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How an A.I. that draws digits “collapses” after being trained on its own output
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<h1 id="when-ais-output-is-a-threat-to-ai-itself"><a href="https://www.nytimes.com/interactive/2024/08/26/upshot/ai-synthetic-data.html">When A.I.’s Output Is a Threat to A.I. Itself</a><a class="headerlink" href="#when-ais-output-is-a-threat-to-ai-itself" title="Permanent link">&para;</a></h1>
<p><strong>Note</strong> - we recommend reading this article on the NY - Times for the best reading experience </p>
<p>As A.I.-generated data becomes harder to detect, it’s increasingly likely to be ingested by future A.I., leading to worse results.</p>
<p>By <a href="https://www.nytimes.com/by/aatish-bhatia">Aatish Bhatia</a></p>
<p>Aatish Bhatia interviewed A.I. researchers, studied research papers and fed an A.I. system its own output.</p>
<p>The internet is becoming awash in words and images generated by artificial intelligence.</p>
<p>Sam Altman, OpenAI’s chief executive, wrote in February that the company generated about <a href="https://x.com/sama/status/1756089361609981993?lang=en">100 billion words per day</a> — a million novels’ worth of text, every day, an unknown share of which finds its way onto the internet.</p>
<p>A.I.-generated text may show up as a restaurant review, a dating profile or a social media post. And it may show up as a news article, too: NewsGuard, a group that tracks online misinformation, recently identified over <a href="https://www.newsguardtech.com/special-reports/ai-tracking-center/">a thousand websites</a> that churn out error-prone <a href="https://www.nytimes.com/2024/06/06/technology/bnn-breaking-ai-generated-news.html">A.I.-generated news articles</a>.</p>
<p>In reality, with no foolproof methods to detect this kind of content, much will simply remain undetected.</p>
<p>All this A.I.-generated information can make it harder for us to know what’s real. And it also poses a problem for A.I. companies. As they trawl the web for new data to train their next models on — an <a href="https://www.nytimes.com/2024/07/19/technology/ai-data-restrictions.html">increasingly challenging task</a> — they’re likely to ingest some of their own A.I.-generated content, creating an unintentional feedback loop in which what was once the output from one A.I. becomes the input for another.</p>
<p>In the long run, this cycle may pose a threat to A.I. itself. <a href="https://www.nature.com/articles/s41586-024-07566-y">Research</a> <a href="https://openreview.net/forum?id=ShjMHfmPs0">has</a> <a href="https://openreview.net/pdf/b07c42e256e6df5c2c52aba4bf28c853110ebb7b.pdf">shown</a> <a href="https://openreview.net/notes/edits/attachment?id=XLIOLMlnqh&amp;name=pdf">that</a> when generative A.I. is trained on a lot of its own output, it can get a lot worse.</p>
<p>Here’s a simple illustration of what happens when an A.I. system is trained on its own output, over and over again:</p>
<p>This is part of a data set of 60,000 handwritten digits.</p>
<p>When we trained an A.I. to mimic those digits, its output looked like this.</p>
<p>This new set was made by an A.I. trained on the previous A.I.-generated digits. What happens if this process continues?</p>
<p>After 20 generations of training new A.I.s on their predecessors’ output, the digits blur and start to erode.</p>
<p>After 30 generations, they converge into a single shape.</p>
<p>While this is a simplified example, it illustrates a problem on the horizon.</p>
<p>Imagine a medical-advice chatbot that lists fewer diseases that match your symptoms, because it was trained on a narrower spectrum of medical knowledge generated by previous chatbots. Or an A.I. history tutor that ingests A.I.-generated propaganda and can no longer separate fact from fiction.</p>
<p>Just as a <a href="https://www.newyorker.com/tech/annals-of-technology/chatgpt-is-a-blurry-jpeg-of-the-web">copy of a copy can drift away</a> from the original, when generative A.I. is trained on its own content, its output can also drift away from reality, growing further apart from the original data that it was intended to imitate.</p>
