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Miscellaneous Aspects of Machine Learning · Representation Learning

Zhuo Huang, Gang Niu, Bo Han, Masashi Sugiyama, Tongliang Liu

The world is understood from various modalities, such as appearance, sound, language, etc. Since each modality only partially represents objects in a certain physical meaning, leveraging additional ones is beneficial in both theory and practice. However, exploiting novel modalities normally requires cross-modal pairs corresponding to the same instance, which is extremely resource-consuming and sometimes even impossible, making knowledge exploration of novel modalities largely restricted. To seek practical multi-modal learning, here we study Out-of-Modal (OOM) Generalization as an initial attempt to generalize to an unknown modality without given instance-level modal correspondence. Specifically, we consider Semi-Supervised and Unsupervised scenarios of OOM Generalization, where the first has scarce correspondences and the second has none, and propose connect & explore (COX) to solve these problems. COX first connects OOM data and known In-Modal (IM) data through a variational information bottleneck framework to extract shared information. Then, COX leverages the shared knowledge to create emergent correspondences, which is theoretically justified from an information-theoretic perspective. As a result, the label information on OOM data emerges along with the correspondences, which help explore the OOM data with unknown knowledge, thus benefiting generalization results. We carefully evaluate the proposed COX method under various OOM generalization scenarios, verifying its effectiveness and extensibility.

Applications · Computer Vision

Yuxin Dai, Qi Wang, Jingsen Zhu, xi db, Yuchi Huo, Chen Qian, Ying He

We introduce MIRReS, a novel two-stage inverse rendering framework thatjointly reconstructs and optimizes explicit geometry, materials, and lightingfrom multi-view images. Unlike previous methods that rely on implicit irradiance fields or oversimplified ray tracing, our method begins with an initialstage that extracts an explicit triangular mesh. In the second stage, we refine this representation using a physically-based inverse rendering modelwith multi-bounce path tracing and Monte Carlo integration. This enables our method to accurately estimate indirect illumination effects, including self-shadowing and internal reflections, leading to a more preciseintrinsic decomposition of shape, material, and lighting. To address thenoise issue in Monte Carlo integration, we incorporate reservoir sampling,improving convergence and enabling efficient gradient-based optimizationwith low sample counts. Through both qualitative and quantitative assessments across various scenarios, especially those with complex shadows,we demonstrate that our method achieves state-of-the-art decompositionperformance. Furthermore, our optimized explicit geometry seamlesslyintegrates with modern graphics engines supporting downstream applications such as scene editing, relighting, and material editing.

Social Aspects · Trustworthy Machine Learning

Hangtao Zhang, Chenyu Zhu, Xianlong Wang, Ziqi Zhou, Changgan Yin, Minghui Li, Lulu Xue, Yichen Wang, Shengshan Hu, Aishan Liu 等

Embodied AI represents systems where AI is integrated into physical entities. Multimodal Large Language Model (LLM), which exhibits powerful language understanding abilities, has been extensively employed in embodied AI by facilitating sophisticated task planning. However, a critical safety issue remains overlooked: could these embodied LLMs perpetrate harmful behaviors? In response, we introduce BadRobot, the first attack paradigm designed to jailbreak robotic manipulation, making embodied LLMs violate safety and ethical constraints through typical voice-based user-system interactions. Specifically, three vulnerabilities are exploited to achieve this type of attack: (i) manipulation of LLMs within robotic systems, (ii) misalignment between linguistic outputs and physical actions, and (iii) unintentional hazardous behaviors caused by world knowledge's flaws. Furthermore, we construct a benchmark of various malicious physical action queries to evaluate BadRobot's attack performance. Based on this benchmark, extensive experiments against existing prominent embodied LLM frameworks (e.g., Voxposer, Code as Policies, and ProgPrompt) demonstrate the effectiveness of our BadRobot. We emphasize that addressing this emerging vulnerability is crucial for the secure deployment of LLMs in robotics.Warning: This paper contains harmful AI-generated language and aggressive actions.

