diff --git a/docs/.buildinfo b/docs/.buildinfo
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--- /dev/null
+++ b/docs/.buildinfo
@@ -0,0 +1,4 @@
+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 8c66866e4e6daa0996d712fe951a8221
+tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/docs/.nojekyll b/docs/.nojekyll
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index 0000000..e69de29
diff --git a/docs/_sources/index.rst.txt b/docs/_sources/index.rst.txt
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+++ b/docs/_sources/index.rst.txt
@@ -0,0 +1,15 @@
+.. Lightning-AI-Sandbox documentation master file, created by
+   sphinx-quickstart on Wed Mar 25 21:34:07 2020.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+.. include:: readme.rst
+
+
+.. toctree::
+   :maxdepth: 1
+   :name: start
+   :caption: Start here
+
+   strategy_advanced
+   strategy_expert
diff --git a/docs/_sources/readme.rst.txt b/docs/_sources/readme.rst.txt
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+++ b/docs/_sources/readme.rst.txt
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+Lightning + Hivemind
+====================
+
+Collaborative Training tries to solve the need for top-tier multi-GPU
+servers by allowing you to train across unreliable machines, such as
+local machines or even preemptible cloud computing across the internet.
+
+Under the hood, we use
+`Hivemind <https://github.com/learning-at-home/hivemind>`__, which
+provides de-centralized training across the internet.
+
+To use Collaborative Training, you need first to have this extension.
+
+.. code:: bash
+
+   pip install -U lightning-Hivemind
+
+The ``HivemindStrategy`` accumulates gradients from all collaborating
+processes until they reach a ``target_batch_size``. By default, we use
+the batch size of the first batch to determine what each local machine
+batch contributes towards the ``target_batch_size``. Once the
+``target_batch_size`` is reached, an optimizer step is made on all
+processes.
+
+When using ``HivemindStrategy``, note that you cannot use gradient
+accumulation (``accumulate_grad_batches``). This is because Hivemind
+manages accumulation internally.
+
+.. code:: py
+
+   from lightning import Trainer
+   from lightning_hivemind.strategy import HivemindStrategy
+
+   trainer = Trainer(strategy=HivemindStrategy(target_batch_size=8192), accelerator="gpu", devices=1)
+
+Followed by:
+
+.. code:: bash
+
+   python train.py
+   # Other machines can connect by running the same command:
+   # INITIAL_PEERS=... python train.py
+   # or passing the peers to the strategy:"
+   # HivemindStrategy(initial_peers=...)"
+
+A helper message is printed once your training begins, showing you how
+to train on other machines using the same code.
diff --git a/docs/_sources/strategy_advanced.rst.txt b/docs/_sources/strategy_advanced.rst.txt
new file mode 100644
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--- /dev/null
+++ b/docs/_sources/strategy_advanced.rst.txt
@@ -0,0 +1,97 @@
+.. _hivemind_intermediate:
+
+Training on unreliable mixed GPUs across the internet (Advanced)
+================================================================
+
+Reducing Communication By Overlapping Communication
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+We can reduce the impact of communication across all machines by overlapping communication with our training iterations. In short, we enable communication to happen
+in the background of training.
+
+Overlap Gradient and State Averaging
+""""""""""""""""""""""""""""""""""""
+
+When the target batch size is reached, all processes that are included in the step send gradients and model states to each other. By enabling some flags through
+the strategy, communication can happen in the background. This allows training to continue (with slightly outdated weights) but provides us the means
+to overlap communication with computation.
+
+.. warning::
+    Enabling overlapping communication means convergence will slightly be affected.
+
+.. note::
+    Enabling these flags means that you must pass in a ``scheduler_fn`` to the ``HivemindStrategy`` instead of relying on a scheduler from ``configure_optimizers``.
+    The optimizer is re-created by Hivemind, and as a result, the scheduler has to be re-created.
+
+.. code-block:: python
+
+    import torch
+    from functools import partial
+    from pytorch_lightning import Trainer
+    from lightning_hivemind.strategy import HivemindStrategy
+
+    trainer = Trainer(
+        strategy=HivemindStrategy(
+            target_batch_size=8192,
+            delay_state_averaging=True,
+            delay_grad_averaging=True,
+            delay_optimizer_step=True,
+            offload_optimizer=True,  # required to delay averaging
+            scheduler_fn=partial(torch.optim.lr_scheduler.ExponentialLR, gamma=...),
+        ),
+        accelerator="gpu",
+        devices=1,
+    )
+
+
+Reducing GPU Memory requirements by re-using buffers & CPU offloading
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+We can also offload the optimizer state to the CPU whilst re-using gradient buffers to reduce the memory requirement for machines.
+
+Offloading Optimizer State to the CPU
+"""""""""""""""""""""""""""""""""""""
+
+Offloading the Optimizer state to the CPU works the same as Deepspeed Zero-stage-2-offload, where we save GPU memory by keeping all optimizer states on the CPU.
+
+.. note::
+    Enabling these flags means that you must pass in a ``scheduler_fn`` to the ``HivemindStrategy`` instead of relying on a scheduler from ``configure_optimizers``.
+    The optimizer is re-created by Hivemind, and as a result, the scheduler has to be re-created.
+
+    We suggest enabling offloading and overlapping communication to hide the additional overhead from having to communicate with the CPU.
+
+.. code-block:: python
+
+    import torch
+    from functools import partial
+    from pytorch_lightning import Trainer
+    from lightning_hivemind.strategy import HivemindStrategy
+
+    trainer = Trainer(
+        strategy=HivemindStrategy(
+            target_batch_size=8192,
+            offload_optimizer=True,
+            scheduler_fn=partial(torch.optim.lr_scheduler.ExponentialLR, gamma=...),
+        ),
+        accelerator="gpu",
+        devices=1,
+    )
+
+
+Re-using Gradient Buffers
+"""""""""""""""""""""""""
+
+By default, Hivemind accumulates gradients in a separate buffer. This means additional GPU memory is required to store gradients. You can enable re-using the model parameter gradient buffers by passing ``reuse_grad_buffers=True`` to the ``HivemindStrategy``.
+
+.. warning::
+    The ``HivemindStrategy`` will override ``zero_grad`` in your ``LightningModule`` to have no effect. This is because gradients are accumulated in the model
+    and Hivemind manages when they need to be cleared.
+
+.. code-block:: python
+
+    from pytorch_lightning import Trainer
+    from lightning_hivemind.strategy import HivemindStrategy
+
+    trainer = Trainer(
+        strategy=HivemindStrategy(target_batch_size=8192, reuse_grad_buffers=True), accelerator="gpu", devices=1
+    )
diff --git a/docs/_sources/strategy_expert.rst.txt b/docs/_sources/strategy_expert.rst.txt
new file mode 100644
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--- /dev/null
+++ b/docs/_sources/strategy_expert.rst.txt
@@ -0,0 +1,85 @@
+.. _hivemind_expert:
+
+Training on unreliable mixed GPUs across the internet (Expert)
+==============================================================
+
+Using Compression to Optimize Communications
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Below are some ways to reduce communication when training collaboratively. As the size of your model increase, bottlenecks in communication become more apparent.
+
+Compress Gradients & State
+""""""""""""""""""""""""""
+
+Hivemind allows you to compress gradients and states before sending them to other machines. This helps reduce the communication overhead substantially when training across the internet.
+
+Below, we enable Float16 compression, which compresses gradients and states to Float16 before sending it to other machines.
+
+.. note::
+    Compressing gradients can affect convergence if you're lowering the precision (i.e training in Float32, but compressing gradients to FP16).
+
+.. code-block:: python
+
+    from hivemind import Float16Compression
+    from pytorch_lightning import Trainer
+    from lightning_hivemind.strategy import HivemindStrategy
+
+    trainer = Trainer(
+        strategy=HivemindStrategy(
+            target_batch_size=target_batch_size,
+            grad_compression=Float16Compression(),
+            state_averaging_compression=Float16Compression(),
+        ),
+        accelerator="gpu",
+        devices=1,
+    )
+
+A slightly more advanced scheme is dynamic compression based on value size. Below, we enable 8-bit quantization for large numbers, and Float16 compression for small values, reducing communication bottlenecks even further.
+
+Size Adaptive Compression has been used in a variety of Hivemind applications and has shown success, but does quantize gradients further, meaning we lose precision when compressing.
+
+.. code-block:: python
+
+    from hivemind import Float16Compression, Uniform8BitQuantization
+    from pytorch_lightning import Trainer
+    from lightning_hivemind.strategy import HivemindStrategy
+
+    # compresses values above threshold with 8bit Quantization, lower with Float16
+    compression = SizeAdaptiveCompression(
+        threshold=2 ** 16 + 1, less=Float16Compression(), greater_equal=Uniform8BitQuantization()
+    )
+    trainer = Trainer(
+        strategy=HivemindStrategy(
+            target_batch_size=target_batch_size,
+            grad_compression=compression,
+            state_averaging_compression=compression,
+        ),
+        accelerator="gpu",
+        devices=1,
+    )
+
+
+PowerSGD
+""""""""
+
+`PowerSGD <https://arxiv.org/abs/1905.13727>`_ is a technique to reduce distributed communication of gradients across processes.
+In short, PowerSGD uses a low-rank approximation to compress gradients before running an `all-reduce` step to sync gradients across all processes.
+
+.. note::
+    Though PowerSGD can impact convergence, it can also substantially reduce communication between processes.