<p>In a <a href="https://www.nature.com/articles/s41586-024-07566-y">paper</a> published last month in the journal Nature, a group of researchers in Britain and Canada showed how this process results in a narrower range of A.I. output over time — an early stage of what they called “model collapse.”</p>
<p>The eroding digits we just saw show this collapse. When untethered from human input, the A.I. output dropped in quality (the digits became blurry) and in diversity (they grew similar).</p>
<h3 id="how-an-ai-that-draws-digits-collapses-after-being-trained-on-its-own-output">How an A.I. that draws digits “collapses” after being trained on its own output<a class="headerlink" href="#how-an-ai-that-draws-digits-collapses-after-being-trained-on-its-own-output" title="Permanent link">&para;</a></h3>
<table>
<thead>
<tr>
<th></th>
<th>“3”</th>
<th>“4”</th>
<th>“6”</th>
<th>“8”</th>
<th>“9”</th>
</tr>
</thead>
<tbody>
<tr>
<td>Handwritten digits</td>
<td><img alt="digit 3 mnist" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_3_mnist_bg.png" /></td>
<td><img alt="digit 4 mnist" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_4_mnist_bg.png" /></td>
<td><img alt="digit 6 mnist" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_6_mnist_bg.png" /></td>
<td><img alt="digit 8 mnist" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_8_mnist_bg.png" /></td>
<td><img alt="digit 9 mnist" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_9_mnist_bg.png" /></td>
</tr>
<tr>
<td>Initial A.I. output</td>
<td><img alt="digit 3 gen_0" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_3_gen_0_bg.png" /></td>
<td><img alt="digit 4 gen_0" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_4_gen_0_bg.png" /></td>
<td><img alt="digit 6 gen_0" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_6_gen_0_bg.png" /></td>
<td><img alt="digit 8 gen_0" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_8_gen_0_bg.png" /></td>
<td><img alt="digit 9 gen_0" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_9_gen_0_bg.png" /></td>
</tr>
<tr>
<td>After 10 generations</td>
<td><img alt="digit 3 gen_10" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_3_gen_10_bg.png" /></td>
<td><img alt="digit 4 gen_10" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_4_gen_10_bg.png" /></td>
<td><img alt="digit 6 gen_10" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_6_gen_10_bg.png" /></td>
<td><img alt="digit 8 gen_10" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_8_gen_10_bg.png" /></td>
<td><img alt="digit 9 gen_10" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_9_gen_10_bg.png" /></td>
</tr>
<tr>
<td>After 20 generations</td>
<td><img alt="digit 3 gen_20" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_3_gen_20_bg.png" /></td>
<td><img alt="digit 4 gen_20" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_4_gen_20_bg.png" /></td>
<td><img alt="digit 6 gen_20" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_6_gen_20_bg.png" /></td>
<td><img alt="digit 8 gen_20" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_8_gen_20_bg.png" /></td>
<td><img alt="digit 9 gen_20" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_9_gen_20_bg.png" /></td>
</tr>
<tr>
<td>After 30 generations</td>
<td><img alt="digit 3 gen_30" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_3_gen_30_bg.png" /></td>
<td><img alt="digit 4 gen_30" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_4_gen_30_bg.png" /></td>
<td><img alt="digit 6 gen_30" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_6_gen_30_bg.png" /></td>
<td><img alt="digit 8 gen_30" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_8_gen_30_bg.png" /></td>
<td><img alt="digit 9 gen_30" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digit_9_gen_30_bg.png" /></td>
</tr>
</tbody>
</table>
<p>If only some of the training data were A.I.-generated, the decline would be slower or more subtle. But it would still occur, researchers say, unless the synthetic data was complemented with a lot of new, real data.</p>
<h2 id="degenerative-ai">Degenerative A.I.<a class="headerlink" href="#degenerative-ai" title="Permanent link">&para;</a></h2>
