The Secret of Fractal Patterns Revealing AI's Limitations: A New Discovery Approaching Unpredictability

Using the same materials, in the same order, and teaching in the same way. Even then, it doesn't guarantee that the resulting AI will behave exactly the same.

In human learning, this might not be surprising. But what if a computer, with its predetermined calculation steps, has its final results swayed by even the slightest difference in starting points?

A research team from the University of Sydney has provided new insights into understanding this issue. The key lies in "fractals," patterns that continue to reveal complexity even when magnified.

According to research introduced by Phys.org on November 5, 2026, the variability in AI learning outcomes cannot be fully explained by differences in hardware or random numbers from external sources. There might be a mathematical structure inherent in the way neural networks learn that makes predicting results difficult.

It wasn't just computer malfunctions causing the issue

The research was conducted by Professor Pulin Gong and doctoral candidate Andrew Ly from the School of Physics at the University of Sydney. The findings were published in the academic journal "Nature Machine Intelligence."

Neural networks learn by adjusting numerous internal values, or parameters. For instance, when distinguishing images, they gradually update these values based on the discrepancy between predictions and correct answers, aiming for better judgment.

In this learning process, the order in which data is presented and minor computational differences can affect the results. Therefore, if results don't match, it's natural to first check random numbers or the computational environment.

This research delved into issues beyond that.

Even in a "deterministic" environment where data and learning procedures are aligned, and the same input and state yield the same computational results, a slight change in initial parameters can lead learning to a different outcome.

Here, it's necessary to distinguish between "completely identical conditions" and "almost identical conditions."

This research does not claim that results change without reason even with completely identical initial states and deterministic procedures. The issue lies in the fact that even when minimizing tiny differences at the starting point, the differences in results do not diminish as expected.

Thinking of AI learning as a "color-coded map"

To understand the research, it's helpful to replace AI learning with a map.

Imagine each point on the map represents a combination of parameters at the start of learning. As learning progresses from there, the location that reaches a certain result is colored blue, and another result is colored orange.

The collection of starting points leading to the same result is called an "attraction basin" in mathematics.

If the blue and orange regions are neatly separated, the situation is relatively simple. If you place the starting point far enough from the boundary in a blue area, you can expect to reach the blue result even with slight deviations.

However, the research team focused on a structure where orange dots intrude into the blue region, and blue dots intrude into the orange region.

Even in areas that appear to be the same color when viewed broadly, different colors emerge upon magnification. Further magnification reveals points leading to different destinations intricately intermingled.

Such structures are referred to as "riddled basins." In Japanese, it can be imagined as attraction basins with holes leading to different results everywhere.

Even if you examine the starting point in detail, there is still fine intermingling beyond that. This is where the difficulty in predicting learning outcomes lies.

The meaning of "no improvement even with 10 billion times precision"

The research team investigated approximately 500,000 learning instances, including networks used for image recognition and text processing.

According to the introduction article, in a relatively large image recognition network, even when the starting point was set with 10 billion times precision, no measurable improvement in reproducibility was observed.

Typically, one would think that reducing errors would stabilize results. Measuring position accurately makes it easier to reach the destination, and measuring ingredients accurately makes it easier to recreate the same dish.

However, if starting points leading to different destinations are intermingled at a very fine scale, merely reducing the difference in initial values does not guarantee consistent results.

However, this "10 billion times" does not mean that the computer was made 10 billion times more powerful. Nor does it mean that the experiment involved increasing the learning data by 10 billion times.

The focus is on the precision of the settings at the start of learning. This result does not immediately conclude that "adding computational resources to AI is meaningless."

"About 48%" is not the error rate of AI

Another striking figure stands out.

The introduction article explains that a very small change equivalent to 1 bit in the initial settings of the network led to learning progressing to a different internal configuration in about 48% of cases.

This figure is striking, but it should not be misinterpreted.

It does not mean "AI makes mistakes about 48% of the time," nor does it mean "about 48% of the answers change." It refers to the proportion of learning sets with minor changes that progressed to different internal destinations.

The fact that internal values differ does not necessarily mean that the answers received by users differ. This is because different combinations of parameters can still achieve the same input-output relationship.

Therefore, the research also separately examines differences in predictions after learning, not just internal configurations. In a representative experiment from the publicly available preprint, the proportion of inputs where the predictions of two models diverged stabilized at an average of about 2.9%. This is also a figure specific to certain experimental conditions and does not apply to all AI.

The important thing is not to focus on a single prominent number, but to confirm what was compared and what differed.

Can ease of learning and reproducibility coexist?

The research also highlighted the challenges between performance and reproducibility.

The setting that determines how much to update parameters during learning is called the "learning rate." Roughly speaking, it determines how much to step forward with each correction.

In the reported experiments, settings that allowed for effective learning made it difficult to predict and reproduce results, while lowering the learning rate made it easier to reproduce but reduced the effectiveness of learning.

It's premature to generalize this as "high-performance AI is always unstable." However, changing settings solely to reduce numerical variability might result in losing other desirable properties.

For developers, it's not simply about thinking "lowering the learning rate will solve the problem." It's about determining what level of performance is necessary and what needs to be reproduced, tailored to the application.

