NeurIPS 2024 Papers

Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works have focused on NODEs in concise forms, while numerous physical systems taking straightforward forms in fact belong to their more complex quasi-classes, thus appealing to a class of general NODEs with high scalability and flexibility to model those systems. This however may result in intricate nonlinear properties. In this paper, we introduce ControlSynth Neural ODEs (CSODEs). We show that despite their highly nonlinear nature, convergence can be guaranteed via tractable linear inequalities. In the composition of CSODEs, we introduce an extra control term for learning the potential simultaneous capture of dynamics at different scales, which could be particularly useful for partial differential equation-formulated systems. Finally, we compare several representative NNs with CSODEs on important physical dynamics under the inductive biases of CSODEs, and illustrate that CSODEs have better learning and predictive abilities in these settings.

Solving large-scale sparse linear systems is essential in fields like mathematics, science, and engineering. Traditional numerical solvers, mainly based on the Krylov subspace iteration algorithm, suffer from the low-efficiency problem, which primarily arises from the less-than-ideal iteration. To tackle this problem, we propose a novel method, namely **Neur**al **K**rylov **It**era**t**ion (**NeurKItt**), for accelerating linear system solving. Specifically, NeurKItt employs a neural operator to predict the invariant subspace of the linear system and then leverages the predicted subspace to accelerate linear system solving. To enhance the subspace prediction accuracy, we utilize QR decomposition for the neural operator outputs and introduce a novel projection loss function for training. NeurKItt benefits the solving by using the predicted subspace to guide the iteration process, significantly reducing the number of iterations. We provide extensive experiments and comprehensive theoretical analyses to demonstrate the feasibility and efficiency of NeurKItt. In our main experiments, NeurKItt accelerates the solving of linear systems across various settings and datasets, achieving up to a 5.5× speedup in computation time and a 16.1× speedup in the number of iterations.

Molecule inverse folding has been a long-standing challenge in chemistry and biology, with the potential to revolutionize drug discovery and material science. Despite specified models have been proposed for different small- or macro-molecules, few have attempted to unify the learning process, resulting in redundant efforts. Complementary to recent advancements in molecular structure prediction, such as RoseTTAFold All-Atom and AlphaFold3, we propose the unified model UniIF for the inverse folding of all molecules. We do such unification in two levels: 1) Data-Level: We propose a unified block graph data form for all molecules, including the local frame building and geometric feature initialization. 2) Model-Level: We introduce a geometric block attention network, comprising a geometric interaction, interactive attention and virtual long-term dependency modules, to capture the 3D interactions of all molecules. Through comprehensive evaluations across various tasks such as protein design, RNA design, and material design, we demonstrate that our proposed method surpasses state-of-the-art methods on all tasks. UniIF offers a versatile and effective solution for general molecule inverse folding.

Macroscopic observables of a system are of keen interest in real applications such as the design of novel materials. Current methods rely on microscopic trajectory simulations, where the forces on all microscopic coordinates need to be computed or measured. However, this can be computationally prohibitive for realistic systems. In this paper, we propose a method to learn macroscopic dynamics requiring only force computations on a subset of the microscopic coordinates. Our method relies on a sparsity assumption: the force on each microscopic coordinate relies only on a small number of other coordinates. The main idea of our approach is to map the training procedure on the macroscopic coordinates back to the microscopic coordinates, on which partial force computations can be used as stochastic estimation to update model parameters. We provide a theoretical justification of this under suitable conditions. We demonstrate the accuracy, force computation efficiency, and robustness of our method on learning macroscopic closure models from a variety of microscopic systems, including those modeled by partial differential equations or molecular dynamics simulations.

Inverse molecular design with diffusion models holds great potential for advancements in material and drug discovery. Despite success in unconditional molecule generation, integrating multiple properties such as synthetic score and gas permeability as condition constraints into diffusion models remains unexplored. We present the Graph Diffusion Transformer (Graph DiT) for multi-conditional molecular generation. Graph DiT has a condition encoder to learn the representation of numerical and categorical properties and utilizes a Transformer-based graph denoiser to achieve molecular graph denoising under conditions. Unlike previous graph diffusion models that add noise separately on the atoms and bonds in the forward diffusion process, we propose a graph-dependent noise model for training Graph DiT, designed to accurately estimate graph-related noise in molecules. We extensively validate the Graph DiT for multi-conditional polymer and small molecule generation. Results demonstrate our superiority across metrics from distribution learning to condition control for molecular properties. A polymer inverse design task for gas separation with feedback from domain experts further demonstrates its practical utility. The code is available at https://github.com/liugangcode/Graph-DiT.