<p>In one example, the researchers trained a large language model on its own sentences over and over again, asking it to complete the same prompt after each round.</p>
<p>When they asked the A.I. to complete a sentence that started with <strong>“To cook a turkey for Thanksgiving, you…,”</strong> at first, it responded like this:</p>
<p>Even at the outset, the A.I. “hallucinates.” But when the researchers further trained it on its own sentences, it got a lot worse…</p>
<p>An example of text generated by an A.I. model.</p>
<p>After two generations, it started simply printing long lists.</p>
<p>An example of text generated by an A.I. model after being trained on its own sentences for 2 generations.</p>
<p>And after four generations, it began to repeat phrases incoherently.</p>
<p>An example of text generated by an A.I. model after being trained on its own sentences for 4 generations.</p>
<p>“The model becomes poisoned with its own projection of reality,” <a href="https://www.nature.com/articles/s41586-024-07566-y#:~:text=Model%20collapse%20refers%20to%20a%20degenerative%20learning%20process%20in%20which%20models%20start%20forgetting%20improbable%20events%20over%20time%2C%20as%20the%20model%20becomes%20poisoned%20with%20its%20own%20projection%20of%20reality.">the researchers wrote</a> of this phenomenon.</p>
<p>This problem isn’t just confined to text. Another team of researchers at Rice University <a href="https://openreview.net/pdf?id=ShjMHfmPs0">studied</a> what would happen when the kinds of A.I. that generate images are repeatedly trained on their own output — a problem that could already be occurring as A.I.-generated images flood the web.</p>
<p>They found that glitches and image artifacts started to build up in the A.I.’s output, eventually producing distorted images with wrinkled patterns and mangled fingers.</p>
<p>When A.I. image models are trained on their own output, they can produce distorted images, mangled fingers or strange patterns.</p>
<p>A.I.-generated images by <a href="https://openreview.net/pdf?id=ShjMHfmPs0">Sina Alemohammad and others</a>.</p>
<p>“You’re kind of drifting into parts of the space that are like a no-fly zone,” said <a href="https://richb.rice.edu/biography/">Richard Baraniuk</a>, a professor who led the research on A.I. image models.</p>
<p>The researchers found that the only way to stave off this problem was to ensure that the A.I. was also trained on a sufficient supply of new, real data.</p>
<p>While selfies are certainly not in short supply on the internet, there could be categories of images where A.I. output outnumbers genuine data, they said.</p>
<p>For example, A.I.-generated images in the style of van Gogh could outnumber actual photographs of van Gogh paintings in A.I.’s training data, and this may lead to errors and distortions down the road. (Early signs of this problem will be hard to detect because the leading A.I. models are closed to outside scrutiny, the researchers said.)</p>
<h2 id="why-collapse-happens">Why collapse happens<a class="headerlink" href="#why-collapse-happens" title="Permanent link">&para;</a></h2>
<p>All of these problems arise because A.I.-generated data is often a poor substitute for the real thing.</p>
<p>This is sometimes easy to see, like when chatbots state absurd facts or when A.I.-generated hands have too many fingers.</p>
<p>But the differences that lead to model collapse aren’t necessarily obvious — and they can be difficult to detect.</p>
<p>When generative A.I. is “trained” on vast amounts of data, what’s really happening under the hood is that it is assembling a <em>statistical distribution</em> — a set of probabilities that predicts the next word in a sentence, or the pixels in a picture.</p>
<p>For example, when we trained an A.I. to imitate handwritten digits, its output could be arranged into a statistical distribution that looks like this:</p>
<h3 id="distribution-of-ai-generated-data">Distribution of A.I.-generated data<a class="headerlink" href="#distribution-of-ai-generated-data" title="Permanent link">&para;</a></h3>
<p>Examples of<br />
