index.xml

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    <title>Neha Verma</title>
    <link>https://nverma1.github.io/</link>
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    <description>Neha Verma</description>
    <generator>Wowchemy (https://wowchemy.com)</generator><language>en-us</language><lastBuildDate>Sat, 01 Jun 2030 13:00:00 +0000</lastBuildDate>
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      <title>Neha Verma</title>
      <link>https://nverma1.github.io/</link>
    </image>
    
    <item>
      <title>Academic Template</title>
      <link>https://nverma1.github.io/home-unused/demo/</link>
      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/home-unused/demo/</guid>
      <description>&lt;h2 id=&#34;-welcome-to-the-academic-template&#34;&gt;👋 Welcome to the Academic Template&lt;/h2&gt;
&lt;p&gt;The Wowchemy &lt;strong&gt;Academic Resumé Template&lt;/strong&gt; for Hugo empowers you to create your job-winning online resumé and showcase your academic publications.&lt;/p&gt;
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</description>
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      <title>Skills</title>
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      <description></description>
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      <title>Experience</title>
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      <title>Recent &amp; Upcoming Talks</title>
      <link>https://nverma1.github.io/home-unused/talks/</link>
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      <title>Featured Publications</title>
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    <item>
      <title>Example Talk</title>
      <link>https://nverma1.github.io/talk/example-talk/</link>
      <pubDate>Sat, 01 Jun 2030 13:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/talk/example-talk/</guid>
      <description>&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click on the &lt;strong&gt;Slides&lt;/strong&gt; button above to view the built-in slides feature.
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&lt;p&gt;Slides can be added in a few ways:&lt;/p&gt;
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</description>
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    <item>
      <title>Merging Feed Forward Sublayers for Compressed Transformers</title>
      <link>https://nverma1.github.io/publication/merge_ffs/</link>
      <pubDate>Tue, 29 Oct 2024 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/merge_ffs/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
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&lt;div class=&#34;alert alert-note&#34;&gt;
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 --&gt;
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</description>
    </item>
    
