From ca14164f12cc2a452735411b4c31a7ea2caae3f1 Mon Sep 17 00:00:00 2001 From: Alejandro Lembke Barrientos Date: Sat, 12 Sep 2026 14:53:06 -0600 Subject: [PATCH] Adding Lab 4. --- Lab4/Informe_Laboratorio_GAN.pdf | Bin 0 -> 833175 bytes Lab4/Informe_Laboratorio_GAN.tex | 336 ++++ .../Instrucciones_Entrega_Laboratorio_GAN.pdf | Bin 0 -> 159928 bytes Lab4/Plantilla_Informe_Laboratorio_GAN.pdf | Bin 0 -> 790648 bytes Lab4/Plantilla_Informe_Laboratorio_GAN.tex | 192 +++ Lab4/lab_new.ipynb | 1355 +++++++++++++++++ .../gan_mode_collapse/class_distributions.png | Bin 0 -> 64724 bytes .../collapsed_class_distribution.png | Bin 0 -> 45336 bytes .../collapsed_discriminator.pt | Bin 0 -> 561106 bytes .../gan_mode_collapse/collapsed_generator.pt | Bin 0 -> 1464059 bytes .../gan_mode_collapse/collapsed_samples.png | Bin 0 -> 181549 bytes .../gan_mode_collapse/configuration.json | 23 + .../evaluation_classifier.pt | Bin 0 -> 1690513 bytes .../gan_mode_collapse/generator_lambda_0.1.pt | Bin 0 -> 1464081 bytes .../gan_mode_collapse/generator_lambda_0.5.pt | Bin 0 -> 1464081 bytes .../gan_mode_collapse/generator_lambda_0.pt | Bin 0 -> 1464037 bytes .../gan_mode_collapse/generator_lambda_1.pt | Bin 0 -> 1464037 bytes .../gan_mode_collapse/history_lambda_0.1.csv | 6 + .../gan_mode_collapse/history_lambda_0.5.csv | 6 + .../gan_mode_collapse/history_lambda_0.csv | 6 + .../gan_mode_collapse/history_lambda_1.csv | 6 + .../gan_mode_collapse/recovery_metrics.png | Bin 0 -> 107284 bytes .../gan_mode_collapse/recovery_samples.png | Bin 0 -> 219304 bytes .../gan_mode_collapse/recovery_training.png | Bin 0 -> 163782 bytes Lab4/outputs/gan_mode_collapse/results.csv | 6 + .../gan_mode_collapse/summary_table.tex | 11 + README.md | 1 + 27 files changed, 1948 insertions(+) create mode 100644 Lab4/Informe_Laboratorio_GAN.pdf create mode 100644 Lab4/Informe_Laboratorio_GAN.tex create mode 100755 Lab4/Instrucciones_Entrega_Laboratorio_GAN.pdf create mode 100755 Lab4/Plantilla_Informe_Laboratorio_GAN.pdf create mode 100755 Lab4/Plantilla_Informe_Laboratorio_GAN.tex create mode 100755 Lab4/lab_new.ipynb create mode 100644 Lab4/outputs/gan_mode_collapse/class_distributions.png create mode 100644 Lab4/outputs/gan_mode_collapse/collapsed_class_distribution.png create mode 100644 Lab4/outputs/gan_mode_collapse/collapsed_discriminator.pt create mode 100644 Lab4/outputs/gan_mode_collapse/collapsed_generator.pt create mode 100644 Lab4/outputs/gan_mode_collapse/collapsed_samples.png create mode 100644 Lab4/outputs/gan_mode_collapse/configuration.json create mode 100644 Lab4/outputs/gan_mode_collapse/evaluation_classifier.pt create mode 100644 Lab4/outputs/gan_mode_collapse/generator_lambda_0.1.pt create mode 100644 Lab4/outputs/gan_mode_collapse/generator_lambda_0.5.pt create mode 100644 Lab4/outputs/gan_mode_collapse/generator_lambda_0.pt create mode 100644 Lab4/outputs/gan_mode_collapse/generator_lambda_1.pt create mode 100644 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+\usepackage[strings]{underscore} + +\graphicspath{{outputs/gan_mode_collapse/}} +\setlength{\parindent}{0pt} +\setlength{\parskip}{0.6em} +\setlist[enumerate]{leftmargin=*,itemsep=0.8em} + +\newcommand{\answerbox}[1]{% + \par\noindent\textcolor{gray}{\rule{\linewidth}{0.4pt}}% + \vspace{#1}\par\noindent\textcolor{gray}{\rule{\linewidth}{0.4pt}}% +} + +\newcommand{\answer}[1]{\par\noindent\textbf{Respuesta:} #1} + +\newcommand{\resultfigure}[2]{% + \begin{figure}[H] + \centering + \IfFileExists{outputs/gan_mode_collapse/#1}{% + \includegraphics[width=0.96\linewidth,height=0.55\textheight,keepaspectratio]{#1}% + }{% + \fbox{\parbox[c][4cm][c]{0.88\linewidth}{\centering + Ejecute el notebook para generar \texttt{\detokenize{#1}}.