On social media and in reader comments, the focus is on "whether precision solves the problem"

In the social media posts that could be confirmed about this research, the official LinkedIn post by Phys.org highlighted the point that reproducibility did not improve even with 10 billion times precision in initial settings.

The main point of the post is that merely increasing numerical precision does not guarantee consistent learning outcomes, and that the mathematical structure of learning needs to be considered separately from external randomness.

However, this is a research introduction by the media itself and should be distinguished from the reactions of general users.

Separately from social media, reader comments could be confirmed in the public search results of the news sharing site "Cuppa." The reader expressed surprise at the lack of improvement despite significantly increasing precision and questioned whether the problem could be solved solely by improving computational power or hardware.

This is one example of how the research is perceived by readers. On the other hand, the interpretation that "increasing computational power won't solve the problem" is broader than the scope directly confirmed by the experiments. The precision of initial values and the overall effect of computational resources cannot be treated together.

As of November 6, 2026, the publicly available information that could be confirmed did not reveal a large number of social media posts by general users or the distribution of opinions. There is no basis to describe it as "a flood of surprise voices on social media."

Nevertheless, the confirmed posts and comments present a clear question: If AI is calculated more finely and accurately, will it always develop in the same way? This research prompts a reconsideration of that intuition.

What is relevant to AI implementation sites in Japan?

When considering the implications of this research for implementation sites in Japan, it's important to focus on the difference between "working well once" and "reliably working when rebuilt."

For example, imagine AI that detects defects in products in a factory.

Even if the overall accuracy rates of two models are similar, it doesn't necessarily mean they will miss the same products. Comparing only average scores might overlook important differences in the field.

This is not a result demonstrated in Japanese factories, but an example of applying the research's problem awareness to practical work.

In development and evaluation, the following perspectives can be considered:

• Check not only the best performance obtained from a single learning session but also the variability of results from multiple learning sessions.
• Investigate not only accuracy rates but also which inputs lead to different judgments.
• Ensure that the model after retraining does not make different judgments in important cases compared to before.
• Record initial values, settings, and computational environments to enable result comparison.

Even with the mathematical difficulties suggested by the research, the value of recording and verification does not diminish. Rather, it's important to measure the remaining variability after aligning controllable conditions.

Consider separately from "different answers every time" in chat AI

In familiar generative AI, the answer may change even when the same question is asked. One might be tempted to link that experience with this research.

However, the main topic here is how differences in initial conditions affect the "learning stage" of model creation.

The variability in generating text from a trained model is a different stage being addressed. Therefore, this paper alone cannot explain all changes in responses or factual inaccuracies in chat AI.

Also, it's an overreach to read it as "mathematically impossible to reproduce all neural networks."

The research analyzes mechanisms with simplified models and examines features consistent with those mechanisms in more complex networks. Evidence obtained from complex models and general proofs for all AI need to be distinguished.

The value of this discovery is not in labeling all AI as "unpredictable." It lies in showing a path to investigate, mathematically and experimentally, under what conditions and what types of reproducibility are compromised.

For trustworthy AI, evaluation beyond "accuracy rate" is necessary

In AI evaluation, attention tends to focus on high accuracy rates and prominent benchmark results.

However, in systems intended for long-term use, it's crucial to maintain the required quality when updating data for retraining, adjusting settings, or rebuilding in a different environment.

This research suggests that part of this difficulty may stem from the structure of learning itself, rather than mere setting errors or machine quirks.

The researchers also indicate directions for future improvements, such as methods to measure sensitivity and network designs that reduce conditions causing instability. Investigating the limits of prediction is not about giving up on improvements; it's about identifying what needs to change.

The beautiful fractal patterns of blue and orange intermingling. Behind this lies the practical question of how to balance "accurate AI" with "AI that can be repeatedly verified."

Sources and References

1. Phys.org:Introduction of research provided by the University of Sydney. About 500,000 learning experiments, precision of initial settings, the figure of about 48%, and the relationship between learning rate and reproducibility.
   https://phys.org/news/2026-11-fractal-patterns-reveal-hidden-limits.html

2. Nature Machine Intelligence: DOI of the published paper.
   Andrew Ly, Pulin Gong "Fractal basin geometry and the limits to predictability and reproducibility in deep learning." The full text on the publisher's page could not be obtained, so the following publicly available preprint was used for additional technical confirmation.
   https://doi.org/10.1038/s42256-026-01336-3

3. arXiv: Publicly available preprint of the same title, version 2.
   Distinction between differences in internal parameters and predictions, about 2.9% prediction mismatch in representative experiments, and positioning of verification with simplified models and deep networks. There may be differences from the final published version.arxiv.org
   https://arxiv.org/html/2510.05606v2

4. Phys.org official LinkedIn: Introduction of research on social media.
   Confirmed post introducing the point that reproducibility did not improve even with increased numerical precision. Published as a transmission by the media itself, not as a general user impression.LinkedIn
   https://im.linkedin.com/company/phys-org

5. Cuppa: Reader comments on the article sharing page.
   Summary of comments displayed in public search results. The main page could not be obtained, and it is treated as a single reader reaction, not generalized to public opinion or overall SNS trends.Cuppa
   https://www.dailycuppa.com.au/article/fractal-patterns-reveal-hidden-limits-to-ai-predictability-1433159