<strong>initial A.I. output:</strong></p>
<p><img alt="An example of an A.I.-generated digit" src="https://static01.nytimes.com/newsgraphics/2024-04-24-ai-synthetic-data/_big_assets/digitsamples/random_digit_gen_0_0_bg.png" /></p>
<p>The distribution shown here is simplified for clarity.</p>
<p>The peak of this bell-shaped curve represents the most probable A.I. output — in this case, the most typical A.I.-generated digits. The tail ends describe output that is less common.</p>
<p>Notice that when the model was trained on human data, it had a healthy spread of possible outputs, which you can see in the width of the curve above.</p>
<p>But after it was trained on its own output, this is what happened to the curve:</p>
<h3 id="distribution-of-ai-generated-data-when-trained-on-its-own-output">Distribution of A.I.-generated data when trained on its own output<a class="headerlink" href="#distribution-of-ai-generated-data-when-trained-on-its-own-output" title="Permanent link">&para;</a></h3>
<p>It gets taller and narrower. As a result, the model becomes more and more likely to produce a smaller range of output, and the output can drift away from the original data.</p>
<p>Meanwhile, the tail ends of the curve — which contain the rare, unusual or surprising outcomes — fade away.</p>
<p>This is a telltale sign of model collapse: Rare data becomes even rarer.</p>
<p>If this process went unchecked, the curve would eventually become a spike:</p>
<h3 id="distribution-of-ai-generated-data-when-trained-on-its-own-output_1">Distribution of A.I.-generated data when trained on its own output<a class="headerlink" href="#distribution-of-ai-generated-data-when-trained-on-its-own-output_1" title="Permanent link">&para;</a></h3>
<p>This was when all of the digits became identical, and the model completely collapsed.</p>
<h2 id="why-it-matters">Why it matters<a class="headerlink" href="#why-it-matters" title="Permanent link">&para;</a></h2>
<p>This doesn’t mean generative A.I. will grind to a halt anytime soon.</p>
<p>The companies that make these tools are aware of these problems, and they will notice if their A.I. systems start to deteriorate in quality.</p>
<p>But it may slow things down. As <a href="https://www.nytimes.com/2024/07/19/technology/ai-data-restrictions.html">existing sources of data dry up</a> or <a href="https://www.nytimes.com/2024/03/29/opinion/ai-internet-x-youtube.html">become contaminated</a> with A.I. “<a href="https://www.nytimes.com/2024/06/11/style/ai-search-slop.html">slop</a>,” researchers say it makes it harder for newcomers to compete.</p>
<p>A.I.-generated words and images are already beginning to <a href="https://dl.acm.org/doi/10.1145/3649468#:~:text=6.2-,Interconnectedness%20and%20Synthetic%20Media%20Spills,-Another%20facet%20of">flood social media and the wider web</a>. They’re even hiding in some of the data sets used to train A.I., <a href="https://openreview.net/pdf?id=ShjMHfmPs0">the Rice researchers found</a>.</p>
<p>“The web is becoming increasingly a dangerous place to look for your data,” said <a href="https://www.linkedin.com/in/sina-alemohammad-837b0ab6/">Sina Alemohammad</a>, a graduate student at Rice who studied how A.I. contamination affects image models.</p>
<p>Big players will be affected, too. Computer scientists at N.Y.U. found that when there is a lot of A.I.-generated content in the training data, it <a href="https://openreview.net/forum?id=KVvku47shW">takes more computing power</a> to train A.I. — which translates into more energy and more money.</p>
<p>“Models won’t scale anymore as they should be scaling,” said <a href="https://cims.nyu.edu/~kempe/">Julia Kempe</a>, the N.Y.U. professor who led this work.</p>
<p>The leading A.I. models already cost <a href="https://epochai.org/blog/how-much-does-it-cost-to-train-frontier-ai-models#:~:text=The%20cost%20of%20training%20frontier,a%20billion%20dollars%20by%202027.">tens to hundreds of millions of dollars</a> to train, and they <a href="https://www.bloomberg.com/graphics/2024-ai-data-centers-power-grids/">consume staggering amounts of energy</a>, so this can be a sizable problem.</p>