}}% + } + \caption{#2} + \end{figure} +} + +\title{Informe de laboratorio\\Recuperación del colapso de modos en una GAN} +\author{Estudiante: Alejandro Lembke Barrientos} +\date{Carné: 12002840\hfill Fecha: 12 de septiembre de 2026} + +\begin{document} +\maketitle + +\section{Propósito e hipótesis} + +Todos los experimentos de recuperación parten del mismo punto de control con +colapso de modos. La variable independiente es el peso de la pérdida de +diversidad $\lambda_{\mathrm{div}}\in\{0,0.1,0.5,1.0\}$. La función objetivo del +generador es +\[ + \mathcal{L}_G + =\mathcal{L}_{\mathrm{adv}} + +\lambda_{\mathrm{div}}\mathcal{L}_{\mathrm{div}}, + \qquad + \mathcal{L}_{\mathrm{div}} + =-\mathbb{E}\!\left[ + \frac{\lVert G(z_1)-G(z_2)\rVert_1} + {\lVert z_1-z_2\rVert_1+\epsilon} + \right]. +\] + +\begin{enumerate} + \item Antes de observar los resultados, ¿qué valor de + $\lambda_{\mathrm{div}}$ esperaba que funcionara mejor? Explique el beneficio + esperado y un posible riesgo. +\end{enumerate} +\answer{Antes de examinar los resultados, se esperaría que $\lambda_{\mathrm{div}}=0.5$ +ofreciera el mejor equilibrio: suficiente para inducir diversidad entre salidas del +generador sin ser tan agresivo como $\lambda_{\mathrm{div}}=1.0$, que podría penalizar +en exceso la similitud entre salidas y sacrificar realismo. El riesgo esperado era que +un $\lambda_{\mathrm{div}}$ demasiado alto empujara al generador a maximizar la +distancia píxel a píxel mediante ruido o distorsiones en lugar de generar dígitos +genuinamente distintos --- riesgo que, como se detalla más adelante, efectivamente se +materializó, y que además se combinó con una falla mucho más profunda del +entrenamiento adversarial de base.} + +\section{Diagnóstico del punto de control colapsado} + +\resultfigure{collapsed_samples.png}{Muestras del punto de control común con colapso de modos.} +\resultfigure{collapsed_class_distribution.png}{Distribución de dígitos predicha por el clasificador en el punto colapsado.} + +\begin{enumerate}[resume] + \item ¿Qué evidencia visual sugiere colapso de modos? Distinga entre clases + ausentes y apariencias repetidas dentro de una clase representada. +\end{enumerate} +\answer{La evidencia más contundente no es solo el colapso de clases sino que las 64 +muestras mostradas en \texttt{collapsed\_samples.png} son, en su totalidad, ruido +granulado de alta frecuencia sin ninguna forma de dígito reconocible: no hay trazos, +curvas ni contornos identificables como escritura a mano en ninguna de ellas. Desde la +perspectiva del clasificador, \texttt{collapsed\_class\_distribution.png} muestra que el +100\% de la masa se concentra en un único dígito predicho ("8"), es decir, colapso +total de clases. Pero además la impresión de diagnóstico del propio notebook confirma +\texttt{mass on [1, 7]=0.000}: el generador ni siquiera colapsó hacia los dígitos 1 y 7 +que se pretendía inducir. Aquí no se trata de "una clase repetida con variaciones": es +que ninguna clase real está representada, y la aparente uniformidad visual entre +muestras es simplemente ruido de textura similar, no repetición de un dígito legítimo.} + +\begin{enumerate}[resume] + \item Utilice el número de modos y la entropía normalizada para describir el + colapso entre clases. ¿Qué información aporta cada medida? +\end{enumerate} +\answer{El número de modos (1/10) confirma que solo una clase supera el umbral de +frecuencia del 1\%: un colapso binario, todo-o-nada, hacia una sola clase predicha. La +entropía normalizada (0.010, en una escala de 0 a 1 donde 0 significa que toda la masa +recae en una sola clase y 1 significa una distribución perfectamente uniforme entre las +10 clases) cuantifica qué tan extrema es esa concentración: un valor tan cercano a 0 +indica una distribución prácticamente degenerada, no solo "dominada" por una clase sino +casi puntual en ella. El conteo de modos aporta una lectura binaria y fácil de +interpretar (¿cuántas clases "cuentan"?), mientras que la entropía aporta la forma +completa de la distribución, incluso entre las clases que sí superan el umbral; +juntas confirman un colapso extremo y no solo parcial.