arXiv subjects

Anima Anandkumar

Publications and source records attributed to Anima Anandkumar.

At least 73 records · Page 4Linked to original sources

arXiv2025

EcoSpa: Efficient Transformer Training with Coupled Sparsity

Transformers have become the backbone of modern AI, yet their high computational demands pose critical system challenges. While sparse training offers efficiency gains, existing methods fail to preserve critical structural relationships between weight matrices that interact multiplicatively in attention and feed-forward layers. This oversight leads to performance degradation at high sparsity levels. We introduce EcoSpa, an efficient structured sparse training method that jointly evaluates and sparsifies coupled weight matrix pairs, preserving their interaction patterns through aligned row/column removal. EcoSpa introduces a new granularity for calibrating structural component importance and performs coupled estimation and sparsification across both pre-training and fine-tuning scenarios. Evaluations demonstrate substantial improvements: EcoSpa enables efficient training of LLaMA-1B with 50\% memory reduction and 21\% faster training, achieves $2.2\times$ model compression on GPT-2-Medium with $2.4$ lower perplexity, and delivers $1.6\times$ inference speedup. The approach uses standard PyTorch operations, requiring no custom hardware or kernels, making efficient transformer training accessible on commodity hardware.

cs.LG↗

arXiv2025

Enabling Automatic Differentiation with Mollified Graph Neural Operators

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these derivatives remains challenging, with spectral and finite difference methods introducing approximation errors due to finite resolution. Here, we propose the mollified graph neural operator ($m$GNO), the first method to leverage automatic differentiation and compute exact gradients on arbitrary geometries. This enhancement enables efficient training on irregular grids and varying geometries while allowing seamless evaluation of physics losses at randomly sampled points for improved generalization. For a PDE example on regular grids, $m$GNO paired with autograd reduced the L2 relative data error by 20x compared to finite differences, although training was slower. It can also solve PDEs on unstructured point clouds seamlessly, using physics losses only, at resolutions vastly lower than those needed for finite differences to be accurate enough. On these unstructured point clouds, $m$GNO leads to errors that are consistently 2 orders of magnitude lower than machine learning baselines (Meta-PDE, which accelerates PINNs) for comparable runtimes, and also delivers speedups from 1 to 3 orders of magnitude compared to the numerical solver for similar accuracy. $m$GNOs can also be used to solve inverse design and shape optimization problems on complex geometries.

cs.LG↗

arXiv2025

Physics-informed Neural-operator Predictive Control for Drag Reduction in Turbulent Flows

Assessing turbulence control effects for wall friction numerically is a significant challenge since it requires expensive simulations of turbulent fluid dynamics. We instead propose an efficient deep reinforcement learning (RL) framework for modeling and control of turbulent flows. It is model-based RL for predictive control (PC), where both the policy and the observer models for turbulence control are learned jointly using Physics Informed Neural Operators (PINO), which are discretization invariant and can capture fine scales in turbulent flows accurately. Our PINO-PC outperforms prior model-free reinforcement learning methods in various challenging scenarios where the flows are of high Reynolds numbers and unseen, i.e., not provided during model training. We find that PINO-PC achieves a drag reduction of 39.0\% under a bulk-velocity Reynolds number of 15,000, outperforming previous fluid control methods by more than 32\%.

cs.LG↗

arXiv2025

BioNeMo Framework: a modular, high-performance library for AI model development in drug discovery

Artificial Intelligence models encoding biology and chemistry are opening new routes to high-throughput and high-quality in-silico drug development. However, their training increasingly relies on computational scale, with recent protein language models (pLM) training on hundreds of graphical processing units (GPUs). We introduce the BioNeMo Framework to facilitate the training of computational biology and chemistry AI models across hundreds of GPUs. Its modular design allows the integration of individual components, such as data loaders, into existing workflows and is open to community contributions. We detail technical features of the BioNeMo Framework through use cases such as pLM pre-training and fine-tuning. On 256 NVIDIA A100s, BioNeMo Framework trains a three billion parameter BERT-based pLM on over one trillion tokens in 4.2 days. The BioNeMo Framework is open-source and free for everyone to use.

