--- a/writeup/nips2010_submission.tex	Thu Jun 03 13:15:14 2010 -0400
+++ b/writeup/nips2010_submission.tex	Thu Jun 03 13:16:00 2010 -0400
@@ -510,9 +510,10 @@
 
 To provide a baseline of error rate comparison we also estimate human performance
 on both the 62-class task and the 10-class digits task.
-We compare the best MLPs against
-the best SDAs (both models' hyper-parameters are selected to minimize the validation set error), 
-along with a comparison against a precise estimate
+We compare the best Multi-Layer Perceptrons (MLP) against
+the best Stacked Denoising Auto-encoders (SDA), when
+both models' hyper-parameters are selected to minimize the validation set error.
+We also provide a comparison against a precise estimate
 of human performance obtained via Amazon's Mechanical Turk (AMT)
 service (http://mturk.com). 
 AMT users are paid small amounts
@@ -552,7 +553,7 @@
 useful to estimate the effect of a multi-task setting.
 The distribution of the classes in the NIST training and test sets differs
 substantially, with relatively many more digits in the test set, and a more uniform distribution
-of letters in the test set (where the letters are distributed
+of letters in the test set (whereas in the training set they are distributed
 more like in natural text).
 \vspace*{-1mm}
 
@@ -623,8 +624,8 @@
 \subsection{Models and their Hyperparameters}
 \vspace*{-2mm}
 
-The experiments are performed with Multi-Layer Perceptrons (MLP) with a single
-hidden layer and with Stacked Denoising Auto-Encoders (SDA).
+The experiments are performed using MLPs (with a single
+hidden layer) and SDAs.
 \emph{Hyper-parameters are selected based on the {\bf NISTP} validation set error.}
 
 {\bf Multi-Layer Perceptrons (MLP).}
@@ -638,7 +639,8 @@
 Training examples are presented in minibatches of size 20. A constant learning
 rate was chosen among $\{0.001, 0.01, 0.025, 0.075, 0.1, 0.5\}$
 through preliminary experiments (measuring performance on a validation set),
-and $0.1$ was then selected for optimizing on the whole training sets.
+and $0.1$ (which was found to work best) was then selected for optimizing on
+the whole training sets.
 \vspace*{-1mm}
 
 
@@ -674,14 +676,14 @@
 \end{figure}
 
 Here we chose to use the Denoising
-Auto-Encoder~\citep{VincentPLarochelleH2008} as the building block for
+Auto-encoder~\citep{VincentPLarochelleH2008} as the building block for
 these deep hierarchies of features, as it is very simple to train and
 explain (see Figure~\ref{fig:da}, as well as 
 tutorial and code there: {\tt http://deeplearning.net/tutorial}), 
-provides immediate and efficient inference, and yielded results
+provides efficient inference, and yielded results
 comparable or better than RBMs in series of experiments
 \citep{VincentPLarochelleH2008}. During training, a Denoising
-Auto-Encoder is presented with a stochastically corrupted version
+Auto-encoder is presented with a stochastically corrupted version
 of the input and trained to reconstruct the uncorrupted input,
 forcing the hidden units to represent the leading regularities in
 the data. Once it is trained, in a purely unsupervised way, 
@@ -744,7 +746,7 @@
 Figure~\ref{fig:error-rates-charts} summarizes the results obtained,
 comparing humans, the three MLPs (MLP0, MLP1, MLP2) and the three SDAs (SDA0, SDA1,
 SDA2), along with the previous results on the digits NIST special database
-19 test set from the literature respectively based on ARTMAP neural
+19 test set from the literature, respectively based on ARTMAP neural
 networks ~\citep{Granger+al-2007}, fast nearest-neighbor search
 ~\citep{Cortes+al-2000}, MLPs ~\citep{Oliveira+al-2002-short}, and SVMs
 ~\citep{Milgram+al-2005}.  More detailed and complete numerical results
@@ -780,8 +782,8 @@
 for the SDA.  Note that to simplify these multi-task experiments, only the original
 NIST dataset is used. For example, the MLP-digits bar shows the relative
 percent improvement in MLP error rate on the NIST digits test set 
-is $100\% \times$ (1 - single-task
-model's error / multi-task model's error).  The single-task model is
+is $100\% \times$ (single-task
+model's error / multi-task model's error - 1).  The single-task model is
 trained with only 10 outputs (one per digit), seeing only digit examples,
 whereas the multi-task model is trained with 62 outputs, with all 62
 character classes as examples.  Hence the hidden units are shared across