Take two arrangements of atoms in space. They are not the same shape, and no rotation, reflection, or translation turns one into the other. Yet feed both into the machinery that most modern atomic-scale machine learning depends on, and the numbers that come out are exactly the same. Michelangelo Domina and Michele Ceriotti of EPFL report examples where that indistinguishability survives even when the descriptors are built from clusters of up to seven neighboring atoms, far past the point where every previously known example of the problem breaks down.
The preprint appeared on arXiv on July 29, 2026. It has not been peer reviewed.
To see why this matters, it helps to know what a descriptor is. If you want a computer to predict the energy of a molecule, or how a crystal will deform, you first have to hand it the structure in a form it can work with. Raw coordinates will not do, because the same physical arrangement written down in a rotated frame gives different numbers, and the model would have to learn from scratch that the two are the same thing. So the field converts each atom's surroundings into a list of quantities that do not change under rotation. One popular family, as the authors describe it, amounts to taking a histogram of the distances to neighboring atoms, then of the triangles formed with pairs of neighbors, then quadrilaterals, and so on up a ladder of increasing complexity.
The ladder was supposed to be a safety net. Researchers already knew the bottom rungs leak: with two, three, or four neighbors, you can find pairs of genuinely different structures that produce identical descriptors. These are called descriptor degeneracies, and a model that sees two structures as identical cannot possibly assign them different energies. But every degeneracy anyone had published could be broken by climbing a rung, by taking bigger clusters of neighbors into account. That made the incompleteness feel like a technicality rather than a wall.
Domina and Ceriotti's examples push the wall much further out. Seven neighbors is a lot of neighbors, and computing descriptors at that order is expensive enough that few practitioners would ever go there. The authors go further still: at what they call a practical level of discretization, meaning the resolution at which these histograms are actually chopped into bins in working code, their structures stay indistinguishable to arbitrary order. Climbing the ladder does not save you. The discretization itself is the leak.
The part about the language model
The construction, once you have it, rests on results that have been sitting in the literature for decades, in fields that do not talk much to chemical physics. The authors did not stumble on those results by reading widely. They say a large language model found the references and recognized why they bore on the descriptor problem, and that the examples were discovered with the model's assistance.
That is a narrower and more interesting claim than the usual one about AI in science. Nobody here is saying the model proved a theorem or ran a simulation. What it did was translate: it held a question posed in the vocabulary of one community and located an answer written in the vocabulary of another. Domina and Ceriotti argue this is where such models are unusually well suited, and they frame their own paper as a demonstration of the pattern rather than a one-off. Their phrasing is that AI can accelerate the process by which a lucky discovery in one field becomes a major result in a different one. It is a claim about literature search and recognition, not about machine creativity, and the paper offers a single worked case in support of it.
Why it matters
Machine-learning models of atoms are no longer a curiosity. They are used to screen candidate battery materials, to simulate proteins, to study how crystals melt, all at speeds that direct quantum-mechanical calculation cannot approach. Every one of those models begins by turning a structure into descriptors. If two different structures can arrive at the same descriptors, then somewhere in the model's world those structures are the same object, and no amount of training data will separate them.
How often that bites in practice is a separate question, and this preprint does not answer it. The structures here were constructed deliberately to be pathological. They are existence proofs, not a survey of how common the problem is in real materials databases. Still, the previous reassuring story, that you could always resolve a degeneracy by going to higher order, no longer holds in general. Anyone building or trusting these models now has a sharper sense of where the guarantees actually end.
The methodological point may travel further than the chemistry. Fields accumulate results that would matter enormously somewhere else, if only someone happened to read both literatures. The authors offer a concrete instance of a model doing that reading, and it is worth watching whether the pattern holds up beyond one paper.