cs.LG↗

arXiv2025

Sequential Controlled Langevin Diffusions

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers.

stat.ML↗

arXiv2025

The Personality Illusion: Revealing Dissociation Between Self-Reports & Behavior in LLMs

Personality traits have long been studied as predictors of human behavior. Recent advances in Large Language Models (LLMs) suggest similar patterns may emerge in artificial systems, with advanced LLMs displaying consistent behavioral tendencies resembling human traits like agreeableness and self-regulation. Understanding these patterns is crucial, yet prior work primarily relied on simplified self-reports and heuristic prompting, with little behavioral validation. In this study, we systematically characterize LLM personality across three dimensions: (1) the dynamic emergence and evolution of trait profiles throughout training stages; (2) the predictive validity of self-reported traits in behavioral tasks; and (3) the impact of targeted interventions, such as persona injection, on both self-reports and behavior. Our findings reveal that instructional alignment (e.g., RLHF, instruction tuning) significantly stabilizes trait expression and strengthens trait correlations in ways that mirror human data. However, these self-reported traits do not reliably predict behavior, and observed associations often diverge from human patterns. While persona injection successfully steers self-reports in the intended direction, it exerts little or inconsistent effect on actual behavior. By distinguishing surface-level trait expression from behavioral consistency, our findings challenge assumptions about LLM personality and underscore the need for deeper evaluation in alignment and interpretability.

cs.AI↗

arXiv2025

Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems.

cs.LG↗

arXiv2025

Geometric Operator Learning with Optimal Transport

We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our approach generalizes discretized meshes to mesh density functions, formulating geometry embedding as an OT problem that maps these functions to a uniform density in a reference space. Compared to previous methods relying on interpolation or shared deformation, our OT-based method employs instance-dependent deformation, offering enhanced flexibility and effectiveness. For 3D simulations focused on surfaces, our OT-based neural operator embeds the surface geometry into a 2D parameterized latent space. By performing computations directly on this 2D representation of the surface manifold, it achieves significant computational efficiency gains compared to volumetric simulation. Experiments with Reynolds-averaged Navier-Stokes equations (RANS) on the ShapeNet-Car and DrivAerNet-Car datasets show that our method achieves better accuracy and also reduces computational expenses in terms of both time and memory usage compared to existing machine learning models. Additionally, our model demonstrates significantly improved accuracy on the FlowBench dataset, underscoring the benefits of employing instance-dependent deformation for datasets with highly variable geometries.

cs.LG↗

arXiv2025

Scale-Consistent Learning for Partial Differential Equations

Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot generalize outside the training data; for example, a trained ML model for the Navier-Stokes equations only works for a fixed Reynolds number ($Re$) on a pre-defined domain. To overcome these limitations, we propose a data augmentation scheme based on scale-consistency properties of PDEs and design a scale-informed neural operator that can model a wide range of scales. Our formulation leverages the facts: (i) PDEs can be rescaled, or more concretely, a given domain can be re-scaled to unit size, and the parameters and the boundary conditions of the PDE can be appropriately adjusted to represent the original solution, and (ii) the solution operators on a given domain are consistent on the sub-domains. We leverage these facts to create a scale-consistency loss that encourages matching the solutions evaluated on a given domain and the solution obtained on its sub-domain from the rescaled PDE. Since neural operators can fit to multiple scales and resolutions, they are the natural choice for incorporating scale-consistency loss during training of neural PDE solvers. We experiment with scale-consistency loss and the scale-informed neural operator model on the Burgers' equation, Darcy Flow, Helmholtz equation, and Navier-Stokes equations. With scale-consistency, the model trained on $Re$ of 1000 can generalize to $Re$ ranging from 250 to 10000, and reduces the error by 34% on average of all datasets compared to baselines.

