NeurIPS 2022 论文列表

Conference on Neural Information Processing Systems

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Multi-layer State Evolution Under Random Convolutional Design

Max Daniels, Cedric Gerbelot, Florent Krzakala, Lenka Zdeborova

展开摘要

Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstruction algorithms under generative priors is, however, challenging. For generative priors with fully connected layers and Gaussian i.i.d. weights, this was achieved by the multi-layer approximate message (ML-AMP) algorithm via a rigorous state evolution. However, practical generative priors are typically convolutional, allowing for computational benefits and inductive biases, and so the Gaussian i.i.d. weight assumption is very limiting. In this paper, we overcome this limitation and establish the state evolution of ML-AMP for random convolutional layers. We prove in particular that random convolutional layers belong to the same universality class as Gaussian matrices. Our proof technique is of an independent interest as it establishes a mapping between convolutional matrices and spatially coupled sensing matrices used in coding theory.

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Inherently Explainable Reinforcement Learning in Natural Language

Xiangyu Peng, Mark Riedl, Prithviraj Ammanabrolu

展开摘要

We focus on the task of creating a reinforcement learning agent that is inherently explainable---with the ability to produce immediate local explanations by thinking out loud while performing a task and analyzing entire trajectories post-hoc to produce temporally extended explanations. This Hierarchically Explainable Reinforcement Learning agent (HEX-RL), operates in Interactive Fictions, text-based game environments in which an agent perceives and acts upon the world using textual natural language. These games are usually structured as puzzles or quests with long-term dependencies in which an agent must complete a sequence of actions to succeed---providing ideal environments in which to test an agent's ability to explain its actions. Our agent is designed to treat explainability as a first-class citizen, using an extracted symbolic knowledge graph-based state representation coupled with a Hierarchical Graph Attention mechanism that points to the facts in the internal graph representation that most influenced the choice of actions. Experiments show that this agent provides significantly improved explanations over strong baselines, as rated by human participants generally unfamiliar with the environment, while also matching state-of-the-art task performance.

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On the Effectiveness of Persistent Homology

Renata Turkes, Guido Montufar, Nina Otter

展开摘要

Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known for which classes of problems it is most effective, or to what extent it can detect geometric or topological features. The goal of this work is to identify some types of problems where PH performs well or even better than other methods in data analysis. We consider three fundamental shape analysis tasks: the detection of the number of holes, curvature and convexity from 2D and 3D point clouds sampled from shapes. Experiments demonstrate that PH is successful in these tasks, outperforming several baselines, including PointNet, an architecture inspired precisely by the properties of point clouds. In addition, we observe that PH remains effective for limited computational resources and limited training data, as well as out-of-distribution test data, including various data transformations and noise. For convexity detection, we provide a theoretical guarantee that PH is effective for this task in $\mathbb{R}^d$, and demonstrate the detection of a convexity measure on the FLAVIA dataset of plant leaf images. Due to the crucial role of shape classification in understanding mathematical and physical structures and objects, and in many applications, the findings of this work will provide some knowledge about the types of problems that are appropriate for PH, so that it can --- to borrow the words from Wigner 1960 --- ``remain valid in future research, and extend, to our pleasure", but to our lesser bafflement, to a variety of applications.

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GAMA: Generative Adversarial Multi-Object Scene Attacks

Abhishek Aich, Calvin-Khang Ta, Akash A Gupta, Chengyu Song, Srikanth Krishnamurthy, M. Salman Asif, Amit Roy-Chowdhury

展开摘要

The majority of methods for crafting adversarial attacks have focused on scenes with a single dominant object (e.g., images from ImageNet). On the other hand, natural scenes include multiple dominant objects that are semantically related. Thus, it is crucial to explore designing attack strategies that look beyond learning on single-object scenes or attack single-object victim classifiers. Due to their inherent property of strong transferability of perturbations to unknown models, this paper presents the first approach of using generative models for adversarial attacks on multi-object scenes. In order to represent the relationships between different objects in the input scene, we leverage upon the open-sourced pre-trained vision-language model CLIP (Contrastive Language-Image Pre-training), with the motivation to exploit the encoded semantics in the language space along with the visual space. We call this attack approach Generative Adversarial Multi-object Attacks (GAMA). GAMA demonstrates the utility of the CLIP model as an attacker's tool to train formidable perturbation generators for multi-object scenes. Using the joint image-text features to train the generator, we show that GAMA can craft potent transferable perturbations in order to fool victim classifiers in various attack settings. For example, GAMA triggers ~16% more misclassification than state-of-the-art generative approaches in black-box settings where both the classifier architecture and data distribution of the attacker are different from the victim. Our code is available here: https://abhishekaich27.github.io/gama.html

