Large Language Models scaling exponents: Succi & Coveney arXiv

Sauro Succi, Peter V. Coveney and Alex Hansen posted a paper to arXiv (arXiv:2606.24504) on 23 Jun 2026 arguing that the smallness of current large language model (LLM) scaling exponents points to an unsustainable regime in terms of energy resources. The 11-page manuscript includes two figures and examines whether a non-zero loss-floor, the so-called "pedestal effect", explains away the small exponents.

What did the paper find?

The paper finds that current LLM scaling exponents are small enough to indicate an unsustainable energy trajectory, and that correcting for a non-zero loss in the infinite-data limit does not eliminate the problem. The authors state the small exponents remain problematic even if one attributes their magnitude to a numerical bias caused by neglecting a non-zero loss function at infinite data, the paper’s so-called "pedestal effect".

The manuscript frames this as a practical energy concern: small scaling exponents mean diminishing returns from increasing model size or data lead to very large energy costs to achieve incremental performance gains. The authors present their argument across 11 pages and support it with two figures; they stress the pedestal correction reduces but does not remove the unsustainability issue.

How do the authors support their claim?

The authors use analytical discussion and analogy to phenomenological models of fluid turbulence to comment on how data smoothness or roughness affects scaling exponents. They argue that the smoothness (or roughness) of the training data can change the measured scaling exponents and that insights from turbulence models illuminate these dependencies.

The paper lays out why a pedestal cannot simply be treated as a numerical artefact removable by recalibration: even accounting for a non-zero asymptotic loss, the effective exponent governing resource versus performance scaling remains small enough to raise energy concerns. The turbulence analogy is used to show that intrinsic properties of the data distribution influence how exponents behave, so measurement and interpretation require attention to data regularity and modelling assumptions.

The submission metadata on arXiv confirms the authorship (Sauro Succi, Peter V. Coveney, Alex Hansen), the identifier arXiv:2606.24504, and the submission date of 23 Jun 2026. The paper is presented as 11 pages with two figures, and is available in PDF and experimental HTML formats on arXiv.

Why it matters

If the paper’s core claim holds, the industry trajectory of scaling model and dataset size for incremental performance gains may face practical limits set by energy consumption rather than algorithmic or data availability constraints. That reframes the scaling debate: the mathematical slope of performance improvements now ties directly to environmental and economic cost estimates. Policymakers, data-center planners, and research labs that budget energy for large training runs would be most affected.

The authors’ emphasis on a persistent issue even after pedestal correction highlights that technical fixes aimed solely at measurement bias may not address the underlying energy arithmetic implied by the exponents. The turbulence analogy suggests some part of the problem stems from the properties of the data itself, not just training protocol or model parametrization.

What to watch

Look for follow-up empirical studies that estimate LLM scaling exponents while explicitly accounting for non-zero asymptotic loss and data smoothness, and for community responses that test the turbulence-based arguments. Also watch for discussions or analyses that quantify energy cost trajectories linked to empirically measured exponents.