Unsupervised Domain Adaptation (UDA) has attracted a lot of attention in the last ten years. The emergence of Domain Invariant Representations (IR) has improved drastically the transferability of representations from a labelled source domain to a new and unlabelled target domain. However, a potential pitfall of this approach, namely the presence of \textit{label shift}, has been brought to light. Some works address this issue with a relaxed version of domain invariance obtained by weighting samples, a strategy often referred to as Importance Sampling. From our point of view, the theoretical aspects of how Importance Sampling and Invariant Representations interact in UDA have not been studied in depth. In the present work, we present a bound of the target risk which incorporates both weights and invariant representations. Our theoretical analysis highlights the role of inductive bias in aligning distributions across domains. We illustrate it on standard benchmarks by proposing a new learning procedure for UDA. We observed empirically that weak inductive bias makes adaptation more robust. The elaboration of stronger inductive bias is a promising direction for new UDA algorithms.
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 …
Carleton University（卡尔顿大学）；CIFAR AI Chair（CIFAR人工智能讲席）；Amii（阿尔伯塔机器智能研究所）
Unsupervised domain adaptation reduces the reliance on data annotation in deep learning by adapting knowledge from a source to a target domain. For privacy and efficiency concerns, source-free domain adaptation extends unsupervised domain adaptation by adapting a pre-trained source model to an unlabeled target domain without accessing the source data. However, most existing source-free domain adaptation methods to date focus on the transductive setting, where the target training set is also the testing set. In this paper, we address source-free domain adaptation in the more realistic inductive…
New York University（纽约大学）；UC San Diego（加州大学圣迭戈分校）；Amazon, Cambridge（亚马逊剑桥）
The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation. This inference is analytic and f…
Characterising the Inductive Biases of Neural Networks on Boolean Data
Department of Theoretical Physics, University of Oxford, UK（理论物理系，牛津大学）；Department of Theoretical Chemistry, University of Oxford, UK（理论化学系，牛津大学）；Green Templeton College, University of Oxford, UK（格林·泰尔顿学院，牛津大学）；Department of Computer Science, University of Oxford, UK（计算机科学系，牛津大学）
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…
OnePlanet Research Center（OnePlanet研究中心）；imec-the Netherlands（荷兰微电子研究中心（imec荷兰分部））；Google Research（谷歌研究院）；Donders Institute for Brain, Cognition and Behaviour（唐德斯大脑、认知与行为研究所）；Radboud University（拉德堡德大学）
Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose embedded-model flows (EMF), which alternate general-purpose transformations with structured layers that embed domain-specific inductive biases. These layers are automatically constructed by converting user-specified differentiable probabilistic models into equivalent bijective transformations. We also introduce gated structured layers, which allow bypassing the parts o…
Sorbonne universités（索邦大学）；Université de technologie de Compiègne（贡比涅技术大学）；CNRS（法国国家科学研究中心）；Heudiasyc（人机交互与自动化实验室）
In inductive transfer learning, fine-tuning pre-trained convolutional networks substantially outperforms training from scratch. When using fine-tuning, the underlying assumption is that the pre-trained model extracts generic features, which are at least partially relevant for solving the target task, but would be difficult to extract from the limited amount of data available on the target task. However, besides the initialization with the pre-trained model and the early stopping, there is no mechanism in fine-tuning for retaining the features learned on the source task. In this paper, we inves…
ETH Zurich（苏黎世联邦理工学院）；ETH AI Center（苏黎世联邦理工学院人工智能中心）；Max-Planck-Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in this paper we caution against a strong inductive bias for interpolation in the presence of noise: While a stronger inductive bias encourages a simpler structure that is more aligned with the ground truth, it also increases the detrimental effect of noise. Specifically, for both linear regression and classification with a sparse ground truth, we prove that min…
Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation fails with standard feed-forward networks on binary vectors. Even when trained with maximal training data, standard networks do not reliably detect equality.We introduce differential rectifier (DR) units that we add to the network in different configurations. The DR units create an inductive bias in the networks, so that they do learn to generalise, even from …
