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From 03d230f846da096d618e6bf444a864c9dc87e85c Mon Sep 17 00:00:00 2001
From: GitHub Action <41898282+github-actions[bot]@users.noreply.github.com>
Date: Mon, 15 Jul 2024 08:35:02 +0000
Subject: [PATCH] update pub [ci skip]
---
.all-contributorsrc | 45 -
.github/FUNDING.yml | 12 -
.github/ISSUE_TEMPLATE/bug_report.md | 38 -
.github/ISSUE_TEMPLATE/feature_request.md | 20 -
.github/stale.yml | 18 -
.github/workflows/deploy-image.yml | 32 -
.github/workflows/deploy.yml | 42 -
.nojekyll | 0
404.html | 10 +-
Gemfile | 25 -
_bibliography/papers.bib | 580 -
_config.yml | 329 -
_data/coauthors.yml | 34 -
_data/cv.yml | 97 -
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_includes/cv/map.html | 8 -
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_includes/cv/time_table.html | 59 -
_includes/figure.html | 26 -
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_includes/head.html | 31 -
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_includes/news.html | 31 -
_includes/pagination.html | 17 -
_includes/people.html | 36 -
_includes/people_horizontal.html | 43 -
_includes/projects.html | 36 -
_includes/projects_horizontal.html | 43 -
_includes/scripts/analytics.html | 18 -
_includes/scripts/bootstrap.html | 3 -
_includes/scripts/jquery.html | 2 -
_includes/scripts/masonry.html | 6 -
_includes/scripts/mathjax.html | 13 -
_includes/scripts/misc.html | 14 -
_includes/selected_papers.html | 5 -
_includes/social.html | 57 -
_layouts/about.html | 76 -
_layouts/archive-category.html | 27 -
_layouts/archive-tag.html | 27 -
_layouts/archive-year.html | 27 -
_layouts/bib.html | 209 -
_layouts/cv.html | 35 -
_layouts/default.html | 34 -
_layouts/distill.html | 111 -
_layouts/none.html | 1 -
_layouts/page.html | 16 -
_layouts/post.html | 61 -
_news/announcement_1.md | 7 -
_news/announcement_2.md | 7 -
_pages/_cv.md | 8 -
_pages/_dropdown.md | 13 -
_pages/_projects.md | 58 -
_pages/_teaching.md | 12 -
_pages/about.md | 33 -
_pages/people.md | 58 -
_pages/publications.md | 18 -
_people/bowen_wang.md | 9 -
_people/chang_ma.md | 9 -
_people/chenxin_an.md | 9 -
_people/hongjing_su.md | 9 -
_people/jiacheng_ye.md | 9 -
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_people/lei_li.md | 9 -
_people/lin_zheng.md | 9 -
_people/lingpeng_kong.md | 9 -
_people/mukao_li.md | 9 -
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_people/qintong_li.md | 9 -
_people/sansa_gong.md | 9 -
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_people/tao_yu.md | 9 -
_people/tianbao_xie.md | 9 -
_people/who_next.md | 9 -
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_people/xueliang_zhao.md | 9 -
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_people/yiheng_xu.md | 9 -
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_projects/6_project.md | 80 -
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assets/css/main.css.map | 1 +
assets/css/main.scss | 15 -
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delete mode 100755 bin/cibuild
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delete mode 100755 bin/dockerhub_run.sh
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diff --git a/.all-contributorsrc b/.all-contributorsrc
deleted file mode 100644
index bc6a910..0000000
--- a/.all-contributorsrc
+++ /dev/null
@@ -1,45 +0,0 @@
-{
- "files": [
- "README.md"
- ],
- "imageSize": 100,
- "commit": false,
- "contributorsPerLine": 7,
- "projectName": "al-folio",
- "projectOwner": "alshedivat",
- "repoType": "github",
- "repoHost": "https://github.com",
- "badgeTemplate": "[core_contributors]: https://img.shields.io/badge/core_contributors-<%= contributors.length %>-orange.svg 'Number of core contributors'",
- "contributorTemplate": "\">\" width=\"<%= options.imageSize %>px;\" alt=\"\"/>