Peng Xia, Siwei Han, Shi Qiu, Yiyang Zhou, Zhaoyang Wang, Wenhao Zheng, Zhaorun Chen, Chenhang Cui, Mingyu Ding, Linjie Li 等

Interleaved multimodal comprehension and generation, enabling models to produce and interpret both images and text in arbitrary sequences, have become a pivotal area in multimodal learning. Despite significant advancements, the evaluation of this capability remains insufficient. Existing benchmarks suffer from limitations in data scale, scope, and evaluation depth, while current evaluation metrics are often costly or biased, lacking in reliability for practical applications. To address these challenges, we introduce MMIE, a large-scale knowledge-intensive benchmark for evaluating interleaved multimodal comprehension and generation in Large Vision-Language Models (LVLMs). MMIE comprises 20K meticulously curated multimodal queries, spanning 3 categories, 12 fields, and 102 subfields, including mathematics, coding, physics, literature, health, and arts. It supports both interleaved inputs and outputs, offering a mix of multiple-choice and open-ended question formats to evaluate diverse competencies. Moreover, we propose a reliable automated evaluation metric, leveraging a scoring model fine-tuned with human-annotated data and systematic evaluation criteria, aimed at reducing bias and improving evaluation accuracy. Extensive experiments demonstrate the effectiveness of our benchmark and metrics in providing a comprehensive evaluation of interleaved LVLMs. Specifically, we evaluate eight LVLMs, revealing that even the best models show significant room for improvement, with most achieving only moderate results. We believe MMIE will drive further advancements in the development of interleaved LVLMs.

Deep Learning · Everything Else

Peng Xia, Siwei Han, Shi Qiu, Yiyang Zhou, Zhaoyang Wang, Wenhao Zheng, Zhaorun Chen, Chenhang Cui, Mingyu Ding, Linjie Li 等

Interleaved multimodal comprehension and generation, enabling models to produce and interpret both images and text in arbitrary sequences, have become a pivotal area in multimodal learning. Despite significant advancements, the evaluation of this capability remains insufficient. Existing benchmarks suffer from limitations in data scale, scope, and evaluation depth, while current evaluation metrics are often costly or biased, lacking in reliability for practical applications. To address these challenges, we introduce MMIE, a large-scale knowledge-intensive benchmark for evaluating interleaved multimodal comprehension and generation in Large Vision-Language Models (LVLMs). MMIE comprises 20K meticulously curated multimodal queries, spanning 3 categories, 12 fields, and 102 subfields, including mathematics, coding, physics, literature, health, and arts. It supports both interleaved inputs and outputs, offering a mix of multiple-choice and open-ended question formats to evaluate diverse competencies. Moreover, we propose a reliable automated evaluation metric, leveraging a scoring model fine-tuned with human-annotated data and systematic evaluation criteria, aimed at reducing bias and improving evaluation accuracy. Extensive experiments demonstrate the effectiveness of our benchmark and metrics in providing a comprehensive evaluation of interleaved LVLMs. Specifically, we evaluate eight LVLMs, revealing that even the best models show significant room for improvement, with most achieving only moderate results. We believe MMIE will drive further advancements in the development of interleaved LVLMs.

Deep Learning · Large Language Models

Ruochen Jiao, Shaoyuan Xie, Justin Yue, TAKAMI SATO, Lixu Wang, Yixuan Wang, Qi Alfred Chen, Qi Zhu

