NeurIPS 2024 Papers

Solving a polynomial system, or computing an associated Gröbner basis, has been a fundamental task in computational algebra. However, it is also known for its notorious doubly exponential time complexity in the number of variables in the worst case. This paper is the first to address the learning of Gröbner basis computation with Transformers. The training requires many pairs of a polynomial system and the associated Gröbner basis, raising two novel algebraic problems: random generation of Gröbner bases and transforming them into non-Gröbner ones, termed as backward Gröbner problem. We resolve these problems with 0-dimensional radical ideals, the ideals appearing in various applications. Further, we propose a hybrid input embedding to handle coefficient tokens with continuity bias and avoid the growth of the vocabulary set. The experiments show that our dataset generation method is a few orders of magnitude faster than a naive approach, overcoming a crucial challenge in learning to compute Gröbner bases, and Gröbner computation is learnable in a particular class.

Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient’s anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.

Top-2 methods have become popular in solving the best arm identification (BAI) problem. The best arm, or the arm with the largest mean amongst finitely many, is identified through an algorithm that at any sequential step independently pulls the empirical best arm, with a fixed probability $\beta$, and pulls the best challenger arm otherwise. The probability of incorrect selection is guaranteed to lie below a specified $\delta>0$. Information theoretic lower bounds on sample complexity are well known for BAI problem and are matched asymptotically as $\delta\to 0$ by computationally demanding plug-in methods. The above top 2 algorithm for any $\beta\in(0, 1)$ has sample complexity within a constant of the lower bound. However, determining the optimal β that matches the lower bound has proven difficult. In this paper, we address this and propose an optimal top-2 type algorithm. We consider a function of allocations anchored at a threshold. If it exceeds the threshold then the algorithm samples the empirical best arm. Otherwise, it samples the challenger arm. We show that the proposed algorithm is optimal as $\delta\to 0$. Our analysis relies on identifying a limiting fluid dynamics of allocations that satisfy a series of ordinary differential equations pasted together and that describe the asymptotic path followed by our algorithm. We rely on the implicit function theorem to show existence and uniqueness of these fluid ode’s and to show that the proposed algorithm remains close to the ode solution.

Scaling has been a critical factor in improving model performance and generalization across various fields of machine learning. It involves how a model’s performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in scaling other types of machine learning models, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations, predicting the energy and forces between atoms in molecules and materials based on atomic configurations. The dominant paradigm in this field is to incorporate numerous physical domain constraints into the model, such as symmetry constraints like rotational equivariance. We contend that these increasingly complex domain constraints inhibit the scaling ability of NNIPs, and such strategies are likely to cause model performance to plateau in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling properties and strategies. Our findings indicate that scaling the model through attention mechanisms is both efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a novel multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency---at least 10x speed up in inference time, 5x less in memory usage---compared to existing NNIP models. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). After training EScAIP, we test its ability to learn rotational equivariance by predicting forces on new, unseen atomistic systems before and after rotation. The model's force predictions exactly match the rotated forces, suggesting that it has precisely learned rotational equivariance. Finally, we emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept towards developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

Pedestrian trajectory prediction is crucial for several applications such as robotics and self-driving vehicles. Significant progress has been made in the past decade thanks to the availability of pedestrian trajectory datasets, which enable trajectory prediction methods to learn from pedestrians' past movements and predict future trajectories. However, these datasets and methods typically assume that the observed trajectory sequence is complete, ignoring real-world issues such as sensor failure, occlusion, and limited fields of view that can result in missing values in observed trajectories. To address this challenge, we present TrajImpute, a pedestrian trajectory prediction dataset that simulates missing coordinates in the observed trajectory, enhancing real-world applicability. TrajImpute maintains a uniform distribution of missing data within the observed trajectories. In this work, we comprehensively examine several imputation methods to reconstruct the missing coordinates and benchmark them for imputing pedestrian trajectories. Furthermore, we provide a thorough analysis of recent trajectory prediction methods and evaluate the performance of these models on the imputed trajectories. Our experimental evaluation of the imputation and trajectory prediction methods offers several valuable insights. Our dataset provides a foundational resource for future research on imputation-aware pedestrian trajectory prediction, potentially accelerating the deployment of these methods in real-world applications. Publicly accessible links to the datasets and code files are available at https://github.com/Pranav-chib/TrajImpute.