cs.LG↗

arXiv2025

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

cs.LG↗

arXiv2025

FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale

FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting. The approach is designed to respect spherical geometry and to accurately model the spatially correlated probabilistic nature of the problem, resulting in stable spectra and realistic dynamics across multiple scales. FourCastNet 3 delivers forecasting accuracy that surpasses leading conventional ensemble models and rivals the best diffusion-based methods, while producing forecasts 8 to 60 times faster than these approaches. In contrast to other ML approaches, FourCastNet 3 demonstrates excellent probabilistic calibration and retains realistic spectra, even at extended lead times of up to 60 days. All of these advances are realized using a purely convolutional neural network architecture tailored for spherical geometry. Scalable and efficient large-scale training on 1024 GPUs and more is enabled by a novel training paradigm for combined model- and data-parallelism, inspired by domain decomposition methods in classical numerical models. Additionally, FourCastNet 3 enables rapid inference on a single GPU, producing a 60-day global forecast at 0.25°, 6-hourly resolution in under 4 minutes. Its computational efficiency, medium-range probabilistic skill, spectral fidelity, and rollout stability at subseasonal timescales make it a strong candidate for improving meteorological forecasting and early warning systems through large ensemble predictions.

cs.LG↗

arXiv2025

Robust Representation Consistency Model via Contrastive Denoising

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85$\times$ on average. Codes are available at: https://github.com/jiachenlei/rRCM.

cs.CV↗

arXiv2025

High precision PINNs in unbounded domains: application to singularity formulation in PDEs

We investigate the high-precision training of Physics-Informed Neural Networks (PINNs) in unbounded domains, with a special focus on applications to singularity formulation in PDEs. We propose a modularized approach and study the choices of neural network ansatz, sampling strategy, and optimization algorithm. When combined with rigorous computer-assisted proofs and PDE analysis, the numerical solutions identified by PINNs, provided they are of high precision, can serve as a powerful tool for studying singularities in PDEs. For 1D Burgers equation, our framework can lead to a solution with very high precision, and for the 2D Boussinesq equation, which is directly related to the singularity formulation in 3D Euler and Navier-Stokes equations, we obtain a solution whose loss is $4$ digits smaller than that obtained in \cite{wang2023asymptotic} with fewer training steps. We also discuss potential directions for pushing towards machine precision for higher-dimensional problems.

cs.LG↗

arXiv2025

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

cs.LG↗

arXiv2025

Easy2Hard-Bench: Standardized Difficulty Labels for Profiling LLM Performance and Generalization

While generalization over tasks from easy to hard is crucial to profile language models (LLMs), the datasets with fine-grained difficulty annotations for each problem across a broad range of complexity are still blank. Aiming to address this limitation, we present Easy2Hard-Bench, a consistently formatted collection of 6 benchmark datasets spanning various domains, such as mathematics and programming problems, chess puzzles, and reasoning questions. Each problem within these datasets is annotated with numerical difficulty scores. To systematically estimate problem difficulties, we collect abundant performance data on attempts to each problem by humans in the real world or LLMs on the prominent leaderboard. Leveraging the rich performance data, we apply well-established difficulty ranking systems, such as Item Response Theory (IRT) and Glicko-2 models, to uniformly assign numerical difficulty scores to problems. Moreover, datasets in Easy2Hard-Bench distinguish themselves from previous collections by a higher proportion of challenging problems. Through extensive experiments with six state-of-the-art LLMs, we provide a comprehensive analysis of their performance and generalization capabilities across varying levels of difficulty, with the aim of inspiring future research in LLM generalization. The datasets are available at https://huggingface.co/datasets/furonghuang-lab/Easy2Hard-Bench.

