ICLR 2023 Papers

While neural architecture search (NAS) is an intensely-researched area, approaches typically still suffer from either (i) high computational costs or (ii) lack of robustness across datasets and experiments. Furthermore, most methods start searching for an optimal architecture from scratch, ignoring prior knowledge. This is in contrast to the manual design process by researchers and engineers that leverage previous deep learning experiences by, e.g., transferring architectures from previously solved, related problems. We propose to adopt this human design strategy and introduce a novel surrogate for NAS, that is meta-learned across prior architecture evaluations across different datasets. We utilizes Bayesian Optimization (BO) with deep-kernel Gaussian Processes, graph neural networks for the architecture embeddings and a transformer-based set encoder of datasets. As a result, our method consistently achieves state-of-the-art results on six computer vision datasets, while being as fast as one-shot NAS methods.

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor theoretical justifications, and require iterative manual tuning. We propose a principled multiple shooting technique for neural ODEs that splits the trajectories into manageable short segments, which are optimized in parallel, while ensuring probabilistic control on continuity over consecutive segments. We derive variational inference for our shooting-based latent neural ODE models and propose amortized encodings of irregularly sampled trajectories with a transformer-based recognition network with temporal attention and relative positional encoding. We demonstrate efficient and stable training, and state-of-the-art performance on multiple large-scale benchmark datasets.

We develop ShiftMatch, a new training-data-dependent likelihood for robustness to corruption in Bayesian neural networks (BNNs). ShiftMatch is inspired by the training-data-dependent “EmpCov” priors from Izmailov et al. (2021a), and efficiently matches test-time spatial correlations to those at training time. Critically, ShiftMatch is designed to leave the neural network’s training time likelihood unchanged, allowing it to use publicly available samples from pre-trained BNNs. Using pre-trained HMC samples, ShiftMatch gives strong performance improvements on CIFAR-10-C, outperforms EmpCov priors (though ShiftMatch uses extra information from a minibatch of corrupted test points), and is perhaps the first Bayesian method capable of convincingly outperforming plain deep ensembles.

Sharpness-aware minimization (SAM) and related adversarial deep-learning methods can drastically improve generalization, but their underlying mechanisms are not yet fully understood. Here, we establish SAM as a relaxation of the Bayes objective where the expected negative-loss is replaced by the optimal convex lower bound, obtained by using the so-called Fenchel biconjugate. The connection enables a new Adam-like extension of SAM to automatically obtain reasonable uncertainty estimates, while sometimes also improving its accuracy. By connecting adversarial and Bayesian methods, our work opens a new path to robustness.

Transformer models have achieved profound success in prediction tasks in a wide range of applications in natural language processing, speech recognition and computer vision. Extending Transformer’s success to safety-critical domains requires calibrated uncertainty estimation which remains under-explored. To address this, we propose Sparse Gaussian Process attention (SGPA), which performs Bayesian inference directly in the output space of multi-head attention blocks (MHAs) in transformer to calibrate its uncertainty. It replaces the scaled dot-product operation with a valid symmetric kernel and uses sparse Gaussian processes (SGP) techniques to approximate the posterior processes of MHA outputs. Empirically, on a suite of prediction tasks on text, images and graphs, SGPA-based Transformers achieve competitive predictive accuracy, while noticeably improving both in-distribution calibration and out-of-distribution robustness and detection.

The transferability of adversarial examples across deep neural networks (DNNs) is the crux of many black-box attacks. Many prior efforts have been devoted to improving the transferability via increasing the diversity in inputs of some substitute models. In this paper, by contrast, we opt for the diversity in substitute models and advocate to attack a Bayesian model for achieving desirable transferability. Deriving from the Bayesian formulation, we develop a principled strategy for possible finetuning, which can be combined with many off-the-shelf Gaussian posterior approximations over DNN parameters. Extensive experiments have been conducted to verify the effectiveness of our method, on common benchmark datasets, and the results demonstrate that our method outperforms recent state-of-the-arts by large margins (roughly 19% absolute increase in average attack success rate on ImageNet), and, by combining with these recent methods, further performance gain can be obtained. Our code: https://github.com/qizhangli/MoreBayesian-attack.

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

We propose a general-purpose variational algorithm that forms a natural analogue of Stein variational gradient descent (SVGD) in function space. While SVGD successively updates a set of particles to match a target density, the method introduced here of Stein functional variational gradient descent (SFVGD) updates a set of particle functions to match a target stochastic process (SP). The update step is found by minimizing the functional derivative of the Kullback-Leibler divergence between SPs. SFVGD can either be used to train Bayesian neural networks (BNNs) or for ensemble gradient boosting. We show the efficacy of training BNNs with SFVGD on various real-world datasets.

