NeurIPS 2022 论文列表

Conference on Neural Information Processing Systems

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Retrieve, Reason, and Refine: Generating Accurate and Faithful Patient Instructions

Fenglin Liu, Bang Yang, Chenyu You, Xian Wu, Shen Ge, Zhangdaihong Liu, Xu Sun, Yang Yang, David A. Clifton

展开摘要

The "Patient Instruction" (PI), which contains critical instructional information provided both to carers and to the patient at the time of discharge, is essential for the patient to manage their condition outside hospital. An accurate and easy-to-follow PI can improve the self-management of patients which can in turn reduce hospital readmission rates. However, writing an appropriate PI can be extremely time consuming for physicians, and is subject to being incomplete or error-prone for (potentially overworked) physicians. Therefore, we propose a new task that can provide an objective means of avoiding incompleteness, while reducing clinical workload: the automatic generation of the PI, which is imagined as being a document that the clinician can review, modify, and approve as necessary (rather than taking the human "out of the loop"). We build a benchmark clinical dataset and propose the Re$^3$Writer, which imitates the working patterns of physicians to first retrieve related working experience from historical PIs written by physicians, then reason related medical knowledge. Finally, it refines the retrieved working experience and reasoned medical knowledge to extract useful information, which is used to generate the PI for previously-unseen patient according to their health records during hospitalization. Our experiments show that, using our method, the performance of 6 different models can be substantially boosted across all metrics, with up to 20%, 11%, and 19% relative improvements in BLEU-4, ROUGE-L, and METEOR, respectively. Meanwhile, we show results from human evaluations to measure the effectiveness in terms of its usefulness for clinical practice. The code is available at https://github.com/AI-in-Health/Patient-Instructions.

Accept
RLIP: Relational Language-Image Pre-training for Human-Object Interaction Detection

Hangjie Yuan, Jianwen Jiang, Samuel Albanie, Tao Feng, Ziyuan Huang, Dong Ni, Mingqian Tang

展开摘要

The task of Human-Object Interaction (HOI) detection targets fine-grained visual parsing of humans interacting with their environment, enabling a broad range of applications. Prior work has demonstrated the benefits of effective architecture design and integration of relevant cues for more accurate HOI detection. However, the design of an appropriate pre-training strategy for this task remains underexplored by existing approaches. To address this gap, we propose $\textit{Relational Language-Image Pre-training}$ (RLIP), a strategy for contrastive pre-training that leverages both entity and relation descriptions. To make effective use of such pre-training, we make three technical contributions: (1) a new $\textbf{Par}$allel entity detection and $\textbf{Se}$quential relation inference (ParSe) architecture that enables the use of both entity and relation descriptions during holistically optimized pre-training; (2) a synthetic data generation framework, Label Sequence Extension, that expands the scale of language data available within each minibatch; (3) ambiguity-suppression mechanisms, Relation Quality Labels and Relation Pseudo-Labels, to mitigate the influence of ambiguous/noisy samples in the pre-training data. Through extensive experiments, we demonstrate the benefits of these contributions, collectively termed RLIP-ParSe, for improved zero-shot, few-shot and fine-tuning HOI detection performance as well as increased robustness to learning from noisy annotations. Code will be available at https://github.com/JacobYuan7/RLIP.

Accept
GenerSpeech: Towards Style Transfer for Generalizable Out-Of-Domain Text-to-Speech

