通用机器学习 · supervised learning

We currently do not have an understanding of semi-supervised learning (SSL) objectives such as pseudo-labelling and entropy minimization as log-likelihoods, which precludes the development of e.g. Bayesian SSL. Here, we note that benchmark image datasets such as CIFAR-10 are carefully curated, and we formulate SSL objectives as a log-likelihood in a generative model of data curation. We show that SSL objectives, from entropy minimization and pseudo-labelling, to state-of-the-art techniques similar to FixMatch can be understood as lower-bounds on our principled log-likelihood. We are thus able to introduce a Bayesian extension of SSL, which gives considerable improvements over standard SSL in the setting of 40 labelled points on CIFAR-10, with performance of $92.2\pm 0.3\%$ vs $88.6\%$ in the original FixMatch paper. Finally, our theory suggests that SSL is effective in part due to the statistical patterns induced by data curation. This provides an explanation of past results which show SSL performs better on clean datasets without any ``out of distribution'' examples. Confirming these results we find that SSL gave much larger performance improvements on curated than on uncurated data, using matched curated and uncurated datasets based on Galaxy Zoo 2.

Learning mappings between infinite-dimensional function spaces have achieved empirical success in many disciplines of machine learning, including generative modeling, functional data analysis, causal inference, and multi-agent reinforcement learning. In this paper, we study the statistical limit of learning a Hilbert-Schmidt operator between two infinite-dimensional Sobolev reproducing kernel Hilbert spaces. We establish the information-theoretic lower bound in terms of the Sobolev Hilbert-Schmidt norm and show that a regularization that learns the spectral components below the bias contour and ignores the ones above the variance contour can achieve the optimal learning rate. At the same time, the spectral components between the bias and variance contours give us flexibility in designing computationally feasible machine learning algorithms. Based on this observation, we develop a multilevel kernel operator learning algorithm that is optimal when learning linear operators between infinite-dimensional function spaces.

The critical challenge of Semi-Supervised Learning (SSL) is how to effectively leverage the limited labeled data and massive unlabeled data to improve the model's generalization performance. In this paper, we first revisit the popular pseudo-labeling methods via a unified sample weighting formulation and demonstrate the inherent quantity-quality trade-off problem of pseudo-labeling with thresholding, which may prohibit learning. To this end, we propose SoftMatch to overcome the trade-off by maintaining both high quantity and high quality of pseudo-labels during training, effectively exploiting the unlabeled data. We derive a truncated Gaussian function to weight samples based on their confidence, which can be viewed as a soft version of the confidence threshold. We further enhance the utilization of weakly-learned classes by proposing a uniform alignment approach. In experiments, SoftMatch shows substantial improvements across a wide variety of benchmarks, including image, text, and imbalanced classification.

Unlike vision and language data which usually has a unique format, molecules can naturally be characterized using different chemical formulations. One can view a molecule as a 2D graph or define it as a collection of atoms located in a 3D space. For molecular representation learning, most previous works designed neural networks only for a particular data format, making the learned models likely to fail for other data formats. We believe a general-purpose neural network model for chemistry should be able to handle molecular tasks across data modalities. To achieve this goal, in this work, we develop a novel Transformer-based Molecular model called Transformer-M, which can take molecular data of 2D or 3D formats as input and generate meaningful semantic representations. Using the standard Transformer as the backbone architecture, Transformer-M develops two separated channels to encode 2D and 3D structural information and incorporate them with the atom features in the network modules. When the input data is in a particular format, the corresponding channel will be activated, and the other will be disabled. By training on 2D and 3D molecular data with properly designed supervised signals, Transformer-M automatically learns to leverage knowledge from different data modalities and correctly capture the representations. We conducted extensive experiments for Transformer-M. All empirical results show that Transformer-M can simultaneously achieve strong performance on 2D and 3D tasks, suggesting its broad applicability. The code and models will be made publicly available at https://github.com/lsj2408/Transformer-M.

