arXiv subjects

Yaïr Hein

Publications and source records attributed to Yaïr Hein.

4 recordsLinked to original sources

arXiv2026

Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark

While large language models (LLMs) with reasoning capabilities are progressing rapidly on high-school math competitions and coding, can they reason effectively through complex, open-ended challenges found in frontier physics research? And crucially, what kinds of reasoning tasks do physicists want LLMs to assist with? To address these questions, we present the CritPt (Complex Research using Integrated Thinking - Physics Test, pronounced "critical point"), the first benchmark designed to test LLMs on unpublished, research-level reasoning tasks that broadly covers modern physics research areas, including condensed matter, quantum physics, atomic, molecular & optical physics, astrophysics, high energy physics, mathematical physics, statistical physics, nuclear physics, nonlinear dynamics, fluid dynamics and biophysics. CritPt consists of 71 composite research challenges designed to simulate full-scale research projects at the entry level, which are also decomposed to 190 simpler checkpoint tasks for more fine-grained insights. All problems are newly created by 50+ active physics researchers based on their own research. Every problem is hand-curated to admit a guess-resistant and machine-verifiable answer and is evaluated by an automated grading pipeline heavily customized for advanced physics-specific output formats. We find that while current state-of-the-art LLMs show early promise on isolated checkpoints, they remain far from being able to reliably solve full research-scale challenges: the best average accuracy among base models is only 5.7%, achieved by GPT-5 (high), moderately rising to around 10% when equipped with coding tools. Through the realistic yet standardized evaluation offered by CritPt, we highlight a large disconnect between current model capabilities and realistic physics research demands, offering a foundation to guide the development of scientifically grounded AI tools.

cs.AI↗

arXiv2026

Size-structured populations with growth fluctuations: Feynman--Kac formula and decoupling

We study a size-structured population model in which individual cells grow at a rate determined by a fluctuating internal variable (e.g., gene expression levels). Many previous models of phenotypically heterogeneous populations can be viewed as special cases of this model, and it has previously been observed that the internal variable decouples from cell size under certain conditions. In this work, we generalize these results and connect them to the Feynman-Kac formula, which yields relationships between the lineage dynamics and population distribution in branching processes. To this end, we derive conditions for decoupling, both in the lineage and population ensemble. When decoupling occurs in both ensembles, the size dynamics can be transformed, via a random time change, into a growth-homogeneous process, and expectations can be evaluated through an exponential tilting procedure that follows from the Feynman-Kac formula. We further characterize weaker, ensemble-specific forms of decoupling that hold in either the lineage or the population ensemble, but not both. We provide a more general interpretation of tilted expectations in terms of the mass-weighted phenotype distribution

cond-mat.stat-mech↗

arXiv2024

Asymptotic decoupling of population growth rate and cell size distribution

The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells, leading to correlations between the growth rates of cells across generations. Division sizes of cells are also stochastic and correlated across generations due to a phenomenon known as cell size regulation. Fluctuations and correlations from both growth and division processes affect the population dynamics of an exponentially growing culture. Here, we provide analytic solutions for the population dynamics of cells with continuously fluctuating growth rates coupled with a generic model of cell-size regulation. We show that in balanced growth, the effects of growth and division processes decouple; the population growth rate only depends on the single-cell growth rate process, and the population cell size distribution only depends on the model of division and cell size regulation. The population growth rate is always higher than the average single-cell growth rate, and the difference increases with growth rate variability and its correlation time. This difference also sets the timescale for the population to reach its steady state. We provide analytical solutions for oscillations in population growth rate and traveling waves in size distribution during this approach to the steady state.

q-bio.PE↗

arXiv2024

Competition between transient oscillations and early stochasticity in exponentially growing populations

It has been recently shown that the exponential growth rate of a population of bacterial cells starting from a single cell shows transient oscillations due to early synchronized bursts of division. These oscillations are enhanced by cell size regulation and contain information about single-cell growth statistics. Here, we report a phase transition in these oscillations as a function of growth rate variability. Below the transition point, these oscillations become asymptotically deterministic and can be measured experimentally, while above the transition point, the stochasticity in population growth dominates the oscillations and masks all the information about single cell growth statistics. The analytically calculated transition point, which roughly corresponds to $13\%$ variability in single-cell growth rate, falls within physiologically relevant parameters. Additionally, we show that the oscillations can stochastically emerge even when the initial state contains multiple cells with out-of-phase division cycles. We show that the amplitude and the phase of these oscillations are stochastic and would vary across repeated measurements with the same initial conditions. We provide analytic expressions as well as numerical estimates for the typical oscillation amplitude and the number of generations before the amplitude falls below a given measurement threshold for E. coli in multiple growth conditions.

q-bio.PE↗