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\begin{document}
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\clearpage  % (title) =========================================
\color{blue}
\begin{center}
{\bf How can we design a more intelligent path-planning?}
\hspace*{,5in}\\
\color{black}
\bigskip
\hspace*{1in}\\
\begin{Large}
Akira Imada  \\
\bigskip
Brest State Technical University (Belarus)
\end{Large}
\end{center}


\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Is AI really intelligent?}\\
\bigskip
\color{black}
{\Large
\bigskip
They might be more \color{red} efficient \color{black}and/or \color{red}effective \color{black} than human\\ but still \color{red}less intelligent\color{black}, at least so far.}
\end{center}



\clearpage  % =========================================
\vspace*{.02in}
\begin{center} 
\color{blue}
{\bf What is intelligence?}\\
\color{black}
{\Large 
$\Downarrow$ \\
Intelligence should be 
\color{red}
spontaneous\color{black}, \color{red}flexible\color{black}, and/or \color{red} unpredictable\color{black},\\ \color{black}more or less.}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf ``I beg your pardon?''}\\
\hspace*{1in}\\
\color{black}
{\Large 
Intelligent people try a \color{red}different 
\color{black}explanation for an easier understanding\\
\bigskip
while \\
others just repeat the \color{red}same \color{black}expression, maybe with a louder voice.}
\end{center}


\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Let's make an agent to be spontaneous!}\\
\bigskip
\color{black}
{\Large
\bigskip
Behaviors might \color{red}differ \color{black}even in a \color{red}similar \color{black}situations.}
\end{center}


\clearpage  % =========================================
\vspace*{.01in}
\begin{center} 
\color{blue}
{\bf Goal is
}\\
\bigskip
\color{black}
{\Large
\bigskip
to make an agent behave \color{red} differently \color{black}even when it encounters \\ the \color{red}same \color{black}situation as before.
}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Path Planning as a benchmark
}\\
\hspace*{1in}\\
\color{black}
{\Large 
An agent plans a shortest path from start to goal.
}
\end{center}


%% one candidate approach is ...
\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Genetic Algorithm (GA)}\\
\bigskip
\color{black}
{\Large
%% $\Downarrow$\\
\bigskip
Agent decides actions following its \color{red} chromosome\\
\color{black}
\bigskip
e.g., with  chromosomes like}\\
\color{black}
{\Large  \color{green}(4 1 1 2 1 3 2 3 3 4 2 1 3 4 3 2 3 3 2 1 1 3 2 1 3 ...)\\
\color{black}indicates the agent a route to be followed.} 
\end{center}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Random walk evolved to be minimized}\\
\end{center}
\begin{figure}[bhtp]
\begin{center}
   \includegraphics[width=5cm,height=6cm]{trace-96-start.eps}
   \includegraphics[width=5cm,height=6cm]{trace-96-end-new.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center}\color{blue}
{\bf Task was easy}\\
%%{\bf Evolution successful}\\
%%Though number of steps grows linearly}\\
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=6cm]{evolution-96-new.eps}
%%\includegraphics[width=6cm,height=6cm]{navi-1-new.eps}
\end{center}
\end{figure}


\clearpage  % =========================================
\begin{center} 
{\Large (An interpretation of GA from robotics point of view)}\\
\color{blue}
{\bf Edelman's Neural Darwinism (1978)}\\
\color{black}
\hspace*{1in}\\
{\Large 
Assume evolution in an agent's brain in advance the action.\\
(e.g. 100 \color{red}random \color{black}chromosomes to be evolved)\\
%% of up, down, right, and left)\\
$\Downarrow$\\
after a convergence\\
$\Downarrow$\\
Agent acts following \color{red}the best \color{black}chromosome.}
\end{center}

\clearpage  % =========================================
\begin{center}\color{blue}
{\bf {\Large Route can be different from run to run, if any.}}
\end{center}
\begin{figure}[bhtp]
\begin{center}
   \includegraphics[width=5cm,height=6cm]{shortest.eps}
   \includegraphics[width=5cm,height=6cm]{shortest-2.eps}
   \includegraphics[width=5cm,height=6cm]{shortest-3.eps}
\end{center}
\end{figure}




%% so far so good but ...
\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf It's not so realistic, however.}\\
\hspace*{1in}\\
\color{black}
{\Large 
No one, these days, believe this really happens. \\
\bigskip
It takes a too long time to be a reality if the task is hard. \\
$\Downarrow$\\
Let's dismiss GA now.}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf What about NN?}\\
\hspace*{1in}\\
\color{black}
{\Large 
With fixed weights\\
$\Downarrow$\\
An identical behavior in an identical situation.\\
\bigskip\bigskip
\color{red}
What if we modify weights during action? \\
\color{black} (Floreano et al. 2000)
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\hspace*{1in}\\
\color{blue}
{\Large
{\bf (1) \\
\bigskip
Recurrent McCullough-Pitts Neurons \\
\bigskip
with Sigmoid}\\
}
\end{center}



