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<h1 class="title">Batch size vs Gradient accumulation</h1>
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Understanding of batch size and gradient accumulation steps
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<p>Gradient accumulation means accumulating gradients over several mini-batches and updating the model weights afterward. When the samples in each batch are diverse, this technique doesn’t significantly impact learning.</p>
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<p>This method allows for effective training with larger effective batch sizes without needing proportionally larger memory. Here’s why:</p>
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<ol type="1">
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<li><p><strong>Memory Consumption with Batch Size</strong>: The primary reason increasing the batch size impacts memory is due to the storage requirements for intermediate activations. When you forward propagate a batch through a network, you have to store the activations at each layer for each sample in the batch, because these activations are used during backpropagation to compute gradients. Therefore, larger batches mean more activations, leading to greater GPU memory consumption.</p></li>
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<li><p><strong>Gradient Accumulation</strong>: With gradient accumulation, you’re effectively simulating a larger batch size by accumulating gradients over several smaller batches (or micro-batches). However, at any given time, you’re only forward and backward propagating a micro-batch. This means you only store activations for the micro-batch, not the full accumulated batch. As a result, you can simulate the effect of a larger batch size without the memory cost of storing activations for a large batch.</p></li>
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<p><strong>Example 1:</strong> Micro batch size: 3 Gradient accumulation steps: 2 Number of GPUs: 3 Total batch size = 3 * 2 * 3 = 18</p>
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<pre><code>| GPU 1 | GPU 2 | GPU 3 |
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|----------------|----------------|----------------|
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| S1, S2, S3 | S4, S5, S6 | S7, S8, S9 |
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| e1, e2, e3 | e4, e5, e6 | e7, e8, e9 |
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|----------------|----------------|----------------|
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| → (accumulate) | → (accumulate) | → (accumulate) |
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|----------------|----------------|----------------|
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| S10, S11, S12 | S13, S14, S15 | S16, S17, S18 |
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| e10, e11, e12 | e13, e14, e15 | e16, e17, e18 |
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|----------------|----------------|----------------|
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| → (apply) | → (apply) | → (apply) |
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Accumulated gradient for the weight w1 after the second iteration (considering all GPUs):
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Total gradient for w1 = e1 + e2 + e3 + e4 + e5 + e6 + e7 + e8 + e9 + e10 + e11 + e12 + e13 + e14 + e15 + e16 + e17 + e18
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Weight update for w1:
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w1_new = w1_old - learning rate x (Total gradient for w1 / 18)</code></pre>
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<p><strong>Example 2:</strong> Micro batch size: 2 Gradient accumulation steps: 1 Number of GPUs: 3 Total batch size = 2 * 1 * 3 = 6</p>
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<pre><code>| GPU 1 | GPU 2 | GPU 3 |
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|-----------|-----------|-----------|
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| S1, S2 | S3, S4 | S5, S6 |
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| e1, e2 | e3, e4 | e5, e6 |
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|-----------|-----------|-----------|
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| → (apply) | → (apply) | → (apply) |
