ICLR 2023 论文列表

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the performance gap between pure machine learning approaches to that of the best numerical or hybrid solvers. This is achieved with new representations – separable spectral layers and improved residual connections – and a combination of training strategies such as the Markov assumption, Gaussian noise, and cosine learning rate decay. On several challenging benchmark PDEs on regular grids, structured meshes, and point clouds, the F-FNO can scale to deeper networks and outperform both the FNO and the geo-FNO, reducing the error by 83% on the Navier-Stokes problem, 31% on the elasticity problem, 57% on the airfoil flow problem, and 60% on the plastic forging problem. Compared to the state-of-the-art pseudo-spectral method, the F-FNO can take a step size that is an order of magnitude larger in time and achieve an order of magnitude speedup to produce the same solution quality.

It is well-known that for sparse linear bandits, when ignoring the dependency on sparsity which is much smaller than the ambient dimension, the worst-case minimax regret is $\widetilde{\Theta}\left(\sqrt{dT}\right)$ where $d$ is the ambient dimension and $T$ is the number of rounds. On the other hand, in the benign setting where there is no noise and the action set is the unit sphere, one can use divide-and-conquer to achieve $\widetilde{\mathcal O}(1)$ regret, which is (nearly) independent of $d$ and $T$. In this paper, we present the first variance-aware regret guarantee for sparse linear bandits: $\widetilde{\mathcal O}\left(\sqrt{d\sum_{t=1}^T \sigma_t^2} + 1\right)$, where $\sigma_t^2$ is the variance of the noise at the $t$-th round. This bound naturally interpolates the regret bounds for the worst-case constant-variance regime (i.e., $\sigma_t \equiv \Omega(1)$) and the benign deterministic regimes (i.e., $\sigma_t \equiv 0$). To achieve this variance-aware regret guarantee, we develop a general framework that converts any variance-aware linear bandit algorithm to a variance-aware algorithm for sparse linear bandits in a "black-box" manner. Specifically, we take two recent algorithms as black boxes to illustrate that the claimed bounds indeed hold, where the first algorithm can handle unknown-variance cases and the second one is more efficient.

Generative Pre-trained Transformer models, known as GPT or OPT, set themselves apart through breakthrough performance across complex language modelling tasks, but also by their extremely high computational and storage costs. Specifically, due to their massive size, even inference for large, highly-accurate GPT models may require multiple performant GPUs, which limits the usability of such models. While there is emerging work on relieving this pressure via model compression, the applicability and performance of existing compression techniques is limited by the scale and complexity of GPT models. In this paper, we address this challenge, and propose OPTQ, a new one-shot weight quantization method based on approximate second-order information, that is both highly-accurate and highly-efficient. Specifically, OPTQ can quantize GPT models with 175 billion parameters in approximately four GPU hours, reducing the bitwidth down to 3 or 4 bits per weight, with negligible accuracy degradation relative to the uncompressed baseline. Our method more than doubles the compression gains relative to previously-proposed one-shot quantization methods, preserving accuracy, allowing us for the first time to execute an 175 billion-parameter model inside a single GPU for generative inference. Moreover, we also show that our method can still provide reasonable accuracy in the extreme quantization regime, in which weights are quantized to 2-bit or even ternary quantization levels. We show experimentally that these improvements can be leveraged for end-to-end inference speedups over FP16, of around 3.25x when using high-end GPUs (NVIDIA A100) and 4.5x when using more cost-effective ones (NVIDIA A6000). The implementation is available at https://github.com/IST-DASLab/gptq.

