Some tweaks after first practice.

1 files changed, 15 insertions, 3 deletions

diff --git a/ictp-saifr_colloquium.tex b/ictp-saifr_colloquium.tex
index d883ed8..1eca601 100644
--- a/ictp-saifr_colloquium.tex
+++ b/ictp-saifr_colloquium.tex
@@ -389,7 +389,7 @@
       \[
         0=y_i-\hat f(x_i\mid\pmb a)\qquad\text{for all $1\leq i\leq M$}
       \]
-      with $N$ unknowns $\pmb a=[a_1,\ldots, a_N]$ gives a manifold of $N-M$ dimensions
+      with $N$ unknowns $\pmb a=[a_1,\ldots, a_N]$ gives a manifold of $DlN-M$ dimensions
 
       \medskip
 
@@ -848,8 +848,8 @@
   \begin{tikzpicture}
     \draw (0,0) node[align=center] {Overparameterization works\\\includegraphics[width=3cm]{figs/fit_overparamfit_abs2.pdf}};
     \draw (4,2) node[align=center] {Gradient descent\\implicitly regularizes\\\includegraphics[height=2cm]{figs/fit_gradient_5.pdf}};
-    \draw (-4,2) node[align=center] {Neural networks\\are good bases\\\includegraphics[height=2cm]{figs/fit_basis_abs.pdf}};
-    \draw (-4,-2) node[align=center] {Data is sparse\\and high-dimensional\\\includegraphics[height=2cm]{figs/fit_data_abs2.pdf}};
+    \draw (-4,2) node[align=center] {Neural networks\\are good models\\\includegraphics[height=2cm]{figs/fit_basis_abs.pdf}};
+    \draw (-4,-2) node[align=center] {Data is sparse, low-noise,\\and high-dimensional\\\includegraphics[height=2cm]{figs/fit_data_abs2.pdf}};
     \draw (4,-2) node[align=center] {SGD finds\\high-entropy solutions\\\includegraphics[height=2cm]{figs/gradient_vs_sgd_4.png}};
   \end{tikzpicture}
 \end{frame}
@@ -1301,6 +1301,11 @@
   \framesubtitle{Conclusions and future directions}
   \begin{columns}
     \begin{column}{0.5\textwidth}
+
+      Many outstanding questions:
+
+      \bigskip
+
       \textbf{How do these structures interact with dynamics?}
 
       \bigskip
@@ -1312,6 +1317,13 @@
       \textbf{How do topological properties of solutions correlate with their quality?}
     \end{column}
     \begin{column}{0.5\textwidth}
+      \begin{tikzpicture}[scale=0.6, every node/.style={scale=0.6}]
+        \draw (0,0) node[align=center] {Overparameterization works\\\includegraphics[width=3cm]{figs/fit_overparamfit_abs2.pdf}};
+        \draw (4,2) node[align=center] {Gradient descent\\implicitly regularizes\\\includegraphics[height=2cm]{figs/fit_gradient_5.pdf}};
+        \draw (-4,2) node[align=center] {Neural networks\\are good models\\\includegraphics[height=2cm]{figs/fit_basis_abs.pdf}};
+        \draw (-4,-2) node[align=center] {Data is sparse, low-noise,\\and high-dimensional\\\includegraphics[height=2cm]{figs/fit_data_abs2.pdf}};
+        \draw (4,-2) node[align=center] {SGD finds\\high-entropy solutions\\\includegraphics[height=2cm]{figs/gradient_vs_sgd_4.png}};
+      \end{tikzpicture}
     \end{column}
   \end{columns}
 \end{frame}