+
+.. code-block:: python
+
+    from pytorch_lightning import Trainer
+    from lightning_hivemind.strategy import HivemindStrategy
+    from functools import partial
+    from hivemind.optim.power_sgd_averager import PowerSGDGradientAverager
+
+    trainer = Trainer(
+        strategy=HivemindStrategy(
+            target_batch_size=8192,
+            grad_averager_factory=partial(PowerSGDGradientAverager, averager_rank=32, min_compression_ratio=0.5),
+        ),
+        accelerator="gpu",
+        devices=1,
+    )
diff --git a/docs/_static/basic.css b/docs/_static/basic.css
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index 0000000..7577acb
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+ul.simple ul p {
+    margin-top: 0;
+}
+
+ol.simple > li:not(:first-child) > p,
+ul.simple > li:not(:first-child) > p {
+    margin-top: 0;
+}
+
+ol.simple p,
+ul.simple p {
+    margin-bottom: 0;
+}
+
+aside.footnote > span,
+div.citation > span {
+    float: left;
+}
+aside.footnote > span:last-of-type,
+div.citation > span:last-of-type {
+  padding-right: 0.5em;
+}
+aside.footnote > p {
+  margin-left: 2em;
+}
+div.citation > p {
+  margin-left: 4em;
+}
+aside.footnote > p:last-of-type,
+div.citation > p:last-of-type {
+    margin-bottom: 0em;
+}
+aside.footnote > p:last-of-type:after,
+div.citation > p:last-of-type:after {
+    content: "";
+    clear: both;
+}
+
+dl.field-list {
+    display: grid;
+    grid-template-columns: fit-content(30%) auto;
+}
+
+dl.field-list > dt {
+    font-weight: bold;
+    word-break: break-word;
+    padding-left: 0.5em;
+    padding-right: 5px;
+}
+
+dl.field-list > dd {
+    padding-left: 0.5em;
+    margin-top: 0em;
+    margin-left: 0em;
+    margin-bottom: 0em;
+}
+
+dl {
+    margin-bottom: 15px;
+}
+
+dd > :first-child {
+    margin-top: 0px;
+}
+
+dd ul, dd table {
+    margin-bottom: 10px;
+}
+
+dd {
+    margin-top: 3px;
+    margin-bottom: 10px;
+    margin-left: 30px;
+}
+
+dl > dd:last-child,
+dl > dd:last-child > :last-child {
+    margin-bottom: 0;
+}
+
+dt:target, span.highlighted {
+    background-color: #fbe54e;
+}
+
+rect.highlighted {
+    fill: #fbe54e;
+}
+
+dl.glossary dt {
+    font-weight: bold;
+    font-size: 1.1em;
+}
+
+.versionmodified {
+    font-style: italic;
+}
+
+.system-message {
+    background-color: #fda;
+    padding: 5px;
+    border: 3px solid red;
+}
+
+.footnote:target  {
+    background-color: #ffa;
+}
+
+.line-block {
+    display: block;
+    margin-top: 1em;
+    margin-bottom: 1em;
+}
+
+.line-block .line-block {
+    margin-top: 0;
+    margin-bottom: 0;
+    margin-left: 1.5em;
+}
+
+.guilabel, .menuselection {
+    font-family: sans-serif;
+}
+
+.accelerator {
+    text-decoration: underline;
+}
+
+.classifier {
+    font-style: oblique;
+}
+
+.classifier:before {
+    font-style: normal;
+    margin: 0 0.5em;
+    content: ":";
+    display: inline-block;
+}
+
+abbr, acronym {
+    border-bottom: dotted 1px;
+    cursor: help;
+}
+
+/* -- code displays --------------------------------------------------------- */
+
+pre {
+    overflow: auto;
+    overflow-y: hidden;  /* fixes display issues on Chrome browsers */
+}
+
+pre, div[class*="highlight-"] {
+    clear: both;
+}
+
+span.pre {
+    -moz-hyphens: none;
+    -ms-hyphens: none;
+    -webkit-hyphens: none;
+    hyphens: none;
+    white-space: nowrap;
+}
+
+div[class*="highlight-"] {
+    margin: 1em 0;
+}
+
+td.linenos pre {
+    border: 0;
+    background-color: transparent;
+    color: #aaa;
+}
+
+table.highlighttable {
+    display: block;
+}
+
+table.highlighttable tbody {
+    display: block;
+}
+
+table.highlighttable tr {
+    display: flex;
+}
+
+table.highlighttable td {
+    margin: 0;
+    padding: 0;
+}
+
+table.highlighttable td.linenos {
+    padding-right: 0.5em;
+}
+
+table.highlighttable td.code {
+    flex: 1;
+    overflow: hidden;
+}
+
+.highlight .hll {
+    display: block;
+}
+
+div.highlight pre,
+table.highlighttable pre {
+    margin: 0;
+}
+
+div.code-block-caption + div {
+    margin-top: 0;
+}
+
+div.code-block-caption {
+    margin-top: 1em;
+    padding: 2px 5px;
+    font-size: small;
+}
+
+div.code-block-caption code {
+    background-color: transparent;
+}
+
+table.highlighttable td.linenos,
+span.linenos,
+div.highlight span.gp {  /* gp: Generic.Prompt */
+  user-select: none;
+  -webkit-user-select: text; /* Safari fallback only */
+  -webkit-user-select: none; /* Chrome/Safari */
+  -moz-user-select: none; /* Firefox */
+  -ms-user-select: none; /* IE10+ */
+}
+
+div.code-block-caption span.caption-number {
+    padding: 0.1em 0.3em;
+    font-style: italic;
+}
+
+div.code-block-caption span.caption-text {
+}
+
+div.literal-block-wrapper {
+    margin: 1em 0;
+}
+
+code.xref, a code {
+    background-color: transparent;
+    font-weight: bold;
+}
+
+h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
+    background-color: transparent;
+}
+
+.viewcode-link {
+    float: right;
+}
+
+.viewcode-back {
+    float: right;
+    font-family: sans-serif;
+}
+
+div.viewcode-block:target {
+    margin: -1px -10px;
+    padding: 0 10px;
+}
+
+/* -- math display ---------------------------------------------------------- */
+
+img.math {
+    vertical-align: middle;
+}
+
+div.body div.math p {
+    text-align: center;
+}
+
+span.eqno {
+    float: right;
+}
+
+span.eqno a.headerlink {
+    position: absolute;
+    z-index: 1;
+}
+
+div.math:hover a.headerlink {
+    visibility: visible;
+}
+
+/* -- printout stylesheet --------------------------------------------------- */
+
+@media print {
+    div.document,
+    div.documentwrapper,
+    div.bodywrapper {
+        margin: 0 !important;
+        width: 100%;
+    }
+
+    div.sphinxsidebar,
+    div.related,
+    div.footer,
+    #top-link {
+        display: none;
+    }
+}
\ No newline at end of file
diff --git a/docs/_static/copybutton.js b/docs/_static/copybutton.js
new file mode 100644
index 0000000..453363c
--- /dev/null
+++ b/docs/_static/copybutton.js
@@ -0,0 +1,64 @@
+/* Copied from the official Python docs: https://docs.python.org/3/_static/copybutton.js */
+$(document).ready(function() {
+    /* Add a [>>>] button on the top-right corner of code samples to hide
+     * the >>> and ... prompts and the output and thus make the code
+     * copyable. */
+    var div = $('.highlight-python .highlight,' +
+                '.highlight-python3 .highlight,' +
+                '.highlight-pycon .highlight,' +
+                '.highlight-default .highlight');
+    var pre = div.find('pre');
+
+    // get the styles from the current theme
+    pre.parent().parent().css('position', 'relative');
+    var hide_text = 'Hide the prompts and output';
+    var show_text = 'Show the prompts and output';
+    var border_width = pre.css('border-top-width');
+    var border_style = pre.css('border-top-style');
+    var border_color = pre.css('border-top-color');
+    var button_styles = {
+        'cursor':'pointer', 'position': 'absolute', 'top': '0', 'right': '0',
+        'border-color': border_color, 'border-style': border_style,
+        'border-width': border_width, 'color': border_color, 'text-size': '75%',
+        'font-family': 'monospace', 'padding-left': '0.2em', 'padding-right': '0.2em',
+        'border-radius': '0 3px 0 0'
+    }
+
+    // create and add the button to all the code blocks that contain >>>
+    div.each(function(index) {
+        var jthis = $(this);
+        if (jthis.find('.gp').length > 0) {
+            var button = $('<span class="copybutton">&gt;&gt;&gt;</span>');
+            button.css(button_styles)
+            button.attr('title', hide_text);
+            button.data('hidden', 'false');
+            jthis.prepend(button);
+        }
+        // tracebacks (.gt) contain bare text elements that need to be
+        // wrapped in a span to work with .nextUntil() (see later)
+        jthis.find('pre:has(.gt)').contents().filter(function() {
+            return ((this.nodeType == 3) && (this.data.trim().length > 0));
+        }).wrap('<span>');
+    });
+
+    // define the behavior of the button when it's clicked
+    $('.copybutton').click(function(e){
+        e.preventDefault();
+        var button = $(this);
+        if (button.data('hidden') === 'false') {
+            // hide the code output
+            button.parent().find('.go, .gp, .gt').hide();
+            button.next('pre').find('.gt').nextUntil('.gp, .go').css('visibility', 'hidden');
+            button.css('text-decoration', 'line-through');
+            button.attr('title', show_text);
+            button.data('hidden', 'true');
+        } else {
+            // show the code output
+            button.parent().find('.go, .gp, .gt').show();
+            button.next('pre').find('.gt').nextUntil('.gp, .go').css('visibility', 'visible');
+            button.css('text-decoration', 'none');
+            button.attr('title', hide_text);
+            button.data('hidden', 'false');
+        }
+    });
+});
diff --git a/docs/_static/css/theme.css b/docs/_static/css/theme.css
new file mode 100644
index 0000000..a784b0e
--- /dev/null
+++ b/docs/_static/css/theme.css
@@ -0,0 +1,8 @@
+/*!
+ * Bootstrap v4.6.1 (https://getbootstrap.com/)
+ * Copyright 2011-2021 The Bootstrap Authors
+ * Copyright 2011-2021 Twitter, Inc.
+ * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+ */:root{--blue: #007bff;--indigo: #6610f2;--purple: #6f42c1;--pink: #e83e8c;--red: #dc3545;--orange: #fd7e14;--yellow: #ffc107;--green: #28a745;--teal: #20c997;--cyan: #17a2b8;--white: #fff;--gray: #6c757d;--gray-dark: #343a40;--primary: #007bff;--secondary: #6c757d;--success: #28a745;--info: #17a2b8;--warning: #ffc107;--danger: #dc3545;--light: #f8f9fa;--dark: #343a40;--breakpoint-xs: 0;--breakpoint-sm: 576px;--breakpoint-md: 768px;--breakpoint-lg: 992px;--breakpoint-xl: 1200px;--font-family-sans-serif: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, "Noto Sans", "Liberation Sans", sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol", "Noto Color Emoji";--font-family-monospace: SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", 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+
+/*# sourceMappingURL=theme.css.map */
diff --git a/docs/_static/doctools.js b/docs/_static/doctools.js
new file mode 100644
index 0000000..d06a71d
--- /dev/null
+++ b/docs/_static/doctools.js
@@ -0,0 +1,156 @@
+/*
+ * doctools.js
+ * ~~~~~~~~~~~
+ *
+ * Base JavaScript utilities for all Sphinx HTML documentation.
+ *
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+"use strict";
+
+const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([
+  "TEXTAREA",
+  "INPUT",
+  "SELECT",
+  "BUTTON",
+]);
+
+const _ready = (callback) => {
+  if (document.readyState !== "loading") {
+    callback();
+  } else {
+    document.addEventListener("DOMContentLoaded", callback);
+  }
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const Documentation = {
+  init: () => {
+    Documentation.initDomainIndexTable();
+    Documentation.initOnKeyListeners();
+  },
+
+  /**
+   * i18n support
+   */
+  TRANSLATIONS: {},
+  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
+  LOCALE: "unknown",
+
+  // gettext and ngettext don't access this so that the functions
+  // can safely bound to a different name (_ = Documentation.gettext)
+  gettext: (string) => {
+    const translated = Documentation.TRANSLATIONS[string];
+    switch (typeof translated) {
+      case "undefined":
+        return string; // no translation
+      case "string":
+        return translated; // translation exists
+      default:
+        return translated[0]; // (singular, plural) translation tuple exists
+    }
+  },
+
+  ngettext: (singular, plural, n) => {
+    const translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated !== "undefined")
+      return translated[Documentation.PLURAL_EXPR(n)];
+    return n === 1 ? singular : plural;
+  },
+
+  addTranslations: (catalog) => {
+    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
+    Documentation.PLURAL_EXPR = new Function(
+      "n",
+      `return (${catalog.plural_expr})`
+    );
+    Documentation.LOCALE = catalog.locale;
+  },
+
+  /**
+   * helper function to focus on search bar
+   */
+  focusSearchBar: () => {
+    document.querySelectorAll("input[name=q]")[0]?.focus();
+  },
+
+  /**
+   * Initialise the domain index toggle buttons
+   */
+  initDomainIndexTable: () => {
+    const toggler = (el) => {
+      const idNumber = el.id.substr(7);
+      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
+      if (el.src.substr(-9) === "minus.png") {
+        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
+        toggledRows.forEach((el) => (el.style.display = "none"));
+      } else {
+        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
+        toggledRows.forEach((el) => (el.style.display = ""));
+      }
+    };
+
+    const togglerElements = document.querySelectorAll("img.toggler");
+    togglerElements.forEach((el) =>
+      el.addEventListener("click", (event) => toggler(event.currentTarget))
+    );
+    togglerElements.forEach((el) => (el.style.display = ""));
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
+  },
+
+  initOnKeyListeners: () => {
+    // only install a listener if it is really needed
+    if (
+      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
+      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
+    )
+      return;
+
+    document.addEventListener("keydown", (event) => {
+      // bail for input elements
+      if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return;
+      // bail with special keys
+      if (event.altKey || event.ctrlKey || event.metaKey) return;
+
+      if (!event.shiftKey) {
+        switch (event.key) {
+          case "ArrowLeft":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const prevLink = document.querySelector('link[rel="prev"]');
+            if (prevLink && prevLink.href) {
+              window.location.href = prevLink.href;
+              event.preventDefault();
+            }
+            break;
+          case "ArrowRight":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const nextLink = document.querySelector('link[rel="next"]');
+            if (nextLink && nextLink.href) {
+              window.location.href = nextLink.href;
+              event.preventDefault();
+            }
+            break;
+        }
+      }
+
+      // some keyboard layouts may need Shift to get /
+      switch (event.key) {
+        case "/":
+          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+          Documentation.focusSearchBar();
+          event.preventDefault();
+      }
+    });
+  },
+};
+
+// quick alias for translations
+const _ = Documentation.gettext;
+
+_ready(Documentation.init);
diff --git a/docs/_static/documentation_options.js b/docs/_static/documentation_options.js
new file mode 100644
index 0000000..e49ed18
--- /dev/null
+++ b/docs/_static/documentation_options.js
@@ -0,0 +1,14 @@
+var DOCUMENTATION_OPTIONS = {
+    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
+    VERSION: '0.1.0',
+    LANGUAGE: 'en',
+    COLLAPSE_INDEX: false,
+    BUILDER: 'html',
+    FILE_SUFFIX: '.html',
+    LINK_SUFFIX: '.html',
+    HAS_SOURCE: true,
+    SOURCELINK_SUFFIX: '.txt',
+    NAVIGATION_WITH_KEYS: false,
+    SHOW_SEARCH_SUMMARY: true,
+    ENABLE_SEARCH_SHORTCUTS: true,
+};
\ No newline at end of file
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diff --git a/docs/_static/js/react/react.jsx b/docs/_static/js/react/react.jsx
new file mode 100644
index 0000000..edb2a4b
--- /dev/null
+++ b/docs/_static/js/react/react.jsx
@@ -0,0 +1,60 @@
+const useState = React.useState;
+
+function getComponentProps(node) {
+  const attributeNames = node.getAttributeNames();
+  const props = {};
+  for (const attributeName of attributeNames) {
+    if (attributeName.startsWith("data-")) {
+      const propName = attributeName.slice(5);
+      props[propName] = node.getAttribute(attributeName);
+    }
+  }
+  return props;
+}
+
+function mountComponent(querySelector, Component) {
+  const containers = document.querySelectorAll(querySelector);
+  for (const container of containers) {
+    const props = getComponentProps(container);
+    const root = ReactDOM.createRoot(container);
+    root.render(<Component {...props} />);
+  }
+}
+
+// LikeButtonWithTitle Component
+
+function LikeButtonWithTitle({ title, margin, padding }) {
+  const [likeCount, setLikeCount] = useState(100500);
+  return (
+    <button onClick={() => setLikeCount(likeCount + 1)} style={{ margin, padding }}>
+      Like {title} {likeCount}
+    </button>
+  );
+}
+
+mountComponent(".LikeButtonWithTitle", LikeButtonWithTitle);
+
+
+// ReactGreeter component
+
+function ReactGreeter() {
+  const [name, setName] = useState("");
+  const onSubmit = (event) => {
+    event.preventDefault();
+    alert(`Hello, ${name}!`);
+  };
+  return (
+    <form onSubmit={onSubmit}>
+      <input
+        type="text"
+        placeholder="Enter your name"
+        required
+        value={name}
+        onChange={(event) => setName(event.target.value)}
+      />
+      <button type="submit" disabled={!name}>Submit</button>
+    </form>
+  );
+}
+
+mountComponent(".ReactGreeter", ReactGreeter);
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+// @license-end
diff --git a/docs/_static/js/vendor/bootstrap.min.js b/docs/_static/js/vendor/bootstrap.min.js
new file mode 100644
index 0000000..b4dda1d
--- /dev/null
+++ b/docs/_static/js/vendor/bootstrap.min.js
@@ -0,0 +1,7 @@
+/*!
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+  * Copyright 2011-2021 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors)
+  * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+  */
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t=this;this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._showBackdrop((function(){o.default(document.body).removeClass(ft),t._resetAdjustments(),t._resetScrollbar(),o.default(t._element).trigger(gt)}))},e._removeBackdrop=function(){this._backdrop&&(o.default(this._backdrop).remove(),this._backdrop=null)},e._showBackdrop=function(t){var 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+//# sourceMappingURL=bootstrap.min.js.map
diff --git a/docs/_static/js/vendor/popper.min.js b/docs/_static/js/vendor/popper.min.js
new file mode 100644
index 0000000..bb1aaae
--- /dev/null
+++ b/docs/_static/js/vendor/popper.min.js
@@ -0,0 +1,5 @@
+/*
+ Copyright (C) Federico Zivolo 2020
+ Distributed under the MIT License (license terms are at http://opensource.org/licenses/MIT).
