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Mikhail Pavlov

Publications and source records attributed to Mikhail Pavlov.

14 recordsLinked to original sources
arXiv2025

Towards $W_3$ classical blocks with semi-degenerate operators

We consider 4-point $W_3$ classical blocks focusing on the blocks level-1 and level-2 semi-degenerate operators. We derive BPZ-type equations for the auxiliary 5-point blocks with one additional fully degenerate operator. The monodromy properties of these equations are encoded by the accessory parameters, related to the 4-point $W_3$ classical blocks. We solve the BPZ-type equations via heavy-light perturbation theory and find the accessory parameters, which allows us to obtain the explicit expressions for the considered class of classical blocks.

hep-th↗
arXiv2023

Global torus blocks in the necklace channel

We continue studying of global conformal blocks on the torus in a special (necklace) channel. Functions of such multi-point blocks are explicitly found under special conditions on the blocks' conformal dimensions. We have verified that these blocks satisfy the Casimir equations, which were derived in previous studies.

hep-th↗
arXiv2022

Example of the $4$-pt non-vacuum $\mathcal{W}_3$ classical block

In this note, we study a special case of the $4$-pt non-vacuum classical block associated with the $\mathcal{W}_3$ algebra. We formulate the monodromy problem for the block and derive monodromy equations within the heavy-light approximation. Fixing the remaining functional arbitrariness using parameters of the $4$-pt vacuum $\mathcal{W}_3$ block, we compute the $4$-pt non-vacuum $\mathcal{W}_3$ block function.

hep-th↗
arXiv2022

Torus conformal blocks and Casimir equations in the necklace channel

We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram) and trivalent vertices forming trivalent trees attached to the necklace. Then, the $n$-point torus conformal block in any channel can be obtained by acting with a number of OPE operators on the $k$-point torus block in the necklace channel at $k=1,...,n$. Focusing on the necklace channel, we go to the large-$c$ regime, where the Virasoro algebra truncates to the $sl(2, \mathbb{R})$ subalgebra, and obtain the system of the Casimir equations for the respective $k$-point global conformal block. In the plane limit, when the torus modular parameter $q\to 0$, we explicitly find the Casimir equations on a plane which define the $(k+2)$-point global conformal block in the comb channel. Finally, we formulate the general scheme to find Casimir equations for global torus blocks in arbitrary channels.

hep-th↗
arXiv2021

Evaluating Large Language Models Trained on Code

We introduce Codex, a GPT language model fine-tuned on publicly available code from GitHub, and study its Python code-writing capabilities. A distinct production version of Codex powers GitHub Copilot. On HumanEval, a new evaluation set we release to measure functional correctness for synthesizing programs from docstrings, our model solves 28.8% of the problems, while GPT-3 solves 0% and GPT-J solves 11.4%. Furthermore, we find that repeated sampling from the model is a surprisingly effective strategy for producing working solutions to difficult prompts. Using this method, we solve 70.2% of our problems with 100 samples per problem. Careful investigation of our model reveals its limitations, including difficulty with docstrings describing long chains of operations and with binding operations to variables. Finally, we discuss the potential broader impacts of deploying powerful code generation technologies, covering safety, security, and economics.

cs.LG↗
arXiv2021

Large-$c$ conformal $(n \leq 6)$-point blocks with superlight weights and holographic Steiner trees

In this note we study CFT$_2$ Virasoro conformal blocks with heavy operators in the large-$c$ limit in the context of AdS$_3$/CFT$_2$ correspondence. We compute the lengths of the holographic Steiner trees dual to the $5$-point and $6$-point conformal blocks using the superlight approximation when one or more dimensions are much less than the others. These results are generalized for $N$-point holographic Steiner trees dual to $(N+1)$-point conformal blocks with superlight weights.

hep-th↗
arXiv2021

Zero-Shot Text-to-Image Generation

Text-to-image generation has traditionally focused on finding better modeling assumptions for training on a fixed dataset. These assumptions might involve complex architectures, auxiliary losses, or side information such as object part labels or segmentation masks supplied during training. We describe a simple approach for this task based on a transformer that autoregressively models the text and image tokens as a single stream of data. With sufficient data and scale, our approach is competitive with previous domain-specific models when evaluated in a zero-shot fashion.