As large language models (LLMs) develop increasingly sophisticated capabilities and find applications in medical settings, it becomes important to assess their medical safety due to their far-reaching implications for personal and public health, patient safety, and human rights. However, there is little to no understanding of the notion of medical safety in the context of LLMs, let alone how to evaluate and improve it. To address this gap, we first define the notion of medical safety in LLMs based on the Principles of Medical Ethics set forth by the American Medical Association. We then leverage this understanding to introduce MedSafetyBench, the first benchmark dataset designed to measure the medical safety of LLMs. We demonstrate the utility of MedSafetyBench by using it to evaluate and improve the medical safety of LLMs. Our results show that publicly-available medical LLMs do not meet standards of medical safety and that fine-tuning them using MedSafetyBench improves their medical safety while preserving their medical performance. By introducing this new benchmark dataset, our work enables a systematic study of the state of medical safety in LLMs and motivates future work in this area, paving the way to mitigate the safety risks of LLMs in medicine. The benchmark dataset and code are available at https://github.com/AI4LIFE-GROUP/med-safety-bench.

Quantization of diffusion models has attracted considerable attention due to its potential to enable various applications on resource-constrained mobile devices. However, given the cumulative nature of quantization errors in quantized diffusion models, overall performance may still decline even with efforts to minimize quantization error at each sampling step. Recent studies have proposed several methods to address accumulated quantization error, yet these solutions often suffer from limited applicability due to their underlying assumptions or only partially resolve the issue due to an incomplete understanding. In this work, we introduce a novel perspective by conceptualizing quantization error as a "stepback" in the denoising process. We investigate how the accumulation of quantization error can distort the sampling trajectory, resulting in a notable decrease in model performance. To address this challenge, we introduce StepbaQ, a method that calibrates the sampling trajectory and counteracts the adverse effects of accumulated quantization error through a sampling step correction mechanism. Notably, StepbaQ relies solely on statistics of quantization error derived from a small calibration dataset, highlighting its strong applicability. Our experimental results demonstrate that StepbaQ can serve as a plug-and-play technique to enhance the performance of diffusion models quantized by off-the-shelf tools without modifying the quantization settings. For example, StepbaQ significantly improves the performance of the quantized SD v1.5 model by 7.30 in terms of FID on SDprompts dataset under the common W8A8 setting, and it enhances the performance of the quantized SDXL-Turbo model by 17.31 in terms of FID on SDprompts dataset under the challenging W4A8 setting.

We present DrivAerNet++, the largest and most comprehensive multimodal dataset for aerodynamic car design. DrivAerNet++ comprises 8,000 diverse car designs modeled with high-fidelity computational fluid dynamics (CFD) simulations. The dataset includes diverse car configurations such as fastback, notchback, and estateback, with different underbody and wheel designs to represent both internal combustion engines and electric vehicles. Each entry in the dataset features detailed 3D meshes, parametric models, aerodynamic coefficients, and extensive flow and surface field data, along with segmented parts for car classification and point cloud data. This dataset supports a wide array of machine learning applications including data-driven design optimization, generative modeling, surrogate model training, CFD simulation acceleration, and geometric classification. With more than 39 TB of publicly available engineering data, DrivAerNet++ fills a significant gap in available resources, providing high-quality, diverse data to enhance model training, promote generalization, and accelerate automotive design processes. Along with rigorous dataset validation, we also provide ML benchmarking results on the task of aerodynamic drag prediction, showcasing the breadth of applications supported by our dataset. This dataset is set to significantly impact automotive design and broader engineering disciplines by fostering innovation and improving the fidelity of aerodynamic evaluations. Dataset and code available at: https://github.com/Mohamedelrefaie/DrivAerNet

