Meta-learning that uses implicit gradient have provided an exciting alternative to standard techniques which depend on the trajectory of the inner loop training. Implicit meta-learning (IML), however, require computing $2^{nd}$ order gradients, particularly the Hessian which is impractical to compute for modern deep learning models. Various approximations for the Hessian were proposed but a systematic comparison of their compute cost, stability, generalization of solution found and estimation accuracy were largely overlooked. In this study, we start by conducting a systematic comparative analysis of the various approximation methods and their effect when incorporated into IML training routines. We establish situations where catastrophic forgetting is exhibited in IML and explain their cause in terms of the inability of the approximations to estimate the curvature at convergence points. Sources of IML training instability are demonstrated and remedied. A detailed analysis of the effeciency of various inverse Hessian-vector product approximation methods is also provided. Subsequently, we use the insights gained to propose and evaluate a novel semi-supervised learning algorithm that learns to inductively weigh consistency regularization losses. We show how training a "Confidence Network" to extract domain specific features can learn to up-weigh useful images and down-weigh out-of-distribution samples. Results outperform the baseline FixMatch performance.
Johns Hopkins University（约翰斯·霍普金斯大学）；University of California, Berkeley（加州大学伯克利分校）；Microsoft Research AI（微软人工智能研究院）；Princeton University（普林斯顿大学）
How do learners acquire languages from the limited data available to them? This process must involve some inductive biases - factors that affect how a learner generalizes - but it is unclear which inductive biases can explain observed patterns in language acquisition. To facilitate computational modeling aimed at addressing this question, we introduce a framework for giving particular linguistic inductive biases to a neural network model; such a model can then be used to empirically explore the effects of those inductive biases. This framework disentangles universal inductive biases, which are…
Link prediction for knowledge graphs aims to predict missing connections between entities. Prevailing methods are limited to a transductive setting and hard to process unseen entities. The recent proposed subgraph-based models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet. However, these methods require abundant known facts of training triplets and perform poorly on relationships that only have a few triplets. In this paper, we propose Meta-iKG, a novel subgraph-based meta-learner for few-shot inductive relation reasoning. Meta-iKG utilizes …
Domain alignment is currently the most prevalent solution to unsupervised domain-adaptation tasks and are often being presented as minimizers of some theoretical upper-bounds on risk in the target domain. However, further works revealed severe inadequacies between theory and practice: we consolidate this analysis and confirm that imposing domain invariance on features is neither necessary nor sufficient to obtain low target risk. We instead argue that successful deep domain adaptation rely largely on hidden inductive biases found in the common practice, such as model pre-training or design of …
Ludwig Maximilian University of Munich（慕尼黑大学）；Siemens AG（西门子股份公司）；Technical University of Munich（慕尼黑工业大学）
Knowledge graph completion (KGC) aims to predict the missing links among knowledge graph (KG) entities. Though various methods have been developed for KGC, most of them can only deal with the KG entities seen in the training set and cannot perform well in predicting links concerning novel entities in the test set. Similar problem exists in temporal knowledge graphs (TKGs), and no previous temporal knowledge graph completion (TKGC) method is developed for modeling newly-emerged entities. Compared to KGs, TKGs require temporal reasoning techniques for modeling, which naturally increases the diff…
A central goal of meta-learning is to find a learning rule that enables fast adaptation across a set of tasks, by learning the appropriate inductive bias for that set. Most meta-learning algorithms try to find a \textit{global} learning rule that encodes this inductive bias. However, a global learning rule represented by a fixed-size representation is prone to meta-underfitting or -overfitting since the right representational power for a task set is difficult to choose a priori. Even when chosen correctly, we show that global, fixed-size representations often fail when confronted with certain …
The goal of optimization-based meta-learning is to find a single initialization shared across a distribution of tasks to speed up the process of learning new tasks. Conditional meta-learning seeks task-specific initialization to better capture complex task distributions and improve performance. However, many existing conditional methods are difficult to generalize and lack theoretical guarantees. In this work, we propose a new perspective on conditional meta-learning via structured prediction. We derive task-adaptive structured meta-learning (TASML), a principled framework that yields task-spe…
Machine learning methods adapt the parameters of a model, constrained to lie in a given model class, by using a fixed learning procedure based on data or active observations. Adaptation is done on a per-task basis, and retraining is needed when the system configuration changes. The resulting inefficiency in terms of data and training time requirements can be mitigated, if domain knowledge is available, by selecting a suitable model class and learning procedure, collectively known as inductive bias. However, it is generally difficult to encode prior knowledge into an inductive bias, particularl…
MIT（麻省理工学院）；Stanford University（斯坦福大学）；National University of Singapore（新加坡国立大学）