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Accumulated gradient for the weight w1 (considering all GPUs):
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Total gradient for w1 = e1 + e2 + e3 + e4 + e5 + e6
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Weight update for w1:
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w1_new = w1_old - learning rate × (Total gradient for w1 / 6)</code></pre>
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return true;
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||
}
|
||
}
|
||
return false;
|
||
}
|
||
const onCopySuccess = function(e) {
|
||
// button target
|
||
const button = e.trigger;
|
||
// don't keep focus
|
||
button.blur();
|
||
// flash "checked"
|
||
button.classList.add('code-copy-button-checked');
|
||
var currentTitle = button.getAttribute("title");
|
||
button.setAttribute("title", "Copied!");
|
||
let tooltip;
|
||
if (window.bootstrap) {
|
||
button.setAttribute("data-bs-toggle", "tooltip");
|
||
button.setAttribute("data-bs-placement", "left");
|
||
button.setAttribute("data-bs-title", "Copied!");
|
||
tooltip = new bootstrap.Tooltip(button,
|
||
{ trigger: "manual",
|
||
customClass: "code-copy-button-tooltip",
|
||
offset: [0, -8]});
|
||
tooltip.show();
|
||
}
|
||
setTimeout(function() {
|
||
if (tooltip) {
|
||
tooltip.hide();
|
||
button.removeAttribute("data-bs-title");
|
||
button.removeAttribute("data-bs-toggle");
|
||
button.removeAttribute("data-bs-placement");
|
||
}
|
||
button.setAttribute("title", currentTitle);
|
||
button.classList.remove('code-copy-button-checked');
|
||
}, 1000);
|
||
// clear code selection
|
||
e.clearSelection();
|
||
}
|
||
const getTextToCopy = function(trigger) {
|
||
const codeEl = trigger.previousElementSibling.cloneNode(true);
|
||
for (const childEl of codeEl.children) {
|
||
if (isCodeAnnotation(childEl)) {
|
||
childEl.remove();
|
||
}
|
||
}
|
||
return codeEl.innerText;
|
||
}
|
||
const clipboard = new window.ClipboardJS('.code-copy-button:not([data-in-quarto-modal])', {
|
||
text: getTextToCopy
|
||
});
|
||
clipboard.on('success', onCopySuccess);
|
||
if (window.document.getElementById('quarto-embedded-source-code-modal')) {
|
||
const clipboardModal = new window.ClipboardJS('.code-copy-button[data-in-quarto-modal]', {
|
||
text: getTextToCopy,
|
||
container: window.document.getElementById('quarto-embedded-source-code-modal')
|
||
});
|
||
clipboardModal.on('success', onCopySuccess);
|
||
}
|
||
var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
|
||
var mailtoRegex = new RegExp(/^mailto:/);
|
||
var filterRegex = new RegExp("https:\/\/axolotl-ai-cloud\.github\.io\/axolotl\/");
|
||
var isInternal = (href) => {
|
||
return filterRegex.test(href) || localhostRegex.test(href) || mailtoRegex.test(href);
|
||
}
|
||
// Inspect non-navigation links and adorn them if external
|
||
var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool):not(.about-link)');
|
||
for (var i=0; i<links.length; i++) {
|
||
const link = links[i];
|
||
if (!isInternal(link.href)) {
|
||
// undo the damage that might have been done by quarto-nav.js in the case of
|
||
// links that we want to consider external
|
||
if (link.dataset.originalHref !== undefined) {
|
||
link.href = link.dataset.originalHref;
|
||
}
|
||
}
|
||
}
|
||
function tippyHover(el, contentFn, onTriggerFn, onUntriggerFn) {
|
||
const config = {
|
||
allowHTML: true,
|
||
maxWidth: 500,
|
||
delay: 100,
|
||
arrow: false,
|
||
appendTo: function(el) {
|
||
return el.parentElement;
|
||
},
|
||
interactive: true,
|
||
interactiveBorder: 10,
|
||
theme: 'quarto',
|
||
placement: 'bottom-start',
|
||
};
|
||
if (contentFn) {
|
||
config.content = contentFn;
|
||
}
|
||
if (onTriggerFn) {
|
||
config.onTrigger = onTriggerFn;
|
||
}
|
||
if (onUntriggerFn) {
|
||
config.onUntrigger = onUntriggerFn;
|
||
}
|
||
window.tippy(el, config);
|
||
}
|
||
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
|
||
for (var i=0; i<noterefs.length; i++) {
|
||
const ref = noterefs[i];
|
||
tippyHover(ref, function() {
|
||
// use id or data attribute instead here
|
||
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
|
||
try { href = new URL(href).hash; } catch {}
|
||
const id = href.replace(/^#\/?/, "");
|
||
const note = window.document.getElementById(id);
|
||
