arXiv subjects

Gautam Singh

Publications and source records attributed to Gautam Singh.

At least 19 recordsLinked to original sources

arXiv2026

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the variational form is implemented using a Petrov-Galerkin formulation. Dirichlet boundary conditions are imposed directly, while the source terms are computed using automatic differentiation. Computational experiments on standard two-dimensional problems demonstrate that the proposed method achieves high accuracy in both the maximum and L_2 norms. These results confirm the efficiency and robustness of the Petrov-Galerkin VPINN approach in accurately capturing the multiscale features of two-dimensional SPPs.

math.NA↗

arXiv2026

Learning Reasoning World Models for Parallel Code

Large language models have shown remarkable ability in serial code generation, but they still struggle with parallel code for which training data is comparatively scarce. A common remedy is to use coding agents that interact with external tools, but tool calls can be costly and sometimes impractical, e.g., for partially written code. We propose Parallel-Code World Models (PCWMs), reasoning LLMs that aim to predict tool outcomes directly from parallel source code. To train PCWMs, we design a novel exploration and data generation pipeline that samples diverse parallel-coding problems and candidate implementations across multiple domains, then executes them via tools to record data races and performance profiles. From these, we synthesize reasoning traces that causally connect source code to observed tool outcomes. Fine-tuning on the resulting data yields noticeable gains, with a 7B-parameter world model improving from 64.3% to 72.8% accuracy in race-outcome prediction, while an 8B-parameter model improves in a performance profiling task from 49.3% to 58.6% accuracy. Furthermore, when open-weight models were tasked with fixing data races, world-model feedback improved their race-fixing rates relative to self-feedback by 2.7%-9.1% using our 7B-parameter world model and by 6.1%-11.1% using our 14B-parameter world model. Our results suggest that reasoning world models may have the potential to serve alongside external tool calls in parallel-coding agents.

cs.SE↗

arXiv2025

From Diffraction to Refraction: a coherence-based conceptual framework

Refraction, traditionally viewed as a geometric event occurring at material interfaces, is now being re-examined through the lens of coherence. Recent studies in optics and photonics, including coherence tomography, Moire interference, and coherence-engineered diffraction, indicate that phase organization alone can bend light even without index discontinuities. Fraunhofer-based analyses further show that angular deflection can arise from intrinsic phase curvature within homogeneous media. Here we introduce a coherence-based constitutive framework that systematizes these observations: refraction can occur inside a bulk medium when coherence itself provides the effective boundary. Two near-frequency structured beams write and probe a shared phase field, revealing reproducible angular rotation and coherence-lensing whose direction and magnitude follow the spectral detuning. The key detuning coefficient is: Krc = 2 * pi * (1/lambda_r - 1/lambda_w). The compact coherence-refraction relation n2 * sin(theta_t) - n1 * sin(theta_i) = Krc_parallel / k0, with k0 = 2 * pi / lambda_r, retains the form of Snell's law while extending it to coherence-driven regimes. This is not a new law but a quantitative rule linking tangential phase matching to observable deflection within homogeneous media.

physics.optics↗

arXiv2025

Development and Analysis of Chien-Physics-Informed Neural Networks for Singular Perturbation Problems

In this article, we employ Chien-Physics Informed Neural Networks (C-PINNs) to obtain solutions for singularly perturbed convection-diffusion equations, reaction-diffusion equations, and their coupled forms in both one and two-dimensional settings. While PINNs have emerged as a powerful tool for solving various types of differential equations, their application to singular perturbation problems (SPPs) presents significant challenges. These challenges arise because a small perturbation parameter multiplies the highest-order derivatives, leading to sharp gradient changes near the boundary layer. To overcome these difficulties, we apply C-PINNs, a modified version of the standard PINNs framework, which is specifically designed to address singular perturbation problems. Our study shows that C-PINNs provide a more accurate solution for SPPs, demonstrating better performance than conventional methods.

math.NA↗

arXiv2025

A Variational Physics-Informed Neural Network Framework Using Petrov-Galerkin Method for Solving Singularly Perturbed Boundary Value Problems

This work proposes a Variational Physics-Informed Neural Network (VPINN) framework that integrates the Petrov-Galerkin formulation with deep neural networks (DNNs) for solving one-dimensional singularly perturbed boundary value problems (BVPs) and parabolic partial differential equations (PDEs) involving one or two small parameters. The method adopts a nonlinear approximation in which the trial space is defined by neural network functions, while the test space is constructed from hat functions. The weak formulation is constructed using localized test functions, with interface penalty terms introduced to enhance numerical stability and accurately capture boundary layers. Dirichlet boundary conditions are imposed via hard constraints, and source terms are computed using automatic differentiation. Numerical experiments on benchmark problems demonstrate the effectiveness of the proposed method, showing significantly improved accuracy in both the $L_2$ and maximum norms compared to the standard VPINN approach for one-dimensional singularly perturbed differential equations (SPDEs).