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The Sample Complexity of One-Hidden-Layer Neural Networks

Gal Vardi, Ohad Shamir, Nathan Srebro

展开摘要

We study norm-based uniform convergence bounds for neural networks, aiming at a tight understanding of how these are affected by the architecture and type of norm constraint, for the simple class of scalar-valued one-hidden-layer networks, and inputs bounded in Euclidean norm. We begin by proving that in general, controlling the spectral norm of the hidden layer weight matrix is insufficient to get uniform convergence guarantees (independent of the network width), while a stronger Frobenius norm control is sufficient, extending and improving on previous work. Motivated by the proof constructions, we identify and analyze two important settings where (perhaps surprisingly) a mere spectral norm control turns out to be sufficient: First, when the network's activation functions are sufficiently smooth (with the result extending to deeper networks); and second, for certain types of convolutional networks. In the latter setting, we study how the sample complexity is additionally affected by parameters such as the amount of overlap between patches and the overall number of patches.

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Open High-Resolution Satellite Imagery: The WorldStrat Dataset – With Application to Super-Resolution

Julien Cornebise, Ivan Orsolic, Freddie Kalaitzis

展开摘要

Analyzing the planet at scale with satellite imagery and machine learning is a dream that has been constantly hindered by the cost of difficult-to-access highly-representative high-resolution imagery. To remediate this, we introduce here the WorldStratified dataset. The largest and most varied such publicly available dataset, at Airbus SPOT 6/7 satellites' high resolution of up to 1.5 m/pixel, empowered by European Space Agency's Phi-Lab as part of the ESA-funded QueryPlanet project, we curate 10,000 sq km of unique locations to ensure stratified representation of all types of land-use across the world: from agriculture to ice caps, from forests to multiple urbanization densities. We also enrich those with locations typically under-represented in ML datasets: sites of humanitarian interest, illegal mining sites, and settlements of persons at risk. We temporally-match each high-resolution image with multiple low-resolution images from the freely accessible lower-resolution Sentinel-2 satellites at 10 m/pixel. We accompany this dataset with an open-source Python package to: rebuild or extend the WorldStrat dataset, train and infer baseline algorithms, and learn with abundant tutorials, all compatible with the popular EO-learn toolbox. We hereby hope to foster broad-spectrum applications of ML to satellite imagery, and possibly develop from free public low-resolution Sentinel2 imagery the same power of analysis allowed by costly private high-resolution imagery. We illustrate this specific point by training and releasing several highly compute-efficient baselines on the task of Multi-Frame Super-Resolution. License-wise, the high-resolution Airbus imagery is CC-BY-NC, while the labels, Sentinel2 imagery, and trained weights are under CC-BY, and the source code under BSD, to allow for the widest use and dissemination. The dataset is available at \url{https://zenodo.org/record/6810792} and the software package at \url{https://github.com/worldstrat/worldstrat}.

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Hand-Object Interaction Image Generation

Hezhen Hu, Weilun Wang, Wengang Zhou, Houqiang Li

展开摘要

In this work, we are dedicated to a new task, i.e., hand-object interaction image generation, which aims to conditionally generate the hand-object image under the given hand, object and their interaction status. This task is challenging and research-worthy in many potential application scenarios, such as AR/VR games and online shopping, etc. To address this problem, we propose a novel HOGAN framework, which utilizes the expressive model-aware hand-object representation and leverages its inherent topology to build the unified surface space. In this space, we explicitly consider the complex self- and mutual occlusion during interaction. During final image synthesis, we consider different characteristics of hand and object and generate the target image in a split-and-combine manner. For evaluation, we build a comprehensive protocol to access both the fidelity and structure preservation of the generated image. Extensive experiments on two large-scale datasets, i.e., HO3Dv3 and DexYCB, demonstrate the effectiveness and superiority of our framework both quantitatively and qualitatively. The code will be available at https://github.com/play-with-HOI-generation/HOIG.