Progress in machine learning (ML) stems from a combination of data availability, computational resources, and an appropriate encoding of inductive biases. Useful biases often exploit symmetries in the prediction problem, such as convolutional networks relying on translation equivariance. Automatically discovering these useful symmetries holds the potential to greatly improve the performance of ML systems, but still remains a challenge. In this work, we focus on sequential prediction problems and take inspiration from Noether's theorem to reduce the problem of finding inductive biases to meta-l…
Duke University（杜克大学）；UC Berkeley（加州大学伯克利分校）；Princeton University（普林斯顿大学）
Learning-to-learn or meta-learning leverages data-driven inductive bias to increase the efficiency of learning on a novel task. This approach encounters difficulty when transfer is not advantageous, for instance, when tasks are considerably dissimilar or change over time. We use the connection between gradient-based meta-learning and hierarchical Bayes to propose a Dirichlet process mixture of hierarchical Bayesian models over the parameters of an arbitrary parametric model such as a neural network. In contrast to consolidating inductive biases into a single set of hyperparameters, our approac…
Neural Processes (NPs) are a popular class of approaches for meta-learning. Similar to Gaussian Processes (GPs), NPs define distributions over functions and can estimate uncertainty in their predictions. However, unlike GPs, NPs and their variants suffer from underfitting and often have intractable likelihoods, which limit their applications in sequential decision making. We propose Transformer Neural Processes (TNPs), a new member of the NP family that casts uncertainty-aware meta learning as a sequence modeling problem. We learn TNPs via an autoregressive likelihood-based objective and insta…
Huazhong University of Science and Technology（华中科技大学）
Model-Agnostic Meta-Learning (MAML) is a famous few-shot learning method that has inspired many follow-up efforts, such as ANIL and BOIL. However, as an inductive method, MAML is unable to fully utilize the information of query set, limiting its potential of gaining higher generality. To address this issue, we propose a simple yet effective method that generates psuedo-labels adaptively and could boost the performance of the MAML family. The proposed methods, dubbed Generative Pseudo-label based MAML (GP-MAML), GP-ANIL and GP-BOIL, leverage statistics of the query set to improve the performanc…
King’s College London（伦敦国王学院）；Chalmers Institute of Technology（查尔姆斯理工大学）
Meta-learning automatically infers an inductive bias by observing data from a number of related tasks. The inductive bias is encoded by hyperparameters that determine aspects of the model class or training algorithm, such as initialization or learning rate. Meta-learning assumes that the learning tasks belong to a task environment, and that tasks are drawn from the same task environment both during meta-training and meta-testing. This, however, may not hold true in practice. In this paper, we introduce the problem of transfer meta-learning, in which tasks are drawn from a target task environme…
University of Washington（华盛顿大学）；Bogazici University（博阿齐奇大学）；University of California, Riverside（加州大学河滨分校）
An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of the dataset is smaller than that of the model. While the prior literature focuses on the classical supervised setting, this paper aims to demystify overparameterization for meta-learning. Here we have a sequence of linear-regression tasks and we ask: (1) Given earlier tasks, what is the optimal linear representation of features for a new downstream task? and…
Neural networks have been successfully applied in applications with a large amount of labeled data. However, the task of rapid generalization on new concepts with small training data while preserving performances on previously learned ones still presents a significant challenge to neural network models. In this work, we introduce a novel meta learning method, Meta Networks (MetaNet), that learns a meta-level knowledge across tasks and shifts its inductive biases via fast parameterization for rapid generalization. When evaluated on Omniglot and Mini-ImageNet benchmarks, our MetaNet models achie…
Zhejiang University（浙江大学）；Huawei Technologies Co., Ltd.（华为技术有限公司）；State Key Laboratory of Media Convergence Production Technology and Systems（媒体融合生产技术与系统国家重点实验室）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙江大学杭州国际科创中心）；Alibaba-Zhejiang University Joint Institute of Frontier Technologies（阿里巴巴-浙江大学前沿技术联合研究院）
Knowledge graphs (KGs) consisting of a large number of triples have become widespread recently, and many knowledge graph embedding (KGE) methods are proposed to embed entities and relations of a KG into continuous vector spaces. Such embedding methods simplify the operations of conducting various in-KG tasks (e.g., link prediction) and out-of-KG tasks (e.g., question answering). They can be viewed as general solutions for representing KGs. However, existing KGE methods are not applicable to inductive settings, where a model trained on source KGs will be tested on target KGs with entities unsee…
By searching for shared inductive biases across tasks, meta-learning promises to accelerate learning on novel tasks, but with the cost of solving a complex bilevel optimization problem. We introduce and rigorously define the trade-off between accurate modeling and optimization ease in meta-learning. At one end, classic meta-learning algorithms account for the structure of meta-learning but solve a complex optimization problem, while at the other end domain randomized search (otherwise known as joint training) ignores the structure of meta-learning and solves a single level optimization problem…
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a…
University of Zürich（苏黎世大学）；ETH Zürich（苏黎世联邦理工学院）；Mila；University of Montreal（蒙特利尔大学）；ServiceNow
Finding neural network weights that generalize well from small datasets is difficult. A promising approach is to learn a weight initialization such that a small number of weight changes results in low generalization error. We show that this form of meta-learning can be improved by letting the learning algorithm decide which weights to change, i.e., by learning where to learn. We find that patterned sparsity emerges from this process, with the pattern of sparsity varying on a problem-by-problem basis. This selective sparsity results in better generalization and less interference in a range of f…