Rongjie Huang, Yi Ren, Jinglin Liu, Chenye Cui, Zhou Zhao

展开摘要

Style transfer for out-of-domain (OOD) speech synthesis aims to generate speech samples with unseen style (e.g., speaker identity, emotion, and prosody) derived from an acoustic reference, while facing the following challenges: 1) The highly dynamic style features in expressive voice are difficult to model and transfer; and 2) the TTS models should be robust enough to handle diverse OOD conditions that differ from the source data. This paper proposes GenerSpeech, a text-to-speech model towards high-fidelity zero-shot style transfer of OOD custom voice. GenerSpeech decomposes the speech variation into the style-agnostic and style-specific parts by introducing two components: 1) a multi-level style adaptor to efficiently model a large range of style conditions, including global speaker and emotion characteristics, and the local (utterance, phoneme, and word-level) fine-grained prosodic representations; and 2) a generalizable content adaptor with Mix-Style Layer Normalization to eliminate style information in the linguistic content representation and thus improve model generalization. Our evaluations on zero-shot style transfer demonstrate that GenerSpeech surpasses the state-of-the-art models in terms of audio quality and style similarity. The extension studies to adaptive style transfer further show that GenerSpeech performs robustly in the few-shot data setting. Audio samples are available at \url{https://GenerSpeech.github.io/}.

Accept
EPIC-KITCHENS VISOR Benchmark: VIdeo Segmentations and Object Relations

Ahmad Darkhalil, Dandan Shan, Bin Zhu, Jian Ma, Amlan Kar, Richard Ely Locke Higgins, Sanja Fidler, David Fouhey, Dima Damen

展开摘要

We introduce VISOR, a new dataset of pixel annotations and a benchmark suite for segmenting hands and active objects in egocentric video. VISOR annotates videos from EPIC-KITCHENS, which comes with a new set of challenges not encountered in current video segmentation datasets. Specifically, we need to ensure both short- and long-term consistency of pixel-level annotations as objects undergo transformative interactions, e.g. an onion is peeled, diced and cooked - where we aim to obtain accurate pixel-level annotations of the peel, onion pieces, chopping board, knife, pan, as well as the acting hands. VISOR introduces an annotation pipeline, AI-powered in parts, for scalability and quality. In total, we publicly release 272K manual semantic masks of 257 object classes, 9.9M interpolated dense masks, 67K hand-object relations, covering 36 hours of 179 untrimmed videos. Along with the annotations, we introduce three challenges in video object segmentation, interaction understanding and long-term reasoning. For data, code and leaderboards: http://epic-kitchens.github.io/VISOR

Accept
UQGAN: A Unified Model for Uncertainty Quantification of Deep Classifiers trained via Conditional GANs

Philipp Oberdiek, Gernot A. Fink, Matthias Rottmann

展开摘要

We present an approach to quantifying both aleatoric and epistemic uncertainty for deep neural networks in image classification, based on generative adversarial networks (GANs). While most works in the literature that use GANs to generate out-of-distribution (OoD) examples only focus on the evaluation of OoD detection, we present a GAN based approach to learn a classifier that produces proper uncertainties for OoD examples as well as for false positives (FPs). Instead of shielding the entire in-distribution data with GAN generated OoD examples which is state-of-the-art, we shield each class separately with out-of-class examples generated by a conditional GAN and complement this with a one-vs-all image classifier. In our experiments, in particular on CIFAR10, CIFAR100 and Tiny ImageNet, we improve over the OoD detection and FP detection performance of state-of-the-art GAN-training based classifiers. Furthermore, we also find that the generated GAN examples do not significantly affect the calibration error of our classifier and result in a significant gain in model accuracy.

Accept
Multi-fidelity Monte Carlo: a pseudo-marginal approach

Diana Cai, Ryan P Adams

展开摘要

Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is often a function of expensive computations, such as a high-fidelity physical simulation, an intractable integral, or a slowly-converging iterative algorithm. Thus, using an MCMC algorithms with an expensive target density becomes impractical, as these expensive computations need to be evaluated at each iteration of the algorithm. In practice, these computations often approximated via a cheaper, low-fidelity computation, leading to bias in the resulting target density. Multi-fidelity MCMC algorithms combine models of varying fidelities in order to obtain an approximate target density with lower computational cost. In this paper, we describe a class of asymptotically exact multi-fidelity MCMC algorithms for the setting where a sequence of models of increasing fidelity can be computed that approximates the expensive target density of interest. We take a pseudo-marginal MCMC approach for multi-fidelity inference that utilizes a cheaper, randomized-fidelity unbiased estimator of the target fidelity constructed via random truncation of a telescoping series of the low-fidelity sequence of models. Finally, we discuss and evaluate the proposed multi-fidelity MCMC approach on several applications, including log-Gaussian Cox process modeling, Bayesian ODE system identification, PDE-constrained optimization, and Gaussian process parameter inference.

