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Alex
2025-09-10 10:24:33 +02:00
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thesis/main.tex
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@@ -27,10 +27,10 @@
\usepackage{hyperref} \usepackage{hyperref}
\hypersetup{ \hypersetup{
colorlinks = true, % Colours links instead of ugly boxes colorlinks = true,
urlcolor = blue, % Colour for external hyperlinks linkcolor = black,
linkcolor = blue, % Colour of internal links citecolor = black,
citecolor = red % Colour of citations urlcolor = black
} }
% Document % Document
thesis/sections/background.tex
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@@ -582,7 +582,7 @@ such as ovulatory trends spanning multiple days or cycles.
Convolutional neural networks (CNNs) can also be applied to time-series by using 1D convolutions across the temporal dimension. Convolutional neural networks (CNNs) can also be applied to time-series by using 1D convolutions across the temporal dimension.
In this setting, each convolutional filter acts as a learnable temporal pattern detector (e.g. for local peaks, slopes, or motifs). In this setting, each convolutional filter acts as a learnable temporal pattern detector (e.g. for local peaks, slopes, or motifs).
Convolutions exploit the local correlation structure of time series: adjacent measurements are often highly related. Convolutions exploit the local correlation structure of time series: adjacent measurements are often highly related.
As~\cite{lecun_convolutional_1998} note, “time-series have a strong 1D structure – variables that are temporally nearby are highly correlated. As~\citeauthor{lecun_convolutional_1998} note, “time-series have a strong 1D structure – variables that are temporally nearby are highly correlated.
Local correlations are the reason for the well-known advantages of extracting and combining local features”~\cite{lecun_convolutional_1998}. Local correlations are the reason for the well-known advantages of extracting and combining local features”~\cite{lecun_convolutional_1998}.
Convolutional layers enforce locality by restricting each neuron’s receptive field to a contiguous segment of time. Convolutional layers enforce locality by restricting each neuron’s receptive field to a contiguous segment of time.
By adjusting the convolutional stride and using pooling, By adjusting the convolutional stride and using pooling,
@@ -590,7 +590,7 @@ CNNs can downsample the sequence length (reducing resolution) while preserving s
This reduces the input dimensionality for subsequent layers and can speed up training. This reduces the input dimensionality for subsequent layers and can speed up training.
In practice, convolutional architectures have achieved strong performance on sequential tasks. In practice, convolutional architectures have achieved strong performance on sequential tasks.
For example,~\cite{lecun_convolutional_1998} show that a simple Temporal Convolutional Network often outperforms canonical For example,~\citeauthor{lecun_convolutional_1998} showed that a simple Temporal Convolutional Network often outperforms canonical
recurrent models (like LSTMs) across diverse sequence modeling benchmarks. recurrent models (like LSTMs) across diverse sequence modeling benchmarks.
Their experiments suggest that CNNs are “a natural starting point for sequence modeling,” Their experiments suggest that CNNs are “a natural starting point for sequence modeling,”
especially when temporal features are local or multi-scale. especially when temporal features are local or multi-scale.