Diffusion models (DMs) have recently shown outstanding capabilities in modeling complex image distributions, making them expressive image priors for solving Bayesian inverse problems. However, most existing DM-based methods rely on approximations in the generative process to be generic to different inverse problems, leading to inaccurate sample distributions that deviate from the target posterior defined within the Bayesian framework. To harness the generative power of DMs while avoiding such approximations, we propose a Markov chain Monte Carlo algorithm that performs posterior sampling for general inverse problems by reducing it to sampling the posterior of a Gaussian denoising problem. Crucially, we leverage a general DM formulation as a unified interface that allows for rigorously solving the denoising problem with a range of state-of-the-art DMs. We demonstrate the effectiveness of the proposed method on six inverse problems (three linear and three nonlinear), including a real-world black hole imaging problem. Experimental results indicate that our proposed method offers more accurate reconstructions and posterior estimation compared to existing DM-based imaging inverse methods.

Follow-the-Regularized-Leader (FTRL) is a powerful framework for various online learning problems. By designing its regularizer and learning rate to be adaptive to past observations, FTRL is known to work adaptively to various properties of an underlying environment. However, most existing adaptive learning rates are for online learning problems with a minimax regret of $\Theta(\sqrt{T})$ for the number of rounds $T$, and there are only a few studies on adaptive learning rates for problems with a minimax regret of $\Theta(T^{2/3})$, which include several important problems dealing with indirect feedback. To address this limitation, we establish a new adaptive learning rate framework for problems with a minimax regret of $\Theta(T^{2/3})$. Our learning rate is designed by matching the stability, penalty, and bias terms that naturally appear in regret upper bounds for problems with a minimax regret of $\Theta(T^{2/3})$. As applications of this framework, we consider three major problems with a minimax regret of $\Theta(T^{2/3})$: partial monitoring, graph bandits, and multi-armed bandits with paid observations. We show that FTRL with our learning rate and the Tsallis entropy regularizer improves existing Best-of-Both-Worlds (BOBW) regret upper bounds, which achieve simultaneous optimality in the stochastic and adversarial regimes. The resulting learning rate is surprisingly simple compared to the existing learning rates for BOBW algorithms for problems with a minimax regret of $\Theta(T^{2/3})$.

We present an optimal method for encoding cluster assignments of arbitrary data sets. Our method, Random Cycle Coding (RCC), encodes data sequentially and sends assignment information as cycles of the permutation defined by the order of encoded elements. RCC does not require any training and its worst-case complexity scales quasi-linearly with the size of the largest cluster. We characterize the achievable bit rates as a function of cluster sizes and number of elements, showing RCC consistently outperforms previous methods while requiring less compute and memory resources. Experiments show RCC can save up to $2$ bytes per element when applied to vector databases, and removes the need for assigning integer ids to identify vectors, translating to savings of up to $70\%$ in vector database systems for similarity search applications.

Multimodal Sentiment Analysis (MSA) is an important research area that aims to understand and recognize human sentiment through multiple modalities. The complementary information provided by multimodal fusion promotes better sentiment analysis compared to utilizing only a single modality. Nevertheless, in real-world applications, many unavoidable factors may lead to situations of uncertain modality missing, thus hindering the effectiveness of multimodal modeling and degrading the model’s performance. To this end, we propose a Hierarchical Representation Learning Framework (HRLF) for the MSA task under uncertain missing modalities. Specifically, we propose a fine-grained representation factorization module that sufficiently extracts valuable sentiment information by factorizing modality into sentiment-relevant and modality-specific representations through crossmodal translation and sentiment semantic reconstruction. Moreover, a hierarchical mutual information maximization mechanism is introduced to incrementally maximize the mutual information between multi-scale representations to align and reconstruct the high-level semantics in the representations. Ultimately, we propose a hierarchical adversarial learning mechanism that further aligns and adapts the latent distribution of sentiment-relevant representations to produce robust joint multimodal representations. Comprehensive experiments on three datasets demonstrate that HRLF significantly improves MSA performance under uncertain modality missing cases.

