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| <span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mi>w</mi><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">β</mi><mo stretchy="false">)</mo></mrow></msubsup><mo stretchy="false">(</mo><mi>t</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><msubsup><mi>w</mi><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">β</mi><mo stretchy="false">)</mo></mrow></msubsup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>β</mo><mi>Ξ±</mi><mtext>β β</mtext><mfrac><mrow><mi mathvariant="normal">β</mi><mi>E</mi></mrow><mrow><mi mathvariant="normal">β</mi><msubsup><mi>w</mi><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">β</mi><mo stretchy="false">)</mo></mrow></msubsup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">w_{ij}^{(\ell)}(t+1) = w_{ij}^{(\ell)}(t) - \alpha \; \frac{\partial E}{\partial w_{ij}^{(\ell)}(t)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4577719999999998em;vertical-align:-0.4129719999999999em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.4231360000000004em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">β</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">β</span></span><span class="vlist-r"><span class="vlist" style="height:0.4129719999999999em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.4577719999999998em;vertical-align:-0.4129719999999999em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.4231360000000004em;margin-left:-0.02691em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">β</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">β</span></span><span class="vlist-r"><span class="vlist" style="height:0.4129719999999999em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">β</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.7542879999999998em;vertical-align:-0.8741799999999998em;"></span><span class="mord mathdefault" style="margin-right:0.0037em;">Ξ±</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801079999999999em;"><span style="top:-2.44864em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">β</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0590857142857142em;"><span style="top:-2.2134285714285715em;margin-left:-0.02691em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5357142857142856em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span></span></span></span><span style="top:-3.059085714285714em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5357142857142856em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mtight">β</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">β</span></span><span class="vlist-r"><span class="vlist" style="height:0.46117142857142857em;"><span></span></span></span></span></span></span><span class="mopen mtight">(</span><span class="mord mathdefault mtight">t</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">β</span><span class="mord mathdefault mtight" style="margin-right:0.05764em;">E</span></span></span></span></span><span class="vlist-s">β</span></span><span class="vlist-r"><span class="vlist" style="height:0.8741799999999998em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> | |
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