--- a/writeup/nips2010_submission.tex	Tue Jun 01 10:56:40 2010 -0700
+++ b/writeup/nips2010_submission.tex	Tue Jun 01 10:58:15 2010 -0700
@@ -20,7 +20,7 @@
   Recent theoretical and empirical work in statistical machine learning has
   demonstrated the importance of learning algorithms for deep
   architectures, i.e., function classes obtained by composing multiple
-  non-linear transformations. Self-taught learning (exploiting unlabeled
+  non-linear transformations. The self-taught learning (exploiting unlabeled
   examples or examples from other distributions) has already been applied
   to deep learners, but mostly to show the advantage of unlabeled
   examples. Here we explore the advantage brought by {\em out-of-distribution
@@ -74,8 +74,8 @@
 performed similarly or better than previously proposed Restricted Boltzmann
 Machines in terms of unsupervised extraction of a hierarchy of features
 useful for classification.  The principle is that each layer starting from
-the bottom is trained to encode its input (the output of the previous
-layer) and to reconstruct it from a corrupted version of it. After this
+the bottom is trained to encode their input (the output of the previous
+layer) and try to reconstruct it from a corrupted version of it. After this
 unsupervised initialization, the stack of denoising auto-encoders can be
 converted into a deep supervised feedforward neural network and fine-tuned by
 stochastic gradient descent.
@@ -91,8 +91,6 @@
 (but see~\citep{CollobertR2008}). In particular the {\em relative
 advantage} of deep learning for this settings has not been evaluated.
 
-% TODO: Explain why we care about this question.
-
 In this paper we ask the following questions:
 
 %\begin{enumerate}
@@ -117,7 +115,7 @@
 a corresponding shallow and purely supervised architecture?
 %\end{enumerate}
 
-Our experimental results provide evidence to support positive answers to all of these questions.
+The experimental results presented here provide positive evidence towards all of these questions.
 
 \vspace*{-1mm}
 \section{Perturbation and Transformation of Character Images}
@@ -201,7 +199,7 @@
 {\bf Pinch.}
 This GIMP filter is named "Whirl and
 pinch", but whirl was set to 0. A pinch is ``similar to projecting the image onto an elastic
-surface and pressing or pulling on the center of the surface'' (GIMP documentation manual).
+surface and pressing or pulling on the center of the surface''~\citep{GIMP-manual}.
 For a square input image, think of drawing a circle of
 radius $r$ around a center point $C$. Any point (pixel) $P$ belonging to
 that disk (region inside circle) will have its value recalculated by taking
@@ -335,10 +333,9 @@
 service\footnote{http://mturk.com}. 
 AMT users are paid small amounts
 of money to perform tasks for which human intelligence is required.
-Mechanical Turk has been used extensively in natural language processing and vision.
-%processing \citep{SnowEtAl2008} and vision
-%\citep{SorokinAndForsyth2008,whitehill09}. 
-%\citep{SorokinAndForsyth2008,whitehill09}. 
+Mechanical Turk has been used extensively in natural language
+processing \citep{SnowEtAl2008} and vision
+\citep{SorokinAndForsyth2008,whitehill09}. 
 AMT users where presented
 with 10 character images and asked to type 10 corresponding ASCII
 characters. They were forced to make a hard choice among the
@@ -584,7 +581,13 @@
 
 \begin{figure}[h]
 \resizebox{.99\textwidth}{!}{\includegraphics{images/improvements_charts.pdf}}\\
-\caption{Charts corresponding to tables 2 (left) and 3 (right), from Appendix I.}
+\caption{Relative improvement in error rate due to self-taught learning. 
+Left: Improvement (or loss, when negative)
+induced by out-of-distribution examples (perturbed data). 
+Right: Improvement (or loss, when negative) induced by multi-task 
+learning (training on all classes and testing only on either digits,
+upper case, or lower-case). The deep learner (SDA) benefits more from
+both self-taught learning scenarios, compared to the shallow MLP.}
 \label{fig:improvements-charts}
 \end{figure}