Large Language Models (LLMs) have shown significant promise in real-world decision-making tasks for embodied artificial intelligence, especially when fine-tuned to leverage their inherent common sense and reasoning abilities while being tailored to specific applications. However, this fine-tuning process introduces considerable safety and security vulnerabilities, especially in safety-critical cyber-physical systems. In this work, we propose the first comprehensive framework for **B**ackdoor **A**ttacks against **L**LM-based **D**ecision-making systems (BALD) in embodied AI, systematically exploring the attack surfaces and trigger mechanisms. Specifically, we propose three distinct attack mechanisms: *word injection*, *scenario manipulation*, and *knowledge injection*, targeting various components in the LLM-based decision-making pipeline. We perform extensive experiments on representative LLMs (GPT-3.5, LLaMA2, PaLM2) in autonomous driving and home robot tasks, demonstrating the effectiveness and stealthiness of our backdoor triggers across various attack channels, with cases like vehicles accelerating toward obstacles and robots placing knives on beds. Our word and knowledge injection attacks achieve nearly 100\% success rate across multiple models and datasets while requiring only limited access to the system. Our scenario manipulation attack yields success rates exceeding 65\%, reaching up to 90\%, and does not require any runtime system intrusion. We also assess the robustness of these attacks against defenses, revealing their resilience. Our findings highlight critical security vulnerabilities in embodied LLM systems and emphasize the urgent need for safeguarding these systems to mitigate potential risks.

Deep Learning · Large Language Models

Martin Kuo, Jingyang Zhang, Jianyi Zhang, Minxue Tang, Louis DiValentin, Aolin Ding, Jingwei Sun, William Chen, Amin Hass, Tianlong Chen 等

With the rise of large language models (LLMs), increasing research has recognizedtheir risk of leaking personally identifiable information (PII) under maliciousattacks. Although efforts have been made to protect PII in LLMs, existing methodsstruggle to balance privacy protection with maintaining model utility. In this paper,inspired by studies of amnesia in cognitive science, we propose a novel approach,Proactive Privacy Amnesia (PPA), to safeguard PII in LLMs while preserving theirutility. This mechanism works by actively identifying and forgetting key memoriesmost closely associated with PII in sequences, followed by a memory implantingusing suitable substitute memories to maintain the LLM’s functionality. We conductevaluations across multiple models to protect common PII, such as phone numbersand physical addresses, against prevalent PII-targeted attacks, demonstrating thesuperiority of our method compared with other existing defensive techniques. Theresults show that our PPA method completely eliminates the risk of phone numberexposure by 100% and significantly reduces the risk of physical address exposureby 9.8% – 87.6%, all while maintaining comparable model utility performance.

Applications · Robotics

Kojiro Takeyama, Yimeng Liu, Misha Sra

Understanding human locomotion is crucial for AI agents such as robots, particularly in complex indoor home environments. Modeling human trajectories in these spaces requires insight into how individuals maneuver around physical obstacles and manage social navigation dynamics. These dynamics include subtle behaviors influenced by proxemics - the social use of space, such as stepping aside to allow others to pass or choosing longer routes to avoid collisions. Previous research has developed datasets of human motion in indoor scenes, but these are often limited in scale and lack the nuanced social navigation dynamics common in home environments. To address this, we present LocoVR, a dataset of 7000+ two-person trajectories captured in virtual reality from over 130 different indoor home environments. LocoVR provides accurate trajectory and precise spatial information, along with rich examples of socially-motivated movement behaviors. For example, the dataset captures instances of individuals navigating around each other in narrow spaces, adjusting paths to respect personal boundaries in living areas, and coordinating movements in high-traffic zones like entryways and kitchens. Our evaluation shows that LocoVR significantly enhances model performance in three practical indoor tasks utilizing human trajectories, and demonstrates predicting socially-aware navigation patterns in home environments.

Applications · Robotics

Junting Chen, Checheng Yu, Xunzhe Zhou, Tianqi Xu, Yao Mu, Mengkang Hu, Wenqi Shao, Yikai Wang, Guohao Li, Lin Shao

