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<tspan x="213.082031" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">d</tspan>
<tspan x="218.794922" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a"> </tspan>
<tspan x="221.655762" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">a</tspan>
<tspan x="227.170898" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">c</tspan>
<tspan x="232.119141" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">t</tspan>
<tspan x="235.647949" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">i</tspan>
<tspan x="238.148438" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">v</tspan>
<tspan x="243.474609" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">a</tspan>
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<tspan x="255.019043" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">o</tspan>
<tspan x="260.525391" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">n</tspan>
<tspan x="266.229492" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">s</tspan>
<tspan x="270.918457" y="-0.15625" style="font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">,</tspan>
<tspan x="108.830566" y="-0.15625" style="font-style: oblique; font-size: 9px; font-family: 'DejaVu Sans'; fill: #3a3a3a">E</tspan>
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<g id="text_12">
<text style="font-size: 9px; font-family: 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Arial', 'Helvetica', 'Avant Garde', sans-serif; text-anchor: middle; fill: #3a3a3a" x="219.6" y="573.791303" transform="rotate(-0 219.6 573.791303)">and one bottom-up pass reaches it.</text>
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<text style="font-size: 8.6px; font-family: 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Arial', 'Helvetica', 'Avant Garde', sans-serif; text-anchor: middle; fill: #8a8a8a" x="219.6" y="605.716883" transform="rotate(-0 219.6 605.716883)">The free phase adds nothing and changes nothing at inference.</text>
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<text style="font-weight: 700; font-size: 11.5px; font-family: 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Arial', 'Helvetica', 'Avant Garde', sans-serif; text-anchor: middle; fill: #3a3a3a" x="614.88" y="27.155326" transform="rotate(-0 614.88 27.155326)">Nudged phase (training only)</text>
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<!-- add the loss at strength $\beta \ll 1$ and settle again: -->
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<tspan x="22.682495" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">h</tspan>
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<tspan x="90.166016" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">g</tspan>
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<tspan x="99.151001" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">h</tspan>
<tspan x="104.696655" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a"> </tspan>
<tspan x="114.766846" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">≪</tspan>
<tspan x="125.631714" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">1</tspan>
<tspan x="131.19873" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a"> </tspan>
<tspan x="133.980103" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">a</tspan>
<tspan x="139.342041" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">n</tspan>
<tspan x="144.887695" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">d</tspan>
<tspan x="150.441895" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a"> </tspan>
<tspan x="153.223267" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">s</tspan>
<tspan x="157.781982" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">e</tspan>
<tspan x="163.165283" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">t</tspan>
<tspan x="166.596069" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">t</tspan>
<tspan x="170.026855" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">l</tspan>
<tspan x="172.457886" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">e</tspan>
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<tspan x="180.622559" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">a</tspan>
<tspan x="185.984497" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">g</tspan>
<tspan x="191.538696" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">a</tspan>
<tspan x="196.900635" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">i</tspan>
<tspan x="199.331665" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">n</tspan>
<tspan x="204.877319" y="-0.109375" style="font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">:</tspan>
<tspan x="107.478027" y="-0.109375" style="font-style: oblique; font-size: 8.8px; font-family: 'DejaVu Sans'; fill: #8a8a8a">β</tspan>
</text>
</g>
</g>
<g id="text_16">
<!-- $E(z)\ +\ \beta\cdot\mathrm{CE}(\mathrm{logits}(z_3),\,y)$ -->
<g style="fill: #3a3a3a" transform="translate(539.9 88.649213)">
<text>