The Strong Lottery Ticket Hypothesis (SLTH) stipulates the existence of a subnetwork within a sufficiently overparameterized (dense) neural network that---when initialized randomly and without any training---achieves the accuracy of a fully trained target network. Recent works by Da Cunha et. al 2022, Burkholz 2022 demonstrate that the SLTH can be extended to translation equivariant networks---i.e. CNNs---with the same level of overparametrization as needed for the SLTs in dense networks. However, modern neural networks are capable of incorporating more than just translation symmetry, and developing general equivariant architectures such as rotation and permutation has been a powerful design principle. In this paper, we generalize the SLTH to functions that preserve the action of the group $G$---i.e. $G$-equivariant network---and prove, with high probability, that one can approximate any $G$-equivariant network of fixed width and depth by pruning a randomly initialized overparametrized $G$-equivariant network to a $G$-equivariant subnetwork. We further prove that our prescribed overparametrization scheme is optimal and provide a lower bound on the number of effective parameters as a function of the error tolerance. We develop our theory for a large range of groups, including subgroups of the Euclidean $\text{E}(2)$ and Symmetric group $G \leq \mathcal{S}_n$---allowing us to find SLTs for MLPs, CNNs, $\text{E}(2)$-steerable CNNs, and permutation equivariant networks as specific instantiations of our unified framework. Empirically, we verify our theory by pruning overparametrized $\text{E}(2)$-steerable CNNs, $k$-order GNNs, and message passing GNNs to match the performance of trained target networks.

Though Self-supervised learning (SSL) has been widely studied as a promising technique for representation learning, it doesn't generalize well on long-tailed datasets due to the majority classes dominating the feature space. Recent work shows that the long-tailed learning performance could be boosted by sampling extra in-domain (ID) data for self-supervised training, however, large-scale ID data which can rebalance the minority classes are expensive to collect. In this paper, we propose an alternative but easy-to-use and effective solution, \textbf{C}ontrastive with \textbf{O}ut-of-distribution (OOD) data for \textbf{L}ong-\textbf{T}ail learning (COLT), which can effectively exploit OOD data to dynamically re-balance the feature space. We empirically identify the counter-intuitive usefulness of OOD samples in SSL long-tailed learning and principally design a novel SSL method. Concretely, we first localize the `\emph{head}' and `\emph{tail}' samples by assigning a tailness score to each OOD sample based on its neighborhoods in the feature space. Then, we propose an online OOD sampling strategy to dynamically re-balance the feature space. Finally, we enforce the model to be capable of distinguishing ID and OOD samples by a distribution-level supervised contrastive loss. Extensive experiments are conducted on various datasets and several state-of-the-art SSL frameworks to verify the effectiveness of the proposed method. The results show that our method significantly improves the performance of SSL on long-tailed datasets by a large margin, and even outperforms previous work which uses external ID data. Our code is available at \url{https://github.com/JianhongBai/COLT}.

Pseudo-labeling has proven to be a promising semi-supervised learning (SSL) paradigm. Existing pseudo-labeling methods commonly assume that the class distributions of training data are balanced. However, such an assumption is far from realistic scenarios and thus severely limits the performance of current pseudo-labeling methods under the context of class-imbalance. To alleviate this problem, we design a bias adaptive classifier that targets the imbalanced SSL setups. The core idea is to automatically assimilate the training bias caused by class imbalance via the bias adaptive classifier, which is composed of a novel bias attractor and the original linear classifier. The bias attractor is designed as a light-weight residual network and learned through a bi-level learning framework, which enables the bias adaptive classifier to fit imbalanced training data, while the linear classifier can provide unbiased label prediction for each class. We conduct extensive experiments under various imbalanced semi-supervised setups, and the results demonstrate that our method can be applied to different pseudo-labeling models and is superior to current state-of-the-art methods.

