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 formatting (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
+ \begin{femtoBlock}
+ {Guidelines\\}
+ \begin{itemize}
+ \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}
+ \end{femtoBlock}
\end{frame}
-\begin{frame}{Finding the Optimal Parameters} % Slide 9
- % 1 - Quels parametres et pourquoi ?
+\begin{frame}{Parallelization Scheme} % Slide 9
\begin{femtoBlock}
- {What parameters can be optimized?\\}
- Currently:
+ {In practice\\}
\begin{itemize}
- \item Pitch
- \item Delta
- \item Beta
- \item Phi
- \item Lambda
+ \item Simulation code rewritten in C++
+ \item Eigen C++ library for linear algebra operations
+ \item InterProcess~Communication \\
+ $\rightarrow$ {\bf M}essage~{\bf P}assing~{\bf I}nterface
\end{itemize}
- Next:
+ \end{femtoBlock}
+ \smallskip
+ \begin{femtoBlock}
+ {Performance on speech recognition problem\\}
\begin{itemize}
- \item Number of nodes that significantly improve the solution (threshold)
- \item Input filter (convolutional filter for images)
- \item Potentially any parameters
+ \item Same WER $\rightarrow$ similar classification accuracy
+ \item Reduced computation time
\end{itemize}
-
+ \centering
+ \vspace{0.125cm}
+ {\bf We can study problems with huge Matlab computation time}
+ \end{femtoBlock}
+ \medskip
+ \begin{femtoBlock}
+ {Testing a 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 10
+ % 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 (convolution 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 evolutionary 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
-\end{frame}
-
\section{Performances on the MNIST problem}
-\begin{frame}{Application on the MNIST problem} % Slide 12
+\begin{frame}{Application on the MNIST problem} % Slide 11
+ \begin{femtoBlock}
+ {Task of handwritten digits recognition\\}
+ \centering
+ \vspace{0.125cm}
+ National Institute of Standards and Technology database
+ \begin{itemize}
+ \item Training dataset $\rightarrow$ american census bureau employees
+ \item Test dataset $\rightarrow$ american high school students
+ \end{itemize}
+ \end{femtoBlock}
+ \smallskip
+ \begin{femtoBlock}
+ {Mixed-NIST database is widely used in machine learning\\}
+ \centering
+ \vspace{0.125cm}
+ Mixing of both datasets and improved images
+ \begin{columns}
+ \begin{column}{7.5cm}
+ \begin{itemize}
+ \item Datasets
+ \begin{itemize}
+ \item Training $\rightarrow$ 60,000 samples
+ \item Test $\rightarrow$ 10,000 samples
+ \end{itemize}
+ \item Grayscale Images
+ \begin{itemize}
+ \item Normalized to fit into a $20\times20$ pixel bounding box
+ \item Centered and anti-aliased
+ \end{itemize}
+ \end{itemize}
+ \end{column}
+ \begin{column}{3cm}
+ \centering
+ \includegraphics[width=3cm]{mnist.png}
+ \end{column}
+ \end{columns}
+ \end{femtoBlock}
% 1 - Decrire ce qu'est le MNIST
% 2 - Setup de notre reservoir
\end{frame}
-\begin{frame}{Comparison with other approaches} % Slide 13
+\begin{frame}{Performances of the parallel code} % Slide 12
+ % To be completed
+ 10000 images:\\
+ 1000 reservoirs of 2 neurons, error : 3.85\%\\
+ 1 reservoir of 2000 neurons, error : 7.14\%
+ \includegraphics[width=7.5cm]{speedup.pdf}
+\end{frame}
+
+\begin{frame}{Exploring ways to improve the results} % Slide 13
+ % Tableau recapitulant les performances
+\end{frame}
+
+\begin{frame}{Comparison with other approaches} % Slide 14
% 1 - Convolutional Neural Networks
% 2 - Reservoir en pipeline (papier de 2015)
\end{frame}
-\begin{frame}{Comparison with other approaches} % Slide 14
+\begin{frame}{Comparison with other approaches} % Slide 15
% Tableau recapitulant les performances
\end{frame}
\section{Conclusion and perspectives}
-\begin{frame}{Conclusion and perspectives} % Slide 15
-
-
- Many perspectives (we are just beginning)
- Improvement of the code\\
- Test of many ideas : number of comities\\
- One reservoir to learn and another one to learn error and correct
- them\\
- Test other large problems in simulation before in real\\
- => Try to test many configuration and to find optimal parameters
-
+\begin{frame}{Conclusion and perspectives} % Slide 16
+ \begin{femtoBlock}
+ {Results\\}
+ \begin{itemize}
+ \item A parallel code allowing fast simulations
+ \item An evaluation on the MNIST problem
+ \end{itemize}
+ \end{femtoBlock}
+ \begin{femtoBlock}
+ {Future works\\}
+ \begin{itemize}
+ \item Further code improvement
+ \item Use of several reservoirs
+ \begin{itemize}
+ \item Committees
+ \item Correct errors of a reservoir by another one
+ \end{itemize}
+ \end{itemize}
+ \end{femtoBlock}
+ %Many perspectives (we are just beginning)
+ %Improvement of the code\\
+ %Test of many ideas : number of comities\\
+ %One reservoir to learn and another one to learn error and correct
+ %them\\
+ %Test other large problems in simulation before in real\\
+ %=> Try to test many configuration and to find optimal parameters
\end{frame}
\begin{frame}{Thank you for your attention}