<%= contributor.name %>",
- "skipCi": true,
- "contributors": [
- {
- "login": "alshedivat",
- "name": "Maruan",
- "avatar_url": "https://avatars.githubusercontent.com/u/2126561?v=4",
- "profile": "http://maruan.alshedivat.com",
- "contributions": [
- "design",
- "code"
- ]
- },
- {
- "login": "rohandebsarkar",
- "name": "Rohan Deb Sarkar",
- "avatar_url": "https://avatars.githubusercontent.com/u/50144004?v=4",
- "profile": "http://rohandebsarkar.github.io",
- "contributions": [
- "code"
- ]
- },
- {
- "login": "pourmand1376",
- "name": "Amir Pourmand",
- "avatar_url": "https://avatars.githubusercontent.com/u/32064808?v=4",
- "profile": "https://amirpourmand.ir",
- "contributions": [
- "code"
- ]
- }
- ]
-}
diff --git a/.github/FUNDING.yml b/.github/FUNDING.yml
deleted file mode 100644
index c78502f..0000000
--- a/.github/FUNDING.yml
+++ /dev/null
@@ -1,12 +0,0 @@
-# These are supported funding model platforms
-
-github: # Replace with up to 4 GitHub Sponsors-enabled usernames e.g., [user1, user2]
-patreon: # Replace with a single Patreon username
-open_collective: # Replace with a single Open Collective username
-ko_fi: alshedivat
-tidelift: # Replace with a single Tidelift platform-name/package-name e.g., npm/babel
-community_bridge: # Replace with a single Community Bridge project-name e.g., cloud-foundry
-liberapay: # Replace with a single Liberapay username
-issuehunt: # Replace with a single IssueHunt username
-otechie: # Replace with a single Otechie username
-custom: # ['https://www.buymeacoffee.com/TkFxuKo']
diff --git a/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md
deleted file mode 100644
index 511f585..0000000
--- a/.github/ISSUE_TEMPLATE/bug_report.md
+++ /dev/null
@@ -1,38 +0,0 @@
----
-name: Bug report
-about: Create a report to help us improve
-title: ''
-labels: bug
-assignees: ''
-
----
-
-**Acknowledge the following**
-- [ ] I carefully read and followed the [Getting Started](https://github.com/alshedivat/al-folio#getting-started) guide.
-- [ ] I read through [FAQ](https://github.com/alshedivat/al-folio#faq) and searched through the [past issues](https://github.com/alshedivat/al-folio/issues), none of which addressed my issue.
-- [ ] The issue I am raising is a potential bug in al-folio and not just a usage question.
[For usage questions, please post in the [Discussions](https://github.com/alshedivat/al-folio/discussions) instead of raising an issue.]
-
-**Describe the bug**
-A clear and concise description of what the bug is.
-
-**To Reproduce**
-Steps to reproduce the behavior:
-1. Go to '...'
-2. Click on '....'
-3. Scroll down to '....'
-4. See error
-
-**Expected behavior**
-A clear and concise description of what you expected to happen.
-
-**Screenshots**
-If applicable, add screenshots to help explain your problem.
-
-**System (please complete the following information):**
- - OS: [e.g. iOS]
- - Browser (and its version) [e.g. chrome, safari]
- - Jekyll version [e.g. 3.8.7]
-- Ruby version [e.g. 2.6.5]
-
-**Additional context**
-Add any other context about the problem here.
diff --git a/.github/ISSUE_TEMPLATE/feature_request.md b/.github/ISSUE_TEMPLATE/feature_request.md
deleted file mode 100644
index 11fc491..0000000
--- a/.github/ISSUE_TEMPLATE/feature_request.md
+++ /dev/null
@@ -1,20 +0,0 @@
----
-name: Feature request
-about: Suggest an idea for this project
-title: ''
-labels: enhancement
-assignees: ''
-
----
-
-**Is your feature request related to a problem? Please describe.**
-A clear and concise description of what the problem is. Ex. I'm always frustrated when [...]
-
-**Describe the solution you'd like**
-A clear and concise description of what you want to happen.
-
-**Describe alternatives you've considered**
-A clear and concise description of any alternative solutions or features you've considered.
