 @@ def local_elemwise_fusion_op(OP, max_input_fct=lambda node: 1024):
                     _logger.info("%s does not implement the c_code function. As well as being potentially slow, this disables loop fusion of this op." % str(i.owner.op.scalar_op))
                     do_fusion=False
 
-            # Compute the number of inputs in case we fuse this input
-            # The -1 is that replace an existing input with others.
+            # Compute the number of inputs in case we fuse this input.
+            # We subtract 1 because we replace the existing input with the new
+            # inputs from `tmp_input`.
             new_nb_input_ = new_nb_input + len(tmp_input) - 1
-            # If the new input is already an input of the current node, it was already counted.
-            # When new_nb_input was initialized to len(node.inputs)
+
+            # If the new input is already an input of the current node, it was
+            # already counted when `new_nb_input` was initialized to
+            # len(node.inputs).
+            # This can happen when a variable is used both by the Elemwise to
+            # fuse and the current node.
             for x in tmp_input:
                 if x in node.inputs:
                     new_nb_input_ -= 1