The energy consumption for training deep learning models is increasing at an alarming rate due to the growth of training data and model scale, resulting in a negative impact on carbon neutrality. Energy consumption is an especially pressing issue for AutoML algorithms because it usually requires repeatedly training large numbers of computationally intensive deep models to search for optimal configurations. This paper takes one of the most essential steps in developing energy-aware (EA) NAS methods, by providing a benchmark that makes EA-NAS research more reproducible and accessible. Specifically, we present the first large-scale energy-aware benchmark that allows studying AutoML methods to achieve better trade-offs between performance and search energy consumption, named EA-HAS-Bench. EA-HAS-Bench provides a large-scale architecture/hyperparameter joint search space, covering diversified configurations related to energy consumption. Furthermore, we propose a novel surrogate model specially designed for large joint search space, which proposes a Bezier curve-based model to predict learning curves with unlimited shape and length. Based on the proposed dataset, we new energy-aware AutoML method that arms existing AutoML algorithms to consider the search energy consumption, and our experiments show that the modified energy-aware AutoML methods achieve a better trade-off between energy consumption and model performance.

Recent state-of-the-art methods in imbalanced semi-supervised learning (SSL) rely on confidence-based pseudo-labeling with consistency regularization. To obtain high-quality pseudo-labels, a high confidence threshold is typically adopted. However, it has been shown that softmax-based confidence scores in deep networks can be arbitrarily high for samples far from the training data, and thus, the pseudo-labels for even high-confidence unlabeled samples may still be unreliable. In this work, we present a new perspective of pseudo-labeling for imbalanced SSL. Without relying on model confidence, we propose to measure whether an unlabeled sample is likely to be "in-distribution''; i.e., close to the current training data. To decide whether an unlabeled sample is "in-distribution'' or "out-of-distribution'', we adopt the energy score from out-of-distribution detection literature. As training progresses and more unlabeled samples become in-distribution and contribute to training, the combined labeled and pseudo-labeled data can better approximate the true class distribution to improve the model. Experiments demonstrate that our energy-based pseudo-labeling method, InPL, albeit conceptually simple, significantly outperforms confidence-based methods on imbalanced SSL benchmarks. For example, it produces a 4-6% absolute accuracy improvement on CIFAR10-LT when the imbalance ratio is higher than 50. When combined with state-of-the-art long-tailed SSL methods, further improvements are attained. In particular, in one of the most challenging scenarios, InPL achieves a 6.9% accuracy improvement over the best competitor.

Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet space, so the difficulty of solving the coupled PDEs depends on dealing with the coupled mappings between the functions. Towards this end, we propose a \textit{coupled multiwavelets neural operator} (CMWNO) learning scheme by decoupling the coupled integral kernels during the multiwavelet decomposition and reconstruction procedures in the Wavelet space. The proposed model achieves significantly higher accuracy compared to previous learning-based solvers in solving the coupled PDEs including Gray-Scott (GS) equations and the non-local mean field game (MFG) problem. According to our experimental results, the proposed model exhibits a $2X-4X$ improvement relative $L$2 error compared to the best results from the state-of-the-art models.

Boundary conditions (BCs) are important groups of physics-enforced constraints that are necessary for solutions of Partial Differential Equations (PDEs) to satisfy at specific spatial locations. These constraints carry important physical meaning, and guarantee the existence and the uniqueness of the PDE solution. Current neural-network based approaches that aim to solve PDEs rely only on training data to help the model learn BCs implicitly, however, there is no guarantee of BC satisfaction by these models during evaluation. In this work, we propose Boundary enforcing Operator Network (BOON) that enables the BC satisfaction of neural operators by making structural changes to the operator kernel. We provide our refinement procedure, and demonstrate the satisfaction of physics-based BCs such as Dirichlet, Neumann, and periodic by the solutions obtained by BOON. Numerical experiments based on multiple PDEs with a wide variety of applications indicate that the proposed approach ensures satisfaction of BCs, and leads to more accurate solutions over the whole domain. The proposed method exhibits a (2X-20X) improvement in accuracy (0.000084 relative $L^2$ error for Burgers' equation). Code available at: https://github.com/amazon-science/boon.

