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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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+ style="font-size:65%;baseline-shift:sub"
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+ id="tspan2127">maj</tspan> , ∥ζ∥ ≤ δ}</tspan></text>
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+ x="77.230827"
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+ style="font-size:4.23333px;stroke-width:0.264583">unsafe area for synthetic points</tspan></text>
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+ style="font-size:4.23333px;stroke-width:0.258878">D = D<tspan
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+ style="font-size:65%;baseline-shift:sub"
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+ id="tspan958">maj</tspan> ∪ D<tspan
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+ style="font-size:65%;baseline-shift:sub"
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+ id="tspan960">min</tspan> with D<tspan
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+ style="font-size:65%;baseline-shift:sub"
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+ id="tspan962">min</tspan> = {x1, x2, …}</tspan></text>
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+ <ellipse
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+ <text
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+ style="font-size:4.23333px;stroke-width:0.264583"
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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"
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+ id="tspan2300"> The generator learns the shape of the safe area.</tspan></text>
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+ x="57.412422"
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+ y="130.90579"
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+ style="font-size:4.23333px;stroke-width:0.264583">noise →</tspan></text>
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+ 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"
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+ x="66.166405"
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+ y="140.29108"
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+ id="text2191"><tspan
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+ sodipodi:role="line"
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+ id="tspan2189"
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+ x="66.166405"
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+ y="140.29108"
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+ style="font-size:4.23333px;stroke-width:0.264583">x →</tspan></text>
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+ </g>
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+ <text
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+ xml:space="preserve"
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+ 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"
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+ x="98.556824"
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+ y="136.32286"
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+ id="text2199"><tspan
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+ sodipodi:role="line"
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+ id="tspan2197"
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+ x="98.556824"
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+ y="136.32286"
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+ style="font-size:4.23333px;stroke-width:0.264583">→v</tspan></text>
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+ <text
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+ xml:space="preserve"
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+ 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"
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+ x="121.22429"
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+ y="136.49443"
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+ id="text2203"><tspan
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+ sodipodi:role="line"
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+ id="tspan2201"
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+ x="121.22429"
|
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+ y="136.49443"
|
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+ style="font-size:4.23333px;stroke-width:0.264583">with x + v ∈ S(x)</tspan></text>
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+ <g
|
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+ id="g930"
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+ transform="translate(-15.714536,76.52675)">
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+ <text
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+ xml:space="preserve"
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+ 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"
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+ x="97.267754"
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+ y="62.758614"
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+ id="text851"><tspan
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+ sodipodi:role="line"
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+ id="tspan849"
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+ x="97.267754"
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+ y="62.758614"
|
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+ style="stroke-width:0.264583">G</tspan></text>
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+ <rect
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+ style="fill:none;stroke:#000000;stroke-width:0.352778;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0"
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+ id="rect907"
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+ width="20.097038"
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+ height="20.097038"
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+ x="91.715813"
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+ y="48.590046" />
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+ </g>
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+ </g>
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+ </g>
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+</svg>
|
Kristian Schultz
