Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization, and meta-learning, where the objective function involves a nested composition associated with an expectation. While a significant amount of studies has been devoted to studying the convergence behavior of SCO algorithms, there is little work on understanding their generalization, i.e., how these learning algorithms built from training examples would behave on future test examples. In this paper, we provide the stability and generalization analysis of stochastic compositional gradient descent algorithms through the lens of algorithmic stability in the framework of statistical learning theory. Firstly, we introduce a stability concept called compositional uniform stability and establish its quantitative relation with generalization for SCO problems. Then, we establish the compositional uniform stability results for two popular stochastic compositional gradient descent algorithms, namely SCGD and SCSC. Finally, we derive dimension-independent excess risk bounds for SCGD and SCSC by trade-offing their stability results and optimization errors. To the best of our knowledge, these are the first-ever-known results on stability and generalization analysis of stochastic compositional gradient descent algorithms.
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；Ecole Polytechnique Federale de Lausanne（洛桑联邦理工学院）
This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair regression, and the design of queuing systems. Of particular interest is the large-scale setting where an oracle provides the stochastic gradients of the constituent functions, and the goal is to solve the problem with a minimal number of calls to the oracle. Owing to the compositional form, the stochastic gradients provided by the oracle do not yield unbiased …
Indian Institute of Technology, Guwahati（印度理工学院古瓦哈提分校）
Generalization error defines the discriminability and the representation power of a deep model. In this work, we claim that feature space design using deep compositional function plays a significant role in generalization along with explicit and implicit regularizations. Our claims are being established with several image classification experiments. We show that the information loss due to convolution and max pooling can be marginalized with the compositional design, improving generalization performance. Also, we will show that learning rate decay acts as an implicit regularizer in deep model …
The Pennsylvania State University（宾夕法尼亚州立大学）；College of Information Science and Technology（信息科学与技术学院）；Department of Computer Science and Engineering（计算机科学与工程系）
Many machine learning, statistical inference, and portfolio optimization problems require minimization of a composition of expected value functions (CEVF). Of particular interest is the finite-sum versions of such compositional optimization problems (FS-CEVF). Compositional stochastic variance reduced gradient (C-SVRG) methods that combine stochastic compositional gradient descent (SCGD) and stochastic variance reduced gradient descent (SVRG) methods are the state-of-the-art methods for FS-CEVF problems. We introduce compositional stochastic average gradient descent (C-SAG) a novel extension o…
Compositionality is a basic structural feature of both biological and artificial neural networks. Learning compositional functions via gradient descent incurs well known problems like vanishing and exploding gradients, making careful learning rate tuning essential for real-world applications. This paper proves that multiplicative weight updates satisfy a descent lemma tailored to compositional functions. Based on this lemma, we derive Madam -- a multiplicative version of the Adam optimiser -- and show that it can train state of the art neural network architectures without learning rate tuning.…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that the deviation of the slow motion from the averaged equation, after proper rescaling, converges to a stochastic process with Gaussian inputs. This indicates that the slow motion can be approximated in the weak sense by a standard perturbed gradient flow or the continuous-time sto…
Facebook Artificial Intelligence Research（脸书人工智能研究院）；Istituto Italiano di Tecnologia（意大利理工学院）
Neural networks are very powerful learning systems, but they do not readily generalize from one task to the other. This is partly due to the fact that they do not learn in a compositional way, that is, by discovering skills that are shared by different tasks, and recombining them to solve new problems. In this paper, we explore the compositional generalization capabilities of recurrent neural networks (RNNs). We first propose the lookup table composition domain as a simple setup to test compositional behaviour and show that it is theoretically possible for a standard RNN to learn to behave com…
Massachusetts Institute of Technology（麻省理工学院）；Brown University（布朗大学）；Tel-Aviv University（特拉维夫大学）
In this paper, we investigate the Rademacher complexity of deep sparse neural networks, where each neuron receives a small number of inputs. We prove generalization bounds for multilayered sparse ReLU neural networks, including convolutional neural networks. These bounds differ from previous ones, as they consider the norms of the convolutional filters instead of the norms of the associated Toeplitz matrices, independently of weight sharing between neurons. As we show theoretically, these bounds may be orders of magnitude better than standard norm-based generalization bounds and empirically, t…