-
-**Additional context**
-Add any other context or screenshots about the feature request here.
diff --git a/.github/stale.yml b/.github/stale.yml
deleted file mode 100644
index 8ec2004..0000000
--- a/.github/stale.yml
+++ /dev/null
@@ -1,18 +0,0 @@
-# Number of days of inactivity before an issue becomes stale
-daysUntilStale: 60
-# Number of days of inactivity before a stale issue is closed
-daysUntilClose: 7
-# Issues with these labels will never be considered stale
-exemptLabels:
- - pinned
- - security
- - enhancement
-# Label to use when marking an issue as stale
-staleLabel: wontfix
-# Comment to post when marking an issue as stale. Set to `false` to disable
-markComment: >
- This issue has been automatically marked as stale because it has not had
- recent activity. It will be closed if no further activity occurs. Thank you
- for your contributions.
-# Comment to post when closing a stale issue. Set to `false` to disable
-closeComment: false
diff --git a/.github/workflows/deploy-image.yml b/.github/workflows/deploy-image.yml
deleted file mode 100644
index 93321b3..0000000
--- a/.github/workflows/deploy-image.yml
+++ /dev/null
@@ -1,32 +0,0 @@
-name: Docker Image CI
-
-on:
- push:
- branches: [ master ]
- pull_request:
- branches: [ master ]
-
-jobs:
-
- build:
-
- runs-on: ubuntu-latest
-
- steps:
- - name: Checkout
- uses: actions/checkout@v2
- - name: Buildx
- uses: docker/setup-buildx-action@v1
-
- - name: Login
- uses: docker/login-action@v1
- with:
- username: ${{ secrets.DOCKER_USERNAME }}
- password: ${{ secrets.DOCKER_PASSWORD }}
-
- - name: Build and push
- uses: docker/build-push-action@v2
- with:
- context: .
- push: true
- tags: amirpourmand/al-folio
diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml
deleted file mode 100644
index f6455fd..0000000
--- a/.github/workflows/deploy.yml
+++ /dev/null
@@ -1,42 +0,0 @@
-name: deploy
-
-on:
- push:
- branches:
- - master
- - main
- pull_request:
- branches:
- - master
- - main
-
-jobs:
- deploy:
- runs-on: ubuntu-latest
- steps:
- - name: Checkout code
- uses: actions/checkout@v3
- - name: Setup Ruby
- uses: ruby/setup-ruby@v1
- with:
- ruby-version: '3.0.2'
- bundler-cache: true
- - name: Install deps
- run: |
- npm install -g mermaid.cli
- - name: Setup deploy options
- id: setup
- run: |
- git config --global user.name "GitHub Action"
- git config --global user.email "41898282+github-actions[bot]@users.noreply.github.com"
- if [[ ${GITHUB_REF} = refs/pull/*/merge ]]; then # pull request
- echo "::set-output name=SRC_BRANCH::${GITHUB_HEAD_REF}"
- echo "::set-output name=NO_PUSH::--no-push"
- elif [[ ${GITHUB_REF} = refs/heads/* ]]; then # branch, e.g. master, source etc
- echo "::set-output name=SRC_BRANCH::${GITHUB_REF#refs/heads/}"
- fi
- echo "::set-output name=DEPLOY_BRANCH::gh-pages"
- - name: Deploy website
- run: yes | bash bin/deploy --verbose ${{ steps.setup.outputs.NO_PUSH }}
- --src ${{ steps.setup.outputs.SRC_BRANCH }}
- --deploy ${{ steps.setup.outputs.DEPLOY_BRANCH }}
diff --git a/.nojekyll b/.nojekyll
new file mode 100644
index 0000000..e69de29
diff --git a/404.html b/404.html
index 929fc57..1eb4d67 100644
--- a/404.html
+++ b/404.html
@@ -1,9 +1 @@
----
-layout: page
-permalink: /404.html
-title: "Page not found"
-description: "Looks like there has been a mistake. Nothing exists here."
-redirect: true
----
-
-
You will be redirected to the main page within 3 seconds. If not redirected, please click here.
+Looks like there has been a mistake. Nothing exists here.
You will be redirected to the main page within 3 seconds. If not redirected, please click here.
{{ content.name }} | -{{ content.value }} | -
{{ item.date | date: "%b %-d, %Y" }} | -
- {% if item.inline -%}
- {{ item.content | remove: ' ' | remove: ' ' | emojify }} - {%- else -%} - {{ item.title }} - {%- endif %} - |
-
---|
No news so far...
