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@@ -29,18 +29,23 @@
 <p><sup>1</sup> Huawei Noah's Ark Lab, 
 <sup>2</sup> University of Liverpool, 
 <sup>3</sup> King's College London</p>
-<p><a rel="nofollow" href="https://link.springer.com/chapter/10.1007/978-3-031-72949-2_26"><img alt="Static Badge" src="https://img.shields.io/badge/ECCV_2024-APA-blue"></a>
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+<p><a href="https://link.springer.com/chapter/10.1007/978-3-031-72949-2_26"><img alt="Static Badge" src="https://img.shields.io/badge/ECCV_2024-APA-blue"></a>
+<a href="https://arxiv.org/pdf/2407.08567"><img alt="Static Badge" src="https://img.shields.io/badge/arxiv-2407.08567-blue"></a>
+<a href="https://paperswithcode.com/sota/long-tail-learning-on-places-lt?p=adaptive-parametric-activation"><img alt="PWC" src="https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/adaptive-parametric-activation/long-tail-learning-on-places-lt"></a>
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+<a href="https://paperswithcode.com/sota/long-tail-learning-on-imagenet-lt?p=adaptive-parametric-activation"><img alt="PWC" src="https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/adaptive-parametric-activation/long-tail-learning-on-imagenet-lt"></a>
+<a href="https://paperswithcode.com/sota/long-tail-learning-on-inaturalist-2018?p=adaptive-parametric-activation"><img alt="PWC" src="https://img.shields.io/endpoint.svg?url=https://paperswithcode.com/badge/adaptive-parametric-activation/long-tail-learning-on-inaturalist-2018"></a></p>
+</div>
+
+<div class="row">
+    <div class="col-sm">
+      <figure class="image text-center">
+      <img alt="APA activation" src="https://huggingface.co/spaces/konsa15/AGLU/resolve/main/assets/unified_activations_combined.jpg">
+      <figcaption> Figure 1: APA unifies most activation functions under the same formula.</figcaption>
+    </figure>
+    </div>
 </div>
 
-<figure class="image text-center">
-  <img alt="APA activation" src="https://huggingface.co/spaces/konsa15/AGLU/resolve/main/assets/unified_activations_combined.jpg">
-  <figcaption> Figure 1: APA unifies most activation functions under the same formula.</figcaption>
-</figure>
 
  <h3>Abstract</h3>
 
@@ -50,10 +55,15 @@
 <p>The Adaptive Parametric Activation APA is defined as: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mi>P</mi><mi>A</mi><mo stretchy="false">(</mo><mi>z</mi><mo separator="true">,</mo><mi>λ</mi><mo separator="true">,</mo><mi>κ</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mi>λ</mi><mi>e</mi><mi>x</mi><mi>p</mi><mo stretchy="false">(</mo><mo>−</mo><mi>κ</mi><mi>z</mi><mo stretchy="false">)</mo><mo>+</mo><mn>1</mn><msup><mo stretchy="false">)</mo><mfrac><mn>1</mn><mrow><mo>−</mo><mi>λ</mi></mrow></mfrac></msup></mrow>APA(z,λ,κ) = (λ exp(−κz) + 1) ^{\frac{1}{−λ}}</math></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:1em;vertical-align:-0.25em;" class="strut"></span><span class="mord mathnormal">A</span><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span style="margin-right:0.04398em;" class="mord mathnormal">z</span><span class="mpunct">,</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="mord mathnormal">λ</span><span class="mpunct">,</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="mord mathnormal">κ</span><span class="mclose">)</span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:1em;vertical-align:-0.25em;" class="strut"></span><span class="mopen">(</span><span class="mord mathnormal">λ</span><span class="mord mathnormal">e</span><span class="mord mathnormal">x</span><span class="mord mathnormal">p</span><span class="mopen">(</span><span class="mord">−</span><span class="mord mathnormal">κ</span><span style="margin-right:0.04398em;" class="mord mathnormal">z</span><span class="mclose">)</span><span style="margin-right:0.2222em;" class="mspace"></span><span class="mbin">+</span><span style="margin-right:0.2222em;" class="mspace"></span></span><span class="base"><span style="height:1.2312em;vertical-align:-0.25em;" class="strut"></span><span class="mord">1</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span style="height:0.9812em;" class="vlist"><span style="top:-3.3902em;margin-right:0.05em;"><span style="height:3em;" class="pstrut"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span style="height:0.8443em;" class="vlist"><span style="top:-2.656em;"><span style="height:3em;" class="pstrut"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.2255em;"><span style="height:3em;" class="pstrut"></span><span style="border-bottom-width:0.049em;" class="frac-line mtight"></span></span><span style="top:-3.384em;"><span style="height:3em;" class="pstrut"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span style="height:0.4035em;" class="vlist"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span>. APA unifies most activation functions under the same formula as shwon in Figure 1.</p>
 <p>APA can be used insed the intermediate layers using Adaptive Generalised Linear Unit (AGLU): <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>A</mi><mi>G</mi><mi>L</mi><mi>U</mi><mo stretchy="false">(</mo><mi>z</mi><mo separator="true">,</mo><mi>λ</mi><mo separator="true">,</mo><mi>κ</mi><mo stretchy="false">)</mo><mo>=</mo><mi>z</mi><mi>A</mi><mi>P</mi><mi>A</mi><mo stretchy="false">(</mo><mi>z</mi><mo separator="true">,</mo><mi>λ</mi><mo separator="true">,</mo><mi>κ</mi><mo stretchy="false">)</mo></mrow>AGLU(z,λ,κ) = z APA(z,λ,κ)</math></span><span aria-hidden="true" class="katex-html"><span class="base"><span style="height:1em;vertical-align:-0.25em;" class="strut"></span><span class="mord mathnormal">A</span><span class="mord mathnormal">G</span><span style="margin-right:0.10903em;" class="mord mathnormal">LU</span><span class="mopen">(</span><span style="margin-right:0.04398em;" class="mord mathnormal">z</span><span class="mpunct">,</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="mord mathnormal">λ</span><span class="mpunct">,</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="mord mathnormal">κ</span><span class="mclose">)</span><span style="margin-right:0.2778em;" class="mspace"></span><span class="mrel">=</span><span style="margin-right:0.2778em;" class="mspace"></span></span><span class="base"><span style="height:1em;vertical-align:-0.25em;" class="strut"></span><span style="margin-right:0.04398em;" class="mord mathnormal">z</span><span class="mord mathnormal">A</span><span style="margin-right:0.13889em;" class="mord mathnormal">P</span><span class="mord mathnormal">A</span><span class="mopen">(</span><span style="margin-right:0.04398em;" class="mord mathnormal">z</span><span class="mpunct">,</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="mord mathnormal">λ</span><span class="mpunct">,</span><span style="margin-right:0.1667em;" class="mspace"></span><span class="mord mathnormal">κ</span><span class="mclose">)</span></span></span></span>.
 The derivatives of AGLU with respect to κ (top), λ (middle) and z (bottom) are shown in Figure 2:</p>
+
+<div class="row">
+    <div class="col-sm">
 <figure class="image text-center">
   <img alt="AGLU derivatives" src="https://huggingface.co/spaces/konsa15/AGLU/resolve/main/assets/derivative_visualisations.jpg">
   <figcaption> Figure 2: The derivatives of AGLU with respect to κ (top), λ (middle) and z (bottom).</figcaption>
 </figure>
+    </div>
+</div>
 
 
 <h3> Simple Code implementation </h3>