<h2 id="a-hidden-danger">‘A hidden danger’<a class="headerlink" href="#a-hidden-danger" title="Permanent link">&para;</a></h2>
<p>Finally, there’s another threat posed by even the early stages of collapse: an erosion of diversity.</p>
<p>And it’s an outcome that could become more likely as companies try to avoid the glitches and “<a href="https://www.nytimes.com/2023/05/01/business/ai-chatbots-hallucination.html">hallucinations</a>” that often occur with A.I. data.</p>
<p>This is easiest to see when the data matches a form of diversity that we can visually recognize — people’s faces:</p>
<p>This set of A.I. faces was created by the same Rice researchers who produced the distorted faces above.</p>
<p>This time, they tweaked the model to avoid visual glitches.</p>
<p>A grid of A.I.-generated faces showing variations in their poses, expressions, ages and races.</p>
<p>This is the output after they trained a new A.I. on the previous set of faces.</p>
<p>At first glance, it may seem like the model changes worked: The glitches are gone.</p>
<p>After one generation of training on A.I. output, the A.I.-generated faces appear more similar.</p>
<p>After two generations …</p>
<p>After two generations of training on A.I. output, the A.I.-generated faces are less diverse than the original image.</p>
<p>After three generations …</p>
<p>After three generations of training on A.I. output, the A.I.-generated faces grow more similar.</p>
<p>After four generations, the faces all appeared to converge.</p>
<p>After four generations of training on A.I. output, the A.I.-generated faces appear almost identical.</p>
<p>This drop in diversity is “a hidden danger,” Mr. Alemohammad said. “You might just ignore it and then you don’t understand it until it's too late.”</p>
<p>Just as with the digits, the changes are clearest when most of the data is A.I.-generated. With a more realistic mix of real and synthetic data, the decline would be more gradual.</p>
<p>But the problem is relevant to the real world, the researchers said, and will inevitably occur unless A.I. companies go out of their way to avoid their own output.</p>
<p><a href="https://arxiv.org/abs/2311.09807">Related research</a> shows that when A.I. language models are trained on their own words, their vocabulary shrinks and their sentences become less varied in their grammatical structure — a loss of “<a href="https://arxiv.org/abs/2311.09807">linguistic diversity</a>.”</p>
<p>And studies have found that this process can <a href="https://arxiv.org/pdf/2209.03942">amplify biases in the data</a> and is more likely to erase <a href="https://arxiv.org/pdf/2403.07857">data pertaining to minorities</a>.</p>
<h2 id="ways-out">Ways out<a class="headerlink" href="#ways-out" title="Permanent link">&para;</a></h2>
<p>Perhaps the biggest takeaway of this research is that high-quality, diverse data is valuable and hard for computers to emulate.</p>
<p>One solution, then, is for A.I. companies to pay for this data instead of <a href="https://www.nytimes.com/2024/04/06/technology/tech-giants-harvest-data-artificial-intelligence.html">scooping it up from the internet</a>, ensuring both human origin and high quality.</p>
<p>OpenAI and Google have made deals with some publishers or websites to use their data to improve A.I. (The New York Times <a href="https://www.nytimes.com/2023/12/27/business/media/new-york-times-open-ai-microsoft-lawsuit.html">sued OpenAI and Microsoft</a> last year, alleging copyright infringement. <a href="https://www.nytimes.com/2024/02/27/technology/openai-new-york-times-lawsuit.html">OpenAI</a> and <a href="https://www.nytimes.com/2024/03/04/technology/microsoft-ai-copyright-lawsuit.html?action=click&amp;module=RelatedLinks&amp;pgtype=Article">Microsoft say</a> their use of the content is considered fair use under copyright law.)</p>
<p>Better ways to detect A.I. output would also help mitigate these problems.</p>
<p><a href="https://deepmind.google/discover/blog/watermarking-ai-generated-text-and-video-with-synthid/">Google</a> and <a href="https://openai.com/index/understanding-the-source-of-what-we-see-and-hear-online/">OpenAI</a> are working on A.I. “<a href="https://www.nytimes.com/interactive/2023/02/17/business/ai-text-detection.html">watermarking</a>” tools, which introduce hidden patterns that can be used to identify A.I.-generated images and text.</p>