} + +\begin{enumerate}[resume] + \item ¿Las muestras mostradas permiten identificar confiablemente el colapso + dentro de cada clase? Explique qué evidencia adicional se necesita. +\end{enumerate} +\answer{No de forma confiable. Como ninguna de las 64 muestras colapsadas se asemeja a +un dígito real, no existe una forma legítima de "8" (o de cualquier otro dígito) contra +la cual comparar variedad interna; no se puede evaluar colapso \emph{dentro} de una +clase que en realidad nunca se materializó visualmente. Además, la confianza del +clasificador (0.981) es engañosa: el clasificador se entrenó únicamente con dígitos +reales de MNIST y nunca vio ejemplos de ruido no estructurado, por lo que puede emitir +predicciones muy seguras sobre entradas fuera de distribución sin que eso refleje +ninguna semántica real. La evidencia adicional necesaria es exactamente la que se usó +aquí para diagnosticar el problema real: inspección visual directa de las muestras, y +las curvas de pérdida del discriminador durante el preentrenamiento (que muestran +$D\approx0.000$ desde la época 5 de 16, evidenciando que el discriminador saturó y el +generador dejó de recibir señal de gradiente útil mucho antes de llegar a la fase de +colapso dirigido).} + +\section{Resultados de recuperación} + +\IfFileExists{outputs/gan_mode_collapse/summary_table.tex}{% + \begin{table}[H] + \centering + \small + \resizebox{\linewidth}{!}{\input{outputs/gan_mode_collapse/summary_table.tex}} + \caption{Resultados cuantitativos generados por el notebook.} + \end{table} +}{% + \begin{center} + \fbox{\parbox[c][2.2cm][c]{0.88\linewidth}{\centering + Ejecute el notebook para generar + \texttt{outputs/gan\_mode\_collapse/summary\_table.tex}.}} + \end{center} +} + +\resultfigure{recovery_samples.png}{Muestras del punto colapsado y de todas las configuraciones de recuperación.} +\resultfigure{class_distributions.png}{Distribuciones de clases predichas; la línea discontinua indica el umbral de modo.} +\resultfigure{recovery_metrics.png}{Comparación cuantitativa de las configuraciones de recuperación.} + +\begin{enumerate}[resume] + \item ¿Qué configuraciones recuperan el mayor número de clases? ¿Un número + alto de modos implica necesariamente una distribución equilibrada? Utilice + la entropía como evidencia. +\end{enumerate} +\answer{$\lambda_{\mathrm{div}}=0.1$, $0.5$ y $1.0$ recuperan 2/10 modos cada uno +(frente a 1/10 en "Collapsed start" y en $\lambda_{\mathrm{div}}=0$), pero un número +más alto de modos no implica una distribución equilibrada: incluso con 2 modos, la +entropía normalizada máxima observada es apenas 0.058 ($\lambda_{\mathrm{div}}=0.1$), +muy lejos de 1.0 (uniforme). En \texttt{class\_distributions.png} se ve que la clase +dominante ("8") sigue concentrando más del 95\% de la masa en las tres configuraciones +con 2 modos, y la segunda "moda" detectada corresponde al dígito "2" --- ni siquiera a +las clases objetivo (1 o 7) --- y apenas supera el umbral del 1\%. El conteo de modos +por sí solo sugiere una mejora que la entropía matiza fuertemente: la distribución +sigue siendo extremadamente desequilibrada en las cuatro configuraciones.