Accept
Beyond Not-Forgetting: Continual Learning with Backward Knowledge Transfer

Sen Lin, Li Yang, Deliang Fan, Junshan Zhang

展开摘要

By learning a sequence of tasks continually, an agent in continual learning (CL) can improve the learning performance of both a new task and `old' tasks by leveraging the forward knowledge transfer and the backward knowledge transfer, respectively. However, most existing CL methods focus on addressing catastrophic forgetting in neural networks by minimizing the modification of the learnt model for old tasks. This inevitably limits the backward knowledge transfer from the new task to the old tasks, because judicious model updates could possibly improve the learning performance of the old tasks as well. To tackle this problem, we first theoretically analyze the conditions under which updating the learnt model of old tasks could be beneficial for CL and also lead to backward knowledge transfer, based on the gradient projection onto the input subspaces of old tasks. Building on the theoretical analysis, we next develop a ContinUal learning method with Backward knowlEdge tRansfer (CUBER), for a fixed capacity neural network without data replay. In particular, CUBER first characterizes the task correlation to identify the positively correlated old tasks in a layer-wise manner, and then selectively modifies the learnt model of the old tasks when learning the new task. Experimental studies show that CUBER can even achieve positive backward knowledge transfer on several existing CL benchmarks for the first time without data replay, where the related baselines still suffer from catastrophic forgetting (negative backward knowledge transfer). The superior performance of CUBER on the backward knowledge transfer also leads to higher accuracy accordingly.

Accept
PDEBench: An Extensive Benchmark for Scientific Machine Learning

Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, Mathias Niepert

展开摘要

Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and repre- sentative of a wide range of problems. We introduce PDEBENCH, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBENCH comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems con- tribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more real- istic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of ini- tial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBENCH allows researchers to extend the benchmark freely for their own pur- poses using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

Accept
Linear Label Ranking with Bounded Noise

Dimitris Fotakis, Alkis Kalavasis, Vasilis Kontonis, Christos Tzamos

展开摘要

Label Ranking (LR) is the supervised task of learning a sorting function that maps feature vectors $x \in \mathbb{R}^d$ to rankings $\sigma(x) \in \mathbb S_k$ over a finite set of $k$ labels. We focus on the fundamental case of learning linear sorting functions (LSFs) under Gaussian marginals: $x$ is sampled from the $d$-dimensional standard normal and the ground truth ranking $\sigma^\star(x)$ is the ordering induced by sorting the coordinates of the vector $W^\star x$, where $W^\star \in \mathbb{R}^{k \times d}$ is unknown. We consider learning LSFs in the presence of bounded noise: assuming that a noiseless example is of the form $(x, \sigma^\star(x))$, we observe $(x, \pi)$, where for any pair of elements $i \neq j$, the probability that the order of $i, j$ is different in $\pi$ than in $\sigma^\star(x)$ is at most $\eta < 1/2$. We design efficient non-proper and proper learning algorithms that learn hypotheses within normalized Kendall's Tau distance $\epsilon$ from the ground truth with $N= \widetilde{O}(d\log(k)/\epsilon)$ labeled examples and runtime $\mathrm{poly}(N, k)$. For the more challenging top-$r$ disagreement loss, we give an efficient proper learning algorithm that achieves $\epsilon$ top-$r$ disagreement with the ground truth with $N = \widetilde{O}(d k r /\epsilon)$ samples and $\mathrm{poly}(N)$ runtime.

Accept
VectorAdam for Rotation Equivariant Geometry Optimization

Selena Ling, Nicholas Sharp, Alec Jacobson

展开摘要

The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam — when treated as a function that maps initial conditions to optimized results — is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.