Heterogeneous multi-robot systems (HMRS) have emerged as a powerful ap-proach for tackling complex tasks that single robots cannot manage alone. Currentlarge-language-model-based multi-agent systems (LLM-based MAS) have shownsuccess in areas like software development and operating systems, but applyingthese systems to robot control presents unique challenges. In particular, the ca-pabilities of each agent in a multi-robot system are inherently tied to the physicalcomposition of the robots, rather than predefined roles. To address this issue,we introduce a novel multi-agent framework designed to enable effective collab-oration among heterogeneous robots with varying embodiments and capabilities,along with a new benchmark named Habitat-MAS. One of our key designs isRobot Resume: Instead of adopting human-designed role play, we propose a self-prompted approach, where agents comprehend robot URDF files and call robotkinematics tools to generate descriptions of their physics capabilities to guidetheir behavior in task planning and action execution. The Habitat-MAS bench-mark is designed to assess how a multi-agent framework handles tasks that requireembodiment-aware reasoning, which includes 1) manipulation, 2) perception, 3)navigation, and 4) comprehensive multi-floor object rearrangement. The experi-mental results indicate that the robot’s resume and the hierarchical design of ourmulti-agent system are essential for the effective operation of the heterogeneousmulti-robot system within this intricate problem context.

Applications · Physics

Erle Zhu, Yadi Liu, Zhe Zhang, Xujun Li, JinZhou, Xinjie Yu, Minlie Huang, Hongning Wang

Pre-trained on extensive text and image corpora, current Multi-Modal Large Language Models (MLLM) have shown strong capabilities in general visual reasoning tasks. However, their performance is still lacking in physical domains that require understanding diagrams with complex physical structures and quantitative analysis based on multi-modal information. To address this, we develop a new framework, named **M**ulti-Modal Scientific Re**A**soning with **P**hysics Perception and **S**imulation (**MAPS**) based on an MLLM. MAPS decomposes expert-level multi-modal reasoning task into physical diagram understanding via a Physical Perception Model (PPM) and reasoning with physical knowledge via a simulator. The PPM module is obtained by fine-tuning a visual language model using carefully designed synthetic data with paired physical diagrams and corresponding simulation language descriptions. At the inference stage, MAPS integrates the simulation language description of the input diagram provided by PPM and results obtained through a Chain-of-Simulation process with MLLM to derive the underlying rationale and the final answer. Validated using our collected college-level circuit analysis problems, MAPS significantly improves reasoning accuracy of MLLM and outperforms all existing models. The results confirm MAPS offers a promising direction for enhancing multi-modal scientific reasoning ability of MLLMs. We will release our code, model and dataset used for our experiments upon publishing of this paper.

Deep Learning · Generative Models and Autoencoders

Giannis Daras, Yeshwanth Cherapanamjeri, Constantinos C Daskalakis

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g.~in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than $80$ models on data with different corruption levels across three datasets ranging from $30,000$ to $\approx 1.3$M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~$10\%$ of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Applications · Chemistry and Drug Discovery

Daniel Levy, Siba Smarak Panigrahi, Sékou-Oumar Kaba, Qiang Zhu, Kin Long Kelvin Lee, Mikhail Galkin, Santiago Miret, Siamak Ravanbakhsh

Generating novel crystalline materials has potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in determining their physical properties. However, existing crystal generation methods either fail to generate materials that display the symmetries of real-world crystals, or simply replicate the symmetry information from examples in a database. To address this limitation, we propose SymmCD, a novel diffusion-based generative model that explicitly incorporates crystallographic symmetry into the generative process. We decompose crystals into two components and learn their joint distribution through diffusion: 1) the asymmetric unit, the smallest subset of the crystal which can generate the whole crystal through symmetry transformations, and; 2) the symmetry transformations needed to be applied to each atom in the asymmetric unit. We also use a novel and interpretable representation for these transformations, enabling generalization across different crystallographic symmetry groups. We showcase the competitive performance of SymmCD on a subset of the Materials Project, obtaining diverse and valid crystals with realistic symmetries and predicted properties.

Reinforcement Learning · Everything Else

Brent Wallace, Jennie Si

We introduce integral performance approximation (IPA), a new continuous-time reinforcement learning (CT-RL) control method. It leverages an affine nonlinear dynamic model, which partially captures the dynamics of the physical environment, alongside state-action trajectory data to enable optimal control with great data efficiency and robust control performance. Utilizing Kleinman algorithm structures allows IPA to provide theoretical guarantees of learning convergence, solution optimality, and closed-loop stability. Furthermore, we demonstrate the effectiveness of IPA on three CT-RL environments including hypersonic vehicle (HSV) control, which has additional challenges caused by unstable and nonminimum phase dynamics. As a result, we demonstrate that the IPA method leads to new, SOTA control design and performance in CT-RL.

