arXiv subjects

Anurag Sarkar

Publications and source records attributed to Anurag Sarkar.

At least 19 recordsLinked to original sources

arXiv2026

Krylov Complexity in Periodically Driven CFTs and Critical Fermions

We study Krylov construction in periodically driven conformal field theories and their lattice realisations via critical fermions. Two types of driving are considered: a square-wave drive and a continuous sinusoidal drive. Using the Arnoldi construction, we examine Arnoldi coefficients and return amplitudes in periodically driven conformal field theories in the heating and non-heating phases. In the heating phase, the Arnoldi coefficients approach unity exponentially; in contrast, in the non-heating phase, they exhibit oscillatory behaviour. For the lattice realisations, we further analyse the Krylov complexity of the correlation matrix, quasi energy level statistics, and the graph structure induced by the Floquet operator. Although the two drives exhibit similar Krylov growth on the CFT side, their lattice realisations exhibit markedly different spectral and graph signatures, indicating distinct mechanisms governing the transition between the heating and non-heating phases.

hep-th↗

arXiv2026

Finite Automata Extraction: Low-data World Model Learning as Programs from Gameplay Video

World models are defined as a compressed spatial and temporal learned representation of an environment. The learned representation is typically a neural network, making transfer of the learned environment dynamics and explainability a challenge. In this paper, we propose an approach, Finite Automata Extraction (FAE), that learns a neuro-symbolic world model from gameplay video represented as programs in a novel domain-specific language (DSL): Retro Coder. Compared to prior world model approaches, FAE learns a more precise model of the environment and more general code than prior DSL-based approaches.

cs.AI↗

arXiv2025

Classical string profile for a class of DDF amplitudes

In the critical bosonic string theory, we explicitly evaluate the three point scattering amplitude at tree level, of a photon with two massive higher spins. The massive excitations belong to states of the form $A_{-r_1}^{s_1} A_{-r_2}^{s_2}$ where $A_{-n}$ is a DDF creation operator. Next, we take the infinite ``spin'' limit to arrive at the classical string dynamics. We find a rotating ``floppy'' string lying mostly on a plane which develops a transverse kink.

hep-th↗

arXiv2025

Generative Modeling of Individual Behavior at Scale

There has been a growing interest in using AI to model human behavior, particularly in domains where humans interact with this technology. While most existing work models human behavior at an aggregate level, our goal is to model behavior at the individual level. Recent approaches to behavioral stylometry -- or the task of identifying a person from their actions alone -- have shown promise in domains like chess, but these approaches are either not scalable (e.g., fine-tune a separate model for each person) or not generative, in that they cannot generate actions. We address these limitations by framing behavioral stylometry as a multi-task learning problem -- where each task represents a distinct person -- and use parameter-efficient fine-tuning (PEFT) methods to learn an explicit style vector for each person. Style vectors are generative: they selectively activate shared "skill" parameters to generate actions in the style of each person. They also induce a latent space that we can interpret and manipulate algorithmically. In particular, we develop a general technique for style steering that allows us to steer a player's style vector towards a desired property. We apply our approach to two very different games, at unprecedented scales: chess (47,864 players) and Rocket League (2,000 players). We also show generality beyond gaming by applying our method to image generation, where we learn style vectors for 10,177 celebrities and use these vectors to steer their images.

cs.LG↗

arXiv2024

Chaotic and Thermal Aspects in the Highly Excited String S-Matrix

We compute tree level scattering amplitudes involving more than one highly excited states and tachyons in bosonic string theory. We use these amplitudes to understand chaotic and thermal aspects of the excited string states lending support to the Susskind-Horowitz-Polchinski correspondence principle. The unaveraged amplitudes exhibit chaos in the resonance distribution as a function of kinematic parameters, which can be described by random matrix theory. Upon coarse-graining these amplitudes are shown to exponentiate, and capture various thermal features, including features of a stringy version of the eigenstate thermalization hypothesis as well as notions of typicality. Further, we compute the effective string form factor corresponding to the highly excited states, and argue for the random walk behaviour of the long strings.

hep-th↗

arXiv2024

Spectral Form Factors of Topological Phases

Signatures of dynamical quantum phase transitions and chaos can be found in the time evolution of generalized partition functions such as spectral form factors (SFF) and Loschmidt echoes. While a lot of work has focused on the nature of such systems in a variety of strongly interacting quantum theories, in this work, we study their behavior in short-range entangled topological phases, particularly focusing on the role of symmetry-protected topological zero modes. We show, using both analytical and numerical methods, how the existence of such zero modes in any representative system can mask the SFF with large period (akin to generalized Rabi) oscillations, hiding any behavior arising from the bulk of the spectrum. Moreover, in a quenched disordered system, these zero modes fundamentally change the late-time universal behavior reflecting the chaotic signatures of the zero-energy manifold. Our study uncovers the rich physics underlying the interplay of chaotic signatures and topological characteristics in a quantum system.

