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Theory/Probabilistic Methods

Ryan Singh, Christopher L Buckley

Attention mechanisms play a crucial role in cognitive systems by allowing them to flexibly allocate cognitive resources. Transformers, in particular, have become a dominant architecture in machine learning, with attention as their central innovation. However, the underlying intuition and formalism of attention in Transformers is based on ideas of keys and queries in database management systems. In this work, we pursue a structural inference perspective, building upon, and bringing together, previous theoretical descriptions of attention such as; Gaussian Mixture Models, alignment mechanisms and Hopfield Networks. Specifically, we demonstrate that attention can be viewed as inference over an implicitly defined set of possible adjacency structures in a graphical model, revealing the generality of such a mechanism. This perspective unifies different attentional architectures in machine learning and suggests potential modifications and generalizations of attention. Here we investigate two and demonstrate their behaviour on explanatory toy problems: (a) extending the value function to incorporate more nodes of a graphical model yielding a mechanism with a bias toward attending multiple tokens; (b) introducing a geometric prior (with conjugate hyper-prior) over the adjacency structures producing a mechanism which dynamically scales the context window depending on input. Moreover, by describing a link between structural inference and precision-regulation in Predictive Coding Networks, we discuss how this framework can bridge the gap between attentional mechanisms in machine learning and Bayesian conceptions of attention in Neuroscience. We hope by providing a new lens on attention architectures our work can guide the development of new and improved attentional mechanisms.

Probabilistic Methods/Bayesian Models and Methods

Kim Nicoli, Christopher J. Anders, Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kühn, Klaus-Robert Müller, Paolo Stornati, Pan Kessel, Shinichi Nakajima

In this paper, we propose a novel and powerful method to harness Bayesian optimization for variational quantum eigensolvers (VQEs) - a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a *VQE-kernel* which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty.Moreover, we propose a novel acquisition function for Bayesian optimization called \emph{Expected Maximum Improvement over Confident Regions} (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly "observed". As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.

Probabilistic Methods/Bayesian Models and Methods

Kajetan Schweighofer, Lukas Aichberger, Mykyta Ielanskyi, Günter Klambauer, Sepp Hochreiter

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.

Probabilistic Methods/Bayesian Models and Methods

Xingsi Dong, Si Wu

Bayesian brain theory suggests that the brain employs generative models to understand the external world. The sampling-based perspective posits that the brain infers the posterior distribution through samples of stochastic neuronal responses. Additionally, the brain continually updates its generative model to approach the true distribution of the external world. In this study, we introduce the Hierarchical Exponential-family Energy-based (HEE) model, which captures the dynamics of inference and learning. In the HEE model, we decompose the partition function into individual layers and leverage a group of neurons with shorter time constants to sample the gradient of the decomposed normalization term. This allows our model to estimate the partition function and perform inference simultaneously, circumventing the negative phase encountered in conventional energy-based models (EBMs). As a result, the learning process is localized both in time and space, and the model is easy to converge. To match the brain's rapid computation, we demonstrate that neural adaptation can serve as a momentum term, significantly accelerating the inference process. On natural image datasets, our model exhibits representations akin to those observed in the biological visual system. Furthermore, for the machine learning community, our model can generate observations through joint or marginal generation. We show that marginal generation outperforms joint generation and achieves performance on par with other EBMs.

Probabilistic Methods/Variational Inference

Thibault RANDRIANARISOA, Botond Szabo

By now Bayesian methods are routinely used in practice for solving inverse problems. In inverse problems the parameter or signal of interest is observed only indirectly, as an image of a given map, and the observations are typically further corrupted with noise. Bayes offers a natural way to regularize these problems via the prior distribution and provides a probabilistic solution, quantifying the remaining uncertainty in the problem. However, the computational costs of standard, sampling based Bayesian approaches can be overly large in such complex models. Therefore, in practice variational Bayes is becoming increasingly popular. Nevertheless, the theoretical understanding of these methods is still relatively limited, especially in context of inverse problems.In our analysis we investigate variational Bayesian methods for Gaussian process priors to solve linear inverse problems. We consider both mildly and severely ill-posed inverse problems and work with the popular inducing variable variational Bayes approach proposed by Titsias [Titsias, 2009]. We derive posterior contraction rates for the variational posterior in general settings and show that the minimax estimation rate can be attained by correctly tunned procedures. As specific examples we consider a collection of inverse problems including the heat equation, Volterra operator and Radon transform and inducing variable methods based on population and empirical spectral features.