Most approaches for self-supervised learning (SSL) are optimised on curated balanced datasets, e.g. ImageNet, despite the fact that natural data usually exhibits long-tail distributions. In this paper, we analyse the behaviour of one of the most popular variants of SSL, i.e. contrastive methods, on imbalanced data. In particular, we investigate the role of the temperature parameter $\tau$ in the contrastive loss, by analysing the loss through the lens of average distance maximisation, and find that a large $\tau$ emphasises group-wise discrimination, whereas a small $\tau$ leads to a higher degree of instance discrimination. While $\tau$ has thus far been treated exclusively as a constant hyperparameter, in this work, we propose to employ a dynamic $\tau$ and show that a simple cosine schedule can yield significant improvements in the learnt representations. Such a schedule results in a constant `task switching' between an emphasis on instance discrimination and group-wise discrimination and thereby ensures that the model learns both group-wise features, as well as instance-specific details. Since frequent classes benefit from the former, while infrequent classes require the latter, we find this method to consistently improve separation between the classes in long-tail data without any additional computational cost.

Despite the impressive progress of self-supervised learning (SSL), its applicability to low-compute networks has received limited attention. Reported performance has trailed behind standard supervised pre-training by a large margin, barring self-supervised learning from making an impact on models that are deployed on device. Most prior works attribute this poor performance to the capacity bottleneck of the low-compute networks and opt to bypass the problem through the use of knowledge distillation (KD). In this work, we revisit SSL for efficient neural networks, taking a closer at what are the detrimental factors causing the practical limitations, and whether they are intrinsic to the self-supervised low-compute setting. We find that, contrary to accepted knowledge, there is no intrinsic architectural bottleneck, we diagnose that the performance bottleneck is related to the model complexity vs regularization strength trade-off. In particular, we start by empirically observing that the use of local views can have a dramatic impact on the effectiveness of the SSL methods. This hints at view sampling being one of the performance bottlenecks for SSL on low-capacity networks. We hypothesize that the view sampling strategy for large neural networks, which requires matching views in very diverse spatial scales and contexts, is too demanding for low-capacity architectures. We systematize the design of the view sampling mechanism, leading to a new training methodology that consistently improves the performance across different SSL methods (e.g. MoCo-v2, SwAV or DINO), different low-size networks (convolution-based networks, e.g. MobileNetV2, ResNet18, ResNet34 and vision transformer, e.g. ViT-Ti), and different tasks (linear probe, object detection, instance segmentation and semi-supervised learning). Our best models establish new state-of-the-art for SSL methods on low-compute networks despite not using a KD loss term. Code is publicly available at github.com/saic-fi/SSLight.

Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 output dimensions × 50k datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output dimensions).

Semi-supervised learning and weakly supervised learning are important paradigms that aim to reduce the growing demand for labeled data in current machine learning applications. In this paper, we introduce a novel analysis of the classical label propagation algorithm (LPA) (Zhu & Ghahramani, 2002) that moreover takes advantage of useful prior information, specifically probabilistic hypothesized labels on the unlabeled data. We provide an error bound that exploits both the local geometric properties of the underlying graph and the quality of the prior information. We also propose a framework to incorporate multiple sources of noisy information. In particular, we consider the setting of weak supervision, where our sources of information are weak labelers. We demonstrate the ability of our approach on multiple benchmark weakly supervised classification tasks, showing improvements upon existing semi-supervised and weakly supervised methods.

