Two neural networks can receive the same training data and follow the same procedure yet arrive at different internal solutions. A new study from the University of Sydney explores a mathematical reason why tiny differences in their starting conditions can lead to different outcomes.
The researchers describe an intricate training landscape in which starting points that lead to different results can be extremely close together. Their work helps explain a reproducibility problem in the systems they studied. It does not prove that every AI system is unpredictable or that a small change will always produce a different answer.
The research appeared in Nature Machine Intelligence and was described by the University of Sydney on November 6, 2026. It connects AI training with a branch of mathematics concerned with how systems evolve from different starting points.
What does it mean to train a neural network?
A neural network contains adjustable parameters. During training, it processes examples, produces outputs and changes those parameters according to a learning procedure. The aim is to improve its performance on a task, such as recognizing an image or predicting an outcome.
Before training begins, the parameters have initial values. Those values are not usually the final solution. They are a starting point from which the learning algorithm makes many successive adjustments.
Different training runs can vary because of the order of examples, random choices in the algorithm or numerical differences in computing hardware. The Sydney researchers investigated a narrower question: what happens when such external sources of variation are controlled, but the starting parameters differ by an extremely small amount?
A map of possible starting points
The university describes the researchers’ approach using the idea of a map. Imagine each location on the map represents a possible set of initial parameters. Color a point according to the solution reached after training. Points leading to the same outcome form a region known as a basin of attraction.
In a simple landscape, nearby starting points might usually lead to the same final region. Boundaries between regions would still matter, but a point well inside one region could be relatively predictable.
The study found evidence of a more intricate arrangement known as riddled basins in the networks examined. In such a landscape, starting points leading to different outcomes can be interwoven at very small scales. Improving the precision with which the starting point is specified may not make the outcome as predictable as a simple map would suggest.
The word ‘fractal’ describes a pattern with structure at multiple scales. It is not a claim that a neural network is literally a picture of a coastline, or that its behavior is random in every sense. A deterministic process can still be highly sensitive to its starting conditions.
What did the researchers observe?
According to the university, in one larger image-recognition network, making the initial settings vastly more precise did not measurably improve reproducibility. It also reports that changing a starting value by the smallest difference represented in the experiment led to a different internal configuration in about 48% of cases.
Those numbers belong to a particular experimental setting. They are not an estimated error rate for ChatGPT, a medical AI system or neural networks in general. The result concerns the outcome measured by the researchers, including internal configurations, and should not automatically be translated into the same percentage of changed predictions for users.
That distinction matters because two networks can have different parameter values while performing similarly on a test. Conversely, similar average accuracy can hide differences on particular examples. A meaningful assessment depends on which outcome is measured and what the system is used for.
Same accuracy, different mistakes
Consider two hypothetical image classifiers that each score highly on a benchmark. They might agree on most images but disagree on a small subset. If those difficult cases are important, a single average score could conceal a practical difference.
The Sydney study motivates questions like this, but the hypothetical example is not a reported test of a clinical diagnostic system. To know whether two actual models differ in a consequential way, researchers would need to evaluate their predictions on appropriate independent cases and measure the errors relevant to the application.
Reproducibility also has more than one meaning. Scientists might ask whether a training run reaches the same parameters, gives the same predictions, achieves the same average performance or reaches the same scientific conclusion. These are related but distinct standards.
Why not simply make the starting values more precise?
Greater numerical precision can reduce some kinds of rounding error. It cannot necessarily solve sensitivity if the mathematical structure of the training process contains starting points that lead to different outcomes at extremely small separations.
A useful analogy is balancing a pencil on its tip. Tiny differences can affect which way it falls. The analogy is only a starting point: a neural-network training landscape can have many parameters and far more complicated boundaries than a falling pencil.
The researchers’ result suggests that, for the systems and settings examined, simply recording or reproducing the initial values with ever greater precision may not be enough to ensure the same internal outcome. Other choices in the learning process may matter.
The learning-rate trade-off
A learning rate controls the size of an update made during training. A smaller rate generally means the algorithm takes smaller steps, although the overall behavior depends on the optimization method and other settings.
The university reports that reducing the learning rate improved reproducibility in the study but made the networks learn less effectively. That is a trade-off observed in the tested settings, not a universal rule that smaller learning rates are always worse.
For a researcher or developer, the practical question is how to balance performance, stability, training time and the needs of the task. Repeating experiments with different starting conditions can reveal how variable results are. It cannot guarantee that every possible failure has been found.
Does this make AI unreliable?
The study does not justify a blanket conclusion that AI cannot be trusted. It shows why reliability should be measured rather than assumed. A system may perform consistently enough for one use and not for another, depending on the consequences of its errors and the evidence available.
In a low-stakes application, small differences between training runs might matter little. In a medical or safety-critical context, developers need rigorous validation, monitoring and an understanding of where errors occur. The same benchmark score is not a substitute for those tests.
The researchers suggest that future work could explore architectures or training methods that reduce the conditions associated with this sensitivity. Such work would need to demonstrate benefits across relevant tasks rather than assume a result from one network transfers everywhere.
What remains open?
The central finding connects the geometry of training with reproducibility in the networks studied. Open questions include how widely the observed patterns occur, whether different architectures behave similarly, and when changes in internal configuration lead to meaningful differences in outputs.
The broader lesson is about scientific explanation. A model can be governed by a deterministic procedure and still be difficult to predict from nearly identical starting conditions. Understanding that distinction may help researchers design better experiments and communicate what their results do, and do not, guarantee.
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