Accept
Iron: Private Inference on Transformers

Meng Hao, Hongwei Li, Hanxiao Chen, Pengzhi Xing, Guowen Xu, Tianwei Zhang

展开摘要

We initiate the study of private inference on Transformer-based models in the client-server setting, where clients have private inputs and servers hold proprietary models. Our main contribution is to provide several new secure protocols for matrix multiplication and complex non-linear functions like Softmax, GELU activations, and LayerNorm, which are critical components of Transformers. Specifically, we first propose a customized homomorphic encryption-based protocol for matrix multiplication that crucially relies on a novel compact packing technique. This design achieves $\sqrt{m} \times$ less communication ($m$ is the number of rows of the output matrix) over the most efficient work. Second, we design efficient protocols for three non-linear functions via integrating advanced underlying protocols and specialized optimizations. Compared to the state-of-the-art protocols, our recipes reduce about half of the communication and computation overhead. Furthermore, all protocols are numerically precise, which preserve the model accuracy of plaintext. These techniques together allow us to implement \Name, an efficient Transformer-based private inference framework. Experiments conducted on several real-world datasets and models demonstrate that \Name achieves $3 \sim 14\times$ less communication and $3 \sim 11\times$ less runtime compared to the prior art.

Accept
Benchmarking Heterogeneous Treatment Effect Models through the Lens of Interpretability

Jonathan Crabbé, Alicia Curth, Ioana Bica, Mihaela van der Schaar

展开摘要

Estimating personalized effects of treatments is a complex, yet pervasive problem. To tackle it, recent developments in the machine learning (ML) literature on heterogeneous treatment effect estimation gave rise to many sophisticated, but opaque, tools: due to their flexibility, modularity and ability to learn constrained representations, neural networks in particular have become central to this literature. Unfortunately, the assets of such black boxes come at a cost: models typically involve countless nontrivial operations, making it difficult to understand what they have learned. Yet, understanding these models can be crucial -- in a medical context, for example, discovered knowledge on treatment effect heterogeneity could inform treatment prescription in clinical practice. In this work, we therefore use post-hoc feature importance methods to identify features that influence the model's predictions. This allows us to evaluate treatment effect estimators along a new and important dimension that has been overlooked in previous work: We construct a benchmarking environment to empirically investigate the ability of personalized treatment effect models to identify predictive covariates -- covariates that determine differential responses to treatment. Our benchmarking environment then enables us to provide new insight into the strengths and weaknesses of different types of treatment effects models as we modulate different challenges specific to treatment effect estimation -- e.g. the ratio of prognostic to predictive information, the possible nonlinearity of potential outcomes and the presence and type of confounding.

Accept
Disentangling the Predictive Variance of Deep Ensembles through the Neural Tangent Kernel

Seijin Kobayashi, Pau Vilimelis Aceituno, Johannes von Oswald

展开摘要

Identifying unfamiliar inputs, also known as out-of-distribution (OOD) detection, is a crucial property of any decision making process. A simple and empirically validated technique is based on deep ensembles where the variance of predictions over different neural networks acts as a substitute for input uncertainty. Nevertheless, a theoretical understanding of the inductive biases leading to the performance of deep ensemble's uncertainty estimation is missing. To improve our description of their behavior, we study deep ensembles with large layer widths operating in simplified linear training regimes, in which the functions trained with gradient descent can be described by the neural tangent kernel. We identify two sources of noise, each inducing a distinct inductive bias in the predictive variance at initialization. We further show theoretically and empirically that both noise sources affect the predictive variance of non-linear deep ensembles in toy models and realistic settings after training. Finally, we propose practical ways to eliminate part of these noise sources leading to significant changes and improved OOD detection in trained deep ensembles.