- {%- endif %} -{{ people.description }}
-{{ people.description }}
-{{ project.description }}
-{{ project.description }}
-{{ page.subtitle }}
-an archive of posts in this category
-{{ post.date | date: "%b %-d, %Y" }} | -- {{ post.title }} - | -
---|
an archive of posts with this tag
-{{ post.date | date: "%b %-d, %Y" }} | -- {{ post.title }} - | -
---|
an archive of posts from this year
-{{ post.date | date: "%b %-d, %Y" }} | -- {{ post.title }} - | -
---|
{{ page.description }}
-{{ page.description }}
-{{ page.description }}
-
-To estimate the expectation in \eqref{eqn:identity}, one can draw multiple Monte Carlo samples from $\mathcal{N}(\omega;0,\mathbf{I})$ such that $\exp(\mbx^{\top} \mby) \approx \frac{1}{S}\sum_{s=1}^S \xi(\mbx,\omega_s)^{\top}\xi(\mby, \omega_s)$. By substituting such approximation into the softmax attention, we obtain random feature attention (RFA)
Why it is called random feature attention?
- This is due to the fact that the sample average can be written as $\mbphi(\mbx,\mbw)^\top \mbphi(\mby,\mbw)$, where $\mbphi(\mbx,\mbw) \coloneqq 1/\sqrt{S}[\xi(\mbx,\omega_1), \dots, \xi(\mbx, \omega_S)]^\top \in \R^{lS}$. The $\mbphi(\cdot,\cdot)$ can be considered as a feature map transforming the input vector to a new vector representation; as a result, $\mbphi(\cdot,\cdot)$ are conveniently referred to as random features
- Our work aims to address the following research question:
- Given that we already know how to unbiasedly estimate exponential kernels, how do we construct an unbiased estimator for the whole softmax attention?
-
-We answer this question in the affirmative and prove that softmax attention can be rewritten as an expectation of simple RFAs, -$$ -\begin{equation} -\mathsf{SoftmaxAttn}(\mbq_n, \mbK,\mbV) = \sum_{m} \frac{\exp \left(\mathbf{q}_{n}^\top \mathbf{k}_{m} \right)}{\sum_{m'} \exp \left(\mathbf{q}_{n}^\top \mathbf{k}_{m'} \right)} \mathbf{v}_{m}^{\top} = \mathbb{E}_{p_n(\omega)}\left[f_n(\omega)\right],\label{eqn:softmax_as_expectation} -\end{equation} -$$ -where -$$ -\begin{align} -p_n(\omega) &= \sum_{m=1}^M \frac{\exp\left( \mbq_n^\top\mbk_m \right)}{\sum_{m'=1}^M\exp\left( \mbq_n^\top\mbk_{m'} \right)} \mathcal{N}(\omega; \mbq_n + \mbk_m, \mathbf{I}), \label{eqn:ra-density} \\ -f_n(\omega) &= \frac{\xi(\mbq_n,\omega)^\top \sum_{m=1}^M \xi(\mbk_m, \omega) \mbv_{m}^{\top}}{\xi(\mbq_n,\omega)^\top \sum_{m'=1}^M \xi(\mbk_{m'}, \omega)} \label{eqn:ra-function}. -\end{align} -$$ -Intuitively, -
-Notably, our result can be viewed as a neat generalization of random feature approximation, which exhibits a high degree of symmetry: -$$ -\begin{align} - \exp(\mbq_n^\top \mbk_m)\mbv_m^\top &= \mathbb{E}_{q(\omega)}\left[\xi(\mbq_n,\omega)^\top\xi(\mbk_m, \omega)\mbv_m^\top\right] \notag \\ - \sum_{m} \frac{\exp \left(\mathbf{q}_{n}^\top \mathbf{k}_{m} \right)}{\sum_{m'} \exp \left(\mathbf{q}_{n}^\top \mathbf{k}_{m'} \right)} \mathbf{v}_{m}^{\top} &= \mathbb{E}_{p_n(\omega)}\left[\frac{\xi(\mbq_n,\omega)^\top \sum_{m=1}^M \xi(\mbk_m, \omega) \mbv_{m}^{\top}}{\xi(\mbq_n,\omega)^\top \sum_{m'=1}^M \xi(\mbk_{m'}, \omega)}\right].