    <item>
      <title>Understanding CKA</title>
      <link>https://nverma1.github.io/post/cka_walkthrough/</link>
      <pubDate>Fri, 04 Oct 2024 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/post/cka_walkthrough/</guid>
      <description>&lt;details class=&#34;toc-inpage d-print-none  &#34; open&gt;
  &lt;summary class=&#34;font-weight-bold&#34;&gt;Table of Contents&lt;/summary&gt;
  &lt;nav id=&#34;TableOfContents&#34;&gt;
  &lt;ul&gt;
    &lt;li&gt;&lt;a href=&#34;#1-overview&#34;&gt;1. Overview&lt;/a&gt;&lt;/li&gt;
    &lt;li&gt;&lt;a href=&#34;#2-inputs-and-outputs&#34;&gt;2. Inputs and Outputs&lt;/a&gt;&lt;/li&gt;
    &lt;li&gt;&lt;a href=&#34;#3-formula&#34;&gt;3. Formula&lt;/a&gt;&lt;/li&gt;
  &lt;/ul&gt;
&lt;/nav&gt;
&lt;/details&gt;
&lt;h2 id=&#34;1-overview&#34;&gt;1. Overview&lt;/h2&gt;
&lt;p&gt;CKA (Centered Kernel Alignment) is a state-of-the-art tool for measuring the similarity of neural network representations. After reading the original paper, I wanted more intuition about how the CKA formulae capture similarity, so I spent some time breaking it down. This post is a summary of my understanding of CKA, and the derivations I worked out.&lt;/p&gt;
&lt;h2 id=&#34;2-inputs-and-outputs&#34;&gt;2. Inputs and Outputs&lt;/h2&gt;
&lt;p&gt;To run CKA, we must have 2 matrices of activations (aka representations) from the same neural network, or different neural networks.&lt;/p&gt;
&lt;p&gt;Let&amp;rsquo;s call these matrices $X$ and $Y$. Let $X \in \mathbb{R}^{n \times d_1}$ and $Y \in \mathbb{R}^{n \times d_2}$, where $n$ is the number of samples and $d_i$ is the dimensionality of the representations. $d_1$ and $d_2$ can be different, but $n$ must be the same for both matrices, and must be the same corresponding examples.
This means CKA lets us compare the similarity of representations that come from layers of differing widths. We also assume that these matrices have been &lt;em&gt;centered&lt;/em&gt;.&lt;/p&gt;
&lt;h2 id=&#34;3-formula&#34;&gt;3. Formula&lt;/h2&gt;
&lt;p&gt;One formula for (linear) CKA is given by:
$$\text{CKA}(X,Y) = \frac{\lVert Y^TX \rVert_F^2}{\lVert X^TX \rVert_F \lVert Y^TY \rVert_F}$$&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Breaking down the Numerator&lt;/strong&gt; &lt;br/&gt;
Let&amp;rsquo;s first look at the numerator of the formula: $$\lVert Y^TX \rVert_F^2$$
In Section 3 of &lt;a href=&#34;https://arxiv.org/pdf/1905.00414&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Similarity of Neural Network Representations Revisited&lt;/a&gt;, we are shown a way to link from dot products between examples to dot products between features: $$ \frac{\lVert Y^TX \rVert_F^2}{\lVert X^TX \rVert_F \lVert Y^TY \rVert_F} = \langle \text{vec}(XX^T), \text{vec}(YY^T)\rangle$$
This is the key insight of CKA, where a computation comparing the multivariate features between the two matrices can actually translate to computing the similarity between examples, and then comparing the resulting similarity structures. Although we can expand the reduced formulation, it is much more helpful to expand the formuation as follows in order to reach the intuition presented by the authors. &lt;br/&gt;&lt;br/&gt;
We will work this the opposite way here, including more details to understand the intermediate steps. First, we will establish an important property of the Frobenius norm, and of the trace.&lt;/p&gt;
&lt;ol&gt;
&lt;li&gt;
&lt;p&gt;frobenius norm reformulation:
$ \lVert A \rVert_F = \sqrt{\text{Tr}(A^TA)}$&lt;/p&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;trace property (cyclic property):
$\text{Tr}(ABC) = \text{Tr}(CAB) = \text{Tr}(BCA)$&lt;/p&gt;