+ */(function(e,t){'object'==typeof exports&&'undefined'!=typeof module?module.exports=t():'function'==typeof define&&define.amd?define(t):e.Popper=t()})(this,function(){'use strict';function e(e){return e&&'[object Function]'==={}.toString.call(e)}function t(e,t){if(1!==e.nodeType)return[];var o=e.ownerDocument.defaultView,n=o.getComputedStyle(e,null);return t?n[t]:n}function o(e){return'HTML'===e.nodeName?e:e.parentNode||e.host}function n(e){if(!e)return document.body;switch(e.nodeName){case'HTML':case'BODY':return e.ownerDocument.body;case'#document':return e.body;}var i=t(e),r=i.overflow,p=i.overflowX,s=i.overflowY;return /(auto|scroll|overlay)/.test(r+s+p)?e:n(o(e))}function i(e){return e&&e.referenceNode?e.referenceNode:e}function r(e){return 11===e?re:10===e?pe:re||pe}function p(e){if(!e)return document.documentElement;for(var o=r(10)?document.body:null,n=e.offsetParent||null;n===o&&e.nextElementSibling;)n=(e=e.nextElementSibling).offsetParent;var i=n&&n.nodeName;return 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v=ee(Q(s[l]-u,v),0),e.arrowElement=i,e.offsets.arrow=(n={},ae(n,m,$(v)),ae(n,h,''),n),e},element:'[x-arrow]'},flip:{order:600,enabled:!0,fn:function(e,t){if(W(e.instance.modifiers,'inner'))return e;if(e.flipped&&e.placement===e.originalPlacement)return e;var o=v(e.instance.popper,e.instance.reference,t.padding,t.boundariesElement,e.positionFixed),n=e.placement.split('-')[0],i=T(n),r=e.placement.split('-')[1]||'',p=[];switch(t.behavior){case ce.FLIP:p=[n,i];break;case ce.CLOCKWISE:p=G(n);break;case ce.COUNTERCLOCKWISE:p=G(n,!0);break;default:p=t.behavior;}return p.forEach(function(s,d){if(n!==s||p.length===d+1)return e;n=e.placement.split('-')[0],i=T(n);var 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t=e.placement,o=t.split('-')[0],n=e.offsets,i=n.popper,r=n.reference,p=-1!==['left','right'].indexOf(o),s=-1===['top','left'].indexOf(o);return i[p?'left':'top']=r[o]-(s?i[p?'width':'height']:0),e.placement=T(t),e.offsets.popper=g(i),e}},hide:{order:800,enabled:!0,fn:function(e){if(!K(e.instance.modifiers,'hide','preventOverflow'))return e;var t=e.offsets.reference,o=D(e.instance.modifiers,function(e){return'preventOverflow'===e.name}).boundaries;if(t.bottom<o.top||t.left>o.right||t.top>o.bottom||t.right<o.left){if(!0===e.hide)return e;e.hide=!0,e.attributes['x-out-of-boundaries']=''}else{if(!1===e.hide)return e;e.hide=!1,e.attributes['x-out-of-boundaries']=!1}return e}},computeStyle:{order:850,enabled:!0,fn:function(e,t){var o=t.x,n=t.y,i=e.offsets.popper,r=D(e.instance.modifiers,function(e){return'applyStyle'===e.name}).gpuAcceleration;void 0!==r&&console.warn('WARNING: `gpuAcceleration` option moved to `computeStyle` modifier and will not be supported in future versions of 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r=L(i,t,e,o.positionFixed),p=O(o.placement,r,t,e,o.modifiers.flip.boundariesElement,o.modifiers.flip.padding);return t.setAttribute('x-placement',p),V(t,{position:o.positionFixed?'fixed':'absolute'}),o},gpuAcceleration:void 0}}},ge});
+//# sourceMappingURL=popper.min.js.map
diff --git a/docs/_static/language_data.js b/docs/_static/language_data.js
new file mode 100644
index 0000000..250f566
--- /dev/null
+++ b/docs/_static/language_data.js
@@ -0,0 +1,199 @@
+/*
+ * language_data.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * This script contains the language-specific data used by searchtools.js,
+ * namely the list of stopwords, stemmer, scorer and splitter.
+ *
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
+
+
+/* Non-minified version is copied as a separate JS file, is available */
+
+/**
+ * Porter Stemmer
+ */
+var Stemmer = function() {
+
+  var step2list = {
+    ational: 'ate',
+    tional: 'tion',
+    enci: 'ence',
+    anci: 'ance',
+    izer: 'ize',
+    bli: 'ble',
+    alli: 'al',
+    entli: 'ent',
+    eli: 'e',
+    ousli: 'ous',
+    ization: 'ize',
+    ation: 'ate',
+    ator: 'ate',
+    alism: 'al',
+    iveness: 'ive',
+    fulness: 'ful',
+    ousness: 'ous',
+    aliti: 'al',
+    iviti: 'ive',
+    biliti: 'ble',
+    logi: 'log'
+  };
+
+  var step3list = {
+    icate: 'ic',
+    ative: '',
+    alize: 'al',
+    iciti: 'ic',
+    ical: 'ic',
+    ful: '',
+    ness: ''
+  };
+
+  var c = "[^aeiou]";          // consonant
+  var v = "[aeiouy]";          // vowel
+  var C = c + "[^aeiouy]*";    // consonant sequence
+  var V = v + "[aeiou]*";      // vowel sequence
+
+  var mgr0 = "^(" + C + ")?" + V + C;                      // [C]VC... is m>0
+  var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$";    // [C]VC[V] is m=1
+  var mgr1 = "^(" + C + ")?" + V + C + V + C;              // [C]VCVC... is m>1
+  var s_v   = "^(" + C + ")?" + v;                         // vowel in stem
+
+  this.stemWord = function (w) {
+    var stem;
+    var suffix;
+    var firstch;
+    var origword = w;
+
+    if (w.length < 3)
+      return w;
+
+    var re;
+    var re2;
+    var re3;
+    var re4;
+
+    firstch = w.substr(0,1);
+    if (firstch == "y")
+      w = firstch.toUpperCase() + w.substr(1);
+
+    // Step 1a
+    re = /^(.+?)(ss|i)es$/;
+    re2 = /^(.+?)([^s])s$/;
+
+    if (re.test(w))
+      w = w.replace(re,"$1$2");
+    else if (re2.test(w))
+      w = w.replace(re2,"$1$2");
+
+    // Step 1b
+    re = /^(.+?)eed$/;
+    re2 = /^(.+?)(ed|ing)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      re = new RegExp(mgr0);
+      if (re.test(fp[1])) {
+        re = /.$/;
+        w = w.replace(re,"");
+      }
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1];
+      re2 = new RegExp(s_v);
+      if (re2.test(stem)) {
+        w = stem;
+        re2 = /(at|bl|iz)$/;
+        re3 = new RegExp("([^aeiouylsz])\\1$");
+        re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+        if (re2.test(w))
+          w = w + "e";
+        else if (re3.test(w)) {
+          re = /.$/;
+          w = w.replace(re,"");
+        }
+        else if (re4.test(w))
+          w = w + "e";
+      }
+    }
+
+    // Step 1c
+    re = /^(.+?)y$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(s_v);
+      if (re.test(stem))
+        w = stem + "i";
+    }
+
+    // Step 2
+    re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step2list[suffix];
+    }
+
+    // Step 3
+    re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step3list[suffix];
+    }
+
+    // Step 4
+    re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
+    re2 = /^(.+?)(s|t)(ion)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      if (re.test(stem))
+        w = stem;
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1] + fp[2];
+      re2 = new RegExp(mgr1);
+      if (re2.test(stem))
+        w = stem;
+    }
+
+    // Step 5
+    re = /^(.+?)e$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      re2 = new RegExp(meq1);
+      re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+      if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
+        w = stem;
+    }
+    re = /ll$/;
+    re2 = new RegExp(mgr1);
+    if (re.test(w) && re2.test(w)) {
+      re = /.$/;
+      w = w.replace(re,"");
+    }
+
+    // and turn initial Y back to y
+    if (firstch == "y")
+      w = firstch.toLowerCase() + w.substr(1);
+    return w;
+  }
+}
+
diff --git a/docs/_static/minus.png b/docs/_static/minus.png
new file mode 100644
index 0000000..d96755f
Binary files /dev/null and b/docs/_static/minus.png differ
diff --git a/docs/_static/nbsphinx-broken-thumbnail.svg b/docs/_static/nbsphinx-broken-thumbnail.svg
new file mode 100644
index 0000000..4919ca8
--- /dev/null
+++ b/docs/_static/nbsphinx-broken-thumbnail.svg
@@ -0,0 +1,9 @@
+<svg xmlns="http://www.w3.org/2000/svg" width="100" height="100">
+  <style>
+    svg { fill: lightcoral; }
+    @media (prefers-color-scheme: dark) {
+      svg { fill: crimson; }
+    }
+  </style>
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new file mode 100644
index 0000000..a3fb27c
--- /dev/null
+++ b/docs/_static/nbsphinx-code-cells.css
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+div.nboutput.container div.prompt *,
+div.nbinput.container div.input_area pre,
+div.nboutput.container div.output_area pre,
+div.nbinput.container div.input_area .highlight,
+div.nboutput.container div.output_area .highlight {
+    border: none;
+    padding: 0;
+    margin: 0;
+    box-shadow: none;
+}
+
+div.nbinput.container > div[class*=highlight],
+div.nboutput.container > div[class*=highlight] {
+    margin: 0;
+}
+
+div.nbinput.container div.prompt *,
+div.nboutput.container div.prompt * {
+    background: none;
+}
+
+div.nboutput.container div.output_area .highlight,
+div.nboutput.container div.output_area pre {
+    background: unset;
+}
+
+div.nboutput.container div.output_area div.highlight {
+    color: unset;  /* override Pygments text color */
+}
+
+/* avoid gaps between output lines */
+div.nboutput.container div[class*=highlight] pre {
+    line-height: normal;
+}
+
+/* input/output containers */
+div.nbinput.container,
+div.nboutput.container {
+    display: -webkit-flex;
+    display: flex;
+    align-items: flex-start;
+    margin: 0;
+    width: 100%;
+}
+@media (max-width: 540px) {
+    div.nbinput.container,
+    div.nboutput.container {
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+}
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+/* input container */
+div.nbinput.container {
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+}
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+div.nblast.container {
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+}
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+/* input prompt */
+div.nbinput.container div.prompt pre,
+/* for sphinx_immaterial theme: */
+div.nbinput.container div.prompt pre > code {
+    color: #307FC1;
+}
+
+/* output prompt */
+div.nboutput.container div.prompt pre,
+/* for sphinx_immaterial theme: */
+div.nboutput.container div.prompt pre > code {
+    color: #BF5B3D;
+}
+
+/* all prompts */
+div.nbinput.container div.prompt,
+div.nboutput.container div.prompt {
+    width: 4.5ex;
+    padding-top: 5px;
+    position: relative;
+    user-select: none;
+}
+
+div.nbinput.container div.prompt > div,
+div.nboutput.container div.prompt > div {
+    position: absolute;
+    right: 0;
+    margin-right: 0.3ex;
+}
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+@media (max-width: 540px) {
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+    div.nboutput.container div.prompt {
+        width: unset;
+        text-align: left;
+        padding: 0.4em;
+    }
+    div.nboutput.container div.prompt.empty {
+        padding: 0;
+    }
+
+    div.nbinput.container div.prompt > div,
+    div.nboutput.container div.prompt > div {
+        position: unset;
+    }
+}
+
+/* disable scrollbars and line breaks on prompts */
+div.nbinput.container div.prompt pre,
+div.nboutput.container div.prompt pre {
+    overflow: hidden;
+    white-space: pre;
+}
+
+/* input/output area */
+div.nbinput.container div.input_area,