Many important problems involving molecular property prediction from 3D structures have limited data, posing a generalization challenge for neural networks. In this paper, we describe a pre-training technique based on denoising that achieves a new state-of-the-art in molecular property prediction by utilizing large datasets of 3D molecular structures at equilibrium to learn meaningful representations for downstream tasks. Relying on the well-known link between denoising autoencoders and score-matching, we show that the denoising objective corresponds to learning a molecular force field -- arising from approximating the Boltzmann distribution with a mixture of Gaussians -- directly from equilibrium structures. Our experiments demonstrate that using this pre-training objective significantly improves performance on multiple benchmarks, achieving a new state-of-the-art on the majority of targets in the widely used QM9 dataset. Our analysis then provides practical insights into the effects of different factors -- dataset sizes, model size and architecture, and the choice of upstream and downstream datasets -- on pre-training.

Few-Shot Learning (FSL) aims to learn a simple and effective bias on limited novel samples. Recently, many methods have been focused on re-training a randomly initialized linear classifier to adapt it to the novel features extracted by the pre-trained feature extractor (called Linear-Probing-based methods). These methods typically assumed the pre-trained feature extractor was robust enough, i.e., finetuning was not needed, and hence the pre-trained feature extractor does not change on the novel samples. However, the unchanged pre-trained feature extractor will distort the features of novel samples because the robustness assumption may not hold, especially on the out-of-distribution samples. To extract the undistorted features, we designed Linear-Probing-Finetuning with Firth-Bias (LP-FT-FB) to yield an accurate bias on the limited samples for better finetuning the pre-trained feature extractor, providing stronger transferring ability. In LP-FT-FB, we further proposed inverse Firth Bias Reduction (i-FBR) to regularize the over-parameterized feature extractor on which FBR does not work well. The proposed i-FBR effectively alleviates the over-fitting problem of the feature extractor in the process of finetuning and helps extract undistorted novel features. To show the effectiveness of the designed LP-FT-FB, we conducted a lot of experiments on the commonly used FSL datasets under different backbones, including in-domain and cross-domain FSL tasks. The experimental results show that the proposed FT-LP-FB outperforms the SOTA FSL methods. The code is available at https://github.com/whzyf951620/LinearProbingFinetuningFirthBias.

Existing approaches to system identification (estimating the physical parameters of an object) from videos assume known object geometries. This precludes their applicability in a vast majority of scenes where object geometries are complex or unknown. In this work, we aim to identify parameters characterizing a physical system from a set of multi-view videos without any assumption on object geometry or topology. To this end, we propose "Physics Augmented Continuum Neural Radiance Fields" (PAC-NeRF), to estimate both the unknown geometry and physical parameters of highly dynamic objects from multi-view videos. We design PAC-NeRF to only ever produce physically plausible states by enforcing the neural radiance field to follow the conservation laws of continuum mechanics. For this, we design a hybrid Eulerian-Lagrangian representation of the neural radiance field, i.e., we use the Eulerian grid representation for NeRF density and color fields, while advecting the neural radiance fields via Lagrangian particles. This hybrid Eulerian-Lagrangian representation seamlessly blends efficient neural rendering with the material point method (MPM) for robust differentiable physics simulation. We validate the effectiveness of our proposed framework on geometry and physical parameter estimation over a vast range of materials, including elastic bodies, plasticine, sand, Newtonian and non-Newtonian fluids, and demonstrate significant performance gain on most tasks.

Ensembling certifiably robust neural networks is a promising approach for improving the \emph{certified robust accuracy} of neural models. Black-box ensembles that assume only query-access to the constituent models (and their robustness certifiers) during prediction are particularly attractive due to their modular structure. Cascading ensembles are a popular instance of black-box ensembles that appear to improve certified robust accuracies in practice. However, we show that the robustness certifier used by a cascading ensemble is unsound. That is, when a cascading ensemble is certified as locally robust at an input $x$ (with respect to $\epsilon$), there can be inputs $x'$ in the $\epsilon$-ball centered at $x$, such that the cascade's prediction at $x'$ is different from $x$ and thus the ensemble is not locally robust. Our theoretical findings are accompanied by empirical results that further demonstrate this unsoundness. We present a new attack against cascading ensembles and show that: (1) there exists an adversarial input for up to 88\% of the samples where the ensemble claims to be certifiably robust and accurate; and (2) the accuracy of a cascading ensemble under our attack is as low as 11\% when it claims to be certifiably robust and accurate on 97\% of the test set. Our work reveals a critical pitfall of cascading certifiably robust models by showing that the seemingly beneficial strategy of cascading can actually hurt the robustness of the resulting ensemble. Our code is available at https://github.com/TristaChi/ensembleKW.