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Learning Options via Compression

Yiding Jiang, Evan Zheran Liu, Benjamin Eysenbach, J Zico Kolter, Chelsea Finn

展开摘要

Identifying statistical regularities in solutions to some tasks in multi-task reinforcement learning can accelerate the learning of new tasks. Skill learning offers one way of identifying these regularities by decomposing pre-collected experiences into a sequence of skills. A popular approach to skill learning is maximizing the likelihood of the pre-collected experience with latent variable models, where the latent variables represent the skills. However, there are often many solutions that maximize the likelihood equally well, including degenerate solutions. To address this underspecification, we propose a new objective that combines the maximum likelihood objective with a penalty on the description length of the skills. This penalty incentivizes the skills to maximally extract common structures from the experiences. Empirically, our objective learns skills that solve downstream tasks in fewer samples compared to skills learned from only maximizing likelihood. Further, while most prior works in the offline multi-task setting focus on tasks with low-dimensional observations, our objective can scale to challenging tasks with high-dimensional image observations.

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Sub-exponential time Sum-of-Squares lower bounds for Principal Components Analysis

Aaron Potechin, Goutham Rajendran

展开摘要

Principal Components Analysis (PCA) is a dimension-reduction technique widely used in machine learning and statistics. However, due to the dependence of the principal components on all the dimensions, the components are notoriously hard to interpret. Therefore, a variant known as sparse PCA is often preferred. Sparse PCA learns principal components of the data but enforces that such components must be sparse. This has applications in diverse fields such as computational biology and image processing. To learn sparse principal components, it's well known that standard PCA will not work, especially in high dimensions, and therefore algorithms for sparse PCA are often studied as a separate endeavor. Various algorithms have been proposed for Sparse PCA over the years, but given how fundamental it is for applications in science, the limits of efficient algorithms are only partially understood. In this work, we study the limits of the powerful Sum of Squares (SoS) family of algorithms for Sparse PCA. SoS algorithms have recently revolutionized robust statistics, leading to breakthrough algorithms for long-standing open problems in machine learning, such as optimally learning mixtures of gaussians, robust clustering, robust regression, etc. Moreover, it is believed to be the optimal robust algorithm for many statistical problems. Therefore, for sparse PCA, it's plausible that it can beat simpler algorithms such as diagonal thresholding that have been traditionally used. In this work, we show that this is not the case, by exhibiting strong tradeoffs between the number of samples required, the sparsity and the ambient dimension, for which SoS algorithms, even if allowed sub-exponential time, will fail to optimally recover the component. Our results are complemented by known algorithms in literature, thereby painting an almost complete picture of the behavior of efficient algorithms for sparse PCA. Since SoS algorithms encapsulate many algorithmic techniques such as spectral or statistical query algorithms, this solidifies the message that known algorithms are optimal for sparse PCA. Moreover, our techniques are strong enough to obtain similar tradeoffs for Tensor PCA, another important higher order variant of PCA with applications in topic modeling, video processing, etc.

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Towards Human-Level Bimanual Dexterous Manipulation with Reinforcement Learning

Yuanpei Chen, Tianhao Wu, Shengjie Wang, Xidong Feng, Jiechuan Jiang, Zongqing Lu, Stephen Marcus McAleer, Hao Dong, Song-Chun Zhu, Yaodong Yang

展开摘要

Achieving human-level dexterity is an important open problem in robotics. However, tasks of dexterous hand manipulation even at the baby level are challenging to solve through reinforcement learning (RL). The difficulty lies in the high degrees of freedom and the required cooperation among heterogeneous agents (e.g., joints of fingers). In this study, we propose the Bimanual Dexterous Hands Benchmark (Bi-DexHands), a simulator that involves two dexterous hands with tens of bimanual manipulation tasks and thousands of target objects. Tasks in Bi-DexHands are first designed to match human-level motor skills according to literature in cognitive science, and then are built in Issac Gym; this enables highly efficient RL trainings, reaching 30,000+ FPS by only one single NVIDIA RTX 3090. We provide a comprehensive benchmark for popular RL algorithms under different settings; this includes multi-agent RL, offline RL, multi-task RL, and meta RL. Our results show that PPO type on-policy algorithms can learn to solve simple manipulation tasks that are equivalent up to 48-month human baby (e.g., catching a flying object, opening a bottle), while multi-agent RL can further help to learn manipulations that require skilled bimanual cooperation (e.g., lifting a pot, stacking blocks). Despite the success on each individual task, when it comes to mastering multiple manipulation skills, existing RL algorithms fail to work in most of the multi-task and the few-shot learning tasks, which calls for more future development from the RL community. Our project is open-sourced at https://github.com/PKU-MARL/DexterousHands.

