Added ideas

documentation/SafeArea.svg

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+         style="font-size:4.23333px;stroke-width:0.264583">Safe area for synthetic points. Let us call it S(x) = { x + ζ : ∥ζ∥ ≤ ε } /  {y + ζ : y ∈ D<tspan
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+   id="tspan2127">maj</tspan> , ∥ζ∥ ≤ δ}</tspan></text>
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+   id="tspan958">maj</tspan> ∪ D<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan960">min</tspan> with D<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan962">min</tspan> = {x1, x2, …}</tspan></text>
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+         id="tspan2179">Questions: Can we train a generator so that it produces points respecting S(x) for a given x?</tspan><tspan
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+           style="font-size:4.23333px;stroke-width:0.264583">→v</tspan></text>
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documentation/SelectiveNoise.svg

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+   id="tspan899">i</tspan> →</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="157.04324"
+       y="149.04385"
+       id="text893"><tspan
+         sodipodi:role="line"
+         id="tspan891"
+         x="157.04324"
+         y="149.04385"
+         style="stroke-width:0.264583">→ s</tspan></text>
+    <g
+       id="g920"
+       transform="translate(-92.077932,-5.0253937)">
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="230.29858"
+         y="155.033"
+         id="text889"><tspan
+           sodipodi:role="line"
+           id="tspan887"
+           x="230.29858"
+           y="155.033"
+           style="stroke-width:0.264583">G</tspan></text>
+      <rect
+         style="fill:none;stroke:#000000;stroke-width:0.352778;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
+         id="rect915"
+         width="20.097038"
+         height="20.097038"
+         x="224.21364"
+         y="141.13202" />
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.728681;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+       d="m 20.975113,130.31435 v 52"
+       id="path943" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.247414"
+       x="26.348614"
+       y="23.948597"
+       id="text839"><tspan
+         sodipodi:role="line"
+         id="tspan837"
+         x="26.348614"
+         y="23.948597"
+         style="font-size:4.23333px;stroke-width:0.247414">ν(l,u) → [l,u] randomly</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="26.539278"
+       y="30.392389"
+       id="text843"><tspan
+         sodipodi:role="line"
+         id="tspan841"
+         x="26.539278"
+         y="30.392389"
+         style="font-size:4.23333px;stroke-width:0.264583">e<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan966">i</tspan> = (0, … 0, 1, 0, … 0) with 1 on the i-th position.</tspan></text>
+    <g
+       id="g956">
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.258878"
+         x="13.083162"
+         y="16.410084"
+         id="text835"><tspan
+           sodipodi:role="line"
+           id="tspan833"
+           x="13.083162"
+           y="16.410084"
+           style="font-size:4.23333px;stroke-width:0.258878">Given D = D<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan958">maj</tspan> ∪ D<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan960">min</tspan> with D<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan962">min</tspan> = {x1, x2, …}</tspan></text>
+      <ellipse
+         style="fill:#000000;stroke:none;stroke-width:0.151522;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
+         id="path951"
+         cx="47.541191"
+         cy="13.087456"
+         rx="0.32406601"
+         ry="0.32406366" />
+    </g>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="45.816288"
+       y="74.261429"
+       id="text847"><tspan
+         sodipodi:role="line"
+         id="tspan845"
+         x="45.816288"
+         y="74.261429"
+         style="stroke-width:0.264583">ν(0, 1) • e<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan903">i</tspan> →</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="-88.858269"
+       y="16.537212"
+       id="text867"
+       transform="rotate(-90)"><tspan
+         sodipodi:role="line"
+         id="tspan865"
+         x="-88.858269"
+         y="16.537212"
+         style="font-size:4.23333px;stroke-width:0.264583">training</tspan></text>
+    <g
+       id="g930"
+       transform="translate(25.446948,12.398362)">
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="97.267754"
+         y="62.758614"
+         id="text851"><tspan
+           sodipodi:role="line"
+           id="tspan849"
+           x="97.267754"
+           y="62.758614"
+           style="stroke-width:0.264583">G</tspan></text>
+      <rect
+         style="fill:none;stroke:#000000;stroke-width:0.352778;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
+         id="rect907"
+         width="20.097038"
+         height="20.097038"
+         x="91.715813"
+         y="48.590046" />
+    </g>
+    <g
+       id="g941"
+       transform="translate(23.859448,10.460927)">
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="117.19472"
+         y="63.813942"
+         id="text855"><tspan
+           sodipodi:role="line"
+           id="tspan853"
+           x="117.19472"
+           y="63.813942"
+           style="stroke-width:0.264583">→ s →</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="126.76593"
+         y="83.361435"
+         id="text859"><tspan
+           sodipodi:role="line"
+           id="tspan857"
+           x="126.76593"
+           y="83.361435"
+           style="stroke-width:0.264583">x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan911">i</tspan> →</tspan></text>
+      <g
+         id="g925"
+         transform="translate(-13.105776)">
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="168.73309"
+           y="73.669617"
+           id="text863"><tspan
+             sodipodi:role="line"
+             id="tspan861"
+             x="168.73309"
+             y="73.669617"
+             style="stroke-width:0.264583">D</tspan></text>
+        <rect
+           style="fill:none;stroke:#000000;stroke-width:0.352778;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
+           id="rect913"
+           width="20.097038"
+           height="20.097038"
+           x="162.96596"
+           y="59.763466" />
+      </g>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.72868;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
+       d="M 20.975113,54.793652 V 106.79365"
+       id="path945" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:4.23333px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="-106.57841"
+       y="27.283545"
+       id="text970"
+       transform="rotate(-90)"><tspan
+         sodipodi:role="line"
+         id="tspan968"
+         x="-106.57841"
+         y="27.283545"
+         style="font-size:4.23333px;stroke-width:0.264583">for i in {1, 2, … , ∣D<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan972">min</tspan>∣}</tspan></text>
+  </g>
+</svg>