Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of Order Oracle, which only utilizes order access between function values (possibly with some bounded noise), but without assuming access to their values. As theoretical results, we propose a new approach to create non-accelerated optimization algorithms (obtained by integrating Order Oracle into existing optimization “tools”) in non-convex, convex, and strongly convex settings that are as good as both SOTA coordinate algorithms with first-order oracle and SOTA algorithms with Order Oracle up to logarithm factor. Moreover, using the proposed approach, _we provide the first accelerated optimization algorithm using the Order Oracle_. And also, using an already different approach we provide the asymptotic convergence of _the first algorithm with the stochastic Order Oracle concept_. Finally, our theoretical results demonstrate effectiveness of proposed algorithms through numerical experiments.
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Generative Models
Over the several recent years, there has been a boom in development of Flow Matching (FM) methods for generative modeling. One intriguing property pursued by the community is the ability to learn flows with straight trajectories which realize the Optimal Transport (OT) displacements. Straightness is crucial for the fast integration (inference) of the learned flow's paths. Unfortunately, most existing flow straightening methods are based on non-trivial iterative FM procedures which accumulate the error during training or exploit heuristics based on minibatch OT. To address these issues, we develop and theoretically justify the novel Optimal Flow Matching approach which allows recovering the straight OT displacement for the quadratic transport in just one FM step. The main idea of our approach is the employment of vector field for FM which are parameterized by convex functions. The code of our OFM implementation and the conducted experiments is available at https://github.com/Jhomanik/Optimal-Flow-Matching
Computer Vision
Rendering and reconstruction are long-standing topics in computer vision and graphics. Achieving both high rendering quality and accurate geometry is a challenge. Recent advancements in 3D Gaussian Splatting (3DGS) have enabled high-fidelity novel view synthesis at real-time speeds. However, the noisy and discrete nature of 3D Gaussian primitives hinders accurate surface estimation. Previous attempts to regularize 3D Gaussian normals often degrade rendering quality due to the fundamental disconnect between normal vectors and the rendering pipeline in 3DGS-based methods. Therefore, we introduce Normal-GS, a novel approach that integrates normal vectors into the 3DGS rendering pipeline. The core idea is to model the interaction between normals and incident lighting using the physically-based rendering equation. Our approach re-parameterizes surface colors as the product of normals and a designed Integrated Directional Illumination Vector (IDIV). To optimize memory usage and simplify optimization, we employ an anchor-based 3DGS to implicitly encode locally-shared IDIVs. Additionally, Normal-GS leverages optimized normals and Integrated Directional Encoding (IDE) to accurately model specular effects, enhancing both rendering quality and surface normal precision. Extensive experiments demonstrate that Normal-GS achieves near state-of-the-art visual quality while obtaining accurate surface normals and preserving real-time rendering performance.
Physical Models · Climate
Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation and video prediction. Modern techniques for the solution of these problems typically combine Convolution Neural Networks (CNN) architecture with a time prediction mechanism. However, oftentimes, such approaches underperform in the long-range propagation of information and lack explainability. In this work, we introduce a physically inspired architecture for the solution of such problems. Namely, we propose to augment CNNs with advection by designing a novel semi-Lagrangian push operator. We show that the proposed operator allows for the non-local transformation of information compared with standard convolutional kernels. We then complement it with Reaction and Diffusion neural components to form a network that mimics the Reaction-Advection-Diffusion equation, in high dimensions. We demonstrate the effectiveness of our network on a number of spatio-temporal datasets that show their merit. Our code is available at https://github.com/Siddharth-Rout/deepADRnet.
Physical Models · Physics
Learning complex physical dynamics purely from data is challenging due to the intrinsic properties of systems to be satisfied. Incorporating physics-informed priors, such as in Hamiltonian Neural Networks (HNNs), achieves high-precision modeling for energy-conservative systems. However, real-world systems often deviate from strict energy conservation and follow different physical priors. To address this, we present a framework that achieves high-precision modeling for a wide range of dynamical systems from the numerical aspect, by enforcing Time-Reversal Symmetry (TRS) via a novel regularization term. It helps preserve energies for conservative systems while serving as a strong inductive bias for non-conservative, reversible systems. While TRS is a domain-specific physical prior, we present the first theoretical proof that TRS loss can universally improve modeling accuracy by minimizing higher-order Taylor terms in ODE integration, which is numerically beneficial to various systems regardless of their properties, even for irreversible systems. By integrating the TRS loss within neural ordinary differential equation models, the proposed model TREAT demonstrates superior performance on diverse physical systems. It achieves a significant 11.5% MSE improvement in a challenging chaotic triple-pendulum scenario, underscoring TREAT’s broad applicability and effectiveness.