This paper studies the problem of \emph{entropy identity testing}: given sample access to a distribution $p$ and a fully described distribution $q$ (both are discrete distributions over the support of size $k$), and the promise that either $p = q$ or $ | H(p) - H(q) | \geqslant \varepsilon$, where $H(\cdot)$ denotes the Shannon entropy, a tester needs to distinguish between the two cases with high probability. We establish a near-optimal sample complexity bound of $\tilde{\Theta}(\sqrt{k}/\varepsilon + {1}/{\varepsilon^2}$) for this problem, and show how to apply it to the problem of identity testing for in-degree-$d$ $n$-dimensional Bayesian networks, obtaining an upper bound of $\tilde{O}( {2^{d / 2} n^{3/2}}/{\varepsilon^2} + {n^2}/{\varepsilon^4} )$. This improves on the sample complexity bound of $\tilde{O}(2^{d/2}n^2/\varepsilon^4)$ from Canonne, Diakonikolas, Kane, and Stewart (2020), which required an additional assumption on the structure of the (unknown) Bayesian network.

In density functional theory, charge density is the core attribute of atomic systems from which all chemical properties can be derived. Machine learning methods are promising in significantly accelerating charge density prediction, yet existing approaches either lack accuracy or scalability. We propose a recipe that can achieve both. In particular, we identify three key ingredients: (1) representing the charge density with atomic and virtual orbitals (spherical fields centered at atom/virtual coordinates); (2) using expressive and learnable orbital basis sets (basis function for the spherical fields); and (3) using high-capacity equivariant neural network architecture. Our method achieves state-of-the-art accuracy while being more than an order of magnitude faster than existing methods. Furthermore, our method enables flexible efficiency-accuracy trade-offs by adjusting the model/basis sizes.

Predicting low-energy molecular conformations given a molecular graph is an important but challenging task in computational drug discovery. Existing state- of-the-art approaches either resort to large scale transformer-based models that diffuse over conformer fields, or use computationally expensive methods to gen- erate initial structures and diffuse over torsion angles. In this work, we introduce Equivariant Transformer Flow (ET-Flow). We showcase that a well-designed flow matching approach with equivariance and harmonic prior alleviates the need for complex internal geometry calculations and large architectures, contrary to the prevailing methods in the field. Our approach results in a straightforward and scalable method that directly operates on all-atom coordinates with minimal assumptions. With the advantages of equivariance and flow matching, ET-Flow significantly increases the precision and physical validity of the generated con- formers, while being a lighter model and faster at inference. Code is available https://github.com/shenoynikhil/ETFlow.

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may search an unnecessarily large space and discover less accurate or overly complex equations. In this paper, we propose to leverage symmetry in automated equation discovery to compress the equation search space and improve the accuracy and simplicity of the learned equations. Specifically, we derive equivariance constraints from the time-independent symmetries of ODEs. Depending on the types of symmetries, we develop a pipeline for incorporating symmetry constraints into various equation discovery algorithms, including sparse regression and genetic programming. In experiments across diverse dynamical systems, our approach demonstrates better robustness against noise and recovers governing equations with significantly higher probability than baselines without symmetry.

Large language models can solve tasks that were not present in the training set. This capability is believed to be due to in-context learning and skill composition. In this work, we study the emergence of in-context learning and skill composition in a collection of modular arithmetic tasks. Specifically, we consider a finite collection of linear modular functions $z = a x + b y \text{ mod } p$ labeled by the vector $(a, b) \in \mathbb{Z}_p^2$. We use some of these tasks for pre-training and the rest for out-of-distribution testing. We empirically show that a GPT-style transformer exhibits a transition from in-distribution to out-of-distribution generalization as the number of pre-training tasks increases. We find that the smallest model capable of out-of-distribution generalization requires two transformer blocks, while for deeper models, the out-of-distribution generalization phase is *transient*, necessitating early stopping. Finally, we perform an interpretability study of the pre-trained models, revealing highly structured representations in both attention heads and MLPs; and discuss the learned algorithms. Notably, we find an algorithmic shift in deeper models, as we go from few to many in-context examples.

