+A ``quiz'' is a pair composed of a prompt and a solution, both being
+sequence of tokens.
+
+We differentiate \textbf{world quizzes} that follow pre-defined and
+fixed regularities, and mimic the world's physical and environmental
+patterns that an organism has to grasp to survive, and \textbf{culture
+ quizzes} that are generated by the GPTs, and mimic the knowledge one
+has to master to perform socially.
+
+
+We train five GPTs on a a very large set of ``world quizzes''
+generated randomly. These models are trained to generate both the
+solution given the prompt, and the prompt given the solution.
+
+This is achieved by using for training both ``forward sequences'',
+composed of a token \texttt{[fwd]}, followed by the prompt's tokens,
+followed by another token \texttt{[fwd]}, followed by the solution's
+tokens, or ``backward sequences'' composed of a token \texttt{[bck]},
+followed by the solution's tokens, followed by another token
+\texttt{[bck]}, followed by the prompt's tokens,
+
+\subsection{Generating Culture Quizzes}
+
+When their accuracy get above $95\%$ we generate new quizzes as follows:
+%
+\begin{enumerate}
+
+\item generate a solution (without conditioning) at temperature $T=2$,
+ then generate a prompt for that solution at temperature $T=1/2$, and
+ then generate a solution for that prompt at temperature $T=1/2$.
+
+\item generate one solution for that prompt with each of the $5$ GPTs
+ at temperature $T=1$, if $4$ of them generate the correct solution,
+ validate that quiz and include it in the training data.
+
+\end{enumerate}
+
+This criterion assures that the new quizzes are both solvable and
+sophisticated, and incrementally complexify the culture. Imposing both
+direction prevents the generation of quizzes which are not trivial
+only because the prompt has been randomly degraded.
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\pagebreak
+
+\section{Grid Quizzes}
+
+\subsection{World Quizzes}
+
+We define several types of quizzes and implement algorithmic
+procedures to generate randomly as many examples from each that we
+need.
+
+In these quizzes, the prompt is made of three grids $A, f(A), B$ and
+the solution is a single grid $f(B)$.
+
+\subsubsection{Half Fill}
+
+\pic{pics/task_color_grow.png}{``half fill''}
+
+The first grid contains three rectangles, each with a vertical or an
+horizontal line of another color in its middle. The second grid is
+identical with one of the rectangle having one half filled. The third
+grid contains three rectangles of identical colors as the firs grid,
+of different size and locations. The solution is obtained by filling
+similarly one of the half of a rectangle of the third image.
+
+\subsubsection{Detect}
+
+\pic{pics/task_detect.png}{``detect''}
+
+The first grid contains three rectangles, the second has two pixels of
+same colors located in the top-left corner of two of them. The
+solution is obtained by marking in the fourth image the top-left
+corners of the rectangles of same colors in the third.
+
+\subsubsection{Frame}
+
+\pic{pics/task_frame.png}{``frame''}
+
+The first grid contains three rectangles, and the second is identical
+except that one rectangle has been replaced by its frame. The same
+should be done to the similarly colored rectangles of the third grid
+to obtain the solution.
+
+\subsubsection{Grow}
+
+\pic{pics/task_grow.png}{``grow''}
+
+The first grid contains three rectangles, one of them getting one
+pixel thicker or thinner in the second. The same should be done to the
+similarly colored rectangles of the third grid to get the solution.
+
+\subsubsection{Replace color}
+
+\pic{pics/task_replace_color.png}{``replace color''}
+
+The first grid contains three rectangles, the second is obtained by
+changing one of the colors. The same should be done to the third grid
+to obtain the solution.
+
+\subsubsection{Translate}
+
+\pic{pics/task_translate.png}{``translate''}
+
+The first grid contains three rectangles. The second is obtained by
+displacing one of them by one pixel in both direction. The solution is
+obtained by applying the same motion to the similarly colored
+rectangle in the third grid.
+
+%% \subsubsection{Bounce}
+
+%% \pic{pics/task_bounce.png}{``bounce''}
+
+%% The solution should join the two pixels of same color, with a path of
+%% another color, starting in the direction indicated by a pixel of that
+%% color, and changing direction only when colliding with a pixel of a
+%% third color or one of the lattice border.
+
+%% \subsubsection{count}
+
+%% \pic{pics/task_count.png}{``count''}
+
+%% \subsubsection{scale}
+
+%% \pic{pics/task_scale.png}{``scale''}
+
+%% \subsubsection{trajectory}
+
+%% \pic{pics/task_trajectory.png}{``trajectory''}
+
+\subsection{Culture Quizzes}
+
+We list here some generated quizzes that exhibit features that were not present in the ``world quizzes'' used for training.
+
+\bigskip
+
+\begin{example}
+
+\pic{pics/culture_c_quiz_0110_N4_validated/quiz_63.png}{0110/63}
+
+\pic{pics/culture_c_quiz_0115_N4_validated/quiz_37.png}{0115/37}
+
+The quizzes ``frame'' and ``half fill'' have been combined in a single
+quiz.
+
+\end{example}
+
+\separator
+
+\begin{example}
+
+\pic{pics/culture_c_quiz_0120_N4_validated/quiz_05.png}{0110/05}
+
+The ``frame'' quiz has been generalized to non-rectangular shapes.
+
+\end{example}
+
+\separator
+
+\begin{example}
+
+\pic{pics/culture_c_quiz_0078_N4_validated/quiz_01.png}{0078/01}
+
+\pic{pics/culture_c_quiz_0078_N4_validated/quiz_02.png}{0078/02}
+
+More rectangles were added as distractors.
projects / culture.git / blobdiff