&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;Now, we can rewrite the numerator of the CKA formula as follows:
$$
\begin{align*}
\lVert Y^TX \rVert_F^2 &amp;amp;= \left(\sqrt{\text{Tr}((Y^TX)^T Y^TX)}\right)^2 &amp;amp;&amp;amp; \text{frobenius norm}\\\
&amp;amp;= Tr\left(X^TYY^TX\right) &amp;amp;&amp;amp; \text{sqrt and transpose} \\\
&amp;amp;= Tr\left(XX^TYY^T\right) &amp;amp;&amp;amp; \text{cyclic trace} \\\
&amp;amp;= \sum_i \left(XX^TYY^T\right)_{ii} &amp;amp;&amp;amp; \text{expanding trace} \\\
&amp;amp;= \sum_i \sum_j (XX^T)_{ij} (YY^T)_{ji}&amp;amp;&amp;amp; \text{expanding matmul} \\\
&amp;amp;= \sum_i \sum_j  (XX^T)_{ij} (YY^T)_{ij} &amp;amp;&amp;amp;\text{gram mats symm.} \\\
&amp;amp;= \langle \text{vec}(XX^T), \text{vec}(YY^T)\rangle &amp;amp;&amp;amp; \text{dot product def.}
\end{align*}
$$&lt;br&gt;
Now we have a more complete understanding of the key Equation 1 in the paper, which relates feature similarity to the dot product between similarity structures.&lt;/p&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Connection to the Hilbert Schmidt Independence Criterion&lt;/strong&gt; &lt;br/&gt;
Before formulating the connection to the Hilbert-Schmidt Independence Criterion (HSIC), we&amp;rsquo;ll first recall the definition of the cross-covariance matrix
$$\text{cov}(X,Y) = \frac{1}{n-1}\left(X - \mathbb{E}(X)\right)\left(Y - \mathbb{E}(Y)\right)^T$$ Now, we will connect the trace formulation from above to the covariance matrix. Remember that we assume our data matrices are already centered
$$ \begin{align*}
\lVert \text{cov}(X^T, Y^T)\rVert_F^2 &amp;amp;= \lVert \frac{1}{n-1} X^TY \rVert_F^2&amp;amp;&amp;amp; \text{by def.&amp;amp;center}\\\
&amp;amp;= \frac{1}{(n-1)^2} \lVert Y^TX \rVert_F^2 &amp;amp;&amp;amp; \text{scalar&amp;amp;norm} \\\
&amp;amp; = \frac{1}{(n-1)^2} \text{Tr}\left(XX^TYY^T\right) &amp;amp;&amp;amp; \text{from above}
\end{align*}$$
Now, the HSIC was originaly proposed as a test statistic for determining if variables are independent. We will now go over the empirical estimator of the HSIC, with kernels $K$ and $L$ and centering matrix $H_n = I_n - \frac{1}{n} \mathbb{1}\mathbb{1}^T$ is
$$ \text{HSIC}(K,L) = \frac{1}{(n-1)^2} \text{Tr}(KHLH)$$ However, the HSIC is not invariant to isotropic scaling, defined as $s(X,Y) = s(\alpha X, \beta Y)$ for similarity index $s$. For CKA, we would like this property. Therefore, the authors propose to use a normalized version. We now share the simplifications for a linear kernel CKA, and an arbitrary kernel CKA. For the linear kernel, we have
$$ \text{HSIC}(X,Y) = \frac{1}{(n-1)^2}\text{Tr}(X^TXY^TY) $$ For linear CKA, we get
$$ \begin{align*}
\text{CKA}(X,Y) &amp;amp;= \frac{\text{HSIC}(K,L)}{\sqrt{\text{HSIC}(K,K)\text{HSIC}(L,L)}} \\\
&amp;amp;= \frac{\frac{1}{(n-1)^2} \lVert Y^TX \rVert_F^2}{\sqrt{\frac{1}{(n-1)^2} \lVert X^TX \rVert_F^2 \frac{1}{(n-1)^2} \lVert Y^TY \rVert_F^2} }\\\
&amp;amp;= \frac{\frac{1}{(n-1)^2} \lVert Y^TX \rVert_F^2}{\frac{1}{n-1}\cdot \frac{1}{n-1} \lVert X^TX \rVert_F \lVert Y^TY \rVert_F} \\\
&amp;amp;=  \frac{\lVert Y^TX \rVert_F^2}{\lVert X^TX \rVert_F \lVert Y^TY \rVert_F}
\end{align*} $$ For arbitrary kernel $K, L$, we simplify the CKA as following:
$$ \begin{align*}
CKA(K,L) &amp;amp;= \frac{\text{HSIC}(K,L)}{\sqrt{\text{HSIC}(K,K)\text{HSIC}(L,L)}} \\\
&amp;amp;= \frac{\frac{1}{(n-1)^2} \text{Tr}(KHLH)}{\sqrt{\frac{1}{(n-1)^2}Tr(KHKH)\frac{1}{(n-1)^2}\text{Tr}(LHLH)}} \\\
&amp;amp;= \frac{\text{Tr}(KHLH)}{\sqrt{\text{Tr}(KHKH)\text{Tr}(LHLH)}} \\\
\end{align*}$$&lt;/p&gt;
&lt;/li&gt;
&lt;/ol&gt;
</description>
    </item>
    