Prevailing methods for graphs require abundant label and edge information for learning. When data for a new task are scarce, meta-learning can learn from prior experiences and form much-needed inductive biases for fast adaption to new tasks. Here, we introduce G-Meta, a novel meta-learning algorithm for graphs. G-Meta uses local subgraphs to transfer subgraph-specific information and learn transferable knowledge faster via meta gradients. G-Meta learns how to quickly adapt to a new task using only a handful of nodes or edges in the new task and does so by learning from data points in other gra…
Few-shot or one-shot learning of classifiers requires a significant inductive bias towards the type of task to be learned. One way to acquire this is by meta-learning on tasks similar to the target task. In this paper, we propose UMTRA, an algorithm that performs unsupervised, model-agnostic meta-learning for classification tasks. The meta-learning step of UMTRA is performed on a flat collection of unlabeled images. While we assume that these images can be grouped into a diverse set of classes and are relevant to the target task, no explicit information about the classes or any labels are need…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding spaces the direction of data generally contains richer information than magnitude. Next to this, state-of-the-art few-shot metric methods that compare distances with aggregated class representations, have shown superior performance. Combining these two insights, we propose to meta-learn classification of embedded points by regressing the closest approximation …
Semi-supervised node classification on graphs is an important research problem, with many real-world applications in information retrieval such as content classification on a social network and query intent classification on an e-commerce query graph. While traditional approaches are largely transductive, recent graph neural networks (GNNs) integrate node features with network structures, thus enabling inductive node classification models that can be applied to new nodes or even new graphs in the same feature space. However, inter-graph differences still exist across graphs within the same dom…
Learned optimizers -- neural networks that are trained to act as optimizers -- have the potential to dramatically accelerate training of machine learning models. However, even when meta-trained across thousands of tasks at huge computational expense, blackbox learned optimizers often struggle with stability and generalization when applied to tasks unlike those in their meta-training set. In this paper, we use tools from dynamical systems to investigate the inductive biases and stability properties of optimization algorithms, and apply the resulting insights to designing inductive biases for bl…
Logical frameworks and meta-languages form a common substrate for representing, implementing and reasoning about a wide variety of deductive systems of interest in logic and computer science. Their design, implementation and their use in reasoning tasks, ranging from the correctness of software to the properties of formal systems, have been the focus of considerable research over the last two decades. This workshop brings together designers, implementors and practitioners to discuss various aspects impinging on the structure and utility of logical frameworks, including the treatment of variabl…
From CNNs to attention mechanisms, encoding inductive biases into neural networks has been a fruitful source of improvement in machine learning. Adding auxiliary losses to the main objective function is a general way of encoding biases that can help networks learn better representations. However, since auxiliary losses are minimized only on training data, they suffer from the same generalization gap as regular task losses. Moreover, by adding a term to the loss function, the model optimizes a different objective than the one we care about. In this work we address both problems: first, we take …
University of California, Berkeley（加州大学伯克利分校）；LinkedIn（领英）
As a special field in deep learning, Graph Neural Networks (GNNs) focus on extracting intrinsic network features and have drawn unprecedented popularity in both academia and industry. Most of the state-of-the-art GNN models offer expressive, robust, scalable and inductive solutions empowering social network recommender systems with rich network features that are computationally difficult to leverage with graph traversal based methods. Most recent GNNs follow an encoder-decoder paradigm to encode high dimensional heterogeneous information from a subgraph onto one low dimensional embedding space…
University of Edinburgh（爱丁堡大学）；The Alan Turing Institute（艾伦·图灵研究所）
We introduce a new application for inductive logic programming: learning the semantics of programming languages from example evaluations. In this short paper, we explored a simplified task in this domain using the Metagol meta-interpretive learning system. We highlighted the challenging aspects of this scenario, including abstracting over function symbols, nonterminating examples, and learning non-observed predicates, and proposed extensions to Metagol helpful for overcoming these challenges, which may prove useful in other domains.
Chalmers University of Technology（查尔姆斯理工大学）；Kings College London（伦敦国王学院）
Meta-learning optimizes an inductive bias---typically in the form of the hyperparameters of a base-learning algorithm---by observing data from a finite number of related tasks. This paper presents an information-theoretic bound on the generalization performance of any given meta-learner, which builds on the conditional mutual information (CMI) framework of Steinke and Zakynthinou (2020). In the proposed extension to meta-learning, the CMI bound involves a training \textit{meta-supersample} obtained by first sampling $2N$ independent tasks from the task environment, and then drawing $2M$ indepe…
