diff options
Diffstat (limited to 'zif.tex')
| -rw-r--r-- | zif.tex | 20 |
1 files changed, 13 insertions, 7 deletions
@@ -187,7 +187,7 @@ \mu=\frac1N\operatorname{Tr}\operatorname{Hess} H(\boldsymbol x) \] - \bigskip + \smallskip Condition on marginal minima by inserting \[ @@ -506,7 +506,7 @@ \medskip - Jamming of disks in $d$ dimensions: + Rectified activations or jamming of disks: \[ \|\boldsymbol x^i-\boldsymbol x^j\|\geq 2R\qquad i,j=1,\ldots,P \] @@ -697,7 +697,8 @@ \begin{column}{0.5\textwidth} $M$ data points, $N$ parameters, $\alpha=M/N$, $y^\mu=V_0$, $\boldsymbol a^\mu$ spherical $p$-spin coefficients, \[ - f_{\boldsymbol x}(\boldsymbol a^\mu) + V_0 + =f_{\boldsymbol x}(\boldsymbol a^\mu) =H^{(\mu)}_p(\boldsymbol x) \] Average Euler characteristic reduced to integral over $m=\frac1N\boldsymbol x\cdot\boldsymbol x_0$, @@ -726,7 +727,8 @@ \begin{column}{0.5\textwidth} $M$ data points, $N$ parameters, $\alpha=M/N$, $y^\mu=V_0$, $\boldsymbol a^\mu$ spherical $p$-spin coefficients, \[ - f_{\boldsymbol x}(\boldsymbol a^\mu) + V_0 + =f_{\boldsymbol x}(\boldsymbol a^\mu) =H^{(\mu)}_p(\boldsymbol x) \] Simplest case: $p=1$, $\Omega$ is intersection of random hyperplanes with the sphere @@ -764,7 +766,7 @@ f_{\boldsymbol x}(\boldsymbol a^\mu) =H^{(\mu)}_p(\boldsymbol x) \] - For $p>1$, new phases possible + For $p>1$, new phases are possible \medskip @@ -1048,6 +1050,10 @@ \frametitle{Practical considerations: treating the sum over subsets} \begin{columns} \begin{column}{0.9\textwidth} + Annealed count can be made with or without this trick + + \bigskip + \includegraphics[width=\textwidth]{figs/annealed_compare.pdf} \end{column} \end{columns} @@ -1077,12 +1083,12 @@ \bigskip - $N\to\infty$ gives asymptotically zero curvature for all $\kappa$ + \alert<5>{$N\to\infty$ gives asymptotically zero curvature for all $\kappa$} \end{column} \begin{column}{0.27\textwidth} \begin{overprint} \onslide<1-2>\includegraphics[width=\textwidth]{figs/curvature_demo_1.pdf} - \onslide<3>\includegraphics[width=\textwidth]{figs/curvature_demo_2.pdf} + \onslide<3,5>\includegraphics[width=\textwidth]{figs/curvature_demo_2.pdf} \onslide<4>\includegraphics[width=\textwidth]{figs/curvature_demo_3.pdf} \end{overprint} \end{column} |