cond-mat.str-el↗

arXiv2023

Latent Combinational Game Design

We present latent combinational game design -- an approach for generating playable games that blend a given set of games in a desired combination using deep generative latent variable models. We use Gaussian Mixture Variational Autoencoders (GMVAEs) which model the VAE latent space via a mixture of Gaussian components. Through supervised training, each component encodes levels from one game and lets us define blended games as linear combinations of these components. This enables generating new games that blend the input games as well as controlling the relative proportions of each game in the blend. We also extend prior blending work using conditional VAEs and compare against the GMVAE and additionally introduce a hybrid conditional GMVAE (CGMVAE) architecture which lets us generate whole blended levels and layouts. Results show that these approaches can generate playable games that blend the input games in specified combinations. We use both platformers and dungeon-based games to demonstrate our results.

cs.LG↗

arXiv2023

Procedural Content Generation via Knowledge Transformation (PCG-KT)

We introduce the concept of Procedural Content Generation via Knowledge Transformation (PCG-KT), a new lens and framework for characterizing PCG methods and approaches in which content generation is enabled by the process of knowledge transformation -- transforming knowledge derived from one domain in order to apply it in another. Our work is motivated by a substantial number of recent PCG works that focus on generating novel content via repurposing derived knowledge. Such works have involved, for example, performing transfer learning on models trained on one game's content to adapt to another game's content, as well as recombining different generative distributions to blend the content of two or more games. Such approaches arose in part due to limitations in PCG via Machine Learning (PCGML) such as producing generative models for games lacking training data and generating content for entirely new games. In this paper, we categorize such approaches under this new lens of PCG-KT by offering a definition and framework for describing such methods and surveying existing works using this framework. Finally, we conclude by highlighting open problems and directions for future research in this area.

cs.AI↗

arXiv2022

tile2tile: Learning Game Filters for Platformer Style Transfer

We present tile2tile, an approach for style transfer between levels of tile-based platformer games. Our method involves training models that translate levels from a lower-resolution sketch representation based on tile affordances to the original tile representation for a given game. This enables these models, which we refer to as filters, to translate level sketches into the style of a specific game. Moreover, by converting a level of one game into sketch form and then translating the resulting sketch into the tiles of another game, we obtain a method of style transfer between two games. We use Markov random fields and autoencoders for learning the game filters and apply them to demonstrate style transfer between levels of Super Mario Bros, Kid Icarus, Mega Man and Metroid.

cs.LG↗

arXiv2022

(Half) Wormholes under Irrelevant Deformation

Recently it has been shown by Almheiri and Lin [1] that the reconstruction of black-hole interior is sensitive to knowing the exact coupling of the boundary theory even if the coupling is irrelevant. This motivates us to enlarge the set of the one-time and two-time toy models inspired from the SYK by deforming the same with \textit{irrelevant} coupling. We find that both half-wormholes as well as the wormholes persist in presence of the deformation, leading to a similar mechanism for curing the factorization problem. While for the one time case, the deformed partition function and its moments change by an overall factor, which can completely be absorbed into a renormalization of coupling, for the two time (or coupled one time) SYK we find non-trivial dynamics of the saddles as the couplings are varied. Curiously, the \textit{irrelevant} deformations that we consider can also be thought of as an ensemble average over an overall scaling of the original undeformed Hamiltionian with an appropriate probability distribution, this allows for the possibility that half-wormholes may also be present in suitably defined ensemble of theories.

hep-th↗

arXiv2021

Procedural Content Generation using Behavior Trees (PCGBT)

Behavior trees (BTs) are a popular method for modeling NPC and enemy AI behavior and have been widely used in commercial games. In this work, rather than use BTs to model game playing agents, we use them for modeling game design agents, defining behaviors as content generation tasks rather than in-game actions. Similar to how traditional BTs enable modeling behaviors in a modular and dynamic manner, BTs for PCG enable simple subtrees for generating parts of levels to be combined modularly to form complex trees for generating whole levels as well as generators that can dynamically vary the generated content. We refer to this approach as Procedural Content Generation using Behavior Trees, or PCGBT, and demonstrate it by using BTs to model generators for Super Mario Bros., Mega Man and Metroid levels as well as dungeon layouts and discuss several ways in which this paradigm could be applied and extended in the future.

cs.AI↗

arXiv2021

Generating and Blending Game Levels via Quality-Diversity in the Latent Space of a Variational Autoencoder

Several works have demonstrated the use of variational autoencoders (VAEs) for generating levels in the style of existing games and blending levels across different games. Further, quality-diversity (QD) algorithms have also become popular for generating varied game content by using evolution to explore a search space while focusing on both variety and quality. To reap the benefits of both these approaches, we present a level generation and game blending approach that combines the use of VAEs and QD algorithms. Specifically, we train VAEs on game levels and run the MAP-Elites QD algorithm using the learned latent space of the VAE as the search space. The latent space captures the properties of the games whose levels we want to generate and blend, while MAP-Elites searches this latent space to find a diverse set of levels optimizing a given objective such as playability. We test our method using models for 5 different platformer games as well as a blended domain spanning 3 of these games. We refer to using MAP-Elites for blending as Blend-Elites. Our results show that MAP-Elites in conjunction with VAEs enables the generation of a diverse set of playable levels not just for each individual game but also for the blended domain while illuminating game-specific regions of the blended latent space.