\notag -\end{align} -$$ -Another implication is that we can construct a Monte Carlo estimator to approximate softmax attention in an unbiased way. By drawing $\omega_n \sim p_n(\omega)$, we obtain -$$ -\begin{align} - \mathsf{SoftmaxAttn}(\mbq_n, \mbK,\mbV) - &\approx \frac{\xi(\mbq_n,\omega_n)^\top \sum_{m=1}^M\xi(\mbk_m, \omega_n) \mbv_{m}^{\top}}{ \xi(\mbq_n,\omega_n)^\top \sum_{m'=1}^M\xi(\mbk_{m'}, \omega_n)} \label{eqn:ra}\\ - &\coloneqq \mathsf{RA}\left(\mbq_{n},\mbK,\mbV\right) \notag -\end{align} -$$ -We name such estimator Randomized Attention (RA) since it computes similarity scores with individual randomized mappings (instead of concatenated features). To the best of our knowledge, this is the first result that generalizes the unbiased kernel estimation to unbiased attention estimation. -
- -Remark: - The proof of \eqref{eqn:softmax_as_expectation} is done by first reverse-engineering the formulation of RFA, equating it with self-normalized importance sampling (see below) and then completing the square of Gaussians to derive the density $p_n(\omega)$. The function $f_n(\omega)$ can be solved by substituting the density $p_n(\omega)$ into the equation. See the paper for a detailed proof.
--Importance sampling (IS) is a general approach to approximating expectation $\mathbb{E}_{p_n(\omega)}\left[f_n(\omega)\right]$ when it is difficult to directly draw samples from $p_n(\omega)$. In importance sampling, we use a proposal distribution $q(\omega)$ to draw samples and estimate the quantity as -$$ -\mathbb{E}_{p_n(\omega)}\left[f_n(\omega)\right] = \mathbb{E}_{\omega \sim q(\omega)}\left[\frac{p_n(\omega)}{q(\omega)}f_n(\omega)\right] \approx \frac{1}{S} \sum_{s=1}^S \frac{p_n(\omega)}{q(\omega)} f_n(\omega_s), -$$ -where $\omega_1, \dots, \omega_S \sim q(\omega)$. The self-normalized importance sampling (SNIS) is defined as -$$ -\begin{equation} - \mathbb{E}_{p_n(\omega)}\left[f_n(\omega)\right] \approx \frac{\sum_{s=1}^S\frac{p_n(\omega_s)}{q(\omega_s)}f(\omega_s)}{\sum_{s=1}^S\frac{p_n(\omega_s)}{q(\omega_s)}} = \sum_{s=1}^S\frac{\frac{p_n(\omega_s)}{q(\omega_s)}}{\sum_{s=1}^S\frac{p_n(\omega_s)}{q(\omega_s)}}f(\omega_s). \label{eqn:snis} -\end{equation} -$$ -The name self-normalized comes from the fact that the importance weights $p_n(\omega)/q(\omega)$ are explicitly normalized and sum to 1. -
- - - - -### RFA as SNIS -Our key finding here is that the formulation of RFA can be exactly derived from SNIS. Supposing $p_n(\omega)$ and $f_n(\omega)$ are given in \eqref{eqn:ra-density} and \eqref{eqn:ra-function} respectively, and $q(\omega) = \mathcal{N}(\omega;0,\mathbf{I})$, we have -$$ -\begin{align} -\mathsf{RFA}\left(\mbq_{n},\mbK,\mbV\right) -&= \frac{\sum_{s=1}^S\textcolor{strings}{\xi(\mbq_n,\omega_s)^{\top}\sum_{m=1}^M\xi(\mbk_m, \omega_s)\mbv_{m}^{\top}}}{\sum_{s=1}^S \textcolor{keywords}{\xi(\mbq_n,\omega_s)^{\top}\sum_{m'=1}^M\xi(\mbk_{m'}, \omega_s)}} = \frac{ \sum_{s=1}^S\textcolor{strings}{\frac{p_n(\omega_s)}{q(\omega_s)} f(\omega_s)}}{ \sum_{s=1}^S\textcolor{keywords}{\frac{p_n(\omega_s)}{q(\omega_s)}}}. \label{eqn:rfa-as-snis} -\end{align} -$$ -This formulation provides a new understanding of RFA: it is just a specific instantiation of SNIS estimators for softmax attention, whose proposal distribution $q(\omega)$ is chosen to be standard Gaussian. This reveals one of the possible reasons why RFA does not work well in practice: The plain standard Gaussian proposal in RFA is far away from the true Gaussian mixture (as in RA), which might lead to a large approximation gap. More importantly, this view implies that we can generalize and extend RFA by using other proposal distributions or adopting other estimating schemes!