We assume that a high-dimensional datum, like an image, is a compositional expression of a set of properties, with a complicated non-linear relationship between the datum and its properties. This paper proposes a factorial mixture prior for capturing latent properties, thereby adding structured compositionality to deep generative models. The prior treats a latent vector as belonging to Cartesian product of subspaces, each of which is quantized separately with a Gaussian mixture model. Some mixture components can be set to represent properties as observed random variables whenever labeled prope…
College of Computer, National University of Defense Technology（国防科技大学计算机学院）；Scientific Computing & Imaging Institute, University of Utah（犹他大学科学计算与成像研究所）
The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent has received a considerable amount of studies. Nevertheless, the community paid little attention to its decentralized variants. In this paper, we provide a novel formulation of the decentralized stochastic gradient descent. Leveraging this formulation together with (non)convex optimization theory, we establish the first stability and generalization guarantee…
Northwest University（西北大学）；Southwestern University of Finance and Economics（西南财经大学）；University of Birmingham（伯明翰大学）
Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in solving various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there is no work studying how the models trained by RCD would generalize to test examples. In this paper, we initialize the generalization analysis of RCD by leveraging the powerful tool of algorithmic stability. We establish argument stability bounds of RCD for both convex and strongly convex objectives, from which we develop optimal generalization bounds by showi…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；University of California, Los Angeles（加州大学洛杉矶分校）
Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of compositions of functions. Each composition may introduce an additional expectation. The series of expectations may be nested. Stochastic compositional optimization is gaining popularity in applications such as reinforcement learning and meta learning. This paper presents a new Stochastically Corrected Stochastic Compositional gradient method (SCSC). SCSC runs in a single-time scale with a single loop, uses a fixed batch size, and guarantees to converge at the same rate …
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable and the number of cutting planes invoked by traditional remedies is difficult to bound, leading to convergences guarantees that are sublinear relative to the cumulative number of gradient evaluations. We instead propose a multipoint generalization of the gradient descent iteration for local op…
Carnegie Mellon University（卡内基梅隆大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Washington（华盛顿大学）；University of California Irvine（加州大学欧文分校）；California Institute of Technology（加州理工学院）
We study compositional generalization, viz., the problem of zero-shot generalization to novel compositions of concepts in a domain. Standard neural networks fail to a large extent on compositional learning. We propose Tree Stack Memory Units (Tree-SMU) to enable strong compositional generalization. Tree-SMU is a recursive neural network with Stack Memory Units (\SMU s), a novel memory augmented neural network whose memory has a differentiable stack structure. Each SMU in the tree architecture learns to read from its stack and to write to it by combining the stacks and states of its children th…
Seminar for Statistics, ETH Zurich（苏黎世联邦理工学院统计研讨班）；Facebook AI Research（Facebook人工智能研究）
Contrarily to humans who have the ability to recombine familiar expressions to create novel ones, modern neural networks struggle to do so. This has been emphasized recently with the introduction of the benchmark dataset "gSCAN" (Ruis et al. 2020), aiming to evaluate models' performance at compositional generalization in grounded language understanding. In this work, we challenge the gSCAN benchmark by proposing a simple model that achieves surprisingly good performance on two of the gSCAN test splits. Our model is based on the observation that, to succeed on gSCAN tasks, the agent must (i) id…
Thomas J. Watson Research Center（托马斯·J·沃森研究中心）；IBM Research AI（IBM研究院人工智能）；MIT Media Lab（麻省理工学院媒体实验室）
Compositional and relational learning is a hallmark of human intelligence, but one which presents challenges for neural models. One difficulty in the development of such models is the lack of benchmarks with clear compositional and relational task structure on which to systematically evaluate them. In this paper, we introduce an environment called ConceptWorld, which enables the generation of images from compositional and relational concepts, defined using a logical domain specific language. We use it to generate images for a variety of compositional structures: 2x2 squares, pentominoes, seque…
Despite achieving tremendous success, existing deep learning models have exposed limitations in compositional generalization, the capability to learn compositional rules and apply them to unseen cases in a systematic manner. To tackle this issue, we propose the Neural-Symbolic Stack Machine (NeSS). It contains a neural network to generate traces, which are then executed by a symbolic stack machine enhanced with sequence manipulation operations. NeSS combines the expressive power of neural sequence models with the recursion supported by the symbolic stack machine. Without training supervision o…