cs.LG↗

arXiv2021

Dungeon and Platformer Level Blending and Generation using Conditional VAEs

Variational autoencoders (VAEs) have been used in prior works for generating and blending levels from different games. To add controllability to these models, conditional VAEs (CVAEs) were recently shown capable of generating output that can be modified using labels specifying desired content, albeit working with segments of levels and platformers exclusively. We expand these works by using CVAEs for generating whole platformer and dungeon levels, and blending levels across these genres. We show that CVAEs can reliably control door placement in dungeons and progression direction in platformer levels. Thus, by using appropriate labels, our approach can generate whole dungeons and platformer levels of interconnected rooms and segments respectively as well as levels that blend dungeons and platformers. We demonstrate our approach using The Legend of Zelda, Metroid, Mega Man and Lode Runner.

cs.LG↗

arXiv2020

Conditional Level Generation and Game Blending

Prior research has shown variational autoencoders (VAEs) to be useful for generating and blending game levels by learning latent representations of existing level data. We build on such models by exploring the level design affordances and applications enabled by conditional VAEs (CVAEs). CVAEs augment VAEs by allowing them to be trained using labeled data, thus enabling outputs to be generated conditioned on some input. We studied how increased control in the level generation process and the ability to produce desired outputs via training on labeled game level data could build on prior PCGML methods. Through our results of training CVAEs on levels from Super Mario Bros., Kid Icarus and Mega Man, we show that such models can assist in level design by generating levels with desired level elements and patterns as well as producing blended levels with desired combinations of games.

cs.LG↗

arXiv2020

Exploring Level Blending across Platformers via Paths and Affordances

Techniques for procedural content generation via machine learning (PCGML) have been shown to be useful for generating novel game content. While used primarily for producing new content in the style of the game domain used for training, recent works have increasingly started to explore methods for discovering and generating content in novel domains via techniques such as level blending and domain transfer. In this paper, we build on these works and introduce a new PCGML approach for producing novel game content spanning multiple domains. We use a new affordance and path vocabulary to encode data from six different platformer games and train variational autoencoders on this data, enabling us to capture the latent level space spanning all the domains and generate new content with varying proportions of the different domains.

cs.LG↗

arXiv2020

Game Level Clustering and Generation using Gaussian Mixture VAEs

Variational autoencoders (VAEs) have been shown to be able to generate game levels but require manual exploration of the learned latent space to generate outputs with desired attributes. While conditional VAEs address this by allowing generation to be conditioned on labels, such labels have to be provided during training and thus require prior knowledge which may not always be available. In this paper, we apply Gaussian Mixture VAEs (GMVAEs), a variant of the VAE which imposes a mixture of Gaussians (GM) on the latent space, unlike regular VAEs which impose a unimodal Gaussian. This allows GMVAEs to cluster levels in an unsupervised manner using the components of the GM and then generate new levels using the learned components. We demonstrate our approach with levels from Super Mario Bros., Kid Icarus and Mega Man. Our results show that the learned components discover and cluster level structures and patterns and can be used to generate levels with desired characteristics.

cs.LG↗

arXiv2020

Towards Game Design via Creative Machine Learning (GDCML)

In recent years, machine learning (ML) systems have been increasingly applied for performing creative tasks. Such creative ML approaches have seen wide use in the domains of visual art and music for applications such as image and music generation and style transfer. However, similar creative ML techniques have not been as widely adopted in the domain of game design despite the emergence of ML-based methods for generating game content. In this paper, we argue for leveraging and repurposing such creative techniques for designing content for games, referring to these as approaches for Game Design via Creative ML (GDCML). We highlight existing systems that enable GDCML and illustrate how creative ML can inform new systems via example applications and a proposed system.

cs.CY↗

arXiv2020

Sequential Segment-based Level Generation and Blending using Variational Autoencoders

Existing methods of level generation using latent variable models such as VAEs and GANs do so in segments and produce the final level by stitching these separately generated segments together. In this paper, we build on these methods by training VAEs to learn a sequential model of segment generation such that generated segments logically follow from prior segments. By further combining the VAE with a classifier that determines whether to place the generated segment to the top, bottom, left or right of the previous segment, we obtain a pipeline that enables the generation of arbitrarily long levels that progress in any of these four directions and are composed of segments that logically follow one another. In addition to generating more coherent levels of non-fixed length, this method also enables implicit blending of levels from separate games that do not have similar orientation. We demonstrate our approach using levels from Super Mario Bros., Kid Icarus and Mega Man, showing that our method produces levels that are more coherent than previous latent variable-based approaches and are capable of blending levels across games.

cs.LG↗