arXiv subjects

Sergey Berezin

Publications and source records attributed to Sergey Berezin.

13 recordsLinked to original sources

arXiv2025

Last-passage percolation and product-matrix ensembles

We introduce and study a model of directed last-passage percolation in planar layered environment. This environment is represented by an array of random exponential clocks arranged in blocks, for each block the average waiting times depend only on the local coordinates within the block. The last-passage time, the total time needed to travel from the source to the sink located in a given block, maximized over all the admissible paths, becomes a stochastic process indexed by the number of blocks in the array. We show that this model is integrable, particularly the probability law of the last-passage time process can be determined via a Fredholm determinant of the kernel that also appears in the study of products of random matrices. Further, we identify the scaling limit of the last-passage time process, as the sizes of the blocks become infinitely large and the average waiting times become infinitely small. Finite-dimensional convergence to the continuous-time critical stochastic process of random matrix theory is established.

math.PR↗

arXiv2025

The TIP of the Iceberg: Revealing a Hidden Class of Task-in-Prompt Adversarial Attacks on LLMs

We present a novel class of jailbreak adversarial attacks on LLMs, termed Task-in-Prompt (TIP) attacks. Our approach embeds sequence-to-sequence tasks (e.g., cipher decoding, riddles, code execution) into the model's prompt to indirectly generate prohibited inputs. To systematically assess the effectiveness of these attacks, we introduce the PHRYGE benchmark. We demonstrate that our techniques successfully circumvent safeguards in six state-of-the-art language models, including GPT-4o and LLaMA 3.2. Our findings highlight critical weaknesses in current LLM safety alignments and underscore the urgent need for more sophisticated defence strategies. Warning: this paper contains examples of unethical inquiries used solely for research purposes.

cs.CR↗

arXiv2024

Evading Toxicity Detection with ASCII-art: A Benchmark of Spatial Attacks on Moderation Systems

We introduce a novel class of adversarial attacks on toxicity detection models that exploit language models' failure to interpret spatially structured text in the form of ASCII art. To evaluate the effectiveness of these attacks, we propose ToxASCII, a benchmark designed to assess the robustness of toxicity detection systems against visually obfuscated inputs. Our attacks achieve a perfect Attack Success Rate (ASR) across a diverse set of state-of-the-art large language models and dedicated moderation tools, revealing a significant vulnerability in current text-only moderation systems.

cs.CL↗

arXiv2023

On the definition of toxicity in NLP

The fundamental problem in toxicity detection task lies in the fact that the toxicity is ill-defined. This causes us to rely on subjective and vague data in models' training, which results in non-robust and non-accurate results: garbage in - garbage out. This work suggests a new, stress-level-based definition of toxicity designed to be objective and context-aware. On par with it, we also describe possible ways of applying this new definition to dataset creation and model training.

cs.CL↗

arXiv2023

No offence, Bert -- I insult only humans! Multiple addressees sentence-level attack on toxicity detection neural network

We introduce a simple yet efficient sentence-level attack on black-box toxicity detector models. By adding several positive words or sentences to the end of a hateful message, we are able to change the prediction of a neural network and pass the toxicity detection system check. This approach is shown to be working on seven languages from three different language families. We also describe the defence mechanism against the aforementioned attack and discuss its limitations.

cs.CL↗

arXiv2023

Functional Central Limit Theorems for Constrained Mittag-Leffler Ensemble in Hard Edge Scaling

We consider the hard-edge scaling of the Mittag-Leffler ensemble confined to a fixed disk inside the droplet. Our primary emphasis is on fluctuations of rotationally-invariant additive statistics that depend on the radius and thus give rise to radius-dependent stochastic processes. For the statistics originating from bounded measurable functions, we establish a central limit theorem in the appropriate functional space. By assuming further regularity, we are able to extend the result to a vector functional central limit theorem that additionally includes the first hitting "time" of the radius-dependent statistic. The proof of the first theorem involves an approximation by exponential random variables alongside a coupling technique. The proof of the second result rests heavily on Skorohod's almost sure representation theorem and builds upon a result of Galen Shorack (1973).

math.PR↗

arXiv2023

Named Entity Inclusion in Abstractive Text Summarization

We address the named entity omission - the drawback of many current abstractive text summarizers. We suggest a custom pretraining objective to enhance the model's attention on the named entities in a text. At first, the named entity recognition model RoBERTa is trained to determine named entities in the text. After that, this model is used to mask named entities in the text and the BART model is trained to reconstruct them. Next, the BART model is fine-tuned on the summarization task. Our experiments showed that this pretraining approach improves named entity inclusion precision and recall metrics.

cs.CL↗

arXiv2023

Planar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials

A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are integer. From this orthogonality, we derive several equivalent Riemann-Hilbert problems. The proof is based on the fundamental identity of Lee and Yang, which we establish using a new technique.

math.CA↗

arXiv2021

Gap probability for products of random matrices in the critical regime

The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to α$, $α>0$, a scaling limit emerges. We consider a gap probability for the corresponding limiting determinantal process, namely, the probability that there are no particles in the interval $(a,+\infty)$. We derive a Tracy-Widom-like formula in terms of the unique solution of a certain matrix Riemann-Hilbert problem of size $2 \times 2$. The right-tail asymptotics for this solution is obtained by the Deift-Zhou non-linear steepest descent analysis.

math.PR↗

arXiv2020

On the Rate of Convergence in the Central Limit Theorem for Linear Statistics of Gaussian, Laguerre, and Jacobi Ensembles

Under the Kolmogorov--Smirnov metric, an upper bound on the rate of convergence to the Gaussian distribution is obtained for linear statistics of the matrix ensembles in the case of the Gaussian, Laguerre, and Jacobi weights. The main lemma gives an estimate for the characteristic functions of the linear statistics; this estimate is uniform over the growing interval. The proof of the lemma relies on the Riemann--Hilbert approach.

math.PR↗

arXiv2020

On barycenters of probability measures

A characterization is presented of barycenters of the Radon probability measures supported on a closed convex subset of a given space. A case of particular interest is studied, where the underlying space is itself the space of finite signed Radon measures on a metric compact and where the corresponding support is the convex set of probability measures. For locally compact spaces, a simple characterization is obtained in terms of the relative interior.

math.PR↗

arXiv2019

Skew Brownian motion with dry friction: The Pugachev-Sveshnikov approach

The Caughey-Dieness process, also known as the Brownian motion with two valued drift, is used in theoretical physics as an advanced model of the Brownian particle velocity if the resistant force is assumed to be dry friction. This process also appears in many other fields, such as applied physics, mechanics, astrophysics, and pure mathematics. In the present paper we are concerned with a more general process, skew Brownian motion with dry friction. The probability distribution of the process itself and of its occupation time on the positive half line are studied. The approach based on the Pugachev-Sveshnikov equation is used.

math.PR↗

arXiv2017

On energy dissipation in a friction-controlled slide of a body excited by random motions of the foundation

We study a friction controlled slide of a body excited by random motions of the foundation it is placed on. Specifically, we are interested in quantities such as displacement, traveled distance, and energy loss due to friction. Assuming that the random excitation is switched off at some time, it is shown that the problem can be treated in an analytic, explicit, manner. Particularly, we derive formulas for the moments of the displacement and distance, and also for the average energy loss. To accomplish that we use the Pugachev-Sveshnikov equation for the characteristic function of a continuous random process given by a system of SDEs. This equation is solved by reduction to a parametric Riemann boundary value problem of complex analysis.

math.PR↗