Regular vs Bayes NN
Comparison between regular neural networks and Bayesian neural networks. The diagram illustrates how Bayesian networks incorporate uncertainty in their predictions by treating weights as probability distributions rather than point values, leading to more robust predictions with uncertainty estimates.
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regular-vs-bayes-nn.tex (62 lines)
\documentclass[tikz]{standalone}
\usetikzlibrary{calc}
\def\layersep{3cm}
\newcommand\nn[1]{
% Input layer
\foreach \y in {1,...,2}
\node[neuron, fill=green!40] (i\y-#1) at (0,\y+1) {$i\y$};
% Hidden layer
\foreach \y in {1,...,4}
\path node[neuron, fill=blue!40] (h\y-#1) at (\layersep,\y) {$h\y$};
% Output node
\node[neuron, fill=red!40] (o-#1) at (2*\layersep,2.5) {$o$};
% Connect every node in the input layer with every node in the hidden layer.
\foreach \source in {1,...,2}
\foreach \dest in {1,...,4}
\path (i\source-#1) edge (h\dest-#1);
% Connect every node in the hidden layer with the output layer
\foreach \source in {1,...,4}
\path (h\source-#1) edge (o-#1);
}
\begin{document}
\begin{tikzpicture}[
scale=1.2,
shorten >=1pt,->,draw=black!70, node distance=\layersep,
neuron/.style={circle,fill=black!25,minimum size=20,inner sep=0},
edge/.style 2 args={pos={(mod(#1+#2,2)+1)*0.33}, font=\tiny},
distro/.style 2 args={
edge={#1}{#2}, node contents={}, minimum size=0.6cm, path picture={\draw[double=orange,white,thick,double distance=1pt,shorten >=0pt] plot[variable=\t,domain=-1:1,samples=51] ({\t},{0.2*exp(-100*(\t-0.05*(#1-1))^2 - 3*\t*#2))});}
},
weight/.style 2 args={
edge={#1}{#2}, node contents={\pgfmathparse{0.35*#1-#2*0.15}\pgfmathprintnumber[fixed]{\pgfmathresult}}, fill=white, inner sep=2pt
}
]
\nn{regular}
\begin{scope}[xshift=8cm]
\nn{bayes}
\end{scope}
% Draw weights for all regular edges.
\foreach \i in {1,...,2}
\foreach \j in {1,...,4}
\path (i\i-regular) -- (h\j-regular) node[weight={\i}{\j}];
\foreach \i in {1,...,4}
\path (h\i-regular) -- (o-regular) node[weight={\i}{1}];
% Draw distros for all Bayesian edges.
\foreach \i in {1,...,2}
\foreach \j in {1,...,4}
\path (i\i-bayes) -- (h\j-bayes) node[distro={\i}{\j}];
\foreach \i in {1,...,4}
\path (h\i-bayes) -- (o-bayes) node[distro={\i}{1}];
\end{tikzpicture}
\end{document}
Typst
regular-vs-bayes-nn.typ (216 lines)
#import "@preview/cetz:0.3.4": canvas, draw
#import "@preview/cetz-plot:0.1.1": plot
#import draw: line, circle, content, group, bezier, translate
#set page(width: auto, height: auto, margin: 8pt)
#canvas({
let layer-sep = 3.5 // Horizontal separation between layers
let node-sep = 1.5 // Vertical separation between nodes
let arrow-style = (mark: (end: "stealth", scale: 0.7), stroke: gray + 0.7pt, fill: gray)
// Helper function to draw a neuron
let neuron(pos, fill: white, label: none, name: none) = {
content(
pos,
if label != none { $#label$ },
frame: "circle",
fill: fill,
stroke: none,
radius: 0.4,
padding: 3pt,
name: name,
)
}
// Helper function to calculate line angle and shift along it
let line-shift(start, end, dist) = {
let dx = end.at(0) - start.at(0)
let dy = end.at(1) - start.at(1)
let len = calc.sqrt(dx * dx + dy * dy)
// Return shift vector components
return (
x: dist * dx / len,
y: dist * dy / len,
)
}