State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain over-parameterized regime, the learning dynamics of gradient descent are governed by a certain kernel obtained at initialization, called the neural tangent kernel. We study the inductive bias of learning in such a regime by analyzing this kernel and the corresponding function space (RKHS). In particular, we study smoothness, approximation, and stability proper…
University of Oxford（牛津大学）；University of Edinburgh（爱丁堡大学）
We explain why directly changing the prior can be a surprisingly ineffective mechanism for incorporating inductive biases into VAEs, and introduce a simple and effective alternative approach: Intermediary Latent Space VAEs(InteL-VAEs). InteL-VAEs use an intermediary set of latent variables to control the stochasticity of the encoding process, before mapping these in turn to the latent representation using a parametric function that encapsulates our desired inductive bias(es). This allows us to impose properties like sparsity or clustering on learned representations, and incorporate human knowl…
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）
Full Bayesian posteriors are rarely analytically tractable, which is why real-world Bayesian inference heavily relies on approximate techniques. Approximations generally differ from the true posterior and require diagnostic tools to assess whether the inference can still be trusted. We investigate a new approach to diagnosing approximate inference: the approximation mismatch is attributed to a change in the inductive bias by treating the approximations as exact and reverse-engineering the corresponding prior. We show that the problem is more complicated than it appears to be at first glance, b…
University of Toronto（多伦多大学）；Vector Institute（矢量研究所）
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a useful constraint, both theoretically--to prove convergence and optimality guarantees--and empirically--as an inductive bias. Deep metric learning architectures that respect the triangle inequality rely, almost exclusively, on Euclidean distance in the latent space. Though effective, this fails to model two broad classes of subadditive distances, common in …
University of Cambridge（剑桥大学）；Eötvös Loránd University（罗兰大学）
In gradient descent, changing how we parametrize the model can lead to drastically different optimization trajectories, giving rise to a surprising range of meaningful inductive biases: identifying sparse classifiers or reconstructing low-rank matrices without explicit regularization. This implicit regularization has been hypothesised to be a contributing factor to good generalization in deep learning. However, natural gradient descent is approximately invariant to reparameterization, it always follows the same trajectory and finds the same optimum. The question naturally arises: What happens …
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）
We present experiments demonstrating that some other form of capacity control, different from network size, plays a central role in learning multilayer feed-forward networks. We argue, partially through analogy to matrix factorization, that this is an inductive bias that can help shed light on deep learning.
Many deep reinforcement learning algorithms contain inductive biases that sculpt the agent's objective and its interface to the environment. These inductive biases can take many forms, including domain knowledge and pretuned hyper-parameters. In general, there is a trade-off between generality and performance when algorithms use such biases. Stronger biases can lead to faster learning, but weaker biases can potentially lead to more general algorithms. This trade-off is important because inductive biases are not free; substantial effort may be required to obtain relevant domain knowledge or to …
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
We analyze the inductive bias of gradient descent for weight normalized smooth homogeneous neural nets, when trained on exponential or cross-entropy loss. We analyse both standard weight normalization (SWN) and exponential weight normalization (EWN), and show that the gradient flow path with EWN is equivalent to gradient flow on standard networks with an adaptive learning rate. We extend these results to gradient descent, and establish asymptotic relations between weights and gradients for both SWN and EWN. We also show that EWN causes weights to be updated in a way that prefers asymptotic rel…
Theoretical Investigation on Inductive Bias of Isolation Forest
National Key Laboratory for Novel Software Technology, Nanjing University, China（新型软件技术国家实验室，南京大学）；School of Artificial Intelligence, Nanjing University, China（人工智能学院，南京大学）；School of Intelligence Science and Technology, Nanjing University, China（智能科学与技术学院，南京大学）；College of Computer and Information, Hohai University, China（计算机与信息学院，河海大学）；Key Laboratory of Water Resources Big Data Technology of Ministry of Water Resources, Hohai University, China（水利部水资源大数据技术重点实验室，河海大学）