Recent advancements in visualizing deep neural networks provide insights into their structures and mesh extraction from Continuous Piecewise Affine (CPWA) functions. Meanwhile, developments in neural surface representation learning incorporate non-linear positional encoding, addressing issues like spectral bias; however, this poses challenges in applying mesh extraction techniques based on CPWA functions. Focusing on trilinear interpolating methods as positional encoding, we present theoretical insights and an analytical mesh extraction, showing the transformation of hypersurfaces to flat planes within the trilinear region under the eikonal constraint. Moreover, we introduce a method for approximating intersecting points among three hypersurfaces contributing to broader applications. We empirically validate correctness and parsimony through chamfer distance and efficiency, and angular distance, while examining the correlation between the eikonal loss and the planarity of the hypersurfaces.

Large language models (LLMs) have demonstrated remarkable capabilities in language understanding and generation, leading to their widespread adoption across various fields. Among these, the medical field is particularly well-suited for LLM applications, as many medical tasks can be enhanced by LLMs. Despite the existence of benchmarks for evaluating LLMs in medical question-answering and exams, there remains a notable gap in assessing LLMs' performance in supporting patients throughout their entire hospital visit journey in real-world clinical practice. In this paper, we address this gap by dividing a typical patient's clinical journey into four stages: planning, access, delivery and ongoing care. For each stage, we introduce multiple tasks and corresponding datasets, resulting in a comprehensive benchmark comprising 12 datasets, of which five are newly introduced, and seven are constructed from existing datasets. This proposed benchmark facilitates a thorough evaluation of LLMs' effectiveness across the entire patient journey, providing insights into their practical application in clinical settings. Additionally, we evaluate three categories of LLMs against this benchmark: 1) proprietary LLM services such as GPT-4; 2) public LLMs like QWen; and 3) specialized medical LLMs, like HuatuoGPT2. Through this extensive evaluation, we aim to provide a better understanding of LLMs' performance in the medical domain, ultimately contributing to their more effective deployment in healthcare settings.

Processing multidomain data defined on multiple graphs holds significant potential in various practical applications in computer science. However, current methods are mostly limited to discrete graph filtering operations. Tensorial partial differential equations on graphs (TPDEGs) provide a principled framework for modeling structured data across multiple interacting graphs, addressing the limitations of the existing discrete methodologies. In this paper, we introduce Continuous Product Graph Neural Networks (CITRUS) that emerge as a natural solution to the TPDEG. CITRUS leverages the separability of continuous heat kernels from Cartesian graph products to efficiently implement graph spectral decomposition. We conduct thorough theoretical analyses of the stability and over-smoothing properties of CITRUS in response to domain-specific graph perturbations and graph spectra effects on the performance. We evaluate CITRUS on well-known traffic and weather spatiotemporal forecasting datasets, demonstrating superior performance over existing approaches. The implementation codes are available at https://github.com/ArefEinizade2/CITRUS.

Extracting scientific understanding from particle-physics experiments requires solving diverse learning problems with high precision and good data efficiency. We propose the Lorentz Geometric Algebra Transformer (L-GATr), a new multi-purpose architecture for high-energy physics. L-GATr represents high-energy data in a geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, the symmetry group of relativistic kinematics. At the same time, the architecture is a Transformer, which makes it versatile and scalable to large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics. We then construct the first Lorentz-equivariant generative model: a continuous normalizing flow based on an L-GATr network, trained with Riemannian flow matching. Across our experiments, L-GATr is on par with or outperforms strong domain-specific baselines.

Solar power is a critical source of renewable energy, offering significant potential to lower greenhouse gas emissions and mitigate climate change. However, the cloud induced-variability of solar radiation reaching the earth’s surface presents a challenge for integrating solar power into the grid (e.g., storage and backup management). The new generation of geostationary satellites such as GOES-16 has become an important data source for large-scale and high temporal frequency solar radiation forecasting. However, no machine-learning-ready dataset has integrated geostationary satellite data with fine-grained solar radiation information to support forecasting model development and benchmarking with consistent metrics. We present SolarCube, a new ML-ready benchmark dataset for solar radiation forecasting. SolarCube covers 19 study areas distributed over multiple continents: North America, South America, Asia, and Oceania. The dataset supports short (i.e., 30 minutes to 6 hours) and long-term (i.e., day-ahead or longer) solar radiation forecasting at both point-level (i.e., specific locations of monitoring stations) and area-level, by processing and integrating data from multiple sources, including geostationary satellite images, physics-derived solar radiation, and ground station observations from different monitoring networks over the globe. We also evaluated a set of forecasting models for point- and image-based time-series data to develop performance benchmarks under different testing scenarios. The dataset is available at https://doi.org/10.5281/zenodo.11498739. A Python library is available to conveniently generate different variations of the dataset based on user needs, along with baseline models at https://github.com/Ruohan-Li/SolarCube.

