Updated results, hebrew, abstract, intro, etc.

content/introduction/introduction.tex

@@ -4,14 +4,16 @@ Real-world data is hardly ever perfect. Many real-world datasets suffer a myriad
 
 Gradient based learning methods, like those used to train neural networks, have trouble dealing with such datasets. Standard, per-sample losses (BCE, focal-loss), are confused easily by mislabeled points, as they produce a very large gradient which throws off training. Current attempts at noise-robust losses (GCE, MAE) help smooth these large gradients, yet still optimize on a per-sample basis, targeting per-sample accuracy rather than ranking quality --- leaving them misaligned with AUC even when they do reduce noise sensitivity. 
 
-In this field, optimizing directly for our desired metric (AUC) proves to be useful in dealing with noise. Per-sample losses help optimize each sample on their own, while AUC losses optimize the sample ranking amongst the whole. This helps them make smart tradeoffs while training, and accepting errors.
+Direct AUC optimization is a natural direction here: ranking-based objectives are determined by the relative ordering of scores rather than their absolute values, making them structurally less sensitive to isolated mislabeled samples. Per-sample losses optimize each sample independently, while AUC losses optimize sample ranking across the whole population, allowing the model to make principled tradeoffs even in the presence of label errors.
 
 \section{Contribution}
 
-In this work we introduce the \textsc{ROLL} framework for ROC curve related losses and \textsc{ROLL}-AoC, a noise-robust loss that optimizes AUC \emph{directly}. We show that the loss is more robust to label noise than other methods, and how it handles class-imbalance naturally.
+In this work we introduce the \textsc{ROLL} framework for ROC curve related losses and \textsc{ROLL}-AOC, a noise-robust loss that optimizes AUC \emph{directly}. We show that the loss is more robust to label noise than other methods, and how it handles class-imbalance naturally.
+
+% TODO: Expand introduction to 4--6 pages. Currently too thin -- add motivation, concrete examples, and a clearer narrative arc before submission.
 
 \section{Roadmap}
 
-In this work, we will first review AUC optimization, KDE, imbalanced classification, label noise and existing methods for dealing with it in datasets. We then introduce \textsc{ROLL} and \textsc{ROLL}-AoC, formulate it using KDE distribution approximation, and offer derivations for use in gradient-based learning. Then, we show performance on real world data. Finally, we discuss advantages and disadvantages with regards to other methods, as well as offer avenues for future research.
+In this work, we will first review AUC optimization, KDE, imbalanced classification, label noise and existing methods for dealing with it in datasets. We then introduce \textsc{ROLL} and \textsc{ROLL}-AOC, formulate it using KDE distribution approximation, and offer derivations for use in gradient-based learning. Then, we show performance on real world data. Finally, we discuss advantages and disadvantages with regards to other methods, as well as offer avenues for future research.