Optimization · Convex
Global polynomial optimization is an important tool across applied mathematics, with many applications in operations research, engineering, and the physical sciences. In various settings, the polynomials depend on external parameters that may be random. We discuss a stochastic sum-of-squares (S-SOS) algorithm based on the sum-of-squares hierarchy that constructs a series of semidefinite programs to jointly find strict lower bounds on the global minimum and extracts candidates for parameterized global minimizers. We prove quantitative convergence of the hierarchy as the degree increases and use it to solve unconstrained and constrained polynomial optimization problems parameterized by random variables. By employing n-body priors from condensed matter physics to induce sparsity, we can use S-SOS to produce solutions and uncertainty intervals for sensor network localization problems containing up to 40 variables and semidefinite matrix sizes surpassing 800 x 800.
Physical Models · Physics
In mechanical structures like airplanes, cars and houses, noise is generated and transmitted through vibrations. To take measures to reduce this noise, vibrations need to be simulated with expensive numerical computations. Deep learning surrogate models present a promising alternative to classical numerical simulations as they can be evaluated magnitudes faster, while trading-off accuracy. To quantify such trade-offs systematically and foster the development of methods, we present a benchmark on the task of predicting the vibration of harmonically excited plates. The benchmark features a total of 12,000 plate geometries with varying forms of beadings, material, boundary conditions, load position and sizes with associated numerical solutions. To address the benchmark task, we propose a new network architecture, named \modelname, which predicts vibration patterns of plate geometries given a specific excitation frequency. Applying principles from operator learning and implicit models for shape encoding, our approach effectively addresses the prediction of highly variable frequency response functions occurring in dynamic systems. To quantify the prediction quality, we introduce a set of evaluation metrics and evaluate the method on our vibrating-plates benchmark. Our method outperforms DeepONets, Fourier Neural Operators and more traditional neural network architectures and can be used for design optimization.Code, dataset and visualizations: https://github.com/ecker-lab/Learning_Vibrating_Plates
Deep Learning · Attention Mechanisms
Despite recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling complex physical systems remains under-explored. Learning problems in physical systems are often characterized as discovering operators that map between function spaces based on a few instances of function pairs. This task frequently presents a severely ill-posed PDE inverse problem. In this work, we propose a novel neural operator architecture based on the attention mechanism, which we coin Nonlocal Attention Operator (NAO), and explore its capability towards developing a foundation physical model. In particular, we show that the attention mechanism is equivalent to a double integral operator that enables nonlocal interactions among spatial tokens, with a data-dependent kernel characterizing the inverse mapping from data to the hidden parameter field of the underlying operator. As such, the attention mechanism extracts global prior information from training data generated by multiple systems, and suggests the exploratory space in the form of a nonlinear kernel map. Consequently, NAO can address ill-posedness and rank deficiency in inverse PDE problems by encoding regularization and achieving generalizability. Lastly, we empirically demonstrate the advantages of NAO over baseline neural models in terms of the generalizability to unseen data resolutions and system states. Our work not only suggests a novel neural operator architecture for learning an interpretable foundation model of physical systems, but also offers a new perspective towards understanding the attention mechanism.
Computer Vision · Video Generation
Human image animation aims to generate a human motion video from the inputs of a reference human image and a target motion video. Current diffusion-based image animation systems exhibit high precision in transferring human identity into targeted motion, yet they still exhibit irregular quality in their outputs. Their optimal precision is achieved only when the physical compositions (i.e., scale and rotation) of the human shapes in the reference image and target pose frame are aligned. In the absence of such alignment, there is a noticeable decline in fidelity and consistency. Especially, in real-world environments, this compositional misalignment commonly occurs, posing significant challenges to the practical usage of current systems. To this end, we propose Test-time Procrustes Calibration (TPC), which enhances the robustness of diffusion-based image animation systems by maintaining optimal performance even when faced with compositional misalignment, effectively addressing real-world scenarios. The TPC provides a calibrated reference image for the diffusion model, enhancing its capability to understand the correspondence between human shapes in the reference and target images. Our method is simple and can be applied to any diffusion-based image animation system in a model-agnostic manner, improving the effectiveness at test time without additional training.
Applications
While significant advancements have been made in music generation and differentiable sound synthesis within machine learning and computer audition, the simulation of instrument vibration guided by physical laws has been underexplored. To address this gap, we introduce a novel model for simulating the spatio-temporal motion of nonlinear strings, integrating modal synthesis and spectral modeling within a neural network framework. Our model leverages mechanical properties and fundamental frequencies as inputs, outputting string states across time and space that solve the partial differential equation characterizing the nonlinear string. Empirical evaluations demonstrate that the proposed architecture achieves superior accuracy in string motion simulation compared to existing baseline architectures. The code and demo are available online.