math.NA↗

arXiv2025

Dreamweaver: Learning Compositional World Models from Pixels

Humans have an innate ability to decompose their perceptions of the world into objects and their attributes, such as colors, shapes, and movement patterns. This cognitive process enables us to imagine novel futures by recombining familiar concepts. However, replicating this ability in artificial intelligence systems has proven challenging, particularly when it comes to modeling videos into compositional concepts and generating unseen, recomposed futures without relying on auxiliary data, such as text, masks, or bounding boxes. In this paper, we propose Dreamweaver, a neural architecture designed to discover hierarchical and compositional representations from raw videos and generate compositional future simulations. Our approach leverages a novel Recurrent Block-Slot Unit (RBSU) to decompose videos into their constituent objects and attributes. In addition, Dreamweaver uses a multi-future-frame prediction objective to capture disentangled representations for dynamic concepts more effectively as well as static concepts. In experiments, we demonstrate our model outperforms current state-of-the-art baselines for world modeling when evaluated under the DCI framework across multiple datasets. Furthermore, we show how the modularized concept representations of our model enable compositional imagination, allowing the generation of novel videos by recombining attributes from previously seen objects. cun-bjy.github.io/dreamweaver-website

cs.CV↗

arXiv2024

Slot State Space Models

Recent State Space Models (SSMs) such as S4, S5, and Mamba have shown remarkable computational benefits in long-range temporal dependency modeling. However, in many sequence modeling problems, the underlying process is inherently modular and it is of interest to have inductive biases that mimic this modular structure. In this paper, we introduce SlotSSMs, a novel framework for incorporating independent mechanisms into SSMs to preserve or encourage separation of information. Unlike conventional SSMs that maintain a monolithic state vector, SlotSSMs maintains the state as a collection of multiple vectors called slots. Crucially, the state transitions are performed independently per slot with sparse interactions across slots implemented via the bottleneck of self-attention. In experiments, we evaluate our model in object-centric learning, 3D visual reasoning, and long-context video understanding tasks, which involve modeling multiple objects and their long-range temporal dependencies. We find that our proposed design offers substantial performance gains over existing sequence modeling methods. Project page is available at https://slotssms.github.io/

cs.AI↗

arXiv2024

Parallelized Spatiotemporal Binding

While modern best practices advocate for scalable architectures that support long-range interactions, object-centric models are yet to fully embrace these architectures. In particular, existing object-centric models for handling sequential inputs, due to their reliance on RNN-based implementation, show poor stability and capacity and are slow to train on long sequences. We introduce Parallelizable Spatiotemporal Binder or PSB, the first temporally-parallelizable slot learning architecture for sequential inputs. Unlike conventional RNN-based approaches, PSB produces object-centric representations, known as slots, for all time-steps in parallel. This is achieved by refining the initial slots across all time-steps through a fixed number of layers equipped with causal attention. By capitalizing on the parallelism induced by our architecture, the proposed model exhibits a significant boost in efficiency. In experiments, we test PSB extensively as an encoder within an auto-encoding framework paired with a wide variety of decoder options. Compared to the state-of-the-art, our architecture demonstrates stable training on longer sequences, achieves parallelization that results in a 60% increase in training speed, and yields performance that is on par with or better on unsupervised 2D and 3D object-centric scene decomposition and understanding.

cs.LG↗

arXiv2023

Imagine the Unseen World: A Benchmark for Systematic Generalization in Visual World Models

Systematic compositionality, or the ability to adapt to novel situations by creating a mental model of the world using reusable pieces of knowledge, remains a significant challenge in machine learning. While there has been considerable progress in the language domain, efforts towards systematic visual imagination, or envisioning the dynamical implications of a visual observation, are in their infancy. We introduce the Systematic Visual Imagination Benchmark (SVIB), the first benchmark designed to address this problem head-on. SVIB offers a novel framework for a minimal world modeling problem, where models are evaluated based on their ability to generate one-step image-to-image transformations under a latent world dynamics. The framework provides benefits such as the possibility to jointly optimize for systematic perception and imagination, a range of difficulty levels, and the ability to control the fraction of possible factor combinations used during training. We provide a comprehensive evaluation of various baseline models on SVIB, offering insight into the current state-of-the-art in systematic visual imagination. We hope that this benchmark will help advance visual systematic compositionality.