} + +\begin{enumerate}[resume] + \item Compare la confianza del clasificador. Identifique cualquier compromiso + aparente entre diversidad y calidad. +\end{enumerate} +\answer{La confianza del clasificador baja de forma monótona al subir +$\lambda_{\mathrm{div}}$: 0.981 (colapsado) $\to$ 0.954 ($\lambda=0$) $\to$ 0.933 +($\lambda=0.1$) $\to$ 0.925 ($\lambda=0.5$) $\to$ 0.909 ($\lambda=1.0$). A primera +vista esto parece el compromiso esperado "más diversidad, menos confianza/calidad". +Sin embargo, dado que ninguna configuración produce imágenes reconocibles como +dígitos (Pregunta 2), esta caída no debe interpretarse como una pérdida real de +fidelidad visual respecto a un buen generador: es simplemente la reacción del +clasificador a texturas de ruido ligeramente distintas entre configuraciones, no un +verdadero compromiso diversidad-calidad sobre dígitos válidos.} + +\begin{enumerate}[resume] + \item Compare la diversidad de características con la diversidad dentro de + cada clase. ¿Qué configuraciones mejoran ambas medidas y cuáles mejoran + principalmente una? +\end{enumerate} +\answer{Ambas métricas crecen de forma monótona con $\lambda_{\mathrm{div}}$: +diversidad de características 16.117 $\to$ 16.436 $\to$ 16.687 $\to$ 17.057 $\to$ +17.288, y diversidad intra-clase 11.458 $\to$ 11.539 $\to$ 11.854 $\to$ 12.603 $\to$ +13.533 (de "Collapsed start" a $\lambda_{\mathrm{div}}=1.0$). No hay una configuración +que mejore una medida sin la otra --- $\lambda_{\mathrm{div}}=1.0$ maximiza ambas +simultáneamente --- pero, como se discute en la Pregunta 8, este incremento conjunto +corresponde a generar ruido cada vez más variado, no dígitos genuinamente más +diversos.} + +\begin{enumerate}[resume] + \item Examine las muestras. ¿La mayor diversidad representa variaciones + significativas o solamente ruido, distorsiones o dígitos ambiguos? Describa + dos ejemplos concretos. +\end{enumerate} +\answer{Claramente lo segundo. En \texttt{recovery\_samples.png}, la fila "Collapsed +start" y la fila $\lambda_{\mathrm{div}}=0$ muestran una textura de ruido fino de alta +frecuencia, prácticamente indistinguible entre columnas (ejemplo 1: cualquiera de las +primeras columnas de esas dos filas). En las filas $\lambda_{\mathrm{div}}=0.5$ y +$\lambda_{\mathrm{div}}=1.0$ aparecen algunas manchas de menor frecuencia con un lazo +curvo central, un poco más "gruesas" y menos granuladas que el ruido base (ejemplo 2: +varias columnas de la fila $\lambda_{\mathrm{div}}=1.0$ muestran una forma circular +difusa parecida a un garabato), pero ninguna de estas formas constituye un dígito +reconocible; se trata de ruido de baja frecuencia en vez de ruido de alta frecuencia, +no una diversidad semántica real entre dígitos.} + +\section{Comportamiento durante el entrenamiento} + +\resultfigure{recovery_training.png}{Pérdidas del generador y discriminador durante la recuperación.} + +\begin{enumerate}[resume] + \item ¿Por qué las pérdidas totales del generador para distintos valores de + $\lambda_{\mathrm{div}}$ no deben compararse como si midieran exactamente la + misma función objetivo? +\end{enumerate} +\answer{Porque $\mathcal{L}_G=\mathcal{L}_{\mathrm{adv}}+\lambda_{\mathrm{div}} +\mathcal{L}_{\mathrm{div}}$ combina dos términos con escalas y objetivos distintos, +ponderados por un $\lambda_{\mathrm{div}}$ diferente en cada configuración. Por +construcción, un $\lambda_{\mathrm{div}}$ mayor añade una contribución adicional del +término de diversidad, de modo que dos configuraciones con distinto +$\lambda_{\mathrm{div}}$ no están minimizando la misma función. Comparar sus valores +totales sin separar los componentes adversarial y de diversidad --tal como se ve en +\texttt{recovery\_training.png}, donde $\lambda_{\mathrm{div}}=1.0$ muestra +sistemáticamente el objetivo total más alto-- puede sugerir falsamente que ese modelo +"entrena peor", cuando en realidad solo está pagando un término adicional que los +demás no tienen en la misma magnitud.