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claude refactor + records
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.gitignore

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_site
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.sass-cache
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.jekyll-cache
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# Jekyll build output
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_site/
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.jekyll-cache/
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.jekyll-metadata
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.sass-cache/
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# Bundler
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.bundle/
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vendor/
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# OS files
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.DS_Store
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vendor
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Thumbs.db
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*.swp
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*~
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# IDE/Editor specific
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.idea/
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.vscode/
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*.sublime-*
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# Log files
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*.log

_notes/ai/attention.markdown

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### Grouped-query attention
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<figure>
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<img src="../../../images/notes/gqa.png" class="center">
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<img src="/assets/images/notes/gqa.png" class="center">
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<figcaption align = "center">A nice schematic displaying the difference between multi-head, multi-query, and grouped-query attention.<br>[Source: Figure 2 of <a href="https://arxiv.org/abs/2305.13245">Ainslie et al., 2023</a>.]</figcaption>
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</figure>
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### Multi-head latent attention
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<figure>
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<img src="../../../images/notes/mla.png" class="center">
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<img src="/assets/images/notes/mla.png" class="center">
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<figcaption align = "center" style="max-width: 500px; margin: 0 auto;">Rather than caching each key and value individually, multi-head latent attention (MLA) caches a compressed latent, and then projects this compressed latent to keys and values.<br>[Source: Figure 3 of <a href="https://arxiv.org/abs/2405.04434">DeepSeek-AI, 2024</a>.]</figcaption>
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</figure>
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_pages/about.markdown

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</div>
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<div style="max-width: 210px; margin-left: 40px; margin-top: 40px; flex-basis: content">
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<!-- <figure>
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<img src="../../../images/about/doodle_portrait.jpg" style="border-radius: 3px;">
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<img src="/assets/images/about/doodle_portrait.jpg" style="border-radius: 3px;">
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<figcaption style="font-size: 12px; color: grey; text-align: center; padding-top: 5px;">
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A flattering doodle of my likeness.<br>
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[<i>Doodle of Andy</i> - GK]
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</figcaption>
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</figure> -->
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<figure>
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<img src="../../../images/about/littlefish.jpg" style="border-radius: 3px;">
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<img src="/assets/images/about/littlefish.jpg" style="border-radius: 3px;">
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<figcaption style="font-size: 11px; color: grey; text-align: center; padding-top: 5px;">
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A little fish that I am fond of.<br>
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[<a href="https://www.metmuseum.org/art/collection/search/338694" style="color: inherit;"><i>Big Fish Eat Little Fish</i> - Pieter Bruegel</a>]
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</figcaption>
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</figure>
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<figure style="padding-top: 20px;">
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<img src="../../../images/about/thinker.jpg" style="border-radius: 3px;"/>
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<img src="/assets/images/about/thinker.jpg" style="border-radius: 3px;"/>
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<figcaption style="font-size: 11px; color: grey; text-align: center; padding-top: 5px;">
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All I know is that I know nothing.<br>
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[<a href="https://www.metmuseum.org/art/collection/search/191811" style="color: inherit;"><i>The Thinker</i> - Auguste Rodin</a>]
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- [My favorite papers](/favorites/papers)
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- [My favorite quotes](/favorites/quotes)
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- [My favorite records](/favorites/records)
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<!-- This is the base Jekyll theme. You can find out more info about customizing your Jekyll theme, as well as basic Jekyll usage documentation at [jekyllrb.com](https://jekyllrb.com/)
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_pages/favorite_records.markdown

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_pages/home.markdown

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</div>
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<div style="max-width: 210px; margin-left: 40px; margin-top: 40px; flex-basis: content">
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<figure>
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<img src="../../../images/about/doodle_portrait.jpg" style="border-radius: 3px;">
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<img src="/assets/images/about/doodle_portrait.jpg" style="border-radius: 3px;">
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<figcaption style="font-size: 12px; color: grey; text-align: center; padding-top: 5px;">
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A flattering doodle of my likeness.<br>
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[<i>Doodle of Andy</i> - GK]

_papers/2024-06-17-refusal_dir_paper.markdown

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date: 2024-06-17 10:00:00 -0400
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external_url: https://arxiv.org/abs/2406.11717
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external_site: ArXiv
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external_site_logo_path: /images/misc/arxiv.svg
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external_site_logo_path: /assets/images/misc/arxiv.svg
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---