+div.nboutput.container div.output_area {
+    -webkit-flex: 1;
+    flex: 1;
+    overflow: auto;
+}
+@media (max-width: 540px) {
+    div.nbinput.container div.input_area,
+    div.nboutput.container div.output_area {
+        width: 100%;
+    }
+}
+
+/* input area */
+div.nbinput.container div.input_area {
+    border: 1px solid #e0e0e0;
+    border-radius: 2px;
+    /*background: #f5f5f5;*/
+}
+
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+div.nboutput.container div[class*=MathJax] {
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+}
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+.ansi-default-inverse-bg { background-color: #000000; }
+
+.ansi-bold { font-weight: bold; }
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+
+div.nbinput.container div.input_area div[class*=highlight] > pre,
+div.nboutput.container div.output_area div[class*=highlight] > pre,
+div.nboutput.container div.output_area div[class*=highlight].math,
+div.nboutput.container div.output_area.rendered_html,
+div.nboutput.container div.output_area > div.output_javascript,
+div.nboutput.container div.output_area:not(.rendered_html) > img{
+    padding: 5px;
+    margin: 0;
+}
+
+/* fix copybtn overflow problem in chromium (needed for 'sphinx_copybutton') */
+div.nbinput.container div.input_area > div[class^='highlight'],
+div.nboutput.container div.output_area > div[class^='highlight']{
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+}
+
+/* hide copy button on prompts for 'sphinx_copybutton' extension ... */
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+}
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+  border: none;
+  border-collapse: collapse;
+  border-spacing: 0;
+  color: black;
+  font-size: 12px;
+  table-layout: fixed;
+}
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+div.rendered_html thead {
+  border-bottom: 1px solid black;
+  vertical-align: bottom;
+}
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+div.rendered_html tr,
+div.rendered_html th,
+div.rendered_html td {
+  text-align: right;
+  vertical-align: middle;
+  padding: 0.5em 0.5em;
+  line-height: normal;
+  white-space: normal;
+  max-width: none;
+  border: none;
+}
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+div.rendered_html th {
+  font-weight: bold;
+}
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+div.rendered_html tbody tr:nth-child(odd) {
+  background: #f5f5f5;
+}
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new file mode 100644
index 0000000..365c27a
--- /dev/null
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+    display: grid;
+    grid-template-columns: repeat(auto-fill, minmax(160px, 1fr));
+    gap: 5px;
+    margin-top: 1em;
+    margin-bottom: 1em;
+}
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+    padding: 5px;
+    border: 1px dotted currentColor;
+    border-radius: 2px;
+    text-align: center;
+}
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+}
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+}
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+    justify-content: center;
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+.highlight .gp { color: #000080; font-weight: bold } /* Generic.Prompt */
+.highlight .gs { font-weight: bold } /* Generic.Strong */
+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
+.highlight .gt { color: #0044DD } /* Generic.Traceback */
+.highlight .kc { color: #008000; font-weight: bold } /* Keyword.Constant */
+.highlight .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */
+.highlight .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */
+.highlight .kp { color: #008000 } /* Keyword.Pseudo */
+.highlight .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */
+.highlight .kt { color: #B00040 } /* Keyword.Type */
+.highlight .m { color: #666666 } /* Literal.Number */
+.highlight .s { color: #BA2121 } /* Literal.String */
+.highlight .na { color: #687822 } /* Name.Attribute */
+.highlight .nb { color: #008000 } /* Name.Builtin */
+.highlight .nc { color: #0000FF; font-weight: bold } /* Name.Class */
+.highlight .no { color: #880000 } /* Name.Constant */
+.highlight .nd { color: #AA22FF } /* Name.Decorator */
+.highlight .ni { color: #717171; font-weight: bold } /* Name.Entity */
+.highlight .ne { color: #CB3F38; font-weight: bold } /* Name.Exception */
+.highlight .nf { color: #0000FF } /* Name.Function */
+.highlight .nl { color: #767600 } /* Name.Label */
+.highlight .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */
+.highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */
+.highlight .nv { color: #19177C } /* Name.Variable */
+.highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
+.highlight .w { color: #bbbbbb } /* Text.Whitespace */
+.highlight .mb { color: #666666 } /* Literal.Number.Bin */
+.highlight .mf { color: #666666 } /* Literal.Number.Float */
+.highlight .mh { color: #666666 } /* Literal.Number.Hex */
+.highlight .mi { color: #666666 } /* Literal.Number.Integer */
+.highlight .mo { color: #666666 } /* Literal.Number.Oct */
+.highlight .sa { color: #BA2121 } /* Literal.String.Affix */
+.highlight .sb { color: #BA2121 } /* Literal.String.Backtick */
+.highlight .sc { color: #BA2121 } /* Literal.String.Char */
+.highlight .dl { color: #BA2121 } /* Literal.String.Delimiter */
+.highlight .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */
+.highlight .s2 { color: #BA2121 } /* Literal.String.Double */
+.highlight .se { color: #AA5D1F; font-weight: bold } /* Literal.String.Escape */
+.highlight .sh { color: #BA2121 } /* Literal.String.Heredoc */
+.highlight .si { color: #A45A77; font-weight: bold } /* Literal.String.Interpol */
+.highlight .sx { color: #008000 } /* Literal.String.Other */
+.highlight .sr { color: #A45A77 } /* Literal.String.Regex */
+.highlight .s1 { color: #BA2121 } /* Literal.String.Single */
+.highlight .ss { color: #19177C } /* Literal.String.Symbol */
+.highlight .bp { color: #008000 } /* Name.Builtin.Pseudo */
+.highlight .fm { color: #0000FF } /* Name.Function.Magic */
+.highlight .vc { color: #19177C } /* Name.Variable.Class */
+.highlight .vg { color: #19177C } /* Name.Variable.Global */
+.highlight .vi { color: #19177C } /* Name.Variable.Instance */
+.highlight .vm { color: #19177C } /* Name.Variable.Magic */
+.highlight .il { color: #666666 } /* Literal.Number.Integer.Long */
\ No newline at end of file
diff --git a/docs/_static/searchtools.js b/docs/_static/searchtools.js
new file mode 100644
index 0000000..97d56a7
--- /dev/null
+++ b/docs/_static/searchtools.js
@@ -0,0 +1,566 @@
+/*
+ * searchtools.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for the full-text search.
+ *
+ * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+"use strict";
+
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
+  var Scorer = {
+    // Implement the following function to further tweak the score for each result
+    // The function takes a result array [docname, title, anchor, descr, score, filename]
+    // and returns the new score.
+    /*
+    score: result => {
+      const [docname, title, anchor, descr, score, filename] = result
+      return score
+    },
+    */
+
+    // query matches the full name of an object
+    objNameMatch: 11,
+    // or matches in the last dotted part of the object name
+    objPartialMatch: 6,
+    // Additive scores depending on the priority of the object
+    objPrio: {
+      0: 15, // used to be importantResults
+      1: 5, // used to be objectResults
+      2: -5, // used to be unimportantResults
+    },
+    //  Used when the priority is not in the mapping.
+    objPrioDefault: 0,
+
+    // query found in title
+    title: 15,
+    partialTitle: 7,
+    // query found in terms
+    term: 5,
+    partialTerm: 2,
+  };
+}
+
+const _removeChildren = (element) => {
+  while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+  string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, searchTerms) => {
+  const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+  const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT;
+  const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+  const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+  const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+
+  const [docName, title, anchor, descr, score, _filename] = item;
+
+  let listItem = document.createElement("li");
+  let requestUrl;
+  let linkUrl;
+  if (docBuilder === "dirhtml") {
+    // dirhtml builder
+    let dirname = docName + "/";
+    if (dirname.match(/\/index\/$/))
+      dirname = dirname.substring(0, dirname.length - 6);
+    else if (dirname === "index/") dirname = "";
+    requestUrl = docUrlRoot + dirname;
+    linkUrl = requestUrl;
+  } else {
+    // normal html builders
+    requestUrl = docUrlRoot + docName + docFileSuffix;
+    linkUrl = docName + docLinkSuffix;
+  }
+  let linkEl = listItem.appendChild(document.createElement("a"));
+  linkEl.href = linkUrl + anchor;
+  linkEl.dataset.score = score;
+  linkEl.innerHTML = title;
+  if (descr)
+    listItem.appendChild(document.createElement("span")).innerHTML =
+      " (" + descr + ")";
+  else if (showSearchSummary)
+    fetch(requestUrl)
+      .then((responseData) => responseData.text())
+      .then((data) => {
+        if (data)
+          listItem.appendChild(
+            Search.makeSearchSummary(data, searchTerms)
+          );
+      });
+  Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+  Search.stopPulse();
+  Search.title.innerText = _("Search Results");
+  if (!resultCount)
+    Search.status.innerText = Documentation.gettext(
+      "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+    );
+  else
+    Search.status.innerText = _(
+      `Search finished, found ${resultCount} page(s) matching the search query.`
+    );
+};
+const _displayNextItem = (
+  results,
+  resultCount,
+  searchTerms
+) => {
+  // results left, load the summary and display it
+  // this is intended to be dynamic (don't sub resultsCount)
+  if (results.length) {
+    _displayItem(results.pop(), searchTerms);
+    setTimeout(
+      () => _displayNextItem(results, resultCount, searchTerms),
+      5
+    );
+  }
+  // search finished, update title and status message
+  else _finishSearch(resultCount);
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+  var splitQuery = (query) => query
+      .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+      .filter(term => term)  // remove remaining empty strings
+}
+
+/**
+ * Search Module
+ */
+const Search = {
+  _index: null,
+  _queued_query: null,
+  _pulse_status: -1,
+
+  htmlToText: (htmlString) => {
+    const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html');
+    htmlElement.querySelectorAll(".headerlink").forEach((el) => { el.remove() });
+    const docContent = htmlElement.querySelector('[role="main"]');
+    if (docContent !== undefined) return docContent.textContent;
+    console.warn(
+      "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template."
