Anyone who has trained neural networks knows the frustration: fix the random seed, pin the data order, switch on every determinism flag, and the result can still change. Earlier work found that flipping a single bit in one parameter can produce as much variation as all the usual noise sources combined. A paper in Nature Machine Intelligence by A. Ly and P. Gong offers an explanation drawn from dynamical systems theory, and it is not reassuring for anyone who hoped more precision would fix the problem.
The proposed mechanism is riddled basins. Picture the space of all possible starting weights, coloured by which solution training ends up in. If the colours were separated by clean borders, starting closer to a known point would make the outcome more predictable. In a riddled basin, every starting point that leads to one solution sits arbitrarily close to points that lead to another, at every scale you zoom into, and the mixed region has real volume rather than being a thin boundary. That makes it different from ordinary chaos: chaos makes trajectories diverge over time, while riddling makes the final outcome itself unpredictable however small the starting error.
The authors show this analytically in a minimal network, deriving an uncertainty exponent close to zero, which means sharp increases in initialisation precision buy almost no gain in predictability. They then trained about 500,000 networks across VGG, ResNet and BERT architectures, MNIST, CIFAR-10 and IMDB data, SGD, gradient descent and AdamW, and a range of regularisation methods and activation functions, and found the same signatures throughout. They extend the measure from weights to the functions networks learn, so the effect is not just different weights doing the same thing.
For practitioners, the practical lesson is about reporting. If tiny changes can send training to different solutions, a single training run is an anecdote, and comparisons between models or methods should show spread across several runs. It also offers a common explanation for patterns people have reported separately, such as irreducible run-to-run variation and trade-offs between performance and reproducibility.
The limits are clearly stated. The authors call riddling a candidate organising principle, not a proof for every network, and the deep-network evidence consists of signatures consistent with it rather than the full analytical derivation. The experiments use relatively small benchmark tasks; whether the same picture holds for today's very large language models, trained once at great cost, is not shown here. The paper is peer reviewed and open access, with source data published.