    <item>
      <title>Merging Text Transformer Models from Different Initializations</title>
      <link>https://nverma1.github.io/publication/merge2024/</link>
      <pubDate>Mon, 01 Jul 2024 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/merge2024/</guid>
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</description>
    </item>
    
    <item>
      <title>Exploring Representational Disparities Between Multilingual and Bilingual Translation Models</title>
      <link>https://nverma1.github.io/publication/rep_comb2023/</link>
      <pubDate>Thu, 23 May 2024 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/rep_comb2023/</guid>
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    <item>
      <title>Multilingual Pixel Representations for Translation and Effective Cross-lingual Transfer</title>
      <link>https://nverma1.github.io/publication/liz2023/</link>
      <pubDate>Wed, 06 Dec 2023 00:00:00 +0000</pubDate>
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  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>JHU IWSLT 2023 Dialect Speech Translation System Description</title>
      <link>https://nverma1.github.io/publication/iwslt23_dialect/</link>
      <pubDate>Thu, 13 Jul 2023 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/iwslt23_dialect/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>JHU IWSLT 2023 Multilingual Speech Translation System Description</title>
      <link>https://nverma1.github.io/publication/iwslt23_multi/</link>
      <pubDate>Thu, 13 Jul 2023 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/iwslt23_multi/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>IsoVec: Controlling the Relative Isomorphism of Word Embedding Spaces</title>
      <link>https://nverma1.github.io/publication/emnlp2022/</link>
      <pubDate>Thu, 01 Dec 2022 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/emnlp2022/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>Neural Natural Language Processing for unstructured data in electronic health records: A review</title>
      <link>https://nverma1.github.io/publication/ehr_review/</link>
      <pubDate>Tue, 01 Nov 2022 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/ehr_review/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>Strategies for Adapting Multilingual Pre-training for Domain-Specific Machine Translation</title>
      <link>https://nverma1.github.io/publication/amta2022/</link>
      <pubDate>Thu, 01 Sep 2022 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/amta2022/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>FeTaQA: Free-form Table Question Answering</title>
      <link>https://nverma1.github.io/publication/tacl2022/</link>
      <pubDate>Sat, 01 Jan 2022 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/tacl2022/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>DART: Open-Domain Structured Data Record to Text Generation</title>
      <link>https://nverma1.github.io/publication/naacl2021/</link>
      <pubDate>Tue, 01 Jun 2021 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/naacl2021/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>Improving Low-Resource Cross-lingual Document Retrieval by Reranking with Deep Bilingual Representations</title>
      <link>https://nverma1.github.io/publication/acl2019/</link>
      <pubDate>Mon, 01 Jul 2019 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/publication/acl2019/</guid>
      <description>&lt;!-- &lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Click the &lt;em&gt;Cite&lt;/em&gt; button above to demo the feature to enable visitors to import publication metadata into their reference management software.
  &lt;/div&gt;
&lt;/div&gt;


&lt;div class=&#34;alert alert-note&#34;&gt;
  &lt;div&gt;
    Create your slides in Markdown - click the &lt;em&gt;Slides&lt;/em&gt; button to check out the example.
  &lt;/div&gt;
&lt;/div&gt;
 --&gt;
&lt;!-- Supplementary notes can be added here, including [code, math, and images](https://wowchemy.com/docs/writing-markdown-latex/). --&gt;
</description>
    </item>
    