} + +\begin{enumerate}[resume] + \item ¿Las curvas de pérdida demuestran por sí solas que se resolvió el + colapso de modos? Justifique utilizando los demás resultados. +\end{enumerate} +\answer{No. Las curvas muestran que la pérdida del discriminador se mantiene +extremadamente baja (del orden de $10^{-5}$) durante toda la recuperación en las +cuatro configuraciones, y que la pérdida del generador tiende a subir con las épocas +--comportamiento consistente con un discriminador que domina por completo y un +generador que no recibe gradiente útil. Esto concuerda con la evidencia visual (las +salidas siguen siendo ruido, Pregunta 8) y con las métricas de cobertura (máximo 2/10 +modos, Pregunta 5). Si solo se miraran las curvas de pérdida, sin las imágenes +generadas ni las métricas de cobertura, se podría malinterpretar la caída suave y +monótona de la pérdida del discriminador como "entrenamiento estable", cuando en +realidad refleja que el generador quedó atrapado en un mínimo degenerado desde el +preentrenamiento inicial y nunca se recuperó.} + +\section{Decisión y limitaciones} + +\begin{enumerate}[resume] + \item Seleccione un valor de $\lambda_{\mathrm{div}}$. Defienda la elección + con al menos dos resultados cuantitativos y dos observaciones visuales. +\end{enumerate} +\answer{Se recomienda $\lambda_{\mathrm{div}}=0.1$ dentro de las cuatro +configuraciones evaluadas, con la salvedad explícita de que ninguna resolvió el +colapso de modos de forma satisfactoria (ver limitaciones más abajo). Evidencia +cuantitativa: (1) $\lambda_{\mathrm{div}}=0.1$ logra la entropía normalizada más alta +de las cuatro configuraciones recuperadas (0.058, frente a 0.021 en $\lambda=0$, 0.053 +en $\lambda=0.5$ y 0.047 en $\lambda=1.0$); (2) mantiene la segunda confianza de +clasificador más alta entre las configuraciones con diversidad activa (0.933, solo por +detrás de $\lambda=0$ con 0.954, y por encima de 0.925 y 0.909 de $\lambda=0.5/1.0$). +Evidencia visual: (3) en \texttt{recovery\_samples.png}, la fila $\lambda=0.1$ +conserva una textura similar a la del punto de partida colapsado, sin las manchas de +baja frecuencia más pronunciadas visibles en las filas $\lambda=0.5$ y $\lambda=1.0$; +(4) alcanza el mismo conteo de modos (2/10) que $\lambda=0.5$ y $\lambda=1.0$, por lo +que no hay evidencia de que forzar más diversidad aporte cobertura adicional de +clases, solo más textura de ruido.} + +\begin{enumerate}[resume] + \item Si la fidelidad de las imágenes fuera más importante que la cobertura + de clases, ¿cambiaría su elección? Justifique. +\end{enumerate} +\answer{Sí, cambiaría a $\lambda_{\mathrm{div}}=0$, que conserva la mayor confianza +del clasificador (0.954) y la menor diversidad de características añadida respecto al +punto de partida. En este experimento ningún valor de $\lambda_{\mathrm{div}}>0$ logra +fidelidad visual aceptable (todas las salidas siguen siendo ruido no estructurado), y +el único "beneficio" medible de subirlo es una cobertura de clases apenas mayor (2 vs. +1 modos) que ni siquiera corresponde a los dígitos objetivo (1 y 7). Si la prioridad +fuera evitar cualquier degradación adicional mientras se corrige el problema real (la +divergencia del entrenamiento adversarial), $\lambda_{\mathrm{div}}=0$ sería el punto +de partida más conservador para reentrenar con otros ajustes.