- -## LARA: Generalizing Both RA and RFA -So far, we have two types of estimators available for approximating softmax attention: unbiased RA and biased RFA. Besides the theoretical biasedness, how do they differ in terms of practical modeling behavior? We list a comprehensive comparison to better illustrate their main differences. - -- In terms of **expressiveness**: - - ✔️ RA directly draws from the true distribution $p_n(\omega)$ \eqref{eqn:ra-density}. This makes the mechanism **adaptive** and **query-specific**, since the sampling distribution depends on the query vector. As a result, RA can **specialize** to each query and process the whole sequence at a finer-grained level. - - ❌ RFA suffers from limited capacity, since there is a large discrepancy between the used proposal $q(\omega) = \mathcal{N}(\omega;0,\mathbf{I})$ and the true distribution $p_n(\omega)$; furthermore, $q(\omega)$ captures no contextual information, leading to low sample efficiency. -- In terms of **efficiency**: - - ❌ RA suffers from **quadratic** computational costs. Since the sampling distribution is distinct for each query, we have to draw at least $\mathcal{O}(N)$ samples for all queries; at the same time, we needs to sum over all $M$ key-value pairs at each sampled $\omega_n$ (see \eqref{eqn:ra}), which leads to $\mathcal{O}(NM)$ complexity overall, as is the case for softmax attention; - - ✔️ RFA uses SNIS to avoid computing or sampling from $p_n(\omega)$, which require quadratic-time computation. Drawing from a simpler proposal distribution allows samples to be shared across queries and still resulting in a $\mathcal{O}(M)$ complexity. --LARA takes the following form -$$ -\begin{align} -\mathsf{LARA}\left(\mbq_{n},\mbK,\mbV\right) &= \frac{\sum_{c=1}^C\alpha_{nc}(\omega_c)\frac{p_n(\omega_c)}{q_c(\omega_c)} f_n(\omega_c)}{\sum_{c=1}^C\alpha_{nc}(\omega_c)\frac{p_n(\omega_c)}{q_c(\omega_c)}}.\label{eqn:lara} -\end{align} -$$ -Here, -
Remark: - We provide a detailed discussion about the parameterization of our proposal distributions in Appendix G.3 of our paper. To summarize, we find the key is to let different proposals depend on different sets of query information so that they could be as query-specific as possible. A good default is to divide the whole sequence into $C$ chunks, compute the mean of queries $\{\widetilde{\mbq}_c\}_{c=1}^C$ and keys $\{\widetilde{\mbk}_c\}_{c=1}^C$ within the same chunk, and set $q_c(\omega) = \mcN(\omega;\widetilde{\mbq}_c + \widetilde{\mbk}_c, \mathbf{I})$. We find this choice works well across various benchmarks.