// Helper function to draw a weight label
let weight-label(start, end, ii, jj, offset: 0) = {
let mid-x = (start.at(0) + end.at(0)) / 2
let mid-y = (start.at(1) + end.at(1)) / 2
// Calculate shift along the line
let shift = if offset != 0 {
let s = line-shift(start, end, offset * 0.4)
(s.x, s.y)
} else { (0, 0) }
content(
(mid-x + shift.at(0), mid-y + shift.at(1)),
[#calc.round(0.35 * ii - jj * 0.15, digits: 2)],
frame: "rect",
fill: white,
stroke: none,
padding: 1.5pt,
)
}
// Helper function to draw a Gaussian distribution
let gaussian(start, end, offset: 0, shift: 0) = {
let width = 0.6
let height = 0.25
let x-mid = (start.at(0) + end.at(0)) / 2
let y-mid = (start.at(1) + end.at(1)) / 2
let mu = offset * 0.15
// Calculate shift along the line
let s = if shift != 0 {
line-shift(start, end, shift * 0.4)
} else { (x: 0, y: 0) }
group({
translate((x-mid - width / 2 + s.x, y-mid - height / 2 + s.y))
plot.plot(
size: (width, height),
axis-style: none,
{
plot.add(
style: (stroke: orange + 1pt, fill: orange.lighten(80%)),
domain: (-1, 1),
samples: 50,
x => {
let variance = 0.3 + calc.abs(offset) * 0.1
let peak = 0.8 + calc.rem(calc.abs(offset), 0.4)
peak * calc.exp(-5 * calc.pow(x - mu, 2) / variance)
},
)
},
)
})
}
// Draw regular network
group(
name: "regular",
{
// Input layer
for ii in range(2) {
neuron(
(0, (ii + 1) * node-sep + 1),
fill: rgb("#90EE90"),
label: "ii" + str(ii + 1),
name: "ii" + str(ii + 1),
)
}
// Hidden layer
for ii in range(4) {
neuron(
(layer-sep, (ii + 1) * node-sep),
fill: rgb("#ADD8E6"),
label: "h" + str(ii + 1),
name: "h" + str(ii + 1),
)
}
// Output layer
neuron(
(2 * layer-sep, 2.5 * node-sep),
fill: rgb("#FFB6C6"),
label: "o",
name: "o",
)
// Connect layers with weights
for ii in range(2) {
for jj in range(4) {
let start = ("ii" + str(ii + 1))
let end = ("h" + str(jj + 1))
line(start, end, ..arrow-style)
weight-label(
(0, (ii + 1) * node-sep + 1),
(layer-sep, (jj + 1) * node-sep),
ii + 1,
jj + 1,
offset: if ii == 0 { 1.5 } else { -1 },
)
}
}
for ii in range(4) {
let start = ("h" + str(ii + 1))
line(start, "o", ..arrow-style)
weight-label(
(layer-sep, (ii + 1) * node-sep),
(2 * layer-sep, 2.5 * node-sep),
ii + 1,
1,
)
}
},
)
// Draw Bayesian network
group(
name: "bayes",
{
// Shift everything right
let x-offset = 3 * layer-sep
// Input layer
for ii in range(2) {
neuron(
(x-offset, (ii + 1) * node-sep + 1),
fill: rgb("#90EE90"),
label: "ii" + str(ii + 1),
name: "ii" + str(ii + 1),
)
}
// Hidden layer
for ii in range(4) {
neuron(
(x-offset + layer-sep, (ii + 1) * node-sep),
fill: rgb("#ADD8E6"),
label: "h" + str(ii + 1),
name: "h" + str(ii + 1),
)
}
// Output layer
neuron(
(x-offset + 2 * layer-sep, 2.5 * node-sep),
fill: rgb("#FFB6C6"),
label: "o",
name: "o",
)
// Connect layers with distributions
for ii in range(2) {
for jj in range(4) {
let start = ("ii" + str(ii + 1))
let end = ("h" + str(jj + 1))
line(start, end, ..arrow-style)
gaussian(
(x-offset, (ii + 1) * node-sep + 1),
(x-offset + layer-sep, (jj + 1) * node-sep),
offset: ii - jj,
shift: if ii == 0 { 1.5 } else { -1 },
)
}
}
for ii in range(4) {
let start = ("h" + str(ii + 1))
line(start, "o", ..arrow-style)
gaussian(
(x-offset + layer-sep, (ii + 1) * node-sep),
(x-offset + 2 * layer-sep, 2.5 * node-sep),
offset: ii,
)
}
},
)
})