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+++ b/README.md
@@ -1,7 +1,9 @@
 
 #Introduction#
 
-This package implements a new module nn.DAG which inherits from nn.Container and allows to combine modules in an arbitrary graph without cycle.
+This package implements a new module nn.DAG which inherits from
+nn.Container and allows to combine modules in an arbitrary graph
+without cycle.
 
 ##Example##
 
@@ -42,56 +44,65 @@ which would encode the following graph
 
 and run a forward pass with a random batch of 30 samples.
 
-Note that DAG:connect allows to add a bunch of edges at once. This is particularly useful to add anonymous modules which have a single predecessor and successor.
+Note that DAG:connect allows to add a bunch of edges at once. This is
+particularly useful to add anonymous modules which have a single
+predecessor and successor.
 
 ##Input and output##
 
-If a node has a single successor, its output is sent unchanged as input to that successor. If it has multiple successors, the outputs are collected into a table, and the table is used as input to the successor node. The indexes of the outputs in that table reflects the order of the DAG:connect() commands.
+If a node has a single predecessor, its output is taken as-is. If it
+has multiple predecessors, all the outputs are collected into a table,
+and the table is used as input. The indexes of the outputs in that
+table reflects the order in which the predecessors appeared in the
+DAG:connect() commands.
 
-The expected input (respectively the produced output) is a nested table of inputs reflecting the structure of the nested table of modules provided to DAG:setInput (respectively DAG:setOutput)
+The input to the DAG (respectively the produced output) is a nested
+table of inputs reflecting the structure of the nested table of
+modules provided to DAG:setInput (respectively DAG:setOutput)
 
-So for instance, in the example above, the model expects a tensor as input, since it is the input to the module a, and its output will is a table composed of two tensors, corresponding to the outputs of d and e respectively.
+So for instance, in the example above, the model expects a tensor as
+input, since it is the input to the module a, and its output will is a
+table composed of two tensors, corresponding to the outputs of d and e
+respectively.
 
-#Usage#
+##Usage##
 
-##nn.DAG()##
+###nn.DAG()###
 
 Create a new empty DAG, which inherits from nn.Container.
 
-##nn.DAG:connect([module1 [, module2 [, ...]]])##
+###nn.DAG:connect([module1 [, module2 [, ...]]])###
 
 Add new nodes corresponding to the modules passed as arguments if they
-are not already existing. Add edges between every the nodes
-corresponding to pairs of successive modules.
+are not already existing. Add edges between every two nodes
+corresponding to a pair of successive modules in the arguments.
 
-##nn.DAG:setInput(i)##
+Calling it with n > 2 arguments is strictly equivalent to calling it
+n-1 times on the pairs of successive arguments.
+
+###nn.DAG:setInput(i)###
 
 Defines the content and structure of the input. The argument should be
 either a module, or a (nested) table of module. The input to the DAG
 should be a (nested) table of inputs with the corresponding structure.
 
-##nn.DAG:setOutput(o)##
+###nn.DAG:setOutput(o)###
 
-Same as DAG:setInput.
+Similar to DAG:setInput().
 
-##nn.DAG:print()##
+###nn.DAG:print()###
 
 Prints the list of nodes.
 
-##nn.DAG:saveDot(filename)##
-
-Save a dot file to be used by the Graphviz set of tools for graph visualization.
-
-##nn.DAG:updateOutput(input)##
-
-See the torch documentation.
+###nn.DAG:saveDot(filename)###
 
-##nn.DAG:updateGradInput(input, gradOutput)##
+Save a dot file to be used by the Graphviz set of tools for graph
+visualization. This dot file can than be used for instance to produce
+a pdf file with
 
-See the torch documentation.
-
-##nn.DAG:accGradParameters(input, gradOutput, scale)##
-
-See the torch documentation.
+```
+dot graph.dot -T pdf -o graph.pdf
+```
 
+-- 
 *Francois Fleuret, Jan 13th, 2017*