From 11f14a4763533dbc24b0e98d115071036025d4f6 Mon Sep 17 00:00:00 2001 From: ericmarin Date: Mon, 22 Jun 2026 00:43:45 +0200 Subject: refinement --- chapters/background/01-neural-networks.tex | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) (limited to 'chapters/background/01-neural-networks.tex') diff --git a/chapters/background/01-neural-networks.tex b/chapters/background/01-neural-networks.tex index a1ecad2..dc3e2d4 100644 --- a/chapters/background/01-neural-networks.tex +++ b/chapters/background/01-neural-networks.tex @@ -2,8 +2,8 @@ \label{sec:neural-networks} A neural network is a computational model inspired by biological neural networks. It consists of -connected nodes called neuron, introduced in its early form by Rosenblatt~\cite{rosenblatt1958perceptron}. -\textit{Multi-Layer Perceptrons} is an architecture composed of sequential layers, trained using +connected nodes called neurons, introduced in its early form by Rosenblatt~\cite{rosenblatt1958perceptron}. +The \textit{Multi-Layer Perceptrons} is an architecture composed of sequential layers, trained using backpropagation as popularized by Rumelhart et al.~\cite{rumelhart1986learning}. \subsection{Neuron} @@ -51,7 +51,7 @@ The output $y$ is defined as: \draw[->] (act) -- (y); \end{tikzpicture} - \caption{Mathematical model of an artificial neuron.} + \caption{Graphical representation of a neuron.} \label{fig:single-neuron} \end{figure} @@ -101,14 +101,15 @@ the outputs. \node[above] at (7, 1.2) {Output Layer}; \end{tikzpicture} - \caption{Architecture of a Multi-Layer Perceptron (MLP) with one hidden layer.} + \caption{Architecture of an MLP with one hidden layer.} \label{fig:mlp} \end{figure} -One of the most common activation function is the ReLU, defined as: +One of the most common activation functions is the ReLU, defined as: \begin{equation} \text{ReLU}(z) = \max(0, z) \end{equation} +The framework focuses on MLP with ReLU activation functions. \subsection{Neural Network Verification} The verification problem of a neural network $F: \mathbb{R}^n \to \mathbb{R}^m$ with input constraint -- cgit v1.2.3