Deep Learning · Algorithms
Tensor Train~(TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate computing the TT decomposition with the Alternating Least Squares (ALS) algorithm relying on exact leverage scores sampling. For this purpose, we propose a data structure that allows us to efficiently sample from the tensor with time complexity logarithmic in the product of the tensor dimensions. Our contribution specifically leverages the canonical form of the TT decomposition. By maintaining the canonical form through each iteration of ALS, we can efficiently compute (and sample from) the leverage scores, thus achieving significant speed-up in solving each sketched least-square problem. Experiments on synthetic and real data on dense and sparse tensors demonstrate that our method outperforms SVD-based and ALS-based algorithms.
Physical Models
We introduce multiple physics pretraining (MPP), an autoregressive task-agnostic pretraining approach for physical surrogate modeling of spatiotemporal systems with transformers. In MPP, rather than training one model on a specific physical system, we train a backbone model to predict the dynamics of multiple heterogeneous physical systems simultaneously in order to learn features that are broadly useful across systems and facilitate transfer. In order to learn effectively in this setting, we introduce a shared embedding and normalization strategy that projects the fields of multiple systems into a shared embedding space. We validate the efficacy of our approach on both pretraining and downstream tasks over a broad fluid mechanics-oriented benchmark. We show that a single MPP-pretrained transformer is able to match or outperform task-specific baselines on all pretraining sub-tasks without the need for finetuning. For downstream tasks, we demonstrate that finetuning MPP-trained models results in more accurate predictions across multiple time-steps on systems with previously unseen physical components or higher dimensional systems compared to training from scratch or finetuning pretrained video foundation models. We open-source our code and model weights trained at multiple scales for reproducibility.
Computational Biology
In the past decade, deep conditional generative models have revolutionized the generation of realistic images, extending their application from entertainment to scientific domains. Single-particle cryo-electron microscopy (cryo-EM) is crucial in resolving near-atomic resolution 3D structures of proteins, such as the SARS-COV-2 spike protein. To achieve high-resolution reconstruction, a comprehensive data processing pipeline has been adopted. However, its performance is still limited as it lacks high-quality annotated datasets for training. To address this, we introduce physics-informed generative cryo-electron microscopy (CryoGEM), which for the first time integrates physics-based cryo-EM simulation with a generative unpaired noise translation to generate physically correct synthetic cryo-EM datasets with realistic noises. Initially, CryoGEM simulates the cryo-EM imaging process based on a virtual specimen. To generate realistic noises, we leverage an unpaired noise translation via contrastive learning with a novel mask-guided sampling scheme. Extensive experiments show that CryoGEM is capable of generating authentic cryo-EM images. The generated dataset can be used as training data for particle picking and pose estimation models, eventually improving the reconstruction resolution.
Optimization · Optimization and Learning under Uncertainty
Bayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in particular, the search space of the next query may depend on previous ones. Example challenges arise in the physical sciences in the form of local movement constraints, required monotonicity in certain variables, and transitions influencing the accuracy of measurements. Altogether, such *transition constraints* necessitate a form of planning. This work extends classical Bayesian optimization via the framework of Markov Decision Processes. We iteratively solve a tractable linearization of our utility function using reinforcement learning to obtain a policy that plans ahead for the entire horizon. This is a parallel to the optimization of an *acquisition function in policy space*. The resulting policy is potentially history-dependent and non-Markovian. We showcase applications in chemical reactor optimization, informative path planning, machine calibration, and other synthetic examples.
Datasets and Benchmarks
In recent years, the input context sizes of large language models (LLMs) have increased dramatically. However, existing evaluation methods have not kept pace, failing to comprehensively assess the efficiency of models in handling long contexts. To bridge this gap, we introduce the BABILong benchmark, designed to test language models' ability to reason across facts distributed in extremely long documents. BABILong includes a diverse set of 20 reasoning tasks, including fact chaining, simple induction, deduction, counting, and handling lists/sets. These tasks are challenging on their own, and even more demanding when the required facts are scattered across long natural text. Our evaluations show that popular LLMs effectively utilize only 10-20% of the context and their performance declines sharply with increased reasoning complexity. Among alternatives to in-context reasoning, Retrieval-Augmented Generation methods achieve a modest 60% accuracy on single-fact question answering, independent of context length. Among context extension methods, the highest performance is demonstrated by recurrent memory transformers after fine-tuning, enabling the processing of lengths up to 50 million tokens. The BABILong benchmark is extendable to any length to support the evaluation of new upcoming models with increased capabilities, and we provide splits up to 10 million token lengths.