In the scenario-based Question Answering (QA) task, models are asked to find answers that are appropriate to the user scenarios associated with the question and identify information that is missing from the scenarios but is necessary for the answers to hold. Scenarios commonly include multiple properties of users, such as age, employment status, and income level for the question “How much can I claim from this benefit”. The properties relevant to a potential answer are given in a document, which will state conditions necessary for the answer to hold. Documents also may specify how conditions interact with each other, e.g. with text like “one of the conditions below must apply”. Although understanding the relationship between conditions is crucial for solving this challenging QA task, limited work has been done so far in modeling this. In this paper, we propose the T-Reasoner model, which solves this problem with three jointly learned modules: an entailment module which checks whether a condition has been satisfied by the scenario, a decoding module which locates eligible answers from documents, and a reasoning module which infers the relationship between conditions and performs a reasoning step to determine the logically consistent answers and identify missing conditions. T-Reasoner outperforms strong baselines on a synthetic scenario-based QA dataset and achieves a new state-of-the-art on two scenario-based QA benchmarks, outperforming the prior best models by 3-10 points.

In this paper, we work towards a neural surrogate to model wireless electro-magnetic propagation effects in indoor environments. Such neural surrogates provide a fast, differentiable, and continuous representation of the environment and enables end-to-end optimization for downstream tasks (e.g., network planning). Specifically, the goal of the paper is to render the wireless signal (e.g., time-of-flights, power of each path) in an environment as a function of the sensor's spatial configuration (e.g., placement of transmit and receive antennas). NeRF-based approaches have shown promising results in the visual setting (RGB image signal, with a camera sensor), where the key idea is to algorithmically evaluate the 'global' signal (e.g., using volumetric rendering) by breaking it down in a sequence of 'local' evaluations (e.g., using co-ordinate neural networks). In a similar spirit, we model the time-angle channel impulse response (the global wireless signal) as a superposition of multiple paths. The wireless characteristics (e.g., power) of each path is a result of multiple evaluations of a neural network that learns implicit ray-surface interaction properties. We evaluate our approach in multiple indoor scenarios and demonstrate that our model achieves strong performance (e.g., $<$0.33ns error in time-of-flight predictions). Furthermore, we demonstrate that our neural surrogate whitens the `black-box' wireless simulators, and thus enables inverse rendering applications (e.g., user localization).

Many real-world dynamical systems are associated with first integrals (a.k.a. invariant quantities), which are quantities that remain unchanged over time. The discovery and understanding of first integrals are fundamental and important topics both in the natural sciences and in industrial applications. First integrals arise from the conservation laws of system energy, momentum, and mass, and from constraints on states; these are typically related to specific geometric structures of the governing equations. Existing neural networks designed to ensure such first integrals have shown excellent accuracy in modeling from data. However, these models incorporate the underlying structures, and in most situations where neural networks learn unknown systems, these structures are also unknown. This limitation needs to be overcome for scientific discovery and modeling of unknown systems. To this end, we propose first integral-preserving neural differential equation (FINDE). By leveraging the projection method and the discrete gradient method, FINDE finds and preserves first integrals from data, even in the absence of prior knowledge about underlying structures. Experimental results demonstrate that FINDE can predict future states of target systems much longer and find various quantities consistent with well-known first integrals in a unified manner.