Probabilistic Methods/Bayesian Models and Methods

Qingyao Sun, Kevin Murphy, Sayna Ebrahimi, Alexander D'Amour

Changes in the data distribution at test time can have deleterious effects on the performance of predictive models $p(y|x)$.We consider situations where there are additional meta-data labels (such as group labels), denoted by $z$, that can account for such changes in the distribution.In particular, we assume that the prior distribution $p(y,z)$, which models the dependence between the class label $y$ and the "nuisance" factors $z$, may change across domains, either due to a change in the correlation between these terms, or a change in one of their marginals.However, we assume that the generative model for features $p(x|y,z)$ is invariant across domains.We note that this corresponds to an expanded version of the widely used "label shift" assumption, where the labels now also include the nuisance factors $z$. Based on this observation, we propose a test-time label shift correction that adapts to changes in the joint distribution $p(y, z)$ using EM applied to unlabeled samples from the target domain distribution, $p_t(x)$.Importantly, we are able to avoid fitting a generative model $p(x|y,z)$, and merely need to reweight the outputs of a discriminative model $p_s(y,z|x)$ trained on the source distribution.We evaluate our method, which we call "Test-Time Label-Shift Adaptation" (TTLSA), on several standard image and text datasets, as well as the CheXpert chest X-ray dataset, and show that it improves performance over methods that target invariance to changes in the distribution, as well as baseline empirical risk minimization methods.Code for reproducing experiments is available at https://github.com/nalzok/test-time-label-shift.

Optimization/Zero-order and Black-box Optimization

Alexandre Maraval, Matthieu Zimmer, Antoine Grosnit, Haitham Bou Ammar

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.

Aditi Basu Bal, Ramy Mounir, Sathyanarayanan Aakur, Sudeep Sarkar, Anuj Srivastava

Graph-based representations are becoming increasingly popular for representing and analyzing video data, especially in object tracking and scene understanding applications. Accordingly, an essential tool in this approach is to generate statistical inferences for graphical time series associated with videos. This paper develops a Kalman-smoothing method for estimating graphs from noisy, cluttered, and incomplete data. The main challenge here is to find and preserve the registration of nodes (salient detected objects) across time frames when the data has noise and clutter due to false and missing nodes. First, we introduce a quotient-space representation of graphs that incorporates temporal registration of nodes, and we use that metric structure to impose a dynamical model on graph evolution. Then, we derive a Kalman smoother, adapted to the quotient space geometry, to estimate dense, smooth trajectories of graphs. We demonstrate this framework using simulated data and actual video graphs extracted from the Multiview Extended Video with Activities (MEVA) dataset. This framework successfully estimates graphs despite the noise, clutter, and missed detections. Keywords: motion tracking, graph representations, video graphs, quotient metrics, Kalman smoothing, nonlinear manifolds.

Nan Ding, Xi Chen, Tomer Levinboim, Soravit Changpinyo, Radu Soricut

With the increasing abundance of pretrained models in recent years, the problem of selecting the best pretrained checkpoint for a particular downstream classification task has been gaining increased attention. Although several methods have recently been proposed to tackle the selection problem (e.g. LEEP, H-score), these methods resort to applying heuristics that are not well motivated by learning theory. In this paper we present PACTran, a theoretically grounded family of metrics for pretrained model selection and transferability measurement. We first show how to derive PACTran metrics from the optimal PAC-Bayesian bound under the transfer learning setting. We then empirically evaluate three metric instantiations of PACTran on a number of vision tasks (VTAB) as well as a language-and-vision (OKVQA) task. An analysis of the results shows PACTran is a more consistent and effective transferability measure compared to existing selection methods.

Yuwei Wu, Weixiao Liu, Sipu Ruan, Gregory S. Chirikjian

3D shape abstraction has drawn great interest over the years. Apart from low-level representations such as meshes and voxels, researchers also seek to semantically abstract complex objects with basic geometric primitives. Recent deep learning methods rely heavily on datasets, with limited generality to unseen categories. Furthermore, abstracting an object accurately yet with a small number of primitives still remains a challenge. In this paper, we propose a novel non-parametric Bayesian statistical method to infer an abstraction, consisting of an unknown number of geometric primitives, from a point cloud. We model the generation of points as observations sampled from an infinite mixture of Gaussian Superquadric Taper Models (GSTM). Our approach formulates the abstraction as a clustering problem, in which: 1) each point is assigned to a cluster via the Chinese Restaurant Process (CRP); 2) a primitive representation is optimized for each cluster, and 3) a merging post-process is incorporated to provide a concise representation. We conduct extensive experiments on two datasets. The results indicate that our method outperforms the state-of-the-art in terms of accuracy and is generalizable to various types of objects.