Applications · Computer Vision

Shuyi Jiang, Qihao Zhao, Hossein Rahmani, De Wen Soh, Jun Liu, Na Zhao

Recently, with the development of Neural Radiance Fields and Gaussian Splatting, 3D reconstruction techniques have achieved remarkably high fidelity. However, the latent representations learnt by these methods are highly entangled and lack interpretability. In this paper, we propose a novel part-aware compositional reconstruction method, called GaussianBlock, that enables semantically coherent and disentangled representations, allowing for precise and physical editing akin to building blocks, while simultaneously maintaining high fidelity.Our GaussianBlock introduces a hybrid representation that leverages the advantages of both primitives, known for their flexible actionability and editability, and 3D Gaussians, which excel in reconstruction quality. Specifically, we achieve semantically coherent primitives through a novel attention-guided centering loss derived from 2D semantic priors, complemented by a dynamic splitting and fusion strategy. Furthermore, we utilize 3D Gaussians that hybridize with primitives to refine structural details and enhance fidelity. Additionally, a binding inheritance strategy is employed to strengthen and maintain the connection between the two. Our reconstructed scenes are evidenced to be disentangled, compositional, and compact across diverse benchmarks, enabling seamless, direct and precise editing while maintaining high quality.

Applications · Physics

Yehui Tang, Mabiao Long, Junchi Yan

Quantum state property estimation (QPE) is a fundamental challenge in quantum many-body problems in physics and chemistry, involving the prediction of characteristics such as correlation and entanglement entropy through statistical analysis of quantum measurement data. Recent advances in deep learning have provided powerful solutions, predominantly using auto-regressive models. These models generally assume an intrinsic ordering among qubits, aiming to approximate the classical probability distribution through sequential training. However, unlike natural language, the entanglement structure of qubits lacks an inherent ordering, hurting the motivation of such models. In this paper, we introduce a novel, non-autoregressive generative model called \textbf{\model}, designed for \underline{\textbf{Qua}}ntum state property estimation using \underline{\textbf{Di}}ffusion \underline{\textbf{M}}odels. \model progressively denoises Gaussian noise into the distribution corresponding to the quantum state, encouraging equal, unbiased treatment of all qubits. \model learns to map physical variables to properties of the ground state of the parameterized Hamiltonian during offline training. Afterwards one can sample from the learned distribution conditioned on previously unseen physical variables to collect measurement records and employ post-processing to predict properties of unknown quantum states. We evaluate \model on large-scale QPE tasks using classically simulated data on the 1D anti-ferromagnetic Heisenberg model with the system size up to 100 qubits. Numerical results demonstrate that \model outperforms baseline models, particularly auto-regressive approaches, under conditions of limited measurement data during training and reduced sample complexity during inference.

Deep Learning · Generative Models and Autoencoders

Yongxing Zhang, Donglin Yang, Renjie Liao

The group of permutations $S_n$, also known as the finite symmetric groups, are essential in fields such as combinatorics, physics, and chemistry. However, learning a probability distribution over $S_n$ poses significant challenges due to its intractable size and discrete nature. In this paper, we introduce *SymmetricDiffusers*, a novel discrete diffusion model that simplifies the task of learning a complicated distribution over $S_n$ by decomposing it into learning simpler transitions of the reverse diffusion using deep neural networks. We identify the riffle shuffle as an effective forward transition and provide empirical guidelines for selecting the diffusion length based on the theory of random walks on finite groups. Additionally, we propose a generalized Plackett-Luce (PL) distribution for the reverse transition, which is provably more expressive than the PL distribution. We further introduce a theoretically grounded "denoising schedule" to improve sampling and learning efficiency. Extensive experiments show that our model achieves state-of-the-art or comparable performance on solving tasks including sorting 4-digit MNIST images, jigsaw puzzles, and traveling salesman problems. Our code is released at <https://github.com/DSL-Lab/SymmetricDiffusers>.