<p>But watermarking text <a href="https://www.brookings.edu/articles/detecting-ai-fingerprints-a-guide-to-watermarking-and-beyond/">is challenging</a>, researchers say, because these watermarks can’t always be reliably detected and can <a href="https://www.youtube.com/watch?v=2Kx9jbSMZqA&amp;t=3068s">easily be subverted</a> (they may not survive being translated into another language, for example).</p>
<p>A.I. slop is not the only reason that companies may need to be wary of synthetic data. Another problem is that there are only so many words on the internet.</p>
<p><a href="https://epochai.org/blog/will-we-run-out-of-data-limits-of-llm-scaling-based-on-human-generated-data">Some experts estimate</a> that the largest A.I. models have been trained on a few percent of the available pool of text on the internet. <a href="https://epochai.org/blog/will-we-run-out-of-data-limits-of-llm-scaling-based-on-human-generated-data">They project</a> that these models may run out of public data to sustain their current pace of growth within a decade.</p>
<p>“These models are so enormous that the entire internet of images or conversations is somehow close to being not enough,” Professor Baraniuk said.</p>
<p>To meet their growing data needs, some companies are considering using <a href="https://www.nytimes.com/2024/04/06/technology/ai-data-tech-companies.html">today’s A.I. models to generate data to train tomorrow’s models</a>. But researchers say this can lead to unintended consequences (such as the drop in quality or diversity that we saw above).</p>
<p>There are certain contexts where synthetic data can help A.I.s learn — for example, when output from a larger A.I. model is used to train a smaller one, or when the correct answer can be verified, like the solution to a <a href="https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/">math</a> <a href="https://deepmind.google/discover/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/">problem</a> or the best strategies in <a href="https://deepmind.google/discover/blog/alphazero-shedding-new-light-on-chess-shogi-and-go/">games like chess or Go</a>.</p>
<p>And <a href="https://openreview.net/forum?id=iqoqtNyVta">new</a> <a href="https://arxiv.org/abs/2407.09499">research</a> suggests that when humans curate synthetic data (for example, by ranking A.I. answers and choosing the best one), it can alleviate some of the problems of collapse.</p>
<p>Companies are already spending a lot on curating data, Professor Kempe said, and she believes this will become even more important as they learn about the problems of synthetic data.</p>
<p>But for now, there’s no replacement for the real thing.</p>
<p>About the data</p>
<p>To produce the images of A.I.-generated digits, we followed a procedure <a href="https://arxiv.org/pdf/2305.17493">outlined by researchers</a>. We first trained a type of a neural network known as a <a href="https://en.wikipedia.org/wiki/Variational_autoencoder">variational autoencoder</a> using a standard data set of <a href="https://en.wikipedia.org/wiki/MNIST_database">60,000 handwritten digits</a>.</p>
<p>We then trained a new neural network using only the A.I.-generated digits produced by the previous neural network, and repeated this process in a loop 30 times.</p>
<p>To create the statistical distributions of A.I. output, we used each generation’s neural network to create 10,000 drawings of digits. We then used the first neural network (the one that was trained on the original handwritten digits) to encode these drawings as a set of numbers, known as a “<a href="https://en.wikipedia.org/wiki/Latent_space">latent space</a>” encoding. This allowed us to quantitatively compare the output of different generations of neural networks. For simplicity, we used the average value of this latent space encoding to generate the statistical distributions shown in the article.</p>
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