In recent years, a large number of algorithms for label integration and noise correction have been proposed to infer the unknown true labels of instances in crowdsourcing. They have made great advances in improving the label quality of crowdsourced datasets. However, due to the presence of intractable instances, these algorithms are usually not as significant in improving the model quality as they are in improving the label quality. To improve the model quality, this paper proposes an instance weighting-based bias-variance trade-off (IWBVT) approach. IWBVT at first proposes a novel instance weighting method based on the complementary set and entropy, which mitigates the impact of intractable instances and thus makes the bias and variance of trained models closer to the unknown true results. Then, IWBVT performs probabilistic loss regressions based on the bias-variance decomposition, which achieves the bias-variance trade-off and thus reduces the generalization error of trained models. Experimental results indicate that IWBVT can serve as a universal post-processing approach to significantly improving the model quality of existing state-of-the-art label integration algorithms and noise correction algorithms.

With the arrival of the Noisy Intermediate-Scale Quantum (NISQ) era, Variational Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question. In this paper, we manage to combine the Hamming Weight Preserving ansatz with a topological-aware parity check on physical qubits to enforce error mitigation and further hard constraints. We demonstrate the combination significantly outperforms peer VQA methods on both quantum chemistry problems and constrained combinatorial optimization problems e.g. Quadratic Assignment Problem. Intensive experimental results on both simulators and superconducting quantum processors are provided to verify that the combination of HWP ansatz with parity check is among the most promising candidates to demonstrate quantum advantages in the NISQ era to solve more realistic problems.

Weather forecasting is a fundamental problem for anticipating and mitigating the impacts of climate change. Recently, data-driven approaches for weather forecasting based on deep learning have shown great promise, achieving accuracies that are competitive with operational systems. However, those methods often employ complex, customized architectures without sufficient ablation analysis, making it difficult to understand what truly contributes to their success. Here we introduce Stormer, a simple transformer model that achieves state-of-the art performance on weather forecasting with minimal changes to the standard transformer backbone. We identify the key components of Stormer through careful empirical analyses, including weather-specific embedding, randomized dynamics forecast, and pressure-weighted loss. At the core of Stormer is a randomized forecasting objective that trains the model to forecast the weather dynamics over varying time intervals. During inference, this allows us to produce multiple forecasts for a target lead time and combine them to obtain better forecast accuracy. On WeatherBench 2, Stormer performs competitively at short to medium-range forecasts and outperforms current methods beyond 7 days, while requiring orders-of-magnitude less training data and compute. Additionally, we demonstrate Stormer’s favorable scaling properties, showing consistent improvements in forecast accuracy with increases in model size and training tokens. Code and checkpoints are available at https://github.com/tung-nd/stormer.

Recent progress of deep generative models in the vision and language domain has stimulated significant interest in more structured data generation such as molecules. However, beyond generating new random molecules, efficient exploration and a comprehensive understanding of the vast chemical space are of great importance to molecular science and applications in drug design and materials discovery. In this paper, we propose a new framework, ChemFlow, to traverse chemical space through navigating the latent space learned by molecule generative models through flows. We introduce a dynamical system perspective that formulates the problem as learning a vector field that transports the mass of the molecular distribution to the region with desired molecular properties or structure diversity. Under this framework, we unify previous approaches on molecule latent space traversal and optimization and propose alternative competing methods incorporating different physical priors. We validate the efficacy of ChemFlow on molecule manipulation and single- and multi-objective molecule optimization tasks under both supervised and unsupervised molecular discovery settings. Codes and demos are publicly available on GitHub at [https://github.com/garywei944/ChemFlow](https://github.com/garywei944/ChemFlow).

Fourier Neural Operators (FNOs) have shown promise for solving partial differential equations (PDEs). Typically, FNOs employ separate parameters for different frequency modes to specify tunable kernel integrals in Fourier space, which, yet, results in an undesirably large number of parameters when solving high-dimensional PDEs. A workaround is to abandon the frequency modes exceeding a predefined threshold, but this limits the FNOs' ability to represent high-frequency details and poses non-trivial challenges for hyper-parameter specification. To address these, we propose AMortized Fourier Neural Operator (AM-FNO), where an amortized neural parameterization of the kernel function is deployed to accommodate arbitrarily many frequency modes using a fixed number of parameters. We introduce two implementations of AM-FNO, based on the recently developed, appealing Kolmogorov–Arnold Network (KAN) and Multi-Layer Perceptrons (MLPs) equipped with orthogonal embedding functions respectively. We extensively evaluate our method on diverse datasets from various domains and observe up to 31\% average improvement compared to competing neural operator baselines.