Node classification is a classical graph representation learning task on which Graph Neural Networks (GNNs) have recently achieved strong results. However, it is often believed that standard GNNs only work well for homophilous graphs, i.e., graphs where edges tend to connect nodes of the same class. Graphs without this property are called heterophilous, and it is typically assumed that specialized methods are required to achieve strong performance on such graphs. In this work, we challenge this assumption. First, we show that the standard datasets used for evaluating heterophily-specific models have serious drawbacks, making results obtained by using them unreliable. The most significant of these drawbacks is the presence of a large number of duplicate nodes in the datasets Squirrel and Chameleon, which leads to train-test data leakage. We show that removing duplicate nodes strongly affects GNN performance on these datasets. Then, we propose a set of heterophilous graphs of varying properties that we believe can serve as a better benchmark for evaluating the performance of GNNs under heterophily. We show that standard GNNs achieve strong results on these heterophilous graphs, almost always outperforming specialized models. Our datasets and the code for reproducing our experiments are available at https://github.com/yandex-research/heterophilous-graphs

The saturation effect refers to the phenomenon that the kernel ridge regression (KRR) fails to achieve the information theoretical lower bound when the smoothness of the underground truth function exceeds certain level. The saturation effect has been widely observed in practices and a saturation lower bound of KRR has been conjectured for decades. In this paper, we provide a proof of this long-standing conjecture.

High-quality instance segmentation has shown emerging importance in computer vision. Without any refinement, DCT-Mask directly generates high-resolution masks by compressed vectors. To further refine masks obtained by compressed vectors, we propose for the first time a compressed vector based multi-stage refinement framework. However, the vanilla combination does not bring significant gains, because changes in some elements of the DCT vector will affect the prediction of the entire mask. Thus, we propose a simple and novel method named PatchDCT, which separates the mask decoded from a DCT vector into several patches and refines each patch by the designed classifier and regressor. Specifically, the classifier is used to distinguish mixed patches from all patches, and to correct previously mispredicted foreground and background patches. In contrast, the regressor is used for DCT vector prediction of mixed patches, further refining the segmentation quality at boundary locations. Experiments on COCO show that our method achieves 2.0\%, 3.2\%, 4.5\% AP and 3.4\%, 5.3\%, 7.0\% Boundary AP improvements over Mask-RCNN on COCO, LVIS, and Cityscapes, respectively. It also surpasses DCT-Mask by 0.7\%, 1.1\%, 1.3\% AP and 0.9\%, 1.7\%, 4.2\% Boundary AP on COCO, LVIS and Cityscapes. Besides, the performance of PatchDCT is also competitive with other state-of-the-art methods.

Hyperparameter optimization (HPO) and neural architecture search (NAS) are methods of choice to obtain the best-in-class machine learning models, but in practice they can be costly to run. When models are trained on large datasets, tuning them with HPO or NAS rapidly becomes prohibitively expensive for practitioners, even when efficient multi-fidelity methods are employed. We propose an approach to tackle the challenge of tuning machine learning models trained on large datasets with limited computational resources. Our approach, named PASHA, extends ASHA and is able to dynamically allocate maximum resources for the tuning procedure depending on the need. The experimental comparison shows that PASHA identifies well-performing hyperparameter configurations and architectures while consuming significantly fewer computational resources than ASHA.

This work establishes low test error of gradient flow (GF) and stochastic gradient descent (SGD) on two-layer ReLU networks with standard initialization scale, in three regimes where key sets of weights rotate little (either naturally due to GF and SGD, or due to an artificial constraint), and making use of margins as the core analysis technique. The first regime is near initialization, specifically until the weights have moved by $\mathcal{O}(\sqrt m)$, where $m$ denotes the network width, which is in sharp contrast to the $\mathcal{O}(1)$ weight motion allowed by the Neural Tangent Kernel (NTK); here it is shown that GF and SGD only need a network width and number of samples inversely proportional to the NTK margin, and moreover that GF attains at least the NTK margin itself and in particular escapes bad KKT points of the margin objective, whereas prior work could only establish nondecreasing but arbitrarily small margins. The second regime is the Neural Collapse (NC) setting, where data lies in well-separated groups, and the sample complexity scales with the number of groups; here the contribution over prior work is an analysis of the entire GF trajectory from initialization. Lastly, if the inner layer weights are constrained to change in norm only and can not rotate, then GF with large widths achieves globally maximal margins, and its sample complexity scales with their inverse; this is in contrast to prior work, which required infinite width and a tricky dual convergence assumption.