Datasets and Benchmarks
With the continuous advancement of large language models (LLMs), it is essential to create new benchmarks to evaluate their expanding capabilities and identify areas for improvement. This work focuses on multi-image reasoning, an emerging capability in state-of-the-art LLMs. We introduce ReMI, a dataset designed to assess LLMs' ability to reason with multiple images. This dataset encompasses a diverse range of tasks, spanning various reasoning domains such as math, physics, logic, code, table/chart understanding, and spatial and temporal reasoning. It also covers a broad spectrum of characteristics found in multi-image reasoning scenarios. We have benchmarked several cutting-edge LLMs using ReMI and found a substantial gap between their performance and human-level proficiency. This highlights the challenges in multi-image reasoning and the need for further research. Our analysis also reveals the strengths and weaknesses of different models, shedding light on the types of reasoning that are currently attainable and areas where future models require improvement. We anticipate that ReMI will be a valuable resource for developing and evaluating more sophisticated LLMs capable of handling real-world multi-image understanding tasks.
Applications
Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications.Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training.This work presents a new dataset and benchmark called $\nabla^2$DFT that is based on the nablaDFT.It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models.The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object.All calculations were performed at the DFT level ($\omega$B97X-D/def2-SVP) for each conformation. Moreover, $\nabla^2$DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.
Generative Models · Reasoning
Large Language Models (LLMs) have demonstrated impressive capabilities across a range of scientific tasks including mathematics, physics, and chemistry. Despite their successes, the effectiveness of LLMs in handling complex statistical tasks remains systematically under-explored. To bridge this gap, we introduce StatQA, a new benchmark designed for statistical analysis tasks. StatQA comprises 11,623 examples tailored to evaluate LLMs' proficiency in specialized statistical tasks and their applicability assessment capabilities, particularly for hypothesis testing methods. We systematically experiment with representative LLMs using various prompting strategies and show that even state-of-the-art models such as GPT-4o achieve a best performance of only 64.83%, indicating significant room for improvement. Notably, while open-source LLMs (e.g. LLaMA-3) show limited capability, those fine-tuned ones exhibit marked improvements, outperforming all in-context learning-based methods (e.g. GPT-4o). Moreover, our comparative human experiments highlight a striking contrast in error types between LLMs and humans: LLMs primarily make applicability errors, whereas humans mostly make statistical task confusion errors. This divergence highlights distinct areas of proficiency and deficiency, suggesting that combining LLM and human expertise could lead to complementary strengths, inviting further investigation into their collaborative potential. Our source code and data are available at https://statqa.github.io/.
Reinforcement Learning · Deep RL
Inspired by the diversity and depth of XLand and the simplicity and minimalism of MiniGrid, we present XLand-MiniGrid, a suite of tools and grid-world environments for meta-reinforcement learning research. Written in JAX, XLand-MiniGrid is designed to be highly scalable and can potentially run on GPU or TPU accelerators, democratizing large-scale experimentation with limited resources. Along with the environments, XLand-MiniGrid provides pre-sampled benchmarks with millions of unique tasks of varying difficulty and easy-to-use baselines that allow users to quickly start training adaptive agents. In addition, we have conducted a preliminary analysis of scaling and generalization, showing that our baselines are capable of reaching millions of steps per second during training and validating that the proposed benchmarks are challenging. XLand-MiniGrid is open-source and available at \url{https://github.com/corl-team/xland-minigrid}.
Datasets and Benchmarks
Binary code is pervasive, and binary analysis is a key task in reverse engineering, malware classification, and vulnerability discovery. Unfortunately, while there exist large corpuses of malicious binaries, obtaining high-quality corpuses of benign binaries for modern systems has proven challenging (e.g., due to licensing issues). Consequently, machine learning based pipelines for binary analysis utilize either costly commercial corpuses (e.g., VirusTotal) or open-source binaries (e.g., coreutils) available in limited quantities. To address these issues, we present Assemblage: an extensible cloud-based distributed system that crawls, configures, and builds Windows PE binaries to obtain high-quality binary corpuses suitable for training state-of-the-art models in binary analysis. We have run Assemblage on AWS over the past year, producing 890k Windows PE and 428k Linux ELF binaries across 29 configurations. Assemblage is designed to be both reproducible and extensible, enabling users to publish "recipes" for their datasets, and facilitating the extraction of a wide array of features. We evaluated Assemblage by using its data to train modern learning-based pipelines for compiler provenance and binary function similarity. Our results illustrate the practical need for robust corpuses of high-quality Windows PE binaries in training modern learning-based binary analyses.