Hanwei Fan, Jiandong Mu, Wei Zhang

Pruning is an effective technique for convolutional neural networks (CNNs) model compression, but it is difficult to find the optimal pruning policy due to the large design space. To improve the usability of pruning, many auto pruning methods have been developed. Recently, Bayesian optimization (BO) has been considered to be a competitive algorithm for auto pruning due to its solid theoretical foundation and high sampling efficiency. However, BO suffers from the curse of dimensionality. The performance of BO deteriorates when pruning deep CNNs, since the dimension of the design spaces increase. We propose a novel clustering algorithm that reduces the dimension of the design space to speed up the searching process. Subsequently, a rollback algorithm is proposed to recover the high-dimensional design space so that higher pruning accuracy can be obtained. We validate our proposed method on ResNet, MobileNetV1, and MobileNetV2 models. Experiments show that the proposed method significantly improves the convergence rate of BO when pruning deep CNNs with no increase in running time. The source code is available at https://github.com/fanhanwei/BOCR.

Mingjun Zhao, Shan Lu, Zixuan Wang, Xiaoli Wang, Di Niu

Automated augmentation is an emerging and effective technique to search for data augmentation policies to improve generalizability of deep neural network training. Most existing work focuses on constructing a unified policy applicable to all data samples in a given dataset, without considering sample or class variations. In this paper, we propose a novel two-stage data augmentation algorithm, named Label-Aware AutoAugment (LA3), which takes advantage of the label information, and learns augmentation policies separately for samples of different labels. LA3 consists of two learning stages, where in the first stage, individual augmentation methods are evaluated and ranked for each label via Bayesian Optimization aided by a neural predictor, which allows us to identify effective augmentation techniques for each label under a low search cost. And in the second stage, a composite augmentation policy is constructed out of a selection of effective as well as complementary augmentations, which produces significant performance boost and can be easily deployed in typical model training. Extensive experiments demonstrate that LA3 achieves excellent performance matching or surpassing existing methods on CIFAR-10 and CIFAR-100, and achieves a new state-of-the-art ImageNet accuracy of 79.97% on ResNet-50 among auto-augmentation methods, while maintaining a low computational cost.

Jiamian Wang, Yulun Zhang, Xin Yuan, Ziyi Meng, Zhiqiang Tao

Recently, hyperspectral imaging (HSI) has attracted increasing research attention, especially for the ones based on a coded aperture snapshot spectral imaging (CASSI) system. Existing deep HSI reconstruction models are generally trained on paired data to retrieve original signals upon 2D compressed measurements given by a particular optical hardware mask in CASSI, during which the mask largely impacts the reconstruction performance and could work as a ""model hyperparameter"" governing on data augmentations. This mask-specific training style will lead to a hardware miscalibration issue, which sets up barriers to deploying deep HSI models among different hardware and noisy environments. To address this challenge, we introduce mask uncertainty for HSI with a complete variational Bayesian learning treatment and explicitly model it through a mask decomposition inspired by real hardware. Specifically, we propose a novel Graph-based Self-Tuning (GST) network to reason uncertainties adapting to varying spatial structures of masks among different hardware. Moreover, we develop a bilevel optimization framework to balance HSI reconstruction and uncertainty estimation, accounting for the hyperparameter property of masks. Extensive experimental results validate the effectiveness (over 33/30 dB) of the proposed method under two miscalibration scenarios and demonstrate a highly competitive performance compared with the state-of-the-art well-calibrated methods. Our source code and pre-trained models are available at https://github.com/Jiamian-Wang/mask_uncertainty_spectral_SCI

Zhaopeng Dou, Zhongdao Wang, Weihua Chen, Yali Li, Shengjin Wang

Current person image retrieval methods have achieved great improvements in accuracy metrics. However, they rarely describe the reliability of the prediction. In this paper, we propose an Uncertainty-Aware Learning (UAL) method to remedy this issue. UAL aims at providing reliability-aware predictions by considering data uncertainty and model uncertainty simultaneously. Data uncertainty captures the “noise” inherent in the sample, while model uncertainty depicts the model’s confidence in the sample’s prediction. Specifically, in UAL, (1) we propose a sampling-free data uncertainty learning method to adaptively assign weights to different samples during training, down-weighting the low-quality ambiguous samples. (2) we leverage the Bayesian framework to model the model uncertainty by assuming the parameters of the network follow a Bernoulli distribution. (3) the data uncertainty and the model uncertainty are jointly learned in a unified network, and they serve as two fundamental criteria for the reliability assessment: if a probe is high-quality (low data uncertainty) and the model is confident in the prediction of the probe (low model uncertainty), the final ranking will be assessed as reliable. Experiments under the risk-controlled settings and the multi-query settings show the proposed reliability assessment is effective. Our method also shows superior performance on three challenging benchmarks under the vanilla single query settings. The code is available at: https://github.com/dcp15/UAL

Alexandra Chouldechova, Siqi Deng, Yongxin Wang, Wei Xia, Pietro Perona

We introduce Semi-supervised Performance Evaluation for Face Recognition