State-of-the-art machine learning methods exhibit limited compositional generalization. At the same time, there is a lack of realistic benchmarks that comprehensively measure this ability, which makes it challenging to find and evaluate improvements. We introduce a novel method to systematically construct such benchmarks by maximizing compound divergence while guaranteeing a small atom divergence between train and test sets, and we quantitatively compare this method to other approaches for creating compositional generalization benchmarks. We present a large and realistic natural language quest…
University of Colorado Boulder（科罗拉多大学博尔德分校）；MILA（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Standard methods in deep learning for natural language processing fail to capture the compositional structure of human language that allows for systematic generalization outside of the training distribution. However, human learners readily generalize in this way, e.g. by applying known grammatical rules to novel words. Inspired by work in neuroscience suggesting separate brain systems for syntactic and semantic processing, we implement a modification to standard approaches in neural machine translation, imposing an analogous separation. The novel model, which we call Syntactic Attention, subst…
Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models struggle to do so. In this work, we study compositional generalization in classification tasks and present two main contributions. First, we study ways to convert a natural language sequence-to-sequence dataset to a classification dataset that also requires compositional generalization. Second, we show that providing structural hints (specifically, providing p…
Swing-by Dynamics in Concept Learning and Compositional Generalization
CBS-NTT Physics of Intelligence Program, Harvard University（哈佛大学）；Physics & Informatics Laboratories, NTT Research, Inc.（NTT研究公司）；Computer Science and Engineering, University of Michigan（密歇根大学）；Department of Physics, Harvard University（哈佛大学）
University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Deep learning models struggle with compositional generalization, i.e. the ability to recognize or generate novel combinations of observed elementary concepts. In hopes of enabling compositional generalization, various unsupervised learning algorithms have been proposed with inductive biases that aim to induce compositional structure in learned representations (e.g. disentangled representation and emergent language learning). In this work, we evaluate these unsupervised learning algorithms in terms of how well they enable compositional generalization. Specifically, our evaluation protocol focus…
Does Data Scaling Lead to Visual Compositional Generalization?
Tübingen AI Center, University of Tübingen（图宾根人工智能中心，图宾根大学）；Technical University of Munich（慕尼黑技术大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Max Planck Institute for Intelligent Systems, Tübingen（马克斯·普朗克智能系统研究所，图宾根）
Khoury College of Computer Sciences, Northeastern University（东北大学库利计算机学院）
Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact or no compositional generali…
Provable Compositional Generalization for Object-Centric Learning
University of Tübingen（蒂宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tübingen AI Center（蒂宾根人工智能中心）；ELLIS Institute Tübingen（ELLIS蒂宾根研究所）
Studies of discrete languages emerging when neural agents communicate to solve a joint task often look for evidence of compositional structure. This stems for the expectation that such a structure would allow languages to be acquired faster by the agents and enable them to generalize better. We argue that these beneficial properties are only loosely connected to compositionality. In two experiments, we demonstrate that, depending on the task, non-compositional languages might show equal, or better, generalization performance and acquisition speed than compositional ones. Further research in th…
While mainstream machine learning methods are known to have limited ability to compositionally generalize, new architectures and techniques continue to be proposed to address this limitation. We investigate state-of-the-art techniques and architectures in order to assess their effectiveness in improving compositional generalization in semantic parsing tasks based on the SCAN and CFQ datasets. We show that masked language model (MLM) pre-training rivals SCAN-inspired architectures on primitive holdout splits. On a more complex compositional task, we show that pre-training leads to significant i…
Columbia University（哥伦比亚大学）；IBM TJ Watson Research Center（IBM托马斯·J·沃森研究中心）；Mila - Quebec AI Institute（Mila - 魁北克人工智能研究所）
The field of compositional generalization is currently experiencing a renaissance in AI, as novel problem settings and algorithms motivated by various practical applications are being introduced, building on top of the classical compositional generalization problem. This article aims to provide a comprehensive review of top recent developments in multiple real-life applications of the compositional generalization. Specifically, we introduce a taxonomy of common applications and summarize the state-of-the-art for each of those domains. Furthermore, we identify important current trends and provi…