} + +\begin{enumerate}[resume] + \item Indique una limitación de utilizar un clasificador de MNIST para medir + la cobertura de la GAN y una limitación del diseño experimental. +\end{enumerate} +\answer{\emph{Clasificador:} se entrenó únicamente con dígitos reales de MNIST y nunca +vio ejemplos fuera de esa distribución; frente a entradas de ruido no estructurado +(como las de este experimento) puede emitir predicciones con alta confianza (hasta +0.981) que no reflejan ninguna semántica real de dígito, por lo que las métricas de +"modos" y "entropía" derivadas de sus predicciones pueden ser completamente engañosas +cuando el generador no produce imágenes válidas, como ocurrió aquí. \emph{Diseño +experimental:} las cuatro configuraciones de recuperación parten todas del mismo punto +de control ya deteriorado (\texttt{mass on [1,7]=0.000}, discriminador saturado desde +la época 5 de 16 del preentrenamiento) y solo se entrenan 5 épocas adicionales; este +diseño no permite distinguir si $\lambda_{\mathrm{div}}$ es insuficiente o si el punto +de partida está tan degradado que ningún valor de $\lambda_{\mathrm{div}}$ en ese rango +podría recuperarlo en tan pocas épocas.} + +\begin{enumerate}[resume] + \item Proponga un experimento posterior que fortalezca o cuestione su + conclusión. Indique la variable que modificaría y la evidencia que recopilaría. +\end{enumerate} +\answer{Se propone repetir la fase de preentrenamiento con técnicas de estabilización +(por ejemplo, suavizado de etiquetas para el discriminador, penalización de gradiente, +o una tasa de aprendizaje/capacidad relativa menor para el discriminador) para evitar +que este domine desde la época 5, verificando mediante la pérdida del discriminador +(que debería mantenerse por encima de un piso razonable, no en 0.000) y mediante +inspección visual de \texttt{collapsed\_samples.png} que el punto de control de +partida realmente produzca dígitos reconocibles concentrados en las clases 1 y 7 antes +de aplicar el experimento de recuperación con $\lambda_{\mathrm{div}}$. Si, una vez +logrado un colapso "limpio" y visualmente legible, $\lambda_{\mathrm{div}}=0.1$ sigue +mostrando la mejor entropía sin sacrificar tanta confianza como valores mayores, esto +confirmaría la conclusión actual; si en cambio valores más altos de +$\lambda_{\mathrm{div}}$ logran recuperar clases adicionales reconocibles una vez +resuelto el problema de fondo, la conclusión debería revisarse.} + +\section*{Recomendación final} + +Valor recomendado: $\lambda_{\mathrm{div}}=0.1$ + +Conclusión en una oración: +\answer{Dentro de las cuatro configuraciones evaluadas, $\lambda_{\mathrm{div}}=0.1$ +ofrece el mejor equilibrio relativo entre cobertura de clases (mayor entropía) y +confianza del clasificador, pero ninguna resolvió el colapso de modos real, ya que el +generador quedó atrapado en un régimen de ruido no estructurado desde el +preentrenamiento inicial (discriminador saturado), por lo que se recomienda corregir +ese problema de entrenamiento antes de repetir la comparación de +$\lambda_{\mathrm{div}}$.} + +\end{document} diff --git a/Lab4/Instrucciones_Entrega_Laboratorio_GAN.pdf b/Lab4/Instrucciones_Entrega_Laboratorio_GAN.pdf new file mode 100755 index 0000000000000000000000000000000000000000..fda7624d30db48f574cfd9d4e44450738de17868 GIT binary patch literal 159928 zcma%iLzFNK4BYZt+qP}nwr$(CZQHhO+qP}*_HSR?OE1kSc{wLDNhT!n!lE<`v}}+h z^UEXakSzH0_;!YtklfsmbkZiaX3pmL49pxH`2Wiw=|nB8olP9^=|rs!oK1vHjO>g} zAbEKqotzy_3~V6XH(S)CoVHlud(YJF#b?yPAp+}8k2_^ab66#i5?r3o#DU@U#&qab!>wLVwZU`Y?1(3TvQGJfSo@ScP=rEuRMG;dM_D@;!nF$pn zgR)EUjRs_JyrK2le)7jE6Dv`EEOU-6)SX4Vk=ke z>hLrf<1mSuYyQh8Gia`F>kF9@IN)L!_gdEOs9`3T$XI}O6CKDjC5|ZHar`L>@`{u< z_W*D*V77-TGcMP$0&BSjvp7?>6M3s*hVm$Cwhz=~cHNJ?N=f@-x>Y;P)Lrd%^-MwP z;mtJ33NN)~gkw}Zl`sHGQ%D@_bdgri(42V~9y=9qN4#HNGeJY2q;~#<+OcqGu75c7 z$1q~@*WG6#qLdETFGY(fr;G>YzHTM7-luC5x?dobT=xZ8z+3^mJB6TNTt-Pq)SzLm zJ0_h#d^S%E&J!~Li`ledGA?ky4~IRJwctX|6WbWi8A14M6Me@a<7JV;y)HY1nH)!S zB?Q9++u$3ONgTy}M-_nm%X24T#&wXc1f?%24$n?u$e;;LFI7O+y=BfL2TR=zXcK0E 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