Local SGD is a communication-efficient variant of SGD for large-scale training, where multiple GPUs perform SGD independently and average the model parameters periodically. It has been recently observed that Local SGD can not only achieve the design goal of reducing the communication overhead but also lead to higher test accuracy than the corresponding SGD baseline (Lin et al., 2020b), though the training regimes for this to happen are still in debate (Ortiz et al., 2021). This paper aims to understand why (and when) Local SGD generalizes better based on Stochastic Differential Equation (SDE) approximation. The main contributions of this paper include (i) the derivation of an SDE that captures the long-term behavior of Local SGD in the small learning rate regime, showing how noise drives the iterate to drift and diffuse after it has reached close to the manifold of local minima, (ii) a comparison between the SDEs of Local SGD and SGD, showing that Local SGD induces a stronger drift term that can result in a stronger effect of regularization, e.g., a faster reduction of sharpness, and (iii) empirical evidence validating that having a small learning rate and long enough training time enables the generalization improvement over SGD but removing either of the two conditions leads to no improvement.

Graph neural networks have shown great potential for the description of a variety of chemical systems. However, standard message passing does not explicitly account for long-range and directional interactions, for instance due to electrostatics. In this work, an anisotropic state based on Cartesian multipoles is proposed as an addition to the existing hidden features. With the anisotropic state, message passing can be modified to explicitly account for directional interactions. Compared to existing models, this modification results in relatively little additional computational cost. Most importantly, the proposed formalism offers as a distinct advantage the seamless integration of (1) anisotropic long-range interactions, (2) interactions with surrounding fields and particles that are not part of the graph, and (3) the fast multipole method. As an exemplary use case, the application to quantum mechanics/molecular mechanics (QM/MM) systems is demonstrated.

Algorithmic fairness plays an increasingly critical role in machine learning research. Several group fairness notions and algorithms have been proposed. However, the fairness guarantee of existing fair classification methods mainly depend on specific data distributional assumptions, often requiring large sample sizes, and fairness could be violated when there is a modest number of samples, which is often the case in practice. In this paper, we propose FaiREE, a fair classification algorithm which can satisfy group fairness constraints with finite-sample and distribution-free theoretical guarantees. FaiREE can be adapted to satisfying various group fairness notions (e.g., Equality of Opportunity, Equalized Odds, Demographic Parity, etc.) and achieve the optimal accuracy. These theoretical guarantees are further supported by experiments on both synthetic and real data. FaiREE is shown to have favorable performance over state-of-the-art algorithms.

Multimodal VAEs have recently gained attention as efficient models for weakly-supervised generative learning with multiple modalities. However, all existing variants of multimodal VAEs are affected by a non-trivial trade-off between generative quality and generative coherence. In particular mixture-based models achieve good coherence only at the expense of sample diversity and a resulting lack of generative quality. We present a novel variant of the mixture-of-experts multimodal variational autoencoder that improves its generative quality, while maintaining high semantic coherence. We model shared and modality-specific information in separate latent subspaces, proposing an objective that overcomes certain dependencies on hyperparameters that arise for existing approaches with the same latent space structure. Compared to these existing approaches, we show increased robustness with respect to changes in the design of the latent space, in terms of the capacity allocated to modality-specific subspaces. We show that our model achieves both good generative coherence and high generative quality in challenging experiments, including more complex multimodal datasets than those used in previous works.