Applications · Physics

Zeyu Li, Hongkun Dou, Shen Fang, Wang Han, Yue Deng, Lijun Yang

The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schr\"{o}dinger Bridge (PalSB). This framework leverages a diffusion bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques. The source code can be found at https://github.com/lzy12301/PalSB.

Applications · Computer Vision

Jianqi Chen, Panwen Hu, Xiaojun Chang, Zhenwei Shi, Michael Kampffmeyer, Xiaodan Liang

Recent advancements in human motion synthesis have focused on specific types of motions, such as human-scene interaction, locomotion or human-human interaction, however, there is a lack of a unified system capable of generating a diverse combination of motion types. In response, we introduce *Sitcom-Crafter*, a comprehensive and extendable system for human motion generation in 3D space, which can be guided by extensive plot contexts to enhance workflow efficiency for anime and game designers. The system is comprised of eight modules, three of which are dedicated to motion generation, while the remaining five are augmentation modules that ensure consistent fusion of motion sequences and system functionality. Central to the generation modules is our novel 3D scene-aware human-human interaction module, which addresses collision issues by synthesizing implicit 3D Signed Distance Function (SDF) points around motion spaces, thereby minimizing human-scene collisions without additional data collection costs. Complementing this, our locomotion and human-scene interaction modules leverage existing methods to enrich the system's motion generation capabilities. Augmentation modules encompass plot comprehension for command generation, motion synchronization for seamless integration of different motion types, hand pose retrieval to enhance motion realism, motion collision revision to prevent human collisions, and 3D retargeting to ensure visual fidelity. Experimental evaluations validate the system's ability to generate high-quality, diverse, and physically realistic motions, underscoring its potential for advancing creative workflows. Code and demonstration videos can be found in the supplementary files.

Deep Learning · Self-Supervised Learning

Junyi An, Chao Qu, Yun-Fei Shi, XinHao Liu, Qianwei Tang, Fenglei Cao, Yuan Qi

Graph neural networks (GNNs) have shown considerable promise in computational chemistry. However, the limited availability of molecular data raises concerns regarding GNNs' ability to effectively capture the fundamental principles of physics and chemistry, which constrains their generalization capabilities. To address this challenge, we introduce a novel self-supervised approach termed Equivariant Masked Position Prediction (EMPP), grounded in intramolecular potential and force theory. Unlike conventional attribute masking techniques, EMPP formulates a nuanced position prediction task that is more well-defined and enhances the learning of quantum mechanical features. EMPP also bypasses the approximation of the Gaussian mixture distribution commonly used in denoising methods, allowing for more accurate acquisition of physical properties. Experimental results indicate that EMPP significantly enhances performance of advanced molecular architectures, surpassing state-of-the-art self-supervised approaches. Our code is released in https://github.com/ajy112/EMPP.

Applications · Physics

Honghui Wang, Shiji Song, Gao Huang

Significant advancements have been achieved in PDE modeling using neural fields. Despite their effectiveness, existing methods rely on global modulation, limiting their ability to reconstruct local details. While spatial modulation with vanilla grid-based representations offers a promising alternative, it struggles with inadequate global information modeling and over-fitting to the training spatial domain. To address these challenges, we propose GridMix, a novel approach that models spatial modulation as a mixture of grid-based representations. GridMix effectively explores global structures while preserving locality for fine-grained modulation. Furthermore, we introduce spatial domain augmentation to enhance the robustness of the modulated neural fields against spatial domain variations. With all these innovations,our comprehensive approach culminates in MARBLE, a framework that significantly advancing the capabilities of neural fields in PDE modeling. The effectiveness of MARBLE is extensivelyvalidated on diverse benchmarks encompassing dynamics modeling and geometric prediction.