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Learning Neural Acoustic Fields

Andrew Luo, Yilun Du, Michael J. Tarr, Joshua B. Tenenbaum, Antonio Torralba, Chuang Gan

展开摘要

Our environment is filled with rich and dynamic acoustic information. When we walk into a cathedral, the reverberations as much as appearance inform us of the sanctuary's wide open space. Similarly, as an object moves around us, we expect the sound emitted to also exhibit this movement. While recent advances in learned implicit functions have led to increasingly higher quality representations of the visual world, there have not been commensurate advances in learning spatial auditory representations. To address this gap, we introduce Neural Acoustic Fields (NAFs), an implicit representation that captures how sounds propagate in a physical scene. By modeling acoustic propagation in a scene as a linear time-invariant system, NAFs learn to continuously map all emitter and listener location pairs to a neural impulse response function that can then be applied to arbitrary sounds. We demonstrate NAFs on both synthetic and real data, and show that the continuous nature of NAFs enables us to render spatial acoustics for a listener at arbitrary locations. We further show that the representation learned by NAFs can help improve visual learning with sparse views. Finally we show that a representation informative of scene structure emerges during the learning of NAFs.

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Optimal Dynamic Regret in LQR Control

Dheeraj Baby, Yu-Xiang Wang

展开摘要

We consider the problem of nonstochastic control with a sequence of quadratic losses, i.e., LQR control. We provide an efficient online algorithm that achieves an optimal dynamic (policy) regret of $\tilde{O}(n^{1/3} \mathcal{TV}(M_{1:n}^{2/3} \vee 1)$, where $\mathcal{TV}(M_{1:n})$ is the total variation of any oracle sequence of \emph{Disturbance Action} policies parameterized by $M_1,...,M_n$ --- chosen in hindsight to cater to unknown nonstationarity. The rate improves the best known rate of $\tilde{O}(\sqrt{n (\mathcal{TV}(M_{1:n})+1)} )$ for general convex losses and is information-theoretically optimal for LQR. Main technical components include the reduction of LQR to online linear regression with delayed feedback due to Foster & Simchowitz 2020, as well as a new \emph{proper} learning algorithm with an optimal $\tilde{O}(n^{1/3})$ dynamic regret on a family of "minibatched'' quadratic losses, which could be of independent interest.

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Unpacking Reward Shaping: Understanding the Benefits of Reward Engineering on Sample Complexity

Abhishek Gupta, Aldo Pacchiano, Yuexiang Zhai, Sham M. Kakade, Sergey Levine

展开摘要

The success of reinforcement learning in a variety of challenging sequential decision-making problems has been much discussed, but often ignored in this discussion is the consideration of how the choice of reward function affects the behavior of these algorithms. Most practical RL algorithms require copious amounts of reward engineering in order to successfully solve challenging tasks. The idea of this type of ``reward-shaping'' has been often discussed in the literature and is used in practical instantiations, but there is relatively little formal characterization of how the choice of reward shaping can yield benefits in sample complexity for RL problems. In this work, we build on the framework of novelty-based exploration to provide a simple scheme for incorporating shaped rewards into RL along with an analysis tool to show that particular choices of reward shaping provably improve sample efficiency. We characterize the class of problems where these gains are expected to be significant and show how this can be connected to practical algorithms in the literature. We show that these results hold in practice in experimental evaluations as well, providing an insight into the mechanisms through which reward shaping can significantly improve the complexity of reinforcement learning while retaining asymptotic performance.

