diff options
Diffstat (limited to 'ictp-saifr_colloquium.tex')
| -rw-r--r-- | ictp-saifr_colloquium.tex | 18 |
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} |