if (note) {
|
||
return note.innerHTML;
|
||
} else {
|
||
return "";
|
||
}
|
||
});
|
||
}
|
||
const xrefs = window.document.querySelectorAll('a.quarto-xref');
|
||
const processXRef = (id, note) => {
|
||
// Strip column container classes
|
||
const stripColumnClz = (el) => {
|
||
el.classList.remove("page-full", "page-columns");
|
||
if (el.children) {
|
||
for (const child of el.children) {
|
||
stripColumnClz(child);
|
||
}
|
||
}
|
||
}
|
||
stripColumnClz(note)
|
||
if (id === null || id.startsWith('sec-')) {
|
||
// Special case sections, only their first couple elements
|
||
const container = document.createElement("div");
|
||
if (note.children && note.children.length > 2) {
|
||
container.appendChild(note.children[0].cloneNode(true));
|
||
for (let i = 1; i < note.children.length; i++) {
|
||
const child = note.children[i];
|
||
if (child.tagName === "P" && child.innerText === "") {
|
||
continue;
|
||
} else {
|
||
container.appendChild(child.cloneNode(true));
|
||
break;
|
||
}
|
||
}
|
||
if (window.Quarto?.typesetMath) {
|
||
window.Quarto.typesetMath(container);
|
||
}
|
||
return container.innerHTML
|
||
} else {
|
||
if (window.Quarto?.typesetMath) {
|
||
window.Quarto.typesetMath(note);
|
||
}
|
||
return note.innerHTML;
|
||
}
|
||
} else {
|
||
// Remove any anchor links if they are present
|
||
const anchorLink = note.querySelector('a.anchorjs-link');
|
||
if (anchorLink) {
|
||
anchorLink.remove();
|
||
}
|
||
if (window.Quarto?.typesetMath) {
|
||
window.Quarto.typesetMath(note);
|
||
}
|
||
if (note.classList.contains("callout")) {
|
||
return note.outerHTML;
|
||
} else {
|
||
return note.innerHTML;
|
||
}
|
||
}
|
||
}
|
||
for (var i=0; i<xrefs.length; i++) {
|
||
const xref = xrefs[i];
|
||
tippyHover(xref, undefined, function(instance) {
|
||
instance.disable();
|
||
let url = xref.getAttribute('href');
|
||
let hash = undefined;
|
||
if (url.startsWith('#')) {
|
||
hash = url;
|
||
} else {
|
||
try { hash = new URL(url).hash; } catch {}
|
||
}
|
||
if (hash) {
|
||
const id = hash.replace(/^#\/?/, "");
|
||
const note = window.document.getElementById(id);
|
||
if (note !== null) {
|
||
try {
|
||
const html = processXRef(id, note.cloneNode(true));
|
||
instance.setContent(html);
|
||
} finally {
|
||
instance.enable();
|
||
instance.show();
|
||
}
|
||
} else {
|
||
// See if we can fetch this
|
||
fetch(url.split('#')[0])
|
||
.then(res => res.text())
|
||
.then(html => {
|
||
const parser = new DOMParser();
|
||
const htmlDoc = parser.parseFromString(html, "text/html");
|
||
const note = htmlDoc.getElementById(id);
|
||
if (note !== null) {
|
||
const html = processXRef(id, note);
|
||
instance.setContent(html);
|
||
}
|
||
}).finally(() => {
|
||
instance.enable();
|
||
instance.show();
|
||
});
|
||
}
|
||
} else {
|
||
// See if we can fetch a full url (with no hash to target)
|
||
// This is a special case and we should probably do some content thinning / targeting
|
||
fetch(url)
|
||
.then(res => res.text())
|
||
.then(html => {
|
||
const parser = new DOMParser();
|
||
const htmlDoc = parser.parseFromString(html, "text/html");
|
||
const note = htmlDoc.querySelector('main.content');
|
||
if (note !== null) {
|
||
// This should only happen for chapter cross references
|
||
// (since there is no id in the URL)
|
||
// remove the first header
|
||
if (note.children.length > 0 && note.children[0].tagName === "HEADER") {
|
||
note.children[0].remove();
|
||
}
|
||
const html = processXRef(null, note);
|
||
instance.setContent(html);
|
||
}
|
||
}).finally(() => {
|
||
instance.enable();
|
||
instance.show();
|
||
});
|
||
}
|
||
}, function(instance) {
|
||
});
|
||
}
|
||
let selectedAnnoteEl;
|
||
const selectorForAnnotation = ( cell, annotation) => {
|
||
let cellAttr = 'data-code-cell="' + cell + '"';
|
||
let lineAttr = 'data-code-annotation="' + annotation + '"';
|
||
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
|
||
return selector;
|
||
}
|
||
const selectCodeLines = (annoteEl) => {
|
||
const doc = window.document;
|
||
const targetCell = annoteEl.getAttribute("data-target-cell");
|
||
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
|
||
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
|
||
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
|
||
const lineIds = lines.map((line) => {
|
||
return targetCell + "-" + line;
|
||
})