University of California, Berkeley（加州大学伯克利分校）；CipherMode Labs（CipherMode实验室）；Microsoft Research（微软研究院）
We provide a function space characterization of the inductive bias resulting from minimizing the $\ell_2$ norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting hypothesis on ReLU networks trained using gradient descent. We define an induced regularizer in the function space as the minimum $\ell_2$ norm of weights of a network required to realize a function. For two layer linear convolutional networks with $C$ output channels and kernel size $K$, we show the following: (a) If the inputs to the network are single channeled, …
DeepMind；MIT（麻省理工学院）；Department of Brain and Cognitive Sciences（脑与认知科学系；麻省理工学院）；MIT
While current deep learning systems excel at tasks such as object classification, language processing, and gameplay, few can construct or modify a complex system such as a tower of blocks. We hypothesize that what these systems lack is a "relational inductive bias": a capacity for reasoning about inter-object relations and making choices over a structured description of a scene. To test this hypothesis, we focus on a task that involves gluing pairs of blocks together to stabilize a tower, and quantify how well humans perform. We then introduce a deep reinforcement learning agent which uses obj…
Borrowing from the transformer models that revolutionized the field of natural language processing, self-supervised feature learning for visual tasks has also seen state-of-the-art success using these extremely deep, isotropic networks. However, the typical AI researcher does not have the resources to evaluate, let alone train, a model with several billion parameters and quadratic self-attention activations. To facilitate further research, it is necessary to understand the features of these huge transformer models that can be adequately studied by the typical researcher. One interesting charac…
End-to-end automatic speech recognition (ASR) commonly transcribes audio signals into sequences of characters while its performance is evaluated by measuring the word-error rate (WER). This suggests that predicting sequences of words directly may be helpful instead. However, training with word-level supervision can be more difficult due to the sparsity of examples per label class. In this paper we analyze an end-to-end ASR model that combines a word-and-character representation in a multi-task learning (MTL) framework. We show that it improves on the WER and study how the word-level model can …
South China University of Technology（华南理工大学）；MIT（麻省理工学院）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；Tsinghua University（清华大学）；Shanghai Qi Zhi Institute（上海期智研究院）
Transformers recently are adapted from the community of natural language processing as a promising substitute of convolution-based neural networks for visual learning tasks. However, its supremacy degenerates given an insufficient amount of training data (e.g., ImageNet). To make it into practical utility, we propose a novel distillation-based method to train vision transformers. Unlike previous works, where merely heavy convolution-based teachers are provided, we introduce lightweight teachers with different architectural inductive biases (e.g., convolution and involution) to co-advise the st…
Aligning Inductive Bias for Data-Efficient Generalization in State Space Models
School of Computer Science, National Key Laboratory for Multimedia Information Processing, Peking University, China（计算机学院、多媒体信息处理国家重点实验室、北京大学）；School of Physics, Peking University, China（物理学院、北京大学）
Humans rely less on spurious correlations and trivial cues, such as texture, compared to deep neural networks which lead to better generalization and robustness. It can be attributed to the prior knowledge or the high-level cognitive inductive bias present in the brain. Therefore, introducing meaningful inductive bias to neural networks can help learn more generic and high-level representations and alleviate some of the shortcomings. We propose InBiaseD to distill inductive bias and bring shape-awareness to the neural networks. Our method includes a bias alignment objective that enforces the n…
Vector Institute（向量研究所）；University of Toronto（多伦多大学）；Google Research（谷歌研究院）；University of Cambridge（剑桥大学）
While designing inductive bias in neural architectures has been widely studied, we hypothesize that transformer networks are flexible enough to learn inductive bias from suitable generic tasks. Here, we replace architecture engineering by encoding inductive bias in the form of datasets. Inspired by Peirce's view that deduction, induction, and abduction are the primitives of reasoning, we design three synthetic tasks that are intended to require the model to have these three abilities. We specifically design these tasks to be synthetic and devoid of mathematical knowledge to ensure that only th…