Accept
MORA: Improving Ensemble Robustness Evaluation with Model Reweighing Attack

Yunrui Yu, Xitong Gao, Cheng-Zhong Xu

展开摘要

Adversarial attacks can deceive neural networks by adding tiny perturbations to their input data. Ensemble defenses, which are trained to minimize attack transferability among sub-models, offer a promising research direction to improve robustness against such attacks while maintaining a high accuracy on natural inputs. We discover, however, that recent state-of-the-art (SOTA) adversarial attack strategies cannot reliably evaluate ensemble defenses, sizeably overestimating their robustness. This paper identifies the two factors that contribute to this behavior. First, these defenses form ensembles that are notably difficult for existing gradient-based method to attack, due to gradient obfuscation. Second, ensemble defenses diversify sub-model gradients, presenting a challenge to defeat all sub-models simultaneously, simply summing their contributions may counteract the overall attack objective; yet, we observe that ensemble may still be fooled despite most sub-models being correct. We therefore introduce MORA, a model-reweighing attack to steer adversarial example synthesis by reweighing the importance of sub-model gradients. MORA finds that recent ensemble defenses all exhibit varying degrees of overestimated robustness. Comparing it against recent SOTA white-box attacks, it can converge orders of magnitude faster while achieving higher attack success rates across all ensemble models examined with three different ensemble modes (i.e, ensembling by either softmax, voting or logits). In particular, most ensemble defenses exhibit near or exactly $0\%$ robustness against MORA with $\ell^\infty$ perturbation within $0.02$ on CIFAR-10, and $0.01$ on CIFAR-100. We make MORA open source with reproducible results and pre-trained models; and provide a leaderboard of ensemble defenses under various attack strategies.

Accept
Learning sparse features can lead to overfitting in neural networks

Leonardo Petrini, Francesco Cagnetta, Eric Vanden-Eijnden, Matthieu Wyart

展开摘要

It is widely believed that the success of deep networks lies in their ability to learn a meaningful representation of the features of the data. Yet, understanding when and how this feature learning improves performance remains a challenge: for example, it is beneficial for modern architectures trained to classify images, whereas it is detrimental for fully-connected networks trained for the same task on the same data. Here we propose an explanation for this puzzle, by showing that feature learning can perform worse than lazy training (via random feature kernel or the NTK) as the former can lead to a sparser neural representation. Although sparsity is known to be essential for learning anisotropic data, it is detrimental when the target function is constant or smooth along certain directions of input space. We illustrate this phenomenon in two settings: (i) regression of Gaussian random functions on the $d$-dimensional unit sphere and (ii) classification of benchmark datasets of images. For (i), we compute the scaling of the generalization error with number of training points, and show that methods that do not learn features generalize better, even when the dimension of the input space is large. For (ii), we show empirically that learning features can indeed lead to sparse and thereby less smooth representations of the image predictors. This fact is plausibly responsible for deteriorating the performance, which is known to be correlated with smoothness along diffeomorphisms.

Accept
Mean Estimation with User-level Privacy under Data Heterogeneity

Rachel Cummings, Vitaly Feldman, Audra McMillan, Kunal Talwar

展开摘要

A key challenge in many modern data analysis tasks is that user data is heterogeneous. Different users may possess vastly different numbers of data points. More importantly, it cannot be assumed that all users sample from the same underlying distribution. This is true, for example in language data, where different speech styles result in data heterogeneity. In this work we propose a simple model of heterogeneous user data that differs in both distribution and quantity of data, and we provide a method for estimating the population-level mean while preserving user-level differential privacy. We demonstrate asymptotic optimality of our estimator and also prove general lower bounds on the error achievable in our problem.

Accept
GPT3.int8(): 8-bit Matrix Multiplication for Transformers at Scale

Tim Dettmers, Mike Lewis, Younes Belkada, Luke Zettlemoyer

展开摘要

Large language models have been widely adopted but require significant GPU memory for inference. We develop a procedure for Int8 matrix multiplication for feed-forward and attention projection layers in transformers, which cut the memory needed for inference by half while retaining full precision performance. With our method, a 175B parameter 16/32-bit checkpoint can be loaded, converted to Int8, and used immediately without performance degradation. This is made possible by understanding and working around properties of highly systematic emergent features in transformer language models that dominate attention and transformer predictive performance. To cope with these features, we develop a two-part quantization procedure, {\bf LLM.int8()}. We first use vector-wise quantization with separate normalization constants for each inner product in the matrix multiplication, to quantize most of the features. However, for the emergent outliers, we also include a new mixed-precision decomposition scheme, which isolates the outlier feature dimensions into a 16-bit matrix multiplication while still more than 99.9\% of values are multiplied in 8-bit. Using LLM.int8(), we show empirically it is possible to perform inference in LLMs with up to 175B parameters without any performance degradation. This result makes such models much more accessible, for example making it possible to use OPT-175B/BLOOM on a single server with consumer GPUs. We open source our software.

