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Serguei Popov

Publications and source records attributed to Serguei Popov.

At least 19 recordsLinked to original sources
arXiv2026

Humanity's Last Exam

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

cs.LG↗
arXiv2026

Dynamics of the leftmost particle in heterogeneous semi-infinite exclusion systems

We study the behaviour of the leftmost particle in a semi-infinite particle system on $\mathbb{Z}$, where each particle performs a continuous-time nearest-neighbour random walk, with particle-specific jump rates, subject to the exclusion interaction (i.e., no more than one particle per site). We give conditions, in terms of the jump rates on the system, under which the leftmost particle is recurrent or transient, and develop tools to study its rate of escape in the transient case, including by comparison with an $M/G/\infty$ queue. In particular we show examples in which the leftmost particle can be null recurrent, positive recurrent, ballistically transient, or subdiffusively transient. Finally we indicate the role of the initial condition in determining the dynamics, and show, for example, that sub-ballistic transience can occur started from close-packed initial configurations but not from stationary initial conditions.

math.PR↗
arXiv2026

COMPOSITE-Stem

AI agents hold growing promise for accelerating scientific discovery; yet, a lack of frontier evaluations hinders adoption into real workflows. Expert-written benchmarks have proven effective at measuring AI reasoning, but most at this stage have become saturated and only measure performance on constrained outputs. To help address this gap, we introduce COMPOSITE-STEM, a benchmark of 70 expert-written tasks in physics, biology, chemistry, and mathematics, curated by doctoral-level researchers. Our benchmark combines exact-match grading and criterion-based rubrics with an LLM-as-a-jury grading protocol, allowing more flexible assessment of scientifically meaningful outputs. Using an adapted multimodal Terminus-2 agent harness within the Harbor agentic evaluation framework, we evaluate four frontier models. The top-performing model achieves 21%, demonstrating that COMPOSITE-STEM captures capabilities beyond current agent reach. All tasks are open-sourced with contributor permission to support reproducibility and to promote additional research towards AI's acceleration of scientific progress in these domains.

cs.AI↗
arXiv2025

One-dimensional particle clouds with elastic collisions

We study an interacting particle system of a finite number of labelled particles on the integer lattice, in which particles have intrinsic masses and left/right jump rates. If a particle is the minimal-label particle at its site when it tries to jump left, the jump is executed. If not, `momentum' is transferred to increase the rate of jumping left of the minimal-label particle. Similarly for jumps to the right. The collision rule is `elastic' in the sense that the net rate of flow of mass is independent of the present configuration, in contrast to the exclusion process, for example. We show that the particle masses and jump rates determine explicitly, via a concave majorant of a simple `potential' function associated to the masses and jump rates, a unique partition of the system into maximal stable subsystems. The internal configuration of each stable subsystem remains tight, while the location of each stable subsystem obeys a strong law of large numbers with an explicit speed. We indicate connections to adjacent models, including diffusions with rank-based coefficients.

math.PR↗
arXiv2025

On extinction and survival of the Bak-Sneppen model on arbitrary graphs

We study the discrete Bak-Sneppen model introduced by Barbay and Kenyon (2001) "On the discrete Bak-Sneppen model of self-organized criticality". We extend their results as well as the non-triviality result of Meester and Znamenskiy (2002) for a finite segment of $\mathbb{Z}^1$ with the periodic boundary condition to a large class of graphs, by using coupling between the Bak-Sneppen model and the oriented percolation in a quadrant. This allows us to avoid dealing with the so-called avalanches, thus simplifying many arguments.

math.PR↗
arXiv2025

On the shape of the connected components of the complement of two-dimensional Brownian random interlacements

We study the limiting shape of the connected components of the vacant set of two-dimensional Brownian random interlacements: we prove that the connected component around $x$ is close in distribution to a rescaled \emph{Brownian amoeba} in the regime when the distance from $x\in\mathbb{C}$ to the closest trajectory is small (which, in particular, includes the cases $x\to\infty$ with fixed intensity parameter $α$, and $α\to\infty$ with fixed $x$). We also obtain a new family of martingales built on the conditioned Brownian motion, which may be of independent interest.

math.PR↗
arXiv2024

Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. Under appropriate hypotheses on the jump rates (uniformly bounded rates is sufficient) and started from an initial condition that is a finite perturbation of the close-packed configuration, we give conditions under which the particles evolve as a single, semi-infinite "stable cloud". More precisely, we show that inter-particle separations converge to a product-geometric stationary distribution, and that the location of every particle obeys a strong law of large numbers with the same characteristic speed.