<tspan x="0" y="-0.8125" style="font-style: oblique; font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">E</tspan>
<tspan x="11.752686" y="-0.8125" style="font-style: oblique; font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">z</tspan>
<tspan x="43.860521" y="-0.8125" style="font-style: oblique; font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">β</tspan>
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<tspan x="138.567297" y="-0.8125" style="font-style: oblique; font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">y</tspan>
<tspan x="7.266113" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">(</tspan>
<tspan x="17.789062" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">)</tspan>
<tspan x="28.250207" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">+</tspan>
<tspan x="53.440111" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">⋅</tspan>
<tspan x="59.336107" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">C</tspan>
<tspan x="67.365892" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">E</tspan>
<tspan x="74.632005" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">(</tspan>
<tspan x="79.118578" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">l</tspan>
<tspan x="82.313646" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">o</tspan>
<tspan x="89.349535" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">g</tspan>
<tspan x="96.649339" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">i</tspan>
<tspan x="99.844408" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">t</tspan>
<tspan x="104.353441" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">s</tspan>
<tspan x="110.344896" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">(</tspan>
<tspan x="126.317626" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">)</tspan>
<tspan x="130.804198" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">,</tspan>
<tspan x="145.372961" y="-0.8125" style="font-size: 11.5px; font-family: 'DejaVu Sans'; fill: #3a3a3a">)</tspan>
<tspan x="120.867845" y="1.15625" style="font-size: 8.05px; font-family: 'DejaVu Sans'; fill: #3a3a3a">3</tspan>
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<!-- pull $-\beta\,\nabla\mathrm{CE}$ -->
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<text>
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<tspan x="11.8927" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">l</tspan>
<tspan x="14.497375" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">l</tspan>
<tspan x="17.102051" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e"> </tspan>
<tspan x="20.082092" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">−</tspan>
<tspan x="35.442383" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">∇</tspan>
<tspan x="41.713745" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">C</tspan>
<tspan x="48.259766" y="-0.109375" style="font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">E</tspan>
<tspan x="27.937317" y="-0.109375" style="font-style: oblique; font-size: 9.4px; font-family: 'DejaVu Sans'; fill: #b03a2e">β</tspan>
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<!-- $z_3^{\beta} = z_3 + d_3$ -->
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<tspan x="12.384603" y="-0.475" style="font-size: 10px; font-family: 'DejaVu Sans'; fill: #3a3a3a">=</tspan>
<tspan x="34.636068" y="-0.475" style="font-size: 10px; font-family: 'DejaVu Sans'; fill: #3a3a3a">+</tspan>
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<tspan x="7.716522" y="-3.592188" style="font-size: 6.02px; font-family: 'DejaVu Sans'; fill: #8a8a8a">⊤</tspan>
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<text style="font-weight: 700; font-size: 11px; font-family: 'DejaVu Sans', 'Bitstream Vera Sans', 'Computer Modern Sans Serif', 'Lucida Grande', 'Verdana', 'Geneva', 'Lucid', 'Arial', 'Helvetica', 'Avant Garde', sans-serif; text-anchor: start; fill: #3a3a3a" x="35.136" y="662.442054" transform="rotate(-0 35.136 662.442054)">The update — a difference measurement between the two settled states</text>
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<!-- $\hat{g}\ =\ \left[\ \partial_\theta E(z^{\beta})\ -\ \partial_\theta E(z^{0})\ \right]\,/\,\beta$$\qquad\qquad(\partial_\theta E(z^0)\equiv 0\ \mathrm{here,\ since}\ E=0)$ -->
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<!-- per layer: $\Delta\theta_l\ \propto\ \langle\ d_l\ ,\ \partial f_l(z_{l-1})/\partial\theta_l\ \rangle\ /\ \beta$ -->
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<tspan x="74.977018" y="-0.328125" style="font-size: 10px; font-family: 'DejaVu Sans'; fill: #3a3a3a">∝</tspan>
<tspan x="87.315853" y="-0.328125" style="font-size: 10px; font-family: 'DejaVu Sans'; fill: #3a3a3a">⟨</tspan>
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<tspan x="138.019857" y="1.3125" style="font-size: 7px; font-family: 'DejaVu Sans'; fill: #3a3a3a">−</tspan>
<tspan x="145.248861" y="1.3125" style="font-size: 7px; font-family: 'DejaVu Sans'; fill: #3a3a3a">1</tspan>
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