_posts/2022-05-24-stablecoins.markdown

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Here's a graph showing the volatility of Bitcoin over a two year period from May 2020 - May 2022:
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<img src="../../../images/stablecoins/bitcoin_volatile.png" class="center">
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<img src="/assets/images/stablecoins/bitcoin_volatile.png" class="center">
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<figcaption align = "center">Source: CoinGecko</figcaption>
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Tether initially launched on top of the Bitcoin blockchain[^2], but has since expanded to many blockchains, most notably Ethereum. This means that a user can obtain a representation of a USDT token on any of Tether's supported blockchains.
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<img src="../../../images/stablecoins/usdt_flow.png" class="center">
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<img src="/assets/images/stablecoins/usdt_flow.png" class="center">
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<figcaption align = "center">The flow of funds between USD and USDT</figcaption>
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<figcaption align = "center">[Source: Tether whitepaper]</figcaption>
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Tether Limited regularly publishes the balance of its reserve, comprised primarily of non-digital assets. It also hires 3rd party auditing companies to verify the published values. Tether Limited thus attempts to provide transparency into the assurance that USDT is backed sufficiently by USD. The below figure is the quarterly transparency report released by Tether Limited on March 31, 2022. It displays the breakdown of their reserve by asset type.
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<figure>
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<img src="../../../images/stablecoins/usdt_reserves.png" class="center">
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<img src="/assets/images/stablecoins/usdt_reserves.png" class="center">
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<figcaption align = "center">Tether's reported reserve breakdown as of March 31, 2022</figcaption>
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<figcaption align = "center">[Source: <a href="https://tether.to/en/transparency/">Tether transparency report</a>]</figcaption>
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Despite these clever exchange mechanics, UST eventually met the same fate as all algorithmic stablecoins that came before: it collapsed.
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<img src="../../../images/stablecoins/ust_graph.png" class="center">
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<img src="/assets/images/stablecoins/ust_graph.png" class="center">
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<figcaption align = "center">UST fell from its $1 peg in May 2022</figcaption>
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<figcaption align = "center">[Source: CoinGecko]</figcaption>
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Once knocked below its peg, UST holders became fearful that it would keep dropping - they wanted to get out before the house came down. They rushed to redeem their $$x$$ UST for $$x$$ USD worth of Luna, and then sold this Luna on DEXs. This caused DEXs to be flooded with fresh Luna supply, devaluing the price of Luna. This market devaluation of Luna makes it so that future UST redemptions require the minting of even more Luna, and one can see how the vicious cycle of hyperinflation is born.
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<img src="/assets/images/stablecoins/luna_supply.png" class="center">
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<figcaption align = "center">From 5/10 to 5/13, Luna supply increased over 18,000%</figcaption>
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<figcaption align = "center">[Source: <a href="https://twitter.com/MaxInvestor89/status/1524990394747998208">TerraScope</a>]</figcaption>
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<img src="/assets/images/stablecoins/luna_graph.png" class="center">
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_posts/2022-07-09-zk1.markdown

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Turns out there's a very simple and elegant interactive proof system for quadratic non-residuosity:
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<img src="/assets/images/zk1/ip_nonqr.png" class="center">
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<figcaption align = "center">Interactive proof system for quadratic non-residuosity</figcaption>
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<figcaption align = "center">[Source: <a href="https://youtu.be/6uGimDYZPMw">Lecture 1, Slide 19</a>]</figcaption>
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The following interactive proof system satisfies the definition of perfect ZK (and therefore honest-verifier ZK, since perfect ZK is a stronger definition):
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<img src="../../../images/zk1/zkip_qr.png" class="center">
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<img src="/assets/images/zk1/zkip_qr.png" class="center">
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<figcaption align = "center">Zero-knowledge interactive proof system for quadratic residuosity</figcaption>
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<figcaption align = "center">[Source: <a href="https://youtu.be/6uGimDYZPMw">Lecture 1, Slide 31</a>]</figcaption>
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_posts/2022-08-17-zk2.markdown

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For this post, we will consider a graph with $$n$$ vertices as being represented by an $$n \times n$$ adjacency matrix, where the $$(i,j)^{th}$$ entry is a 1 if the graph contains the edge $$i \rightarrow j$$, and 0 otherwise.
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<img src="/assets/images/zk2/zkp_ham_adjmat.png" class="center">
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<figcaption align = "center">Adjacency matrix representation of a graph G with a Hamiltonian cycle w (bolded)</figcaption>
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<figcaption align = "center">[Source: <a href="https://youtu.be/cQ-BI1WWzjU">Lecture 2, Slide 25</a>]</figcaption>
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<figcaption align = "center">Computationally zero-knowledge proof for HAM</figcaption>
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<figcaption align = "center">[Source: <a href="https://youtu.be/cQ-BI1WWzjU">Lecture 2, Slide 27</a>]</figcaption>
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_posts/2022-10-25-kzg.markdown

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external_url: https://scroll.io/blog/kzg
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external_site: Scroll
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