cs.CV↗
arXiv2020

Holographic variables for CFT$_2$ conformal blocks with heavy operators

We consider large-$c$ $n$-point Virasoro blocks with $n-k$ background heavy operators and $k$ perturbative heavy operators. Conformal dimensions of heavy operators scale linearly with large $c$, while splitting into background/perturbative operators assumes an additional perturbative expansion. Such conformal blocks can be calculated within the monodromy method that basically reduces to solving auxiliary Fuchsian second-order equation and finding monodromy of solutions. We show that there exist particular variables that we call holographic, use of which drastically simplifies the whole analysis. In consequence, we formulate the uniformization property of the large-$c$ blocks which states that in the holographic variables their form depends only on the number of perturbative heavy operators. On the other hand, the holographic variables encode the metric in the bulk space so that the conformal blocks with the same number of perturbative operators are calculated by the same geodesic trees but on different geometries created by the background operators.

hep-th↗
arXiv2019

Four-point conformal blocks with three heavy background operators

We study CFT$_2$ Virasoro conformal blocks of the 4-point correlation function $\langle \mathcal{O}_L \mathcal{O}_H \mathcal{O}_H \mathcal{O}_H \rangle $ with three background operators $\mathcal{O}_H$ and one perturbative operator $\mathcal{O}_L$ of dimensions $Δ_L/Δ_H \ll1$. The conformal block function is calculated in the large central charge limit using the monodromy method. From the holographic perspective, the background operators create $AdS_3$ space with three conical singularities parameterized by dimensions $Δ_H$, while the perturbative operator corresponds to the geodesic line stretched from the boundary to the bulk. The geodesic length calculates the perturbative conformal block. We propose how to address the block/length correspondence problem in the general case of higher-point correlation functions $\langle \mathcal{O}_L \cdots \mathcal{O}_L \mathcal{O}_H \cdots \mathcal{O}_H \rangle $ with arbitrary numbers of background and perturbative operators.

hep-th↗
arXiv2018

Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk

We consider the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-$c$ conformal blocks on the boundary and particle motions in the bulk. The Steiner trees are weighted graphs on the Poincare disk with a number of endpoints and trivalent vertices connected to each other by edges in such a way that an overall length is minimum. We specify a particular class of Steiner trees that we call holographic. Their characteristic property is that a holographic Steiner tree with $N$ endpoints can be inscribed into an $N$-gon with $N-1$ ideal vertices. The holographic Steiner trees are dual to large-$c$ conformal blocks. Particular examples of $N=2,3,4$ Steiner trees as well as their dual conformal blocks are explicitly calculated. We discuss geometric properties of the holographic Steiner trees and their realization in CFT terms. It is shown that connectivity and cuts of the Steiner trees encode the factorization properties of large-$c$ conformal blocks.

hep-th↗
arXiv2018

Learning to Run challenge solutions: Adapting reinforcement learning methods for neuromusculoskeletal environments

In the NIPS 2017 Learning to Run challenge, participants were tasked with building a controller for a musculoskeletal model to make it run as fast as possible through an obstacle course. Top participants were invited to describe their algorithms. In this work, we present eight solutions that used deep reinforcement learning approaches, based on algorithms such as Deep Deterministic Policy Gradient, Proximal Policy Optimization, and Trust Region Policy Optimization. Many solutions use similar relaxations and heuristics, such as reward shaping, frame skipping, discretization of the action space, symmetry, and policy blending. However, each of the eight teams implemented different modifications of the known algorithms.

cs.LG↗
arXiv2018

Run, skeleton, run: skeletal model in a physics-based simulation

In this paper, we present our approach to solve a physics-based reinforcement learning challenge "Learning to Run" with objective to train physiologically-based human model to navigate a complex obstacle course as quickly as possible. The environment is computationally expensive, has a high-dimensional continuous action space and is stochastic. We benchmark state of the art policy-gradient methods and test several improvements, such as layer normalization, parameter noise, action and state reflecting, to stabilize training and improve its sample-efficiency. We found that the Deep Deterministic Policy Gradient method is the most efficient method for this environment and the improvements we have introduced help to stabilize training. Learned models are able to generalize to new physical scenarios, e.g. different obstacle courses.

cs.AI↗
arXiv2015

Deep Attention Recurrent Q-Network

A deep learning approach to reinforcement learning led to a general learner able to train on visual input to play a variety of arcade games at the human and superhuman levels. Its creators at the Google DeepMind's team called the approach: Deep Q-Network (DQN). We present an extension of DQN by "soft" and "hard" attention mechanisms. Tests of the proposed Deep Attention Recurrent Q-Network (DARQN) algorithm on multiple Atari 2600 games show level of performance superior to that of DQN. Moreover, built-in attention mechanisms allow a direct online monitoring of the training process by highlighting the regions of the game screen the agent is focusing on when making decisions.

cs.LG↗