cs.CV↗

arXiv2023

Object-Centric Slot Diffusion

The recent success of transformer-based image generative models in object-centric learning highlights the importance of powerful image generators for handling complex scenes. However, despite the high expressiveness of diffusion models in image generation, their integration into object-centric learning remains largely unexplored in this domain. In this paper, we explore the feasibility and potential of integrating diffusion models into object-centric learning and investigate the pros and cons of this approach. We introduce Latent Slot Diffusion (LSD), a novel model that serves dual purposes: it is the first object-centric learning model to replace conventional slot decoders with a latent diffusion model conditioned on object slots, and it is also the first unsupervised compositional conditional diffusion model that operates without the need for supervised annotations like text. Through experiments on various object-centric tasks, including the first application of the FFHQ dataset in this field, we demonstrate that LSD significantly outperforms state-of-the-art transformer-based decoders, particularly in more complex scenes, and exhibits superior unsupervised compositional generation quality. In addition, we conduct a preliminary investigation into the integration of pre-trained diffusion models in LSD and demonstrate its effectiveness in real-world image segmentation and generation. Project page is available at https://latentslotdiffusion.github.io

cs.CV↗

arXiv2023

Neural Systematic Binder

The key to high-level cognition is believed to be the ability to systematically manipulate and compose knowledge pieces. While token-like structured knowledge representations are naturally provided in text, it is elusive how to obtain them for unstructured modalities such as scene images. In this paper, we propose a neural mechanism called Neural Systematic Binder or SysBinder for constructing a novel structured representation called Block-Slot Representation. In Block-Slot Representation, object-centric representations known as slots are constructed by composing a set of independent factor representations called blocks, to facilitate systematic generalization. SysBinder obtains this structure in an unsupervised way by alternatingly applying two different binding principles: spatial binding for spatial modularity across the full scene and factor binding for factor modularity within an object. SysBinder is a simple, deterministic, and general-purpose layer that can be applied as a drop-in module in any arbitrary neural network and on any modality. In experiments, we find that SysBinder provides significantly better factor disentanglement within the slots than the conventional object-centric methods, including, for the first time, in visually complex scene images such as CLEVR-Tex. Furthermore, we demonstrate factor-level systematicity in controlled scene generation by decoding unseen factor combinations.

cs.CV↗

arXiv2022

Simple Unsupervised Object-Centric Learning for Complex and Naturalistic Videos

Unsupervised object-centric learning aims to represent the modular, compositional, and causal structure of a scene as a set of object representations and thereby promises to resolve many critical limitations of traditional single-vector representations such as poor systematic generalization. Although there have been many remarkable advances in recent years, one of the most critical problems in this direction has been that previous methods work only with simple and synthetic scenes but not with complex and naturalistic images or videos. In this paper, we propose STEVE, an unsupervised model for object-centric learning in videos. Our proposed model makes a significant advancement by demonstrating its effectiveness on various complex and naturalistic videos unprecedented in this line of research. Interestingly, this is achieved by neither adding complexity to the model architecture nor introducing a new objective or weak supervision. Rather, it is achieved by a surprisingly simple architecture that uses a transformer-based image decoder conditioned on slots and the learning objective is simply to reconstruct the observation. Our experiment results on various complex and naturalistic videos show significant improvements compared to the previous state-of-the-art.

cs.CV↗

arXiv2022

Illiterate DALL-E Learns to Compose

Although DALL-E has shown an impressive ability of composition-based systematic generalization in image generation, it requires the dataset of text-image pairs and the compositionality is provided by the text. In contrast, object-centric representation models like the Slot Attention model learn composable representations without the text prompt. However, unlike DALL-E its ability to systematically generalize for zero-shot generation is significantly limited. In this paper, we propose a simple but novel slot-based autoencoding architecture, called SLATE, for combining the best of both worlds: learning object-centric representations that allows systematic generalization in zero-shot image generation without text. As such, this model can also be seen as an illiterate DALL-E model. Unlike the pixel-mixture decoders of existing object-centric representation models, we propose to use the Image GPT decoder conditioned on the slots for capturing complex interactions among the slots and pixels. In experiments, we show that this simple and easy-to-implement architecture not requiring a text prompt achieves significant improvement in in-distribution and out-of-distribution (zero-shot) image generation and qualitatively comparable or better slot-attention structure than the models based on mixture decoders.