- LARA can be equivalently written in a similar way to RA and RFA. We spell it out here to see a systematic comparison among RA, LARA, and RFA:
-$$
-\begin{align}
-\mathsf{RA}\left(\mbq_{n},\mbK,\mbV\right) &= \frac{\xi(\mbq_n,\omega_n)^\top \sum_{m=1}^M\xi(\mbk_m, \omega_n) \mbv_{m}^{\top}}{ \xi(\mbq_n,\omega_n)^\top \sum_{m'=1}^M\xi(\mbk_{m'}, \omega_n)}, &&\textcolor{keywords}{\omega_n \sim p_n(\omega)}\notag\\
-\mathsf{LARA}\left(\mbq_{n},\mbK,\mbV\right) &= \frac{\sum_{c=1}^C \textcolor{strings}{\alpha'_{nc}(\omega_c)} \xi(\mbq_n,\omega_c)^\top \sum_{m=1}^M\xi(\mbk_m, \omega_c) \mbv_{m}^{\top}}{\sum_{c=1}^C \textcolor{strings}{\alpha'_{nc}(\omega_c)} \xi(\mbq_n,\omega_c)^\top \sum_{m=1}^M \xi(\mbk_{m}, \omega_c)}, &&\textcolor{keywords}{\omega_c \sim q_c(\omega)}\notag\\
-\mathsf{RFA}\left(\mbq_{n},\mbK,\mbV\right) &= \frac{ \sum_{s=1}^S\xi(\mbq_n,\omega_s)^{\top}\sum_{m=1}^M\xi(\mbk_m, \omega_s)\mbv_{m}^{\top}}{\sum_{s=1}^S \xi(\mbq_n,\omega_s)^{\top}\sum_{m'=1}^M\xi(\mbk_{m'}, \omega_s)}, &&\textcolor{keywords}{\omega_1,\dots,\omega_S \sim \mcN(\omega;0, \mathbf{I})} \notag
-\end{align}
-$$
-where we denote $\alpha'_{nc}(\omega_c) \coloneqq \alpha_{nc}(\omega_c)\mcN(\omega_c;0, \mathbf{I})/q_c(\omega_c)$ to simplify the notation. Note that their major difference lies in the choice of sampling distributions.
-
-LARA is not designed to be a simple interpolation between RA and RFA; instead, it is a generalized estimation framework that includes both RA and RFA as its special cases. To see this,
-
- We do not grow absolutely, chronologically. We grow sometimes in one dimension, and not in another, unevenly. We grow partially. We are relative. We are mature in one realm, childish in another. - —Anais Nin -- -Fap aliqua qui, scenester pug Echo Park polaroid irony shabby chic ex cardigan church-key Odd Future accusamus. Blog stumptown sartorial squid, gastropub duis aesthetic Truffaut vero. Pinterest tilde twee, odio mumblecore jean shorts lumbersexual. - - - -# Tweet -An example of displaying a tweet: -{% twitter https://twitter.com/rubygems/status/518821243320287232 %} - -# Timeline -An example of pulling from a timeline: -{% twitter https://twitter.com/jekyllrb maxwidth=500 limit=3 %} - -# Additional Details -For more details on using the plugin visit: [jekyll-twitter-plugin](https://github.com/rob-murray/jekyll-twitter-plugin) - - -This theme supports generating various diagrams from a text description using [jekyll-diagrams](https://github.com/zhustec/jekyll-diagrams){:target="\_blank"} plugin. -Below, we generate a few examples of such diagrams using languages such as [mermaid](https://mermaid-js.github.io/mermaid/){:target="\_blank"}, [plantuml](https://plantuml.com/){:target="\_blank"}, [vega-lite](https://vega.github.io/vega-lite/){:target="\_blank"}, etc. - -**Note:** different diagram-generation packages require external dependencies to be installed on your machine. -Also, be mindful of that because of diagram generation the fist time you build your Jekyll website after adding new diagrams will be SLOW. -For any other details, please refer to [jekyll-diagrams](https://github.com/zhustec/jekyll-diagrams){:target="\_blank"} README. - - -## Mermaid - -Install mermaid using `node.js` package manager `npm` by running the following command: -```bash -npm install -g mermaid.cli -``` - -The diagram below was generated by the following code: - -{% raw %} -``` -{% mermaid %} -sequenceDiagram - participant John - participant Alice - Alice->>John: Hello John, how are you? - John-->>Alice: Great! -{% endmermaid %} -``` -{% endraw %} - -{% mermaid %} -sequenceDiagram - participant John - participant Alice - Alice->>John: Hello John, how are you? - John-->>Alice: Great! -{% endmermaid %} - - - -A sample blog page that demonstrates the accessing of github meta data. - -## What does Github-MetaData do? -* Propagates the site.github namespace with repository metadata -* Setting site variables : - * site.title - * site.description - * site.url - * site.baseurl -* Accessing the metadata - duh. -* Generating edittable links. - -## Additional Reading -* If you're recieving incorrect/missing data, you may need to perform a Github API authentication. -* Go through this README for more details on the topic. -* This page highlights all the feilds you can access with github-metadata. -
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