This paper presents a new open-source high-fidelity dataset for Machine Learning (ML) containing 355 geometric variants of the Windsor body, to help the development and testing of ML surrogate models for external automotive aerodynamics. Each Computational Fluid Dynamics (CFD) simulation was run with a GPU-native high-fidelity Wall-Modeled Large-Eddy Simulations (WMLES) using a Cartesian immersed-boundary method using more than 280M cells to ensure the greatest possible accuracy. The dataset contains geometry variants that exhibits a wide range of flow characteristics that are representative of those observed on road-cars. The dataset itself contains the 3D time-averaged volume \& boundary data as well as the geometry and force \& moment coefficients. This paper discusses the validation of the underlying CFD methods as well as contents and structure of the dataset. To the authors knowledge, this represents the first, large-scale high-fidelity CFD dataset for the Windsor body with a permissive open-source license (CC-BY-SA).

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning to high-stakes applications such as medical imaging and weather forecasting. Conditional diffusion models' breakthrough ability to accurately and efficiently sample from the posterior distribution of a dataset now makes uncertainty estimation conceptually straightforward: One need only train and sample from a large ensemble of diffusion models. Unfortunately, training such an ensemble becomes computationally intractable as the complexity of the model architecture grows. In this work we introduce a new approach to ensembling, hyper-diffusion models (HyperDM), which allows one to accurately estimate both epistemic and aleatoric uncertainty with a single model. Unlike existing single-model uncertainty methods like Monte-Carlo dropout and Bayesian neural networks, HyperDM offers prediction accuracy on par with, and in some cases superior to, multi-model ensembles. Furthermore, our proposed approach scales to modern network architectures such as Attention U-Net and yields more accurate uncertainty estimates compared to existing methods. We validate our method on two distinct real-world tasks: x-ray computed tomography reconstruction and weather temperature forecasting.

3D particle tracking velocimetry (PTV) is a key technique for analyzing turbulent flow, one of the most challenging computational problems of our century. At the core of 3D PTV is the dual-frame fluid motion estimation algorithm, which tracks particles across two consecutive frames. Recently, deep learning-based methods have achieved impressive accuracy in dual-frame fluid motion estimation; however, they heavily depend on large volumes of labeled data. In this paper, we introduce a new method that is **completely self-supervised and notably outperforms its fully-supervised counterparts while requiring only 1\% of the training samples (without labels) used by previous methods.** Our method features a novel zero-divergence loss that is specific to the domain of turbulent flow. Inspired by the success of splat operation in high-dimensional filtering and random fields, we propose a splat-based implementation for this loss which is both efficient and effective. The self-supervised nature of our method naturally supports test-time optimization, leading to the development of a tailored Dynamic Velocimetry Enhancer (DVE) module. We demonstrate that strong cross-domain robustness is achieved through test-time optimization on unseen leave-one-out synthetic domains and real physical/biological domains. Code, data and models are available at [https://github.com/Forrest-110/FluidMotionNet](https://github.com/Forrest-110/FluidMotionNet).

We introduce Annealed Multiple Choice Learning (aMCL) which combines simulated annealing with MCL. MCL is a learning framework handling ambiguous tasks by predicting a small set of plausible hypotheses. These hypotheses are trained using the Winner-takes-all (WTA) scheme, which promotes the diversity of the predictions. However, this scheme may converge toward an arbitrarily suboptimal local minimum, due to the greedy nature of WTA. We overcome this limitation using annealing, which enhances the exploration of the hypothesis space during training. We leverage insights from statistical physics and information theory to provide a detailed description of the model training trajectory. Additionally, we validate our algorithm by extensive experiments on synthetic datasets, on the standard UCI benchmark, and on speech separation.

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a derivative-enhanced deep operator network (DE-DeepONet), which leverages derivative information to enhance the solution prediction accuracy and provides a more accurate approximation of solution-to-parameter derivatives, especially when training data are limited. DE-DeepONet explicitly incorporates linear dimension reduction of high dimensional parameter input into DeepONet to reduce training cost and adds derivative loss in the loss function to reduce the number of required parameter-solution pairs. We further demonstrate that the use of derivative loss can be extended to enhance other neural operators, such as the Fourier neural operator (FNO). Numerical experiments validate the effectiveness of our approach.