cs.LG↗

arXiv2025

TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training

Scientific problems require resolving multi-scale phenomena across different resolutions and learning solution operators in infinite-dimensional function spaces. Neural operators provide a powerful framework for this, using tensor-parameterized layers to capture complex, multi-dimensional relationships. However, scaling neural operators to high-resolution problems leads to significant computational demands, making the training of industrial-scale models prohibitive. In this work, we introduce \textbf{TensorGRaD}, a novel method that directly addresses the memory challenges associated with optimizing large tensor-structured weights. Our approach, based on a \texit{robust tensor decomposition}, factorizes gradients as the sum of a low-rank tensor and a sparse one to efficiently capture information within optimizer states, including outliers. Additionally, we provide a recipe for mixed precision training of TensorGRaD, achieving further memory savings without sacrificing accuracy. We showcase the effectiveness of TensorGRaD on Fourier Neural Operators, a class of models crucial for solving partial differential equations (PDE). We provide theoretical guarantees for TensorGRaD, demonstrating its fundamental advantage over matrix-based gradient compression methods. We empirically demonstrate large improvements across various PDE tasks, including the challenging turbulent Navier-Stokes case at a Reynolds number of $10^5$. TensorGRaD reduces total memory usage by over $50\%$ while maintaining and sometimes even improving accuracy.

cs.LG↗

arXiv2025

Lean Copilot: Large Language Models as Copilots for Theorem Proving in Lean

Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers pretrained on a fixed collection of data and offering valuable suggestions at times, it is challenging for them to continually prove novel theorems in a fully autonomous mode, where human insights may be critical. In this paper, we explore LLMs as copilots that assist humans in proving theorems. We introduce Lean Copilot, a general framework for running LLM inference natively in Lean. It enables programmers to build various LLM-based proof automation tools that integrate seamlessly into the workflow of Lean users. Lean users can use our pretrained models or bring their own ones that run either locally (with or without GPUs) or on the cloud. Using Lean Copilot, we build LLM-based tools that suggest proof steps, complete proof goals, and select relevant premises. Experimental results on the Mathematics in Lean textbook demonstrate the effectiveness of our method compared to existing rule-based proof automation in Lean (aesop). When assisting humans, Lean Copilot requires only 2.08 manually-entered proof steps on average (3.86 required by aesop); when automating the theorem proving process, Lean Copilot automates 74.2% proof steps on average, 85% better than aesop (40.1%). We open source all code and artifacts under a permissive MIT license to facilitate further research.

cs.AI↗

arXiv2025

HiPerRAG: High-Performance Retrieval Augmented Generation for Scientific Insights

The volume of scientific literature is growing exponentially, leading to underutilized discoveries, duplicated efforts, and limited cross-disciplinary collaboration. Retrieval Augmented Generation (RAG) offers a way to assist scientists by improving the factuality of Large Language Models (LLMs) in processing this influx of information. However, scaling RAG to handle millions of articles introduces significant challenges, including the high computational costs associated with parsing documents and embedding scientific knowledge, as well as the algorithmic complexity of aligning these representations with the nuanced semantics of scientific content. To address these issues, we introduce HiPerRAG, a RAG workflow powered by high performance computing (HPC) to index and retrieve knowledge from more than 3.6 million scientific articles. At its core are Oreo, a high-throughput model for multimodal document parsing, and ColTrast, a query-aware encoder fine-tuning algorithm that enhances retrieval accuracy by using contrastive learning and late-interaction techniques. HiPerRAG delivers robust performance on existing scientific question answering benchmarks and two new benchmarks introduced in this work, achieving 90% accuracy on SciQ and 76% on PubMedQA-outperforming both domain-specific models like PubMedGPT and commercial LLMs such as GPT-4. Scaling to thousands of GPUs on the Polaris, Sunspot, and Frontier supercomputers, HiPerRAG delivers million document-scale RAG workflows for unifying scientific knowledge and fostering interdisciplinary innovation.

cs.IR↗