CIMeC, University of Trento（特伦托大学心智/脑科学中心）；ICREA（加泰罗尼亚研究与高等教育学院）；Facebook AI Research（脸书人工智能研究院）
Lake and Baroni (2018) introduced the SCAN dataset probing the ability of seq2seq models to capture compositional generalizations, such as inferring the meaning of "jump around" 0-shot from the component words. Recurrent networks (RNNs) were found to completely fail the most challenging generalization cases. We test here a convolutional network (CNN) on these tasks, reporting hugely improved performance with respect to RNNs. Despite the big improvement, the CNN has however not induced systematic rules, suggesting that the difference between compositional and non-compositional behaviour is not …
University of California, Berkeley（加州大学伯克利分校）；Princeton University（普林斯顿大学）
A generally intelligent learner should generalize to more complex tasks than it has previously encountered, but the two common paradigms in machine learning -- either training a separate learner per task or training a single learner for all tasks -- both have difficulty with such generalization because they do not leverage the compositional structure of the task distribution. This paper introduces the compositional problem graph as a broadly applicable formalism to relate tasks of different complexity in terms of problems with shared subproblems. We propose the compositional generalization pro…
Zhejiang University（浙江大学）；Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）
Modern neural machine translation (NMT) models have achieved competitive performance in standard benchmarks such as WMT. However, there still exist significant issues such as robustness, domain generalization, etc. In this paper, we study NMT models from the perspective of compositional generalization by building a benchmark dataset, CoGnition, consisting of 216k clean and consistent sentence pairs. We quantitatively analyze effects of various factors using compound translation error rate, then demonstrate that the NMT model fails badly on compositional generalization, although it performs rem…
Compositional generalization is a basic mechanism in human language learning, but current neural networks lack such ability. In this paper, we conduct fundamental research for encoding compositionality in neural networks. Conventional methods use a single representation for the input sentence, making it hard to apply prior knowledge of compositionality. In contrast, our approach leverages such knowledge with two representations, one generating attention maps, and the other mapping attended input words to output symbols. We reduce the entropy in each representation to improve generalization. Ou…
Peking University（北京大学）；University of Rochester（罗切斯特大学）；Kwai Inc.（快手公司）
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of \textit{Stochastic Recursive Gradient Descent} to design a novel algorithm named SARAH-Compositional, and…
University of Tübingen（图宾根大学）；University of Copenhagen（哥本哈根大学）；Stanford University（斯坦福大学）
Image captioning models are usually evaluated on their ability to describe a held-out set of images, not on their ability to generalize to unseen concepts. We study the problem of compositional generalization, which measures how well a model composes unseen combinations of concepts when describing images. State-of-the-art image captioning models show poor generalization performance on this task. We propose a multi-task model to address the poor performance, that combines caption generation and image--sentence ranking, and uses a decoding mechanism that re-ranks the captions according their sim…
Question answering models struggle to generalize to novel compositions of training patterns, such to longer sequences or more complex test structures. Current end-to-end models learn a flat input embedding which can lose input syntax context. Prior approaches improve generalization by learning permutation invariant models, but these methods do not scale to more complex train-test splits. We propose Grounded Graph Decoding, a method to improve compositional generalization of language representations by grounding structured predictions with an attention mechanism. Grounding enables the model to …
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Boston University（波士顿大学）
Flexible neural sequence models outperform grammar- and automaton-based counterparts on a variety of tasks. However, neural models perform poorly in settings requiring compositional generalization beyond the training data -- particularly to rare or unseen subsequences. Past work has found symbolic scaffolding (e.g. grammars or automata) essential in these settings. We describe R&R, a learned data augmentation scheme that enables a large category of compositional generalizations without appeal to latent symbolic structure. R&R has two components: recombination of original training examples via …
People can learn a new concept and use it compositionally, understanding how to "blicket twice" after learning how to "blicket." In contrast, powerful sequence-to-sequence (seq2seq) neural networks fail such tests of compositionality, especially when composing new concepts together with existing concepts. In this paper, I show how memory-augmented neural networks can be trained to generalize compositionally through meta seq2seq learning. In this approach, models train on a series of seq2seq problems to acquire the compositional skills needed to solve new seq2seq problems. Meta se2seq learning …