+    );
+    return "";
+  },
+
+  init: () => {
+    const query = new URLSearchParams(window.location.search).get("q");
+    document
+      .querySelectorAll('input[name="q"]')
+      .forEach((el) => (el.value = query));
+    if (query) Search.performSearch(query);
+  },
+
+  loadIndex: (url) =>
+    (document.body.appendChild(document.createElement("script")).src = url),
+
+  setIndex: (index) => {
+    Search._index = index;
+    if (Search._queued_query !== null) {
+      const query = Search._queued_query;
+      Search._queued_query = null;
+      Search.query(query);
+    }
+  },
+
+  hasIndex: () => Search._index !== null,
+
+  deferQuery: (query) => (Search._queued_query = query),
+
+  stopPulse: () => (Search._pulse_status = -1),
+
+  startPulse: () => {
+    if (Search._pulse_status >= 0) return;
+
+    const pulse = () => {
+      Search._pulse_status = (Search._pulse_status + 1) % 4;
+      Search.dots.innerText = ".".repeat(Search._pulse_status);
+      if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+    };
+    pulse();
+  },
+
+  /**
+   * perform a search for something (or wait until index is loaded)
+   */
+  performSearch: (query) => {
+    // create the required interface elements
+    const searchText = document.createElement("h2");
+    searchText.textContent = _("Searching");
+    const searchSummary = document.createElement("p");
+    searchSummary.classList.add("search-summary");
+    searchSummary.innerText = "";
+    const searchList = document.createElement("ul");
+    searchList.classList.add("search");
+
+    const out = document.getElementById("search-results");
+    Search.title = out.appendChild(searchText);
+    Search.dots = Search.title.appendChild(document.createElement("span"));
+    Search.status = out.appendChild(searchSummary);
+    Search.output = out.appendChild(searchList);
+
+    const searchProgress = document.getElementById("search-progress");
+    // Some themes don't use the search progress node
+    if (searchProgress) {
+      searchProgress.innerText = _("Preparing search...");
+    }
+    Search.startPulse();
+
+    // index already loaded, the browser was quick!
+    if (Search.hasIndex()) Search.query(query);
+    else Search.deferQuery(query);
+  },
+
+  /**
+   * execute search (requires search index to be loaded)
+   */
+  query: (query) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+    const allTitles = Search._index.alltitles;
+    const indexEntries = Search._index.indexentries;
+
+    // stem the search terms and add them to the correct list
+    const stemmer = new Stemmer();
+    const searchTerms = new Set();
+    const excludedTerms = new Set();
+    const highlightTerms = new Set();
+    const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+    splitQuery(query.trim()).forEach((queryTerm) => {
+      const queryTermLower = queryTerm.toLowerCase();
+
+      // maybe skip this "word"
+      // stopwords array is from language_data.js
+      if (
+        stopwords.indexOf(queryTermLower) !== -1 ||
+        queryTerm.match(/^\d+$/)
+      )
+        return;
+
+      // stem the word
+      let word = stemmer.stemWord(queryTermLower);
+      // select the correct list
+      if (word[0] === "-") excludedTerms.add(word.substr(1));
+      else {
+        searchTerms.add(word);
+        highlightTerms.add(queryTermLower);
+      }
+    });
+
+    if (SPHINX_HIGHLIGHT_ENABLED) {  // set in sphinx_highlight.js
+      localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" "))
+    }
+
+    // console.debug("SEARCH: searching for:");
+    // console.info("required: ", [...searchTerms]);
+    // console.info("excluded: ", [...excludedTerms]);
+
+    // array of [docname, title, anchor, descr, score, filename]
+    let results = [];
+    _removeChildren(document.getElementById("search-progress"));
+
+    const queryLower = query.toLowerCase();
+    for (const [title, foundTitles] of Object.entries(allTitles)) {
+      if (title.toLowerCase().includes(queryLower) && (queryLower.length >= title.length/2)) {
+        for (const [file, id] of foundTitles) {
+          let score = Math.round(100 * queryLower.length / title.length)
+          results.push([
+            docNames[file],
+            titles[file] !== title ? `${titles[file]} > ${title}` : title,
+            id !== null ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
+
+    // search for explicit entries in index directives
+    for (const [entry, foundEntries] of Object.entries(indexEntries)) {
+      if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) {
+        for (const [file, id] of foundEntries) {
+          let score = Math.round(100 * queryLower.length / entry.length)
+          results.push([
+            docNames[file],
+            titles[file],
+            id ? "#" + id : "",
+            null,
+            score,
+            filenames[file],
+          ]);
+        }
+      }
+    }
+
+    // lookup as object
+    objectTerms.forEach((term) =>
+      results.push(...Search.performObjectSearch(term, objectTerms))
+    );
+
+    // lookup as search terms in fulltext
+    results.push(...Search.performTermsSearch(searchTerms, excludedTerms));
+
+    // let the scorer override scores with a custom scoring function
+    if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item)));
+
+    // now sort the results by score (in opposite order of appearance, since the
+    // display function below uses pop() to retrieve items) and then
+    // alphabetically
+    results.sort((a, b) => {
+      const leftScore = a[4];
+      const rightScore = b[4];
+      if (leftScore === rightScore) {
+        // same score: sort alphabetically
+        const leftTitle = a[1].toLowerCase();
+        const rightTitle = b[1].toLowerCase();
+        if (leftTitle === rightTitle) return 0;
+        return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
+      }
+      return leftScore > rightScore ? 1 : -1;
+    });
+
+    // remove duplicate search results
+    // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+    let seen = new Set();
+    results = results.reverse().reduce((acc, result) => {
+      let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+      if (!seen.has(resultStr)) {
+        acc.push(result);
+        seen.add(resultStr);
+      }
+      return acc;
+    }, []);
+
+    results = results.reverse();
+
+    // for debugging
+    //Search.lastresults = results.slice();  // a copy
+    // console.info("search results:", Search.lastresults);
+
+    // print the results
+    _displayNextItem(results, results.length, searchTerms);
+  },
+
+  /**
+   * search for object names
+   */
+  performObjectSearch: (object, objectTerms) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const objects = Search._index.objects;
+    const objNames = Search._index.objnames;
+    const titles = Search._index.titles;
+
+    const results = [];
+
+    const objectSearchCallback = (prefix, match) => {
+      const name = match[4]
+      const fullname = (prefix ? prefix + "." : "") + name;
+      const fullnameLower = fullname.toLowerCase();
+      if (fullnameLower.indexOf(object) < 0) return;
+
+      let score = 0;
+      const parts = fullnameLower.split(".");
+
+      // check for different match types: exact matches of full name or
+      // "last name" (i.e. last dotted part)
+      if (fullnameLower === object || parts.slice(-1)[0] === object)
+        score += Scorer.objNameMatch;
+      else if (parts.slice(-1)[0].indexOf(object) > -1)
+        score += Scorer.objPartialMatch; // matches in last name
+
+      const objName = objNames[match[1]][2];
+      const title = titles[match[0]];
+
+      // If more than one term searched for, we require other words to be
+      // found in the name/title/description
+      const otherTerms = new Set(objectTerms);
+      otherTerms.delete(object);
+      if (otherTerms.size > 0) {
+        const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+        if (
+          [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+        )
+          return;
+      }
+
+      let anchor = match[3];
+      if (anchor === "") anchor = fullname;
+      else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+      const descr = objName + _(", in ") + title;
+
+      // add custom score for some objects according to scorer
+      if (Scorer.objPrio.hasOwnProperty(match[2]))
+        score += Scorer.objPrio[match[2]];
+      else score += Scorer.objPrioDefault;
+
+      results.push([
+        docNames[match[0]],
+        fullname,
+        "#" + anchor,
+        descr,
+        score,
+        filenames[match[0]],
+      ]);
+    };
+    Object.keys(objects).forEach((prefix) =>
+      objects[prefix].forEach((array) =>
+        objectSearchCallback(prefix, array)
+      )
+    );
+    return results;
+  },
+
+  /**
+   * search for full-text terms in the index
+   */
+  performTermsSearch: (searchTerms, excludedTerms) => {
+    // prepare search
+    const terms = Search._index.terms;
+    const titleTerms = Search._index.titleterms;
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const titles = Search._index.titles;
+
+    const scoreMap = new Map();
+    const fileMap = new Map();
+
+    // perform the search on the required terms
+    searchTerms.forEach((word) => {
+      const files = [];
+      const arr = [
+        { files: terms[word], score: Scorer.term },
+        { files: titleTerms[word], score: Scorer.title },
+      ];
+      // add support for partial matches
+      if (word.length > 2) {
+        const escapedWord = _escapeRegExp(word);
+        Object.keys(terms).forEach((term) => {
+          if (term.match(escapedWord) && !terms[word])
+            arr.push({ files: terms[term], score: Scorer.partialTerm });
+        });
+        Object.keys(titleTerms).forEach((term) => {
+          if (term.match(escapedWord) && !titleTerms[word])
+            arr.push({ files: titleTerms[word], score: Scorer.partialTitle });
+        });
+      }
+
+      // no match but word was a required one
+      if (arr.every((record) => record.files === undefined)) return;
+
+      // found search word in contents
+      arr.forEach((record) => {
+        if (record.files === undefined) return;
+
+        let recordFiles = record.files;
+        if (recordFiles.length === undefined) recordFiles = [recordFiles];
+        files.push(...recordFiles);
+
+        // set score for the word in each file
+        recordFiles.forEach((file) => {
+          if (!scoreMap.has(file)) scoreMap.set(file, {});
+          scoreMap.get(file)[word] = record.score;
+        });
+      });
+
+      // create the mapping
+      files.forEach((file) => {
+        if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1)
+          fileMap.get(file).push(word);
+        else fileMap.set(file, [word]);
+      });
+    });
+
+    // now check if the files don't contain excluded terms
+    const results = [];
+    for (const [file, wordList] of fileMap) {
+      // check if all requirements are matched
+
+      // as search terms with length < 3 are discarded
+      const filteredTermCount = [...searchTerms].filter(
+        (term) => term.length > 2
+      ).length;
+      if (
+        wordList.length !== searchTerms.size &&
+        wordList.length !== filteredTermCount
+      )
+        continue;
+
+      // ensure that none of the excluded terms is in the search result
+      if (
+        [...excludedTerms].some(
+          (term) =>
+            terms[term] === file ||
+            titleTerms[term] === file ||
+            (terms[term] || []).includes(file) ||
+            (titleTerms[term] || []).includes(file)
+        )
+      )
+        break;
+
+      // select one (max) score for the file.