    <item>
      <title>Slides</title>
      <link>https://nverma1.github.io/slides/example/</link>
      <pubDate>Tue, 05 Feb 2019 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/slides/example/</guid>
      <description>&lt;h1 id=&#34;create-slides-in-markdown-with-wowchemy&#34;&gt;Create slides in Markdown with Wowchemy&lt;/h1&gt;
&lt;p&gt;&lt;a href=&#34;https://wowchemy.com/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Wowchemy&lt;/a&gt; | &lt;a href=&#34;https://owchemy.com/docs/managing-content/#create-slides&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Documentation&lt;/a&gt;&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;features&#34;&gt;Features&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Efficiently write slides in Markdown&lt;/li&gt;
&lt;li&gt;3-in-1: Create, Present, and Publish your slides&lt;/li&gt;
&lt;li&gt;Supports speaker notes&lt;/li&gt;
&lt;li&gt;Mobile friendly slides&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;controls&#34;&gt;Controls&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;Next: &lt;code&gt;Right Arrow&lt;/code&gt; or &lt;code&gt;Space&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Previous: &lt;code&gt;Left Arrow&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Start: &lt;code&gt;Home&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Finish: &lt;code&gt;End&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Overview: &lt;code&gt;Esc&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Speaker notes: &lt;code&gt;S&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Fullscreen: &lt;code&gt;F&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Zoom: &lt;code&gt;Alt + Click&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href=&#34;https://revealjs.com/pdf-export/&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;PDF Export&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;code-highlighting&#34;&gt;Code Highlighting&lt;/h2&gt;
&lt;p&gt;Inline code: &lt;code&gt;variable&lt;/code&gt;&lt;/p&gt;
&lt;p&gt;Code block:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-python&#34; data-lang=&#34;python&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;n&#34;&gt;porridge&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;=&lt;/span&gt; &lt;span class=&#34;s2&#34;&gt;&amp;#34;blueberry&amp;#34;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;k&#34;&gt;if&lt;/span&gt; &lt;span class=&#34;n&#34;&gt;porridge&lt;/span&gt; &lt;span class=&#34;o&#34;&gt;==&lt;/span&gt; &lt;span class=&#34;s2&#34;&gt;&amp;#34;blueberry&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;:&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;    &lt;span class=&#34;nb&#34;&gt;print&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;(&lt;/span&gt;&lt;span class=&#34;s2&#34;&gt;&amp;#34;Eating...&amp;#34;&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;)&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;hr&gt;
&lt;h2 id=&#34;math&#34;&gt;Math&lt;/h2&gt;
&lt;p&gt;In-line math: $x + y = z$&lt;/p&gt;
&lt;p&gt;Block math:&lt;/p&gt;
&lt;hr&gt;
&lt;h2 id=&#34;fragments&#34;&gt;Fragments&lt;/h2&gt;
&lt;p&gt;Make content appear incrementally&lt;/p&gt;
&lt;pre tabindex=&#34;0&#34;&gt;&lt;code&gt;{{% fragment %}} One {{% /fragment %}}
{{% fragment %}} **Two** {{% /fragment %}}
{{% fragment %}} Three {{% /fragment %}}
&lt;/code&gt;&lt;/pre&gt;&lt;p&gt;Press &lt;code&gt;Space&lt;/code&gt; to play!&lt;/p&gt;
&lt;span class=&#34;fragment &#34; &gt;
  One
&lt;/span&gt;
&lt;span class=&#34;fragment &#34; &gt;
  &lt;strong&gt;Two&lt;/strong&gt;
&lt;/span&gt;
&lt;span class=&#34;fragment &#34; &gt;
  Three
&lt;/span&gt;
&lt;hr&gt;
&lt;p&gt;A fragment can accept two optional parameters:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;code&gt;class&lt;/code&gt;: use a custom style (requires definition in custom CSS)&lt;/li&gt;
&lt;li&gt;&lt;code&gt;weight&lt;/code&gt;: sets the order in which a fragment appears&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;h2 id=&#34;speaker-notes&#34;&gt;Speaker Notes&lt;/h2&gt;
&lt;p&gt;Add speaker notes to your presentation&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-markdown&#34; data-lang=&#34;markdown&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{% speaker_note %}}
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;k&#34;&gt;-&lt;/span&gt; Only the speaker can read these notes
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;k&#34;&gt;-&lt;/span&gt; Press &lt;span class=&#34;sb&#34;&gt;`S`&lt;/span&gt; key to view
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  {{% /speaker_note %}}
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;p&gt;Press the &lt;code&gt;S&lt;/code&gt; key to view the speaker notes!&lt;/p&gt;
&lt;aside class=&#34;notes&#34;&gt;
  &lt;ul&gt;
&lt;li&gt;Only the speaker can read these notes&lt;/li&gt;
&lt;li&gt;Press &lt;code&gt;S&lt;/code&gt; key to view&lt;/li&gt;
&lt;/ul&gt;

&lt;/aside&gt;
&lt;hr&gt;
&lt;h2 id=&#34;themes&#34;&gt;Themes&lt;/h2&gt;
&lt;ul&gt;
&lt;li&gt;black: Black background, white text, blue links (default)&lt;/li&gt;
&lt;li&gt;white: White background, black text, blue links&lt;/li&gt;
&lt;li&gt;league: Gray background, white text, blue links&lt;/li&gt;
&lt;li&gt;beige: Beige background, dark text, brown links&lt;/li&gt;
&lt;li&gt;sky: Blue background, thin dark text, blue links&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;
&lt;ul&gt;
&lt;li&gt;night: Black background, thick white text, orange links&lt;/li&gt;
&lt;li&gt;serif: Cappuccino background, gray text, brown links&lt;/li&gt;
&lt;li&gt;simple: White background, black text, blue links&lt;/li&gt;
&lt;li&gt;solarized: Cream-colored background, dark green text, blue links&lt;/li&gt;
&lt;/ul&gt;
&lt;hr&gt;