|
||
let top = null;
|
||
let height = null;
|
||
let parent = null;
|
||
if (lineIds.length > 0) {
|
||
//compute the position of the single el (top and bottom and make a div)
|
||
const el = window.document.getElementById(lineIds[0]);
|
||
top = el.offsetTop;
|
||
height = el.offsetHeight;
|
||
parent = el.parentElement.parentElement;
|
||
if (lineIds.length > 1) {
|
||
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
|
||
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
|
||
height = bottom - top;
|
||
}
|
||
if (top !== null && height !== null && parent !== null) {
|
||
// cook up a div (if necessary) and position it
|
||
let div = window.document.getElementById("code-annotation-line-highlight");
|
||
if (div === null) {
|
||
div = window.document.createElement("div");
|
||
div.setAttribute("id", "code-annotation-line-highlight");
|
||
div.style.position = 'absolute';
|
||
parent.appendChild(div);
|
||
}
|
||
div.style.top = top - 2 + "px";
|
||
div.style.height = height + 4 + "px";
|
||
div.style.left = 0;
|
||
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
|
||
if (gutterDiv === null) {
|
||
gutterDiv = window.document.createElement("div");
|
||
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
|
||
gutterDiv.style.position = 'absolute';
|
||
const codeCell = window.document.getElementById(targetCell);
|
||
const gutter = codeCell.querySelector('.code-annotation-gutter');
|
||
gutter.appendChild(gutterDiv);
|
||
}
|
||
gutterDiv.style.top = top - 2 + "px";
|
||
gutterDiv.style.height = height + 4 + "px";
|
||
}
|
||
selectedAnnoteEl = annoteEl;
|
||
}
|
||
};
|
||
const unselectCodeLines = () => {
|
||
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
|
||
elementsIds.forEach((elId) => {
|
||
const div = window.document.getElementById(elId);
|
||
if (div) {
|
||
div.remove();
|
||
}
|
||
});
|
||
selectedAnnoteEl = undefined;
|
||
};
|
||
// Handle positioning of the toggle
|
||
window.addEventListener(
|
||
"resize",
|
||
throttle(() => {
|
||
elRect = undefined;
|
||
if (selectedAnnoteEl) {
|
||
selectCodeLines(selectedAnnoteEl);
|
||
}
|
||
}, 10)
|
||
);
|
||
function throttle(fn, ms) {
|
||
let throttle = false;
|
||
let timer;
|
||
return (...args) => {
|
||
if(!throttle) { // first call gets through
|
||
fn.apply(this, args);
|
||
throttle = true;
|
||
} else { // all the others get throttled
|
||
if(timer) clearTimeout(timer); // cancel #2
|
||
timer = setTimeout(() => {
|
||
fn.apply(this, args);
|
||
timer = throttle = false;
|
||
}, ms);
|
||
}
|
||
};
|
||
}
|
||
// Attach click handler to the DT
|
||
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
|
||
for (const annoteDlNode of annoteDls) {
|
||
annoteDlNode.addEventListener('click', (event) => {
|
||
const clickedEl = event.target;
|
||
if (clickedEl !== selectedAnnoteEl) {
|
||
unselectCodeLines();
|
||
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
|
||
if (activeEl) {
|
||
activeEl.classList.remove('code-annotation-active');
|
||
}
|
||
selectCodeLines(clickedEl);
|
||
clickedEl.classList.add('code-annotation-active');
|
||
} else {
|
||
// Unselect the line
|
||
unselectCodeLines();
|
||
clickedEl.classList.remove('code-annotation-active');
|
||
}
|
||
});
|
||
}
|
||
const findCites = (el) => {
|
||
const parentEl = el.parentElement;
|
||
if (parentEl) {
|
||
const cites = parentEl.dataset.cites;
|
||
if (cites) {
|
||
return {
|
||
el,
|
||
cites: cites.split(' ')
|
||
};
|
||
} else {
|
||
return findCites(el.parentElement)
|
||
}
|
||
} else {
|
||
return undefined;
|
||
}
|
||
};
|
||
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
|
||
for (var i=0; i<bibliorefs.length; i++) {
|
||
const ref = bibliorefs[i];
|
||
const citeInfo = findCites(ref);
|
||
if (citeInfo) {
|
||
tippyHover(citeInfo.el, function() {
|
||
var popup = window.document.createElement('div');
|
||
citeInfo.cites.forEach(function(cite) {
|
||
var citeDiv = window.document.createElement('div');
|
||
citeDiv.classList.add('hanging-indent');
|
||
citeDiv.classList.add('csl-entry');
|
||
var biblioDiv = window.document.getElementById('ref-' + cite);
|
||
if (biblioDiv) {
|
||
citeDiv.innerHTML = biblioDiv.innerHTML;
|
||
}
|
||
popup.appendChild(citeDiv);
|
||
});
|
||
return popup.innerHTML;
|
||
});
|
||
}
|
||
}
|
||
});
|
||
</script>
|
||
</div> <!-- /content -->
|
||
|
||
|
||
|
||
|
||
</body></html> |