Accept
Decoupling Classifier for Boosting Few-shot Object Detection and Instance Segmentation

Bin-Bin Gao, Xiaochen Chen, Zhongyi Huang, Congchong Nie, Jun Liu, Jinxiang Lai, GUANNAN JIANG, Xi Wang, Chengjie Wang

展开摘要

This paper focus on few-shot object detection~(FSOD) and instance segmentation~(FSIS), which requires a model to quickly adapt to novel classes with a few labeled instances. The existing methods severely suffer from bias classification because of the missing label issue which naturally exists in an instance-level few-shot scenario and is first formally proposed by us. Our analysis suggests that the standard classification head of most FSOD or FSIS models needs to be decoupled to mitigate the bias classification. Therefore, we propose an embarrassingly simple but effective method that decouples the standard classifier into two heads. Then, these two individual heads are capable of independently addressing clear positive samples and noisy negative samples which are caused by the missing label. In this way, the model can effectively learn novel classes while mitigating the effects of noisy negative samples. Without bells and whistles, our model without any additional computation cost and parameters consistently outperforms its baseline and state-of-the-art by a large margin on PASCAL VOC and MS-COCO benchmarks for FSOD and FSIS tasks.\footnote{\url{https://csgaobb.github.io/Projects/DCFS}.}

Accept
Infinite-Fidelity Coregionalization for Physical Simulation

Shibo Li, Zheng Wang, Robert Kirby, Shandian Zhe

展开摘要

Multi-fidelity modeling and learning is important in physical simulation related applications. It can leverage both low-fidelity and high-fidelity examples for training so as to reduce the cost of data generation yet still achieving good performance. While existing approaches only model finite, discrete fidelities, in practice, the feasible fidelity choice is often infinite, which can correspond to a continuous mesh spacing or finite element length. In this paper, we propose Infinite Fidelity Coregionalization (IFC). Given the data, our method can extract and exploit rich information within infinite, continuous fidelities to bolster the prediction accuracy. Our model can interpolate and/or extrapolate the predictions to novel fidelities that are not covered by the training data. Specifically, we introduce a low-dimensional latent output as a continuous function of the fidelity and input, and multiple it with a basis matrix to predict high-dimensional solution outputs. We model the latent output as a neural Ordinary Differential Equation (ODE) to capture the complex relationships within and integrate information throughout the continuous fidelities. We then use Gaussian processes or another ODE to estimate the fidelity-varying bases. For efficient inference, we reorganize the bases as a tensor, and use a tensor-Gaussian variational posterior approximation to develop a scalable inference algorithm for massive outputs. We show the advantage of our method in several benchmark tasks in computational physics.

Accept
Convergence for score-based generative modeling with polynomial complexity

Holden Lee, Jianfeng Lu, Yixin Tan

展开摘要

Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples. We prove the first polynomial convergence guarantees for the core mechanic behind SGM: drawing samples from a probability density $p$ given a score estimate (an estimate of $\nabla \ln p$) that is accurate in $L^2(p)$. Compared to previous works, we do not incur error that grows exponentially in time or that suffers from a curse of dimensionality. Our guarantee works for any smooth distribution and depends polynomially on its log-Sobolev constant. Using our guarantee, we give a theoretical analysis of score-based generative modeling, which transforms white-noise input into samples from a learned data distribution given score estimates at different noise scales. Our analysis gives theoretical grounding to the observation that an annealed procedure is required in practice to generate good samples, as our proof depends essentially on using annealing to obtain a warm start at each step. Moreover, we show that a predictor-corrector algorithm gives better convergence than using either portion alone.

Accept