math.PR↗
arXiv2024

On transience of $M/G/\infty$ queues

We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also that here (unlike e.g. irreducible Markov chains) it is possible for recurrent and transient states to coexist. We also prove a lower bound on the growth speed in the transient case.

math.PR↗
arXiv2024

Rate of escape of the conditioned two-dimensional simple random walk

We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf arXiv:2102.09636), with the help of a KMT-type coupling adapted to this setup.

math.PR↗
arXiv2023

Dynamics of finite inhomogeneous particle systems with exclusion interaction

We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. We show that the particle jump rates determine explicitly a unique partition of the system into maximal stable sub-systems, and that this partition can be obtained by a linear-time algorithm using only elementary arithmetic. The internal configuration of each stable sub-system possesses an explicit product-geometric limiting distribution, and the location of each stable sub-system obeys a strong law of large numbers with an explicit speed; the characteristic parameters of each stable sub-system are simple functions of the rate parameters for the corresponding particles. For the case where the entire system is stable, we provide a central limit theorem describing the fluctuations around the law of large numbers. Our approach draws on ramifications, in the exclusion context, of classical work of Goodman and Massey on partially-stable Jackson queueing networks.

math.PR↗
arXiv2021

Voting-based probabilistic consensuses and their applications in distributed ledgers

We review probabilistic models known as majority dynamics (also known as threshold Voter Models) and discuss their possible applications for achieving consensus in cryptocurrency systems. In particular, we show that using this approach straightforwardly for practical consensus in Byzantine setting can be problematic and requires extensive further research. We then discuss the FPC consensus protocol which circumvents the problems mentioned above by using external randomness.

cs.DC↗
arXiv2021

Linear competition processes and generalized Polya urns with removals

A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Polya urn model with removals.

math.PR↗
arXiv2020

FPC-BI: Fast Probabilistic Consensus within Byzantine Infrastructures

This paper presents a novel leaderless protocol (FPC-BI: Fast Probabilistic Consensus within Byzantine Infrastructures) with a low communicational complexity and which allows a set of nodes to come to a consensus on a value of a single bit. The paper makes the assumption that part of the nodes are Byzantine, and are thus controlled by an adversary who intends to either delay the consensus, or break it (this defines that at least a couple of honest nodes come to different conclusions). We prove that, nevertheless, the protocol works with high probability when its parameters are suitably chosen. Along this the paper also provides explicit estimates on the probability that the protocol finalizes in the consensus state in a given time. This protocol could be applied to reaching consensus in decentralized cryptocurrency systems. A special feature of it is that it makes use of a sequence of random numbers which are either provided by a trusted source or generated by the nodes themselves using some decentralized random number generating protocol. This increases the overall trustworthiness of the infrastructure. A core contribution of the paper is that it uses a very weak consensus to obtain a strong consensus on the value of a bit, and which can relate to the validity of a transaction.

cs.DC↗
arXiv2020

Transience of conditioned walks on the plane: encounters and speed of escape

We consider the two-dimensional simple random walk conditioned on never hitting the origin, which is,formally speaking, the Doob's $h$-transform of the simple random walk with respect to the potential kernel. We then study the behavior of the future minimum distance of the walk to the origin, and also prove that two independent copies of the conditioned walk, although both transient, will nevertheless meet infinitely many times a.s.

math.PR↗
arXiv2019

Conditioned two-dimensional simple random walk: Green's function and harmonic measure

We study the Doob's $h$-transform of the two-dimensional simple random walk with respect to its potential kernel, which can be thought of as the two-dimensional simple random walk conditioned on never hitting the origin. We derive an explicit formula for the Green's function of this random walk, and also prove a quantitative result on the speed of convergence of the (conditional) entrance measure to the harmonic measure (for the conditioned walk) on a finite set.

math.PR↗
arXiv2019

An improved decoupling inequality for random interlacements

In this paper we obtain a decoupling feature of the random interlacements process $\mathcal{I}^u \subset \mathbb{Z}^d$, at level $u$, $d\geq 3$. More precisely, we show that the trace of the random interlacements process on two disjoint finite sets, $\textsf{F}$ and its translated $\textsf{F}+x$, can be coupled with high probability of success, when $\|x\|$ is large, with the trace of a process of independent excursions, which we call the noodle soup process. As a consequence, we obtain an upper bound on the covariance between two $[0,1]$-valued functions depending on the configuration of the random interlacements on $\textsf{F}$ and $\textsf{F}+x$, respectively. This improves a previous bound obtained by Sznitman in [12].

math.PR↗