+      const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w]));
+      // add result to the result list
+      results.push([
+        docNames[file],
+        titles[file],
+        "",
+        null,
+        score,
+        filenames[file],
+      ]);
+    }
+    return results;
+  },
+
+  /**
+   * helper function to return a node containing the
+   * search summary for a given text. keywords is a list
+   * of stemmed words.
+   */
+  makeSearchSummary: (htmlText, keywords) => {
+    const text = Search.htmlToText(htmlText);
+    if (text === "") return null;
+
+    const textLower = text.toLowerCase();
+    const actualStartPosition = [...keywords]
+      .map((k) => textLower.indexOf(k.toLowerCase()))
+      .filter((i) => i > -1)
+      .slice(-1)[0];
+    const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+    const top = startWithContext === 0 ? "" : "...";
+    const tail = startWithContext + 240 < text.length ? "..." : "";
+
+    let summary = document.createElement("p");
+    summary.classList.add("context");
+    summary.textContent = top + text.substr(startWithContext, 240).trim() + tail;
+
+    return summary;
+  },
+};
+
+_ready(Search.init);
diff --git a/docs/_static/sphinx_highlight.js b/docs/_static/sphinx_highlight.js
new file mode 100644
index 0000000..aae669d
--- /dev/null
+++ b/docs/_static/sphinx_highlight.js
@@ -0,0 +1,144 @@
+/* Highlighting utilities for Sphinx HTML documentation. */
+"use strict";
+
+const SPHINX_HIGHLIGHT_ENABLED = true
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
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new file mode 100644
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--- /dev/null
+++ b/docs/_static/theme_variables.jinja
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+{%- set external_urls = {
+  'github': 'https://github.com/Lightning-AI/lightning-Hivemind',
+  'github_issues': 'https://github.com/Lightning-AI/lightning-Hivemind/issues',
+  'contributing': 'https://github.com/Lightning-AI/lightning/blob/master/CONTRIBUTING.md',
+  'governance': 'https://github.com/Lightning-AI/lightning/blob/master/governance.md',
+  'docs': 'https://lightning-ai.github.io/lightning-Hivemind/',
+  'twitter': 'https://twitter.com/PyTorchLightnin',
+  'discuss': 'https://pytorch-lightning.slack.com',
+  'tutorials': 'https://lightning.ai',
+  'previous_pytorch_versions': 'https://lightning-ai.github.io/lightning-Hivemind/',
+  'home': 'https://lightning-ai.github.io/lightning-Hivemind/',
+  'get_started': 'https://lightning.ai',
+  'features': 'https://lightning-ai.github.io/lightning-Hivemind/',
+  'blog': 'https://www.Lightning-AI.ai/blog',
+  'resources': 'https://lightning.ai',
+  'support': 'https://lightning-ai.github.io/lightning-Hivemind/',
+}
+-%}
diff --git a/docs/genindex.html b/docs/genindex.html
new file mode 100644
index 0000000..8702751
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+++ b/docs/genindex.html
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+
+
+
+<!DOCTYPE html>
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+  <title>Index &mdash; lightning-Hivemind 0.1.0 documentation</title>
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+<li class="toctree-l1"><a class="reference internal" href="strategy_advanced.html">Training on unreliable mixed GPUs across the internet (Advanced)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="strategy_expert.html">Training on unreliable mixed GPUs across the internet (Expert)</a></li>
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+              
+  <section id="lightning-hivemind">
+<h1>Lightning + Hivemind<a class="headerlink" href="#lightning-hivemind" title="Permalink to this heading">¶</a></h1>
+<p>Collaborative Training tries to solve the need for top-tier multi-GPU
+servers by allowing you to train across unreliable machines, such as
+local machines or even preemptible cloud computing across the internet.</p>
+<p>Under the hood, we use
+<a class="reference external" href="https://github.com/learning-at-home/hivemind">Hivemind</a>, which
+provides de-centralized training across the internet.</p>
+<p>To use Collaborative Training, you need first to have this extension.</p>
+<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>pip<span class="w"> </span>install<span class="w"> </span>-U<span class="w"> </span>lightning-Hivemind
+</pre></div>
+</div>
+<p>The <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code> accumulates gradients from all collaborating
+processes until they reach a <code class="docutils literal notranslate"><span class="pre">target_batch_size</span></code>. By default, we use
+the batch size of the first batch to determine what each local machine
+batch contributes towards the <code class="docutils literal notranslate"><span class="pre">target_batch_size</span></code>. Once the
+<code class="docutils literal notranslate"><span class="pre">target_batch_size</span></code> is reached, an optimizer step is made on all
+processes.</p>
+<p>When using <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code>, note that you cannot use gradient
+accumulation (<code class="docutils literal notranslate"><span class="pre">accumulate_grad_batches</span></code>). This is because Hivemind
+manages accumulation internally.</p>
+<div class="highlight-py notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span><span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span><span class="n">target_batch_size</span><span class="o">=</span><span class="mi">8192</span><span class="p">),</span> <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span> <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Followed by:</p>
+<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>python<span class="w"> </span>train.py
+<span class="c1"># Other machines can connect by running the same command:</span>
+<span class="c1"># INITIAL_PEERS=... python train.py</span>
+<span class="c1"># or passing the peers to the strategy:&quot;</span>
+<span class="c1"># HivemindStrategy(initial_peers=...)&quot;</span>
+</pre></div>
+</div>
+<p>A helper message is printed once your training begins, showing you how
+to train on other machines using the same code.</p>
+<div class="toctree-wrapper compound" id="start">
+<p class="caption" role="heading"><span class="caption-text">Start here</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="strategy_advanced.html">Training on unreliable mixed GPUs across the internet (Advanced)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="strategy_expert.html">Training on unreliable mixed GPUs across the internet (Expert)</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="strategy_advanced.html">Training on unreliable mixed GPUs across the internet (Advanced)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="strategy_expert.html">Training on unreliable mixed GPUs across the internet (Expert)</a></li>
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+  <section id="lightning-hivemind">
+<h1>Lightning + Hivemind<a class="headerlink" href="#lightning-hivemind" title="Permalink to this heading">¶</a></h1>
+<p>Collaborative Training tries to solve the need for top-tier multi-GPU
+servers by allowing you to train across unreliable machines, such as
+local machines or even preemptible cloud computing across the internet.</p>
+<p>Under the hood, we use
+<a class="reference external" href="https://github.com/learning-at-home/hivemind">Hivemind</a>, which
+provides de-centralized training across the internet.</p>
+<p>To use Collaborative Training, you need first to have this extension.</p>
+<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>pip<span class="w"> </span>install<span class="w"> </span>-U<span class="w"> </span>lightning-Hivemind
+</pre></div>
+</div>
+<p>The <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code> accumulates gradients from all collaborating
+processes until they reach a <code class="docutils literal notranslate"><span class="pre">target_batch_size</span></code>. By default, we use
+the batch size of the first batch to determine what each local machine
+batch contributes towards the <code class="docutils literal notranslate"><span class="pre">target_batch_size</span></code>. Once the
+<code class="docutils literal notranslate"><span class="pre">target_batch_size</span></code> is reached, an optimizer step is made on all
+processes.</p>
+<p>When using <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code>, note that you cannot use gradient
+accumulation (<code class="docutils literal notranslate"><span class="pre">accumulate_grad_batches</span></code>). This is because Hivemind
+manages accumulation internally.</p>
+<div class="highlight-py notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span><span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span><span class="n">target_batch_size</span><span class="o">=</span><span class="mi">8192</span><span class="p">),</span> <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span> <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Followed by:</p>
+<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>python<span class="w"> </span>train.py
+<span class="c1"># Other machines can connect by running the same command:</span>
+<span class="c1"># INITIAL_PEERS=... python train.py</span>
+<span class="c1"># or passing the peers to the strategy:&quot;</span>
+<span class="c1"># HivemindStrategy(initial_peers=...)&quot;</span>
+</pre></div>
+</div>
+<p>A helper message is printed once your training begins, showing you how
+to train on other machines using the same code.</p>
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+  <section id="training-on-unreliable-mixed-gpus-across-the-internet-advanced">
+<span id="hivemind-intermediate"></span><h1>Training on unreliable mixed GPUs across the internet (Advanced)<a class="headerlink" href="#training-on-unreliable-mixed-gpus-across-the-internet-advanced" title="Permalink to this heading">¶</a></h1>
+<section id="reducing-communication-by-overlapping-communication">
+<h2>Reducing Communication By Overlapping Communication<a class="headerlink" href="#reducing-communication-by-overlapping-communication" title="Permalink to this heading">¶</a></h2>
+<p>We can reduce the impact of communication across all machines by overlapping communication with our training iterations. In short, we enable communication to happen
+in the background of training.</p>
+<section id="overlap-gradient-and-state-averaging">
+<h3>Overlap Gradient and State Averaging<a class="headerlink" href="#overlap-gradient-and-state-averaging" title="Permalink to this heading">¶</a></h3>
+<p>When the target batch size is reached, all processes that are included in the step send gradients and model states to each other. By enabling some flags through
+the strategy, communication can happen in the background. This allows training to continue (with slightly outdated weights) but provides us the means
+to overlap communication with computation.</p>
+<div class="admonition warning">
+<p class="admonition-title">Warning</p>
+<p>Enabling overlapping communication means convergence will slightly be affected.</p>
+</div>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>Enabling these flags means that you must pass in a <code class="docutils literal notranslate"><span class="pre">scheduler_fn</span></code> to the <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code> instead of relying on a scheduler from <code class="docutils literal notranslate"><span class="pre">configure_optimizers</span></code>.
