Fix part 3

1 files changed, 42 insertions, 8 deletions

diff --git a/report/paper.md b/report/paper.md
index c2c1a56..b76ba5b 100644
--- a/report/paper.md
+++ b/report/paper.md
@@ -24,8 +24,6 @@ A significant improvement to this vanilla architecture is Deep Convolutional Gen
 It is possible to artificially balance the number of steps between G and D backpropagation, however we think with a solid GAN structure this step is not
 really needed. Updating D more frequently than G resulted in additional cases of mode collapse due to the vanishing gradient issue. Updating G more
 frequently has not proved to be beneficial either, as the discriminator did not learn how to distinguish real samples from fake samples quickly enough.
-For this reasons the following sections will not present any artificial balancing of G-D training steps, opting for a standard single step update for both
-discriminator and generator.
 
 # DCGAN
 
@@ -84,6 +82,18 @@ Applying Virtual Batch Normalization our Medium DCGAN does not provide observabl
 We evaluated the effect of different dropout rates (results in appendix figures \ref{fig:dcdrop1_1}, \ref{fig:dcdrop1_2}, \ref{fig:dcdrop2_1}, \ref{fig:dcdrop2_2}) and concluded that the optimisation
 of the dropout hyper-parameter is essential for maximising performance. A high dropout rate results in DCGAN producing only artifacts that do not match any specific class due to the generator performing better than the discriminator. Conversely a low dropout rate leads to an initial stabilisation of G-D losses, but ultimately results in instability under the form of oscillation when training for a large number of batches.
 
+Trying different parameters for artificial G-D balancing in the training stage did not achieve any significant benefits as discussed in section I,
+exclusively leading to the generation of more artifacts (figure \ref{fig:baldc}). We also attempted to increase the D training steps with respect to G,
+but no mode collapse was observed even with the shallow model. 
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=12em]{fig/bal4.png}
+\caption{DCGAN Balancing G-D; D/G=3}
+\label{fig:baldc}
+\end{center}
+\end{figure}
+
 While training the different proposed DCGAN architectures, we did not observe mode collapse, indicating the DCGAN is less prone to a collapse compared to our *vanilla GAN*.
 
 # CGAN
@@ -118,8 +128,7 @@ When comparing the three levels of depth for the architectures it is possible to
 a shallow architecture we notice a high oscillation of the generator loss (figure \ref{fig:cshort}), which is being overpowered by the discriminator. Despite this we don't
 experience any issues with vanishing gradient, hence no mode collapse is reached. 
 Similarly, with a deep architecture the discriminator still overpowers the generator, and an equilibrium between the two losses is not achieved. The image quality in both cases is not really high: we can see that even after 20,000 batches the some pictures appear to be slightly blurry (figure \ref{fig:clong}).
-The best compromise is reached for 3 Dense-LeakyReLu-BN blocks as shown in figure \ref{fig:cmed}. It is possible to observe that G-D losses are perfectly balanced,
-and their value goes below 1, meaning the GAN is approaching the theoretical Nash Equilibrium of 0.5.
+The best compromise is reached for 3 Dense-LeakyReLu-BN blocks as shown in figure \ref{fig:cmed}. It is possible to observe that G-D losses are perfectly balanced, and their value goes below 1.
 The image quality is better than the two examples reported earlier, proving that this Medium-depth architecture is the best compromise.
 
 \begin{figure}
@@ -135,13 +144,12 @@ The three levels of dropout rates attempted do not affect the performance signif
 image quality and G-D losses are comparable.
 
 The biggest improvement in performance is obtained through one-sided label smoothing, shifting the true labels form 1 to 0.9 to reinforce discriminator behaviour.
-Using 0.1 instead of zero for the fake labels does not improve performance, as the discriminator loses incentive to do better (generator behaviour is reinforced). Performance results for
-one-sided labels smoothing with true labels = 0.9 are shown in figure \ref{fig:smooth}.
+Using 0.1 instead of zero for the fake labels does not improve performance, as the discriminator loses incentive to do better (generator behaviour is reinforced).
+Performance results for one-sided labels smoothing with true labels = 0.9 are shown in figure \ref{fig:smooth}.
 
 \begin{figure}
 \begin{center}
 \includegraphics[width=24em]{fig/smoothing_ex.png}
-\includegraphics[width=24em]{fig/smoothing.png}
 \caption{One sided label smoothing}
 \label{fig:smooth}
 \end{center}
@@ -152,11 +160,29 @@ mostly unchanged. The biggest change we expect to see is a lower correlation bet
 performance when training a classifier with the generated images from CGAN, as we will obtain more diverse images. Training with a larger batch size 
 would show more significant results, but since we set this parameter to 128 the issue of within-batch correlation is limited.
 
+Similarly to DCGAN, changing the G-D steps did not lead to good quality results as it can be seen in figure \ref{fig:cbalance}, in which we tried to train
+with D/G=15 for 10,000 batches, trying to initialize good discriminator weights, to then revert to a D/G=1, aiming to balance the losses of the two networks. 
+Even in the case of a shallow network, in which mode collapse should have been more likely, we observed diversity between the samples produced for
+the same classes, indicating that mode collapse still did not occur.
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=8em]{fig/bal1.png}
+\includegraphics[width=8em]{fig/bal2.png}
+\includegraphics[width=8em]{fig/bal3.png}
+\caption{CGAN G-D balancing results}
+\label{fig:cbalance}
+\end{center}
+\end{figure}
+
+FIX THIS
 Convolutional CGAN did not achieve better results than our baseline approach for the architecture analyzed, although we believe that 
 it is possible to achieve a better performance by finer tuning of the Convolutional CGAN parameters. Figure \ref{fig:cdcloss} shows a very high oscillation
 of the generator loss, hence the image quality varies a lot at each training step. Attempting LS on this architecture achieved a similar outcome
 when compared to the non-convolutional counterpart.
 
+ADD PIC
+
 # Inception Score
 
 Inception score is calculated as introduced by Tim Salimans et. al [@improved]. However as we are evaluating MNIST, we use LeNet-5 [@lenet]  as the basis of the inceptioen score.
@@ -165,7 +191,7 @@ We use the logits extracted from LeNet:
 $$ \textrm{IS}(x) = \exp(\mathbb{E}_x \left( \textrm{KL} ( p(y\mid x) \| p(y) ) \right) ) $$
 
 We further report the classification accuracy as found with LeNet. For coherence purposes the inception scores were
-calculated training the LeNet classifier under the same conditions across all experiments (100 epochs with SGD optimizer, learning rate = 0.001).
+calculated training the LeNet classifier under the same conditions across all experiments (100 epochs with `SGD`, `learning rate=0.001`).
 
 \begin{table}[H]
 \begin{tabular}{llll}
@@ -458,6 +484,14 @@ $$ L_{\textrm{total}} = \alpha L_{\textrm{LeNet}} + \beta L_{\textrm{generator}}
 \end{center}
 \end{figure}
 
+\begin{figure}[H]
+\begin{center}
+\includegraphics[width=24em]{fig/smoothing.png}
+\caption{CGAN+LS G-D Losses}
+\label{fig:smoothgd}
+\end{center}
+\end{figure}
+
 ## Retrain-Appendix
 
 \begin{figure}[H]