Automatically optimizing the hyperparameters of Machine Learning algorithms is one of the primary open questions in AI. Existing work in Hyperparameter Optimization (HPO) trains surrogate models for approximating the response surface of hyperparameters as a regression task. In contrast, we hypothesize that the optimal strategy for training surrogates is to preserve the ranks of the performances of hyperparameter configurations as a Learning to Rank problem. As a result, we present a novel method that meta-learns neural network surrogates optimized for ranking the configurations' performances while modeling their uncertainty via ensembling. In a large-scale experimental protocol comprising 12 baselines, 16 HPO search spaces and 86 datasets/tasks, we demonstrate that our method achieves new state-of-the-art results in HPO.

We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by advection-dominated partial differential equations. Those systems have slow-decaying Kolmogorov n-width that hinders standard methods, including reduced order modeling, from producing high-fidelity simulations at low cost. In this work, we construct hypernetwork-based latent dynamical models directly on the parameter space of a compact representation network. We leverage the expressive power of the network and a specially designed consistency-inducing regularization to obtain latent trajectories that are both low-dimensional and smooth. These properties render our surrogate models highly efficient at inference time. We show the efficacy of our framework by learning models that generate accurate multi-step rollout predictions at much faster inference speed compared to competitors, for several challenging examples.

Recently, self-supervised learning has attracted great attention, since it only requires unlabeled data for model training. Contrastive learning is one popular method for self-supervised learning and has achieved promising empirical performance. However, the theoretical understanding of its generalization ability is still limited. To this end, we define a kind of $(\sigma,\delta)$-measure to mathematically quantify the data augmentation, and then provide an upper bound of the downstream classification error rate based on the measure. It reveals that the generalization ability of contrastive self-supervised learning is related to three key factors: alignment of positive samples, divergence of class centers, and concentration of augmented data. The first two factors are properties of learned representations, while the third one is determined by pre-defined data augmentation. We further investigate two canonical contrastive losses, InfoNCE and cross-correlation, to show how they provably achieve the first two factors. Moreover, we conduct experiments to study the third factor, and observe a strong correlation between downstream performance and the concentration of augmented data.

Contrastive learning is a cornerstone underlying recent progress in multi-view and multimodal learning, e.g., in representation learning with image/caption pairs. While its effectiveness is not yet fully understood, a line of recent work reveals that contrastive learning can invert the data generating process and recover ground truth latent factors shared between views. In this work, we present new identifiability results for multimodal contrastive learning, showing that it is possible to recover shared factors in a more general setup than the multi-view setting studied previously. Specifically, we distinguish between the multi-view setting with one generative mechanism (e.g., multiple cameras of the same type) and the multimodal setting that is characterized by distinct mechanisms (e.g., cameras and microphones). Our work generalizes previous identifiability results by redefining the generative process in terms of distinct mechanisms with modality-specific latent variables. We prove that contrastive learning can block-identify latent factors shared between modalities, even when there are nontrivial dependencies between factors. We empirically verify our identifiability results with numerical simulations and corroborate our findings on a complex multimodal dataset of image/text pairs. Zooming out, our work provides a theoretical basis for multimodal representation learning and explains in which settings multimodal contrastive learning can be effective in practice.

Recently, it has been shown that neural networks not only approximate the ground-state wave functions of a single molecular system well but can also generalize to multiple geometries. While such generalization significantly speeds up training, each energy evaluation still requires Monte Carlo integration which limits the evaluation to a few geometries. In this work, we address the inference shortcomings by proposing the Potential learning from ab-initio Networks (PlaNet) framework, in which we simultaneously train a surrogate model in addition to the neural wave function. At inference time, the surrogate avoids expensive Monte-Carlo integration by directly estimating the energy, accelerating the process from hours to milliseconds. In this way, we can accurately model high-resolution multi-dimensional energy surfaces for larger systems that previously were unobtainable via neural wave functions. Finally, we explore an additional inductive bias by introducing physically-motivated restricted neural wave function models. We implement such a function with several additional improvements in the new PESNet++ model. In our experimental evaluation, PlaNet accelerates inference by 7 orders of magnitude for larger molecules like ethanol while preserving accuracy. Compared to previous energy surface networks, PESNet++ reduces energy errors by up to 74%.