\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Learning Rule}\\
\begin{figure}[h]
\begin{center}
\includegraphics[width=8cm,height=4cm]{plasticity-new.eps}
\end{center}
\end{figure}
{\Large
\begin{displaymath}
\color{black}w_{ij}(t+1) = w_{ij}(t) + \color{red}f(x_j(t),y_i(t)) \hspace{.2in} \color{black}(x_j, y_i \in [0,1])
\end{displaymath}
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Optimum configuration of learning rules.}\\
\hspace*{1in}\\
\color{black}
{\Large 
\color{red}
\begin{displaymath}
\eta_{ij} x_i y_j \color{black} \hspace{.2in} \mbox{(Hebb, 1949)}
\end{displaymath}
\color{black}
or
\color{red}
\begin{displaymath}
a_{ij} x_iy_j + b_{ij} x_i + c_{ij} y_j + d  \color{black} \hspace{.2in} \mbox{(Durr et~al. 2008)}
%%% it could be more general like this one
\end{displaymath}
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\Large
{\bf Can agents take a different minimum route \\every time following how it feels?}
}
\bigskip
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=6cm]{recurrent-2.eps}
\end{center}
\end{figure}
\end{center}

\clearpage  % =========================================
\begin{center} 
\color{blue}
{\Large
{\bf (2) \\ Recurrent Spiking Neurons}\\
\bigskip
\color{black}
{\Large 
as a more biologically plausible model.}
}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\Large
{\bf An exploration by Integrate \& Fire Model}
\color{black}
\color{red}
\begin{displaymath}
u_i(t) = u_r +(u_i(t - \delta t) - u_r) \exp (- \delta t/ \tau) + \sum_j w_{ij}f_j (t - \delta t)
\end{displaymath}
}
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=4cm]{path-by-hopfield-no-learning.eps}
\end{center}
\end{figure}
\color{black}
{\Large Can it \color{red}learn \color{black}so that path will finish at the goal with minimum length?}
\end{center}

%% the rearning rule here could be ...
\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Spike timing dependent plasticity (STDP)}\\
\bigskip
\color{black}
{\Large A counterpart of \color{red}Hebb Rule \color{black}of McCullough-Pitts Neurons \\for Spiking Neurons.}
\end{center}



\clearpage  % =========================================
\begin{center} \color{blue}
{\bf What is STDP?}
\bigskip
\color{red}
{\Large
      \begin{eqnarray*}
         W(\Delta t) = \left\{
         \begin{array}{ll}\nonumber
         \hspace{.18in}A_{+} \exp (-\Delta t/\tau_{+})
                          & \hspace{.2in}\mbox{if}\hspace{.2in}\Delta t \ge 0\\
         - A_{-} \exp (-\Delta t/\tau_{-})
                          & \hspace{.2in}\mbox{if}\hspace{.2in}\Delta t < 0\\
         \end{array}
         \right.\\
      \end{eqnarray*}
\color{black} where \hspace{.2in} \color{red} $\Delta t = t_{post} - t_{pre}$\\
\bigskip
\color{black}{\large $W(\Delta t)$}}
\begin{figure}[bhtp]
\begin{center}
   \includegraphics[width=12cm,height=3.5cm]{stdp.eps}
\end{center}
\end{figure}
\end{center}
%% Let me skip details, but we simply adjust this coefficient from conection to connection.

\clearpage  % =========================================
\begin{center} \color{blue}
{\bf Reward-modulated STDP Learning}\\
(Florian 2007)
\bigskip
\color{red}
{\Large
\begin{displaymath}
w_{ij} (t + \delta t) = w_{ij} (t) + \gamma r(t + \delta t) \zeta_{ij}(t)
\end{displaymath}
\color{black}
where
\begin{displaymath}
\zeta_{ij} (t) = P^{+}_{ij} (t)f_i(t) + P^{-}_{ij} (t)f_i(t)
\end{displaymath}
\begin{displaymath}
P^{+}_{ij} (t) = P^{+}_{ij} (t-\delta t) \exp (- \delta t/\tau_{+}) + A_{+}f_j(t)
\end{displaymath}
\begin{displaymath}
P^{-}_{ij} (t) = P^{-}_{ij} (t-\delta t) \exp (- \delta t/\tau_{-}) + A_{-}f_j(t)
\end{displaymath}
}
\end{center}
%% Or, we might employ this very elegant learning rule for spiking neurons called ... proposed by ...

\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Looks like a simple toy problem?}\\
\color{red}
\bigskip
{\Large No!}
\end{center}
%% To confess, we started this project with more challanging benchmark, that is, .... In other words we want to maximize the size of loop. But it's found to be extremely difficult and still inmmune to be solved.


%% instead of minimize the route from start to goal
\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf More challenging benchmark}\\
\color{black}
{\Large 
From one point to the \color{red}same \color{black}point \color{red}maximizing \color{black}its route with a limited fuel.}
\end{center}
\begin{figure}[h]
\begin{center}
\includegraphics[width=10cm,height=5cm]{max-loop-5.eps}
\end{center}
\end{figure}




%% real dogs are still more intelligent than robots
\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Brief Summary}

\bigskip
\begin{figure}[h]
\begin{center}
\rotatebox[origin=c]{270}{
\includegraphics[width=2.5cm,height=5cm]{aibo.eps}}
\end{center}
\end{figure}
\color{black}
{\Large We sometimes need \color{red} spontaneous \color{black} and \color{red} unpredictable \color{black} intelligence rather than \color{red} efficiency \color{black} or \color{red}effectiveness \color{black} like in case of SONY's AIBO}
\end{center}


\clearpage  % =========================================
\begin{center} 
\color{blue}
{\bf Robot dog vs. Real dog}\\
\bigskip
\color{black}
{\Large When will a \color{red}robot \color{black}dog be more intelligent than \color{red}real \color{black}dogs?}\\
\end{center}


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\end{document}

