of the neuromorphic simulation code.
Application on the MNIST problem}
-\author{Rapha\"el Couturier, {\bf Michel Salomon}}
+\author{Rapha\"el Couturier, Michel Salomon}
\institute[FEMTO-ST Institute]{\textit{FEMTO-ST - DISC Department - AND Team}}
\begin{itemize}
\item Study the concept of Reservoir Computing
\item Design a faster simulation code
- \item Apply it to a new problem
+ \item Apply it to new problems
\end{itemize}
\end{femtoBlock}
\end{frame}
\centering
\includegraphics[width=7.5cm]{ntc.png}
\begin{itemize}
- \item $\delta_t \rightarrow \mbox{temporal spacing}; \tau_D \rightarrow \mbox{time delay}$
+ \item $\delta \tau \rightarrow \mbox{temporal spacing}; \tau_D \rightarrow \mbox{time delay}$
\item $f(x) \rightarrow \mbox{nonlinear transformation}; h(t) \rightarrow \mbox{impulse response}$
\end{itemize}
\end{femtoBlock}
% Grandes lignes a partir du pdf de Laurent
\begin{femtoBlock}
{Main lines\\}
- \begin{itemize}
- \item Numerical integration to compute the nonlinear transient
- response (runge kuta in C)
- \item[] $\Rightarrow$ computation of matrices $A$ and $B$
- \item Computation of the Readout
- \item Test of the solution (cross validation)
- \end{itemize}
+ \begin{enumerate}
+ \item Pre-processing
+ \begin{itemize}
+ \item Input data formating (1D~vector; sampling period $\rightarrow \delta \tau$)
+ \item $W^I$ initialization (randomly; normalization)
+ \end{itemize}
+ \item Concatenation of 1D~vectors $\rightarrow$ batch processing
+ \item Nonlinear transient computation
+ \begin{itemize}
+ \item Numerical integration using a Runge-Kutta C routine
+ \item Computation of matrices $A$ and $B$
+ \end{itemize}
+ \item Training of the Read-out $\rightarrow$ More-Penrose matrix inversion
+ \item Testing of the solution (cross-validation)
+ \end{enumerate}
\end{femtoBlock}
+ \smallskip
% Inconvenient de ce code => temps de calcul
\begin{femtoBlock}
{Computation time\\}
- 12 min for 500 words recognition (2013)
+ \vspace{0.125cm}
+ \centering
+ 12 min for 306~``neurons'' on a quad-core i7 1,8~GHz (2013)
\end{femtoBlock}
\end{frame}
\section{Parallelization and optimization}
\begin{frame}{Parallelization Scheme} % Slide 8
- \begin{itemize}
- \item Rewrite the code in C++
- \item Parallelization with MPI (Message Passing Interface)
- \item Computation of data response (sound, image) is independent so
- it can be parallelized (computation of matrices A and B)
- \item Different regression tests are also independent
- \item Test of new idea? First test with matlab and then adapt to C++
- with MPI
- \end{itemize}
- % 1 - Comment le paralleliser
- % 2 - Langage et bibliotheque
-\end{frame}
-
-\begin{frame}{Finding the Optimal Parameters} % Slide 9
- % 1 - Quels parametres et pourquoi ?
\begin{femtoBlock}
- {What parameters can be optimized?\\}
- Currently:
+ {Guidelines\\}
\begin{itemize}
- \item Pitch
- \item Delta
- \item Beta
- \item Phi
- \item Lambda
+ \item Reservoir response is independent, whatever the data \\
+ $\rightarrow$ computation of matrices A and B can be parallelized
+ \item Different regression tests are also independent
\end{itemize}
- Next:
+ \end{femtoBlock}
+ \smallskip
+ \begin{femtoBlock}
+ {In practice\\}
\begin{itemize}
- \item Number of nodes that significantly improve the solution (threshold)
- \item Input filter (convolutional filter for images)
- \item Potentially any parameters
+ \item Simulation code rewritten in C++
+ \item {\bf M}essage~{\bf P}assing~{\bf I}nterface~for~InterProcess~Communication
\end{itemize}
-
+ \end{femtoBlock}
+ \smallskip
+ \begin{femtoBlock}
+ {Test of new idea?\\}
+ \vspace{0.25cm}
+ \centering
+ First test with Matlab and then adapt to C++ with MPI
\end{femtoBlock}
\end{frame}
-\begin{frame}{Finding the Optimal Parameters} % Slide 10
- % 2 - Optimisation par recuit simule
+\begin{frame}{Finding Optimal Parameters} % Slide 9
+ % 1 - Quels parametres et pourquoi ?
\begin{femtoBlock}
- {Optimization heuristics\\}
+ {What parameters can be optimized?\\}
\begin{itemize}
- \item Now: Simulated annealing
- \item[] $\Rightarrow$ probabilistic technique for approximating the global optimum of a given function.
- \item Next: maybe other heuristics
+ \item Currently
+ \begin{itemize}
+ \item Pitch of the Read-Out
+ \item Amplitude parameters $\rightarrow \delta; \beta; \phi_0$
+ \item Regression parameter $\rightarrow \lambda$
+ \end{itemize}
+ \item Next
+ \begin{itemize}
+ \item Number of nodes significantly improving the solution (threshold)
+ \item Input data filter (convolutional filter for images)
+ \end{itemize}
\end{itemize}
+ \centering
+ Potentially any parameter can be optimized
\end{femtoBlock}
+ \smallskip
\begin{femtoBlock}
- {Similar results with the SDR problem\\}
+ {Optimization heuristics\\}
+ \begin{itemize}
+ \item Currently $\rightarrow$ simulated annealing \\
+ {\small (probabilistic global search controlled by a cooling schedule)}
+ \item Next $\rightarrow$ other metaheuristics like evolutionay algorithms
+ \end{itemize}
\end{femtoBlock}
\end{frame}
-\begin{frame}{Performances} % Slide 11
- % 1 - Taux d'erreur en terme de classification
- % 2 - Gain en temps d'execution / speedup curve
+\begin{frame}{Performances of the parallel code} % Slide 10
+ \begin{femtoBlock}
+ {Speech recognition problem\\}
+ \begin{itemize}
+ \item Same WER $\rightarrow$ similar classification accuracy
+ \item Reduced computation time $\rightarrow$ speedup...
+ \end{itemize}
+ \centering
+ \vspace{0.25cm}
+ We can study problems with huge Matlab computation time
+ \end{femtoBlock}
\end{frame}
\section{Performances on the MNIST problem}