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A Neural Pre-Conditioning Active Learning Algorithm to Reduce Label Complexity

Seo Taek Kong, Soomin Jeon, Dongbin Na, Jaewon Lee, Hong-Seok Lee, Kyu-Hwan Jung

展开摘要

Deep learning (DL) algorithms rely on massive amounts of labeled data. Semi-supervised learning (SSL) and active learning (AL) aim to reduce this label complexity by leveraging unlabeled data or carefully acquiring labels, respectively. In this work, we primarily focus on designing an AL algorithm but first argue for a change in how AL algorithms should be evaluated. Although unlabeled data is readily available in pool-based AL, AL algorithms are usually evaluated by measuring the increase in supervised learning (SL) performance at consecutive acquisition steps. Because this measures performance gains from both newly acquired instances and newly acquired labels, we propose to instead evaluate the label efficiency of AL algorithms by measuring the increase in SSL performance at consecutive acquisition steps. After surveying tools that can be used to this end, we propose our neural pre-conditioning (NPC) algorithm inspired by a Neural Tangent Kernel (NTK) analysis. Our algorithm incorporates the classifier's uncertainty on unlabeled data and penalizes redundant samples within candidate batches to efficiently acquire a diverse set of informative labels. Furthermore, we prove that NPC improves downstream training in the large-width regime in a manner previously observed to correlate with generalization. Comparisons with other AL algorithms show that a state-of-the-art SSL algorithm coupled with NPC can achieve high performance using very few labeled data.

Accept
Decision-based Black-box Attack Against Vision Transformers via Patch-wise Adversarial Removal

Yucheng Shi, Yahong Han, Yu-an Tan, Xiaohui Kuang

展开摘要

Vision transformers (ViTs) have demonstrated impressive performance and stronger adversarial robustness compared to Convolutional Neural Networks (CNNs). On the one hand, ViTs' focus on global interaction between individual patches reduces the local noise sensitivity of images. On the other hand, the neglect of noise sensitivity differences between image regions by existing decision-based attacks further compromises the efficiency of noise compression, especially for ViTs. Therefore, validating the black-box adversarial robustness of ViTs when the target model can only be queried still remains a challenging problem. In this paper, we theoretically analyze the limitations of existing decision-based attacks from the perspective of noise sensitivity difference between regions of the image, and propose a new decision-based black-box attack against ViTs, termed Patch-wise Adversarial Removal (PAR). PAR divides images into patches through a coarse-to-fine search process and compresses the noise on each patch separately. PAR records the noise magnitude and noise sensitivity of each patch and selects the patch with the highest query value for noise compression. In addition, PAR can be used as a noise initialization method for other decision-based attacks to improve the noise compression efficiency on both ViTs and CNNs without introducing additional calculations. Extensive experiments on three datasets demonstrate that PAR achieves a much lower noise magnitude with the same number of queries.

Accept
Non-identifiability and the Blessings of Misspecification in Models of Molecular Fitness

Eli N Weinstein, Alan Nawzad Amin, Jonathan Frazer, Debora Susan Marks

展开摘要

Understanding the consequences of mutation for molecular fitness and function is a fundamental problem in biology. Recently, generative probabilistic models have emerged as a powerful tool for estimating fitness from evolutionary sequence data, with accuracy sufficient to predict both laboratory measurements of function and disease risk in humans, and to design novel functional proteins. Existing techniques rest on an assumed relationship between density estimation and fitness estimation, a relationship that we interrogate in this article. We prove that fitness is not identifiable from observational sequence data alone, placing fundamental limits on our ability to disentangle fitness landscapes from phylogenetic history. We show on real datasets that perfect density estimation in the limit of infinite data would, with high confidence, result in poor fitness estimation; current models perform accurate fitness estimation because of, not despite, misspecification. Our results challenge the conventional wisdom that bigger models trained on bigger datasets will inevitably lead to better fitness estimation, and suggest novel estimation strategies going forward.

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Meta-ticket: Finding optimal subnetworks for few-shot learning within randomly initialized neural networks