&lt;section data-noprocess data-shortcode-slide
  
      
      data-background-image=&#34;/media/boards.jpg&#34;
  &gt;

&lt;h2 id=&#34;custom-slide&#34;&gt;Custom Slide&lt;/h2&gt;
&lt;p&gt;Customize the slide style and background&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-markdown&#34; data-lang=&#34;markdown&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;slide&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;background-image&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;/media/boards.jpg&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}}
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;slide&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;background-color&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;#0000FF&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}}
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;{{&lt;span class=&#34;p&#34;&gt;&amp;lt;&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;slide&lt;/span&gt; &lt;span class=&#34;na&#34;&gt;class&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;=&lt;/span&gt;&lt;span class=&#34;s&#34;&gt;&amp;#34;my-style&amp;#34;&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;&amp;gt;&lt;/span&gt;}}
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;hr&gt;
&lt;h2 id=&#34;custom-css-example&#34;&gt;Custom CSS Example&lt;/h2&gt;
&lt;p&gt;Let&amp;rsquo;s make headers navy colored.&lt;/p&gt;
&lt;p&gt;Create &lt;code&gt;assets/css/reveal_custom.css&lt;/code&gt; with:&lt;/p&gt;
&lt;div class=&#34;highlight&#34;&gt;&lt;pre tabindex=&#34;0&#34; class=&#34;chroma&#34;&gt;&lt;code class=&#34;language-css&#34; data-lang=&#34;css&#34;&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;.&lt;/span&gt;&lt;span class=&#34;nc&#34;&gt;reveal&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;section&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;h1&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;.&lt;/span&gt;&lt;span class=&#34;nc&#34;&gt;reveal&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;section&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;h2&lt;/span&gt;&lt;span class=&#34;o&#34;&gt;,&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;.&lt;/span&gt;&lt;span class=&#34;nc&#34;&gt;reveal&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;section&lt;/span&gt; &lt;span class=&#34;nt&#34;&gt;h3&lt;/span&gt; &lt;span class=&#34;p&#34;&gt;{&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;  &lt;span class=&#34;k&#34;&gt;color&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;:&lt;/span&gt; &lt;span class=&#34;kc&#34;&gt;navy&lt;/span&gt;&lt;span class=&#34;p&#34;&gt;;&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;span class=&#34;line&#34;&gt;&lt;span class=&#34;cl&#34;&gt;&lt;span class=&#34;p&#34;&gt;}&lt;/span&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&lt;hr&gt;
&lt;h1 id=&#34;questions&#34;&gt;Questions?&lt;/h1&gt;
&lt;p&gt;&lt;a href=&#34;https://github.com/wowchemy/wowchemy-hugo-modules/discussions&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Ask&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;a href=&#34;https://wowchemy.com/docs/managing-content/#create-slides&#34; target=&#34;_blank&#34; rel=&#34;noopener&#34;&gt;Documentation&lt;/a&gt;&lt;/p&gt;
</description>
    </item>
    
    <item>
      <title>Example Project</title>
      <link>https://nverma1.github.io/project/example/</link>
      <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
      <guid>https://nverma1.github.io/project/example/</guid>
      <description>&lt;p&gt;Lorem ipsum dolor sit amet, consectetur adipiscing elit. Duis posuere tellus ac convallis placerat. Proin tincidunt magna sed ex sollicitudin condimentum. Sed ac faucibus dolor, scelerisque sollicitudin nisi. Cras purus urna, suscipit quis sapien eu, pulvinar tempor diam. Quisque risus orci, mollis id ante sit amet, gravida egestas nisl. Sed ac tempus magna. Proin in dui enim. Donec condimentum, sem id dapibus fringilla, tellus enim condimentum arcu, nec volutpat est felis vel metus. Vestibulum sit amet erat at nulla eleifend gravida.&lt;/p&gt;
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      <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
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