cs.CV↗

arXiv2021

Structured World Belief for Reinforcement Learning in POMDP

Object-centric world models provide structured representation of the scene and can be an important backbone in reinforcement learning and planning. However, existing approaches suffer in partially-observable environments due to the lack of belief states. In this paper, we propose Structured World Belief, a model for learning and inference of object-centric belief states. Inferred by Sequential Monte Carlo (SMC), our belief states provide multiple object-centric scene hypotheses. To synergize the benefits of SMC particles with object representations, we also propose a new object-centric dynamics model that considers the inductive bias of object permanence. This enables tracking of object states even when they are invisible for a long time. To further facilitate object tracking in this regime, we allow our model to attend flexibly to any spatial location in the image which was restricted in previous models. In experiments, we show that object-centric belief provides a more accurate and robust performance for filtering and generation. Furthermore, we show the efficacy of structured world belief in improving the performance of reinforcement learning, planning and supervised reasoning.

cs.LG↗

arXiv2020

Robustifying Sequential Neural Processes

When tasks change over time, meta-transfer learning seeks to improve the efficiency of learning a new task via both meta-learning and transfer-learning. While the standard attention has been effective in a variety of settings, we question its effectiveness in improving meta-transfer learning since the tasks being learned are dynamic and the amount of context can be substantially smaller. In this paper, using a recently proposed meta-transfer learning model, Sequential Neural Processes (SNP), we first empirically show that it suffers from a similar underfitting problem observed in the functions inferred by Neural Processes. However, we further demonstrate that unlike the meta-learning setting, the standard attention mechanisms are not effective in meta-transfer setting. To resolve, we propose a new attention mechanism, Recurrent Memory Reconstruction (RMR), and demonstrate that providing an imaginary context that is recurrently updated and reconstructed with interaction is crucial in achieving effective attention for meta-transfer learning. Furthermore, incorporating RMR into SNP, we propose Attentive Sequential Neural Processes-RMR (ASNP-RMR) and demonstrate in various tasks that ASNP-RMR significantly outperforms the baselines.

cs.LG↗

arXiv2020

SPACE: Unsupervised Object-Oriented Scene Representation via Spatial Attention and Decomposition

The ability to decompose complex multi-object scenes into meaningful abstractions like objects is fundamental to achieve higher-level cognition. Previous approaches for unsupervised object-oriented scene representation learning are either based on spatial-attention or scene-mixture approaches and limited in scalability which is a main obstacle towards modeling real-world scenes. In this paper, we propose a generative latent variable model, called SPACE, that provides a unified probabilistic modeling framework that combines the best of spatial-attention and scene-mixture approaches. SPACE can explicitly provide factorized object representations for foreground objects while also decomposing background segments of complex morphology. Previous models are good at either of these, but not both. SPACE also resolves the scalability problems of previous methods by incorporating parallel spatial-attention and thus is applicable to scenes with a large number of objects without performance degradations. We show through experiments on Atari and 3D-Rooms that SPACE achieves the above properties consistently in comparison to SPAIR, IODINE, and GENESIS. Results of our experiments can be found on our project website: https://sites.google.com/view/space-project-page

cs.LG↗

arXiv2020

Fair Transfer of Multiple Style Attributes in Text

To preserve anonymity and obfuscate their identity on online platforms users may morph their text and portray themselves as a different gender or demographic. Similarly, a chatbot may need to customize its communication style to improve engagement with its audience. This manner of changing the style of written text has gained significant attention in recent years. Yet these past research works largely cater to the transfer of single style attributes. The disadvantage of focusing on a single style alone is that this often results in target text where other existing style attributes behave unpredictably or are unfairly dominated by the new style. To counteract this behavior, it would be nice to have a style transfer mechanism that can transfer or control multiple styles simultaneously and fairly. Through such an approach, one could obtain obfuscated or written text incorporated with a desired degree of multiple soft styles such as female-quality, politeness, or formalness. In this work, we demonstrate that the transfer of multiple styles cannot be achieved by sequentially performing multiple single-style transfers. This is because each single style-transfer step often reverses or dominates over the style incorporated by a previous transfer step. We then propose a neural network architecture for fairly transferring multiple style attributes in a given text. We test our architecture on the Yelp data set to demonstrate our superior performance as compared to existing one-style transfer steps performed in a sequence.

cs.CL↗

arXiv2019

Sequential Neural Processes

Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes. However, a large class of problems comprises underlying temporal dependency structures in a sequence of stochastic processes that Neural Processes (NP) do not explicitly consider. In this paper, we propose Sequential Neural Processes (SNP) which incorporates a temporal state-transition model of stochastic processes and thus extends its modeling capabilities to dynamic stochastic processes. In applying SNP to dynamic 3D scene modeling, we introduce the Temporal Generative Query Networks. To our knowledge, this is the first 4D model that can deal with the temporal dynamics of 3D scenes. In experiments, we evaluate the proposed methods in dynamic (non-stationary) regression and 4D scene inference and rendering.

cs.LG↗