Daiki Chijiwa, Shin'ya Yamaguchi, Atsutoshi Kumagai, Yasutoshi Ida

展开摘要

Few-shot learning for neural networks (NNs) is an important problem that aims to train NNs with a few data. The main challenge is how to avoid overfitting since over-parameterized NNs can easily overfit to such small dataset. Previous work (e.g. MAML by Finn et al. 2017) tackles this challenge by meta-learning, which learns how to learn from a few data by using various tasks. On the other hand, one conventional approach to avoid overfitting is restricting hypothesis spaces by endowing sparse NN structures like convolution layers in computer vision. However, although such manually-designed sparse structures are sample-efficient for sufficiently large datasets, they are still insufficient for few-shot learning. Then the following questions naturally arise: (1) Can we find sparse structures effective for few-shot learning by meta-learning? (2) What benefits will it bring in terms of meta-generalization? In this work, we propose a novel meta-learning approach, called Meta-ticket, to find optimal sparse subnetworks for few-shot learning within randomly initialized NNs. We empirically validated that Meta-ticket successfully discover sparse subnetworks that can learn specialized features for each given task. Due to this task-wise adaptation ability, Meta-ticket achieves superior meta-generalization compared to MAML-based methods especially with large NNs.

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Improving GANs with A Dynamic Discriminator

Ceyuan Yang, Yujun Shen, Yinghao Xu, Deli Zhao, Bo Dai, Bolei Zhou

展开摘要

Discriminator plays a vital role in training generative adversarial networks (GANs) via distinguishing real and synthesized samples. While the real data distribution remains the same, the synthesis distribution keeps varying because of the evolving generator, and thus effects a corresponding change of the bi-classification task assigned to the discriminator. We argue that a discriminator with an on-the-fly adjustment on its capacity can better accommodate such a time-varying task. A comprehensive empirical study confirms that the proposed training strategy, termed as DynamicD, improves the synthesis performance without incurring any additional computation cost or training objectives. Two capacity adjusting schemes are developed for training GANs under different data regimes: i) given a sufficient amount of training data, the discriminator benefits from a progressively increased learning capacity, and ii) when the training data is limited, gradually decreasing the layer width mitigates the over-fitting issue of the discriminator. Experiments on both 2D and 3D-aware image synthesis tasks conducted on a range of datasets substantiate the generalizability of our DynamicD as well as its substantial improvement over the baselines. Furthermore, DynamicD is synergistic to other discriminator-improving approaches (including data augmentation, regularizers, and pre-training), and brings continuous performance gain when combined with them for learning GANs. Code will be made publicly available.

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Lifting Weak Supervision To Structured Prediction

Harit Vishwakarma, Frederic Sala

展开摘要

Weak supervision (WS) is a rich set of techniques that produce pseudolabels by aggregating easily obtained but potentially noisy label estimates from various sources. WS is theoretically well-understood for binary classification, where simple approaches enable consistent estimation of pseudolabel noise rates. Using this result, it has been shown that downstream models trained on the pseudolabels have generalization guarantees nearly identical to those trained on clean labels. While this is exciting, users often wish to use WS for \emph{structured prediction}, where the output space consists of more than a binary or multi-class label set: e.g. rankings, graphs, manifolds, and more. Do the favorable theoretical properties of WS for binary classification lift to this setting? We answer this question in the affirmative for a wide range of scenarios. For labels taking values in a finite metric space, we introduce techniques new to weak supervision based on pseudo-Euclidean embeddings and tensor decompositions, providing a nearly-consistent noise rate estimator. For labels in constant-curvature Riemannian manifolds, we introduce new invariants that also yield consistent noise rate estimation. In both cases, when using the resulting pseudolabels in concert with a flexible downstream model, we obtain generalization guarantees nearly identical to those for models trained on clean data. Several of our results, which can be viewed as robustness guarantees in structured prediction with noisy labels, may be of independent interest.

Accept
Learning Energy Networks with Generalized Fenchel-Young Losses

Mathieu Blondel, Felipe Llinares-López, Robert Dadashi, Leonard Hussenot, Matthieu Geist

展开摘要

Energy-based models, a.k.a. energy networks, perform inference by optimizing an energy function, typically parametrized by a neural network. This allows one to capture potentially complex relationships between inputs and outputs. To learn the parameters of the energy function, the solution to that optimization problem is typically fed into a loss function. The key challenge for training energy networks lies in computing loss gradients, as this typically requires argmin/argmax differentiation. In this paper, building upon a generalized notion of conjugate function, which replaces the usual bilinear pairing with a general energy function, we propose generalized Fenchel-Young losses, a natural loss construction for learning energy networks. Our losses enjoy many desirable properties and their gradients can be computed efficiently without argmin/argmax differentiation. We also prove the calibration of their excess risk in the case of linear-concave energies. We demonstrate our losses on multilabel classification and imitation learning tasks.

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