Sleep staging is helpful in assessing sleep quality and diagnosing sleep disorders. However, how to adequately capture the temporal and spatial relations of the brain during sleep remains a challenge. In particular, existing methods cannot adaptively infer spatial-temporal relations of the brain under different sleep stages. In this paper, we propose a novel Bayesian spatial-temporal relation inference neural network, named Bayesian spatial-temporal transformer (BSTT), for sleep staging. Our model is able to adaptively infer brain spatial-temporal relations during sleep for spatial-temporal feature modeling through a well-designed Bayesian relation inference component. Meanwhile, our model also includes a spatial transformer for extracting brain spatial features and a temporal transformer for capturing temporal features. Experiments show that our BSTT outperforms state-of-the-art baselines on ISRUC and MASS datasets. In addition, the visual analysis shows that the spatial-temporal relations obtained by BSTT inference have certain interpretability for sleep staging.

Acquiring labeled data is challenging in many machine learning applications with limited budgets. Active learning gives a procedure to select the most informative data points and improve data efficiency by reducing the cost of labeling. The info-max learning principle maximizing mutual information such as BALD has been successful and widely adapted in various active learning applications. However, this pool-based specific objective inherently introduces a redundant selection and further requires a high computational cost for batch selection. In this paper, we design and propose a new uncertainty measure, Balanced Entropy Acquisition (BalEntAcq), which captures the information balance between the uncertainty of underlying softmax probability and the label variable. To do this, we approximate each marginal distribution by Beta distribution. Beta approximation enables us to formulate BalEntAcq as a ratio between an augmented entropy and the marginalized joint entropy. The closed-form expression of BalEntAcq facilitates parallelization by estimating two parameters in each marginal Beta distribution. BalEntAcq is a purely standalone measure without requiring any relational computations with other data points. Nevertheless, BalEntAcq captures a well-diversified selection near the decision boundary with a margin, unlike other existing uncertainty measures such as BALD, Entropy, or Mean Standard Deviation (MeanSD). Finally, we demonstrate that our balanced entropy learning principle with BalEntAcq consistently outperforms well-known linearly scalable active learning methods, including a recently proposed PowerBALD, a simple but diversified version of BALD, by showing experimental results obtained from MNIST, CIFAR-100, SVHN, and TinyImageNet datasets.

Meta-learning aims to extract useful inductive biases from a set of related datasets. In Bayesian meta-learning, this is typically achieved by constructing a prior distribution over neural network parameters. However, specifying families of computationally viable prior distributions over the high-dimensional neural network parameters is difficult. As a result, existing approaches resort to meta-learning restrictive diagonal Gaussian priors, severely limiting their expressiveness and performance. To circumvent these issues, we approach meta-learning through the lens of functional Bayesian neural network inference which views the prior as a stochastic process and performs inference in the function space. Specifically, we view the meta-training tasks as samples from the data-generating process and formalize meta-learning as empirically estimating the law of this stochastic process. Our approach can seamlessly acquire and represent complex prior knowledge by meta-learning the score function of the data-generating process marginals instead of parameter space priors. In a comprehensive benchmark, we demonstrate that our method achieves state-of-the-art performance in terms of predictive accuracy and substantial improvements in the quality of uncertainty estimates.

How should we intervene on an unknown structural equation model to maximize a downstream variable of interest? This setting, also known as causal Bayesian optimization (CBO), has important applications in medicine, ecology, and manufacturing. Standard Bayesian optimization algorithms fail to effectively leverage the underlying causal structure. Existing CBO approaches assume noiseless measurements and do not come with guarantees. We propose the {\em model-based causal Bayesian optimization algorithm (MCBO)} that learns a full system model instead of only modeling intervention-reward pairs. MCBO propagates epistemic uncertainty about the causal mechanisms through the graph and trades off exploration and exploitation via the optimism principle. We bound its cumulative regret, and obtain the first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization, our acquisition function cannot be evaluated in closed form, so we show how the reparameterization trick can be used to apply gradient-based optimizers. The resulting practical implementation of MCBO compares favorably with state-of-the-art approaches empirically.

Studying the loss landscapes of neural networks is critical to identifying generalizations and avoiding overconfident predictions. Flatness, which measures the perturbation resilience of pre-trained parameters for loss values, is widely acknowledged as an essential predictor of generalization. While the concept of flatness has been formalized as a PAC-Bayes bound, it has been observed that the generalization bounds can vary arbitrarily depending on the scale of the model parameters. Despite previous attempts to address this issue, generalization bounds remain vulnerable to function-preserving scaling transformations or are limited to impractical network structures. In this paper, we introduce new PAC-Bayes prior and posterior distributions invariant to scaling transformations, achieved through the \textit{decomposition of perturbations into scale and connectivity components}. In this way, this approach expands the range of networks to which the resulting generalization bound can be applied, including those with practical transformations such as weight decay with batch normalization. Moreover, we demonstrate that scale-dependency issues of flatness can adversely affect the uncertainty calibration of Laplace approximation, and we propose a solution using our invariant posterior. Our proposed invariant posterior allows for effective measurement of flatness and calibration with low complexity while remaining invariant to practical parameter transformations, also applying it as a reliable predictor of neural network generalization.