+The optimizer is re-created by Hivemind, and as a result, the scheduler has to be re-created.</p>
+</div>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">torch</span>
+<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
+<span class="kn">from</span> <span class="nn">pytorch_lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span>
+    <span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span>
+        <span class="n">target_batch_size</span><span class="o">=</span><span class="mi">8192</span><span class="p">,</span>
+        <span class="n">delay_state_averaging</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="n">delay_grad_averaging</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="n">delay_optimizer_step</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="n">offload_optimizer</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>  <span class="c1"># required to delay averaging</span>
+        <span class="n">scheduler_fn</span><span class="o">=</span><span class="n">partial</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">optim</span><span class="o">.</span><span class="n">lr_scheduler</span><span class="o">.</span><span class="n">ExponentialLR</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=...</span><span class="p">),</span>
+    <span class="p">),</span>
+    <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span>
+    <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+<span class="p">)</span>
+</pre></div>
+</div>
+</section>
+</section>
+<section id="reducing-gpu-memory-requirements-by-re-using-buffers-cpu-offloading">
+<h2>Reducing GPU Memory requirements by re-using buffers &amp; CPU offloading<a class="headerlink" href="#reducing-gpu-memory-requirements-by-re-using-buffers-cpu-offloading" title="Permalink to this heading">¶</a></h2>
+<p>We can also offload the optimizer state to the CPU whilst re-using gradient buffers to reduce the memory requirement for machines.</p>
+<section id="offloading-optimizer-state-to-the-cpu">
+<h3>Offloading Optimizer State to the CPU<a class="headerlink" href="#offloading-optimizer-state-to-the-cpu" title="Permalink to this heading">¶</a></h3>
+<p>Offloading the Optimizer state to the CPU works the same as Deepspeed Zero-stage-2-offload, where we save GPU memory by keeping all optimizer states on the CPU.</p>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>Enabling these flags means that you must pass in a <code class="docutils literal notranslate"><span class="pre">scheduler_fn</span></code> to the <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code> instead of relying on a scheduler from <code class="docutils literal notranslate"><span class="pre">configure_optimizers</span></code>.
+The optimizer is re-created by Hivemind, and as a result, the scheduler has to be re-created.</p>
+<p>We suggest enabling offloading and overlapping communication to hide the additional overhead from having to communicate with the CPU.</p>
+</div>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">torch</span>
+<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
+<span class="kn">from</span> <span class="nn">pytorch_lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span>
+    <span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span>
+        <span class="n">target_batch_size</span><span class="o">=</span><span class="mi">8192</span><span class="p">,</span>
+        <span class="n">offload_optimizer</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+        <span class="n">scheduler_fn</span><span class="o">=</span><span class="n">partial</span><span class="p">(</span><span class="n">torch</span><span class="o">.</span><span class="n">optim</span><span class="o">.</span><span class="n">lr_scheduler</span><span class="o">.</span><span class="n">ExponentialLR</span><span class="p">,</span> <span class="n">gamma</span><span class="o">=...</span><span class="p">),</span>
+    <span class="p">),</span>
+    <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span>
+    <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+<span class="p">)</span>
+</pre></div>
+</div>
+</section>
+<section id="re-using-gradient-buffers">
+<h3>Re-using Gradient Buffers<a class="headerlink" href="#re-using-gradient-buffers" title="Permalink to this heading">¶</a></h3>
+<p>By default, Hivemind accumulates gradients in a separate buffer. This means additional GPU memory is required to store gradients. You can enable re-using the model parameter gradient buffers by passing <code class="docutils literal notranslate"><span class="pre">reuse_grad_buffers=True</span></code> to the <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code>.</p>
+<div class="admonition warning">
+<p class="admonition-title">Warning</p>
+<p>The <code class="docutils literal notranslate"><span class="pre">HivemindStrategy</span></code> will override <code class="docutils literal notranslate"><span class="pre">zero_grad</span></code> in your <code class="docutils literal notranslate"><span class="pre">LightningModule</span></code> to have no effect. This is because gradients are accumulated in the model
+and Hivemind manages when they need to be cleared.</p>
+</div>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pytorch_lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span>
+    <span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span><span class="n">target_batch_size</span><span class="o">=</span><span class="mi">8192</span><span class="p">,</span> <span class="n">reuse_grad_buffers</span><span class="o">=</span><span class="kc">True</span><span class="p">),</span> <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span> <span class="n">devices</span><span class="o">=</span><span class="mi">1</span>
+<span class="p">)</span>
+</pre></div>
+</div>
+</section>
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+<li><a class="reference internal" href="#reducing-communication-by-overlapping-communication">Reducing Communication By Overlapping Communication</a><ul>
+<li><a class="reference internal" href="#overlap-gradient-and-state-averaging">Overlap Gradient and State Averaging</a></li>
+</ul>
+</li>
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+              
+  <section id="training-on-unreliable-mixed-gpus-across-the-internet-expert">
+<span id="hivemind-expert"></span><h1>Training on unreliable mixed GPUs across the internet (Expert)<a class="headerlink" href="#training-on-unreliable-mixed-gpus-across-the-internet-expert" title="Permalink to this heading">¶</a></h1>
+<section id="using-compression-to-optimize-communications">
+<h2>Using Compression to Optimize Communications<a class="headerlink" href="#using-compression-to-optimize-communications" title="Permalink to this heading">¶</a></h2>
+<p>Below are some ways to reduce communication when training collaboratively. As the size of your model increase, bottlenecks in communication become more apparent.</p>
+<section id="compress-gradients-state">
+<h3>Compress Gradients &amp; State<a class="headerlink" href="#compress-gradients-state" title="Permalink to this heading">¶</a></h3>
+<p>Hivemind allows you to compress gradients and states before sending them to other machines. This helps reduce the communication overhead substantially when training across the internet.</p>
+<p>Below, we enable Float16 compression, which compresses gradients and states to Float16 before sending it to other machines.</p>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>Compressing gradients can affect convergence if you’re lowering the precision (i.e training in Float32, but compressing gradients to FP16).</p>
+</div>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">hivemind</span> <span class="kn">import</span> <span class="n">Float16Compression</span>
+<span class="kn">from</span> <span class="nn">pytorch_lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span>
+    <span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span>
+        <span class="n">target_batch_size</span><span class="o">=</span><span class="n">target_batch_size</span><span class="p">,</span>
+        <span class="n">grad_compression</span><span class="o">=</span><span class="n">Float16Compression</span><span class="p">(),</span>
+        <span class="n">state_averaging_compression</span><span class="o">=</span><span class="n">Float16Compression</span><span class="p">(),</span>
+    <span class="p">),</span>
+    <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span>
+    <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+<span class="p">)</span>
+</pre></div>
+</div>
+<p>A slightly more advanced scheme is dynamic compression based on value size. Below, we enable 8-bit quantization for large numbers, and Float16 compression for small values, reducing communication bottlenecks even further.</p>
+<p>Size Adaptive Compression has been used in a variety of Hivemind applications and has shown success, but does quantize gradients further, meaning we lose precision when compressing.</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">hivemind</span> <span class="kn">import</span> <span class="n">Float16Compression</span><span class="p">,</span> <span class="n">Uniform8BitQuantization</span>
+<span class="kn">from</span> <span class="nn">pytorch_lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+
+<span class="c1"># compresses values above threshold with 8bit Quantization, lower with Float16</span>
+<span class="n">compression</span> <span class="o">=</span> <span class="n">SizeAdaptiveCompression</span><span class="p">(</span>
+    <span class="n">threshold</span><span class="o">=</span><span class="mi">2</span> <span class="o">**</span> <span class="mi">16</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">less</span><span class="o">=</span><span class="n">Float16Compression</span><span class="p">(),</span> <span class="n">greater_equal</span><span class="o">=</span><span class="n">Uniform8BitQuantization</span><span class="p">()</span>
+<span class="p">)</span>
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span>
+    <span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span>
+        <span class="n">target_batch_size</span><span class="o">=</span><span class="n">target_batch_size</span><span class="p">,</span>
+        <span class="n">grad_compression</span><span class="o">=</span><span class="n">compression</span><span class="p">,</span>
+        <span class="n">state_averaging_compression</span><span class="o">=</span><span class="n">compression</span><span class="p">,</span>
+    <span class="p">),</span>
+    <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span>
+    <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+<span class="p">)</span>
+</pre></div>
+</div>
+</section>
+<section id="powersgd">
+<h3>PowerSGD<a class="headerlink" href="#powersgd" title="Permalink to this heading">¶</a></h3>
+<p><a class="reference external" href="https://arxiv.org/abs/1905.13727">PowerSGD</a> is a technique to reduce distributed communication of gradients across processes.
+In short, PowerSGD uses a low-rank approximation to compress gradients before running an <cite>all-reduce</cite> step to sync gradients across all processes.</p>
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>Though PowerSGD can impact convergence, it can also substantially reduce communication between processes.</p>
+</div>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">pytorch_lightning</span> <span class="kn">import</span> <span class="n">Trainer</span>
+<span class="kn">from</span> <span class="nn">lightning_hivemind.strategy</span> <span class="kn">import</span> <span class="n">HivemindStrategy</span>
+<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
+<span class="kn">from</span> <span class="nn">hivemind.optim.power_sgd_averager</span> <span class="kn">import</span> <span class="n">PowerSGDGradientAverager</span>
+
+<span class="n">trainer</span> <span class="o">=</span> <span class="n">Trainer</span><span class="p">(</span>
+    <span class="n">strategy</span><span class="o">=</span><span class="n">HivemindStrategy</span><span class="p">(</span>
+        <span class="n">target_batch_size</span><span class="o">=</span><span class="mi">8192</span><span class="p">,</span>
+        <span class="n">grad_averager_factory</span><span class="o">=</span><span class="n">partial</span><span class="p">(</span><span class="n">PowerSGDGradientAverager</span><span class="p">,</span> <span class="n">averager_rank</span><span class="o">=</span><span class="mi">32</span><span class="p">,</span> <span class="n">min_compression_ratio</span><span class="o">=</span><span class="mf">0.5</span><span class="p">),</span>
+    <span class="p">),</span>
+    <span class="n">accelerator</span><span class="o">=</span><span class="s2">&quot;gpu&quot;</span><span class="p">,</span>
+    <span class="n">devices</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+<span class="p">)</span>
+</pre></div>
+</div>
+</section>
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