Tsinghua University（清华大学）；Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；CIFAR AI Chair（CIFAR人工智能讲席）
Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept of simplicity defined in the Chomsky hierarchy. From fundamental connections between Hankel matrices and regular grammars, we propose to use the trace norm of the Hankel matrix, the tightest convex relaxation of its rank, as the spectral regularizer. To cope with the fact that the Hankel matrix is bi-infinite, we propose an unbiased stochastic estimator for…
Structural Disentanglement in Bilinear MLPs via Architectural Inductive Bias
Department of Electrical Engineering, Indian Institute of Technology Roorkee (IIT Roorkee), India；Department of Material Science \& Engineering, IIT Roorkee, India；Mehta Family School of Data Science
Département d’informatique et de recherche opérationnelle（计算机科学与运筹学系）
In this thesis, we try to build a connection between the two schools by introducing syntactic inductive biases for deep learning models. We propose two families of inductive biases, one for constituency structure and another one for dependency structure. The constituency inductive bias encourages deep learning models to use different units (or neurons) to separately process long-term and short-term information. This separation provides a way for deep learning models to build the latent hierarchical representations from sequential inputs, that a higher-level representation is composed of and ca…
Columbia University（哥伦比亚大学）；Flatiron Institute（弗莱托恩研究所）
Understanding the asymptotic behavior of gradient-descent training of deep neural networks is essential for revealing inductive biases and improving network performance. We derive the infinite-time training limit of a mathematically tractable class of deep nonlinear neural networks, gated linear networks (GLNs), and generalize these results to gated networks described by general homogeneous polynomials. We study the implications of our results, focusing first on two-layer GLNs. We then apply our theoretical predictions to GLNs trained on MNIST and show how architectural constraints and the imp…
There have been a lot of interest in the scaling properties of Transformer models. However, not much has been done on the front of investigating the effect of scaling properties of different inductive biases and model architectures. Do model architectures scale differently? If so, how does inductive bias affect scaling behaviour? How does this influence upstream (pretraining) and downstream (transfer)? This paper conducts a systematic study of scaling behaviour of ten diverse model architectures such as Transformers, Switch Transformers, Universal Transformers, Dynamic convolutions, Performers…
With the resurgence of interest in neural networks, representation learning has re-emerged as a central focus in artificial intelligence. Representation learning refers to the discovery of useful encodings of data that make domain-relevant information explicit. Factorial representations identify underlying independent causal factors of variation in data. A factorial representation is compact and faithful, makes the causal factors explicit, and facilitates human interpretation of data. Factorial representations support a variety of applications, including the generation of novel examples, index…
Contrastive learning is a popular form of self-supervised learning that encourages augmentations (views) of the same input to have more similar representations compared to augmentations of different inputs. Recent attempts to theoretically explain the success of contrastive learning on downstream classification tasks prove guarantees depending on properties of {\em augmentations} and the value of {\em contrastive loss} of representations. We demonstrate that such analyses, that ignore {\em inductive biases} of the function class and training algorithm, cannot adequately explain the success of …
University of Cambridge（剑桥大学）；MILA（蒙特利尔学习算法研究所）；McGill University（麦吉尔大学）；Polytechnique Montréal（蒙特利尔综合理工学院）；ServiceNow（ServiceNow公司）
In order to communicate, humans flatten a complex representation of ideas and their attributes into a single word or a sentence. We investigate the impact of representation learning in artificial agents by developing graph referential games. We empirically show that agents parametrized by graph neural networks develop a more compositional language compared to bag-of-words and sequence models, which allows them to systematically generalize to new combinations of familiar features.