Despite the huge success of object detection, the training process still requires an immense amount of labeled data. Although various active learning solutions for object detection have been proposed, most existing works do not take advantage of epistemic uncertainty, which is an important metric for capturing the usefulness of the sample. Also, previous works pay little attention to the attributes of each bounding box (e.g., nearest object, box size) when computing the informativeness of an image. In this paper, we propose a new active learning strategy for object detection that overcomes the shortcomings of prior works. To make use of epistemic uncertainty, we adopt evidential deep learning (EDL) and propose a new module termed model evidence head (MEH), that makes EDL highly compatible with object detection. Based on the computed epistemic uncertainty of each bounding box, we propose hierarchical uncertainty aggregation (HUA) for obtaining the informativeness of an image. HUA realigns all bounding boxes into multiple levels based on the attributes and aggregates uncertainties in a bottom-up order, to effectively capture the context within the image. Experimental results show that our method outperforms existing state-of-the-art methods by a considerable margin.

Active learning has demonstrated data efficiency in many fields. Existing active learning algorithms, especially in the context of batch-mode deep Bayesian active models, rely heavily on the quality of uncertainty estimations of the model, and are often challenging to scale to large batches. In this paper, we propose Batch-BALanCe, a scalable batch-mode active learning algorithm, which combines insights from decision-theoretic active learning, combinatorial information measure, and diversity sampling. At its core, Batch-BALanCe relies on a novel decision-theoretic acquisition function that facilitates differentiation among different equivalence classes. Intuitively, each equivalence class consists of hypotheses (e.g., posterior samples of deep neural networks) with similar predictions, and Batch-BALanCe adaptively adjusts the size of the equivalence classes as learning progresses. To scale up the computation of queries to large batches, we further propose an efficient batch-mode acquisition procedure, which aims to maximize a novel combinatorial information measure defined through the acquisition function. We show that our algorithm can effectively handle realistic multi-class classification tasks, and achieves compelling performance on several benchmark datasets for active learning under both low- and large-batch regimes.

We develop fast distribution-free conformal prediction algorithms for obtaining multivalid coverage on exchangeable data in the batch setting. Multivalid coverage guarantees are stronger than marginal coverage guarantees in two ways: (1) They hold even conditional on group membership---that is, the target coverage level $1-\alpha$ holds conditionally on membership in each of an arbitrary (potentially intersecting) group in a finite collection $\mathcal{G}$ of regions in the feature space. (2) They hold even conditional on the value of the threshold used to produce the prediction set on a given example. In fact multivalid coverage guarantees hold even when conditioning on group membership and threshold value simultaneously. We give two algorithms: both take as input an arbitrary non-conformity score and an arbitrary collection of possibly intersecting groups $\mathcal{G}$, and then can equip arbitrary black-box predictors with prediction sets. Our first algorithm is a direct extension of quantile regression, needs to solve only a single convex minimization problem, and produces an estimator which has group-conditional guarantees for each group in $\mathcal{G}$. Our second algorithm is iterative, and gives the full guarantees of multivalid conformal prediction: prediction sets that are valid conditionally both on group membership and non-conformity threshold. We evaluate the performance of both of our algorithms in an extensive set of experiments.

Implicit processes (IPs) are a generalization of Gaussian processes (GPs). IPs may lack a closed-form expression but are easy to sample from. Examples include, among others, Bayesian neural networks or neural samplers. IPs can be used as priors over functions, resulting in flexible models with well-calibrated prediction uncertainty estimates. Methods based on IPs usually carry out function-space approximate inference, which overcomes some of the difficulties of parameter-space approximate inference. Nevertheless, the approximations employed often limit the expressiveness of the final model, resulting, e.g., in a Gaussian predictive distribution, which can be restrictive. We propose here a multi-layer generalization of IPs called the Deep Variational Implicit process (DVIP). This generalization is similar to that of deep GPs over GPs, but it is more flexible due to the use of IPs as the prior distribution over the latent functions. We describe a scalable variational inference algorithm for training DVIP and show that it outperforms previous IP-based methods and also deep GPs. We support these claims via extensive regression and classification experiments. We also evaluate DVIP on large datasets with up to several million data instances to illustrate its good scalability and performance.

A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data without any inductive biases, but in practice, we often restrict the class of stochastic processes for the ease of estimation. One such restriction is the use of a finite-dimensional latent variable accounting for the uncertainty in the functions drawn from NPs. Some recent works show that this can be improved with more “data-driven” source of uncertainty such as bootstrapping. In this work, we take a different approach based on the martingale posterior, a recently developed alternative to Bayesian inference. For the martingale posterior, instead of specifying prior-likelihood pairs, a predictive distribution for future data is specified. Under specific conditions on the predictive distribution, it can be shown that the uncertainty in the generated future data actually corresponds to the uncertainty of the implicitly defined Bayesian posteriors. Based on this result, instead of assuming any form of the latent variables, we equip a NP with a predictive distribution implicitly defined with neural networks and use the corresponding martingale posteriors as the source of uncertainty. The resulting model, which we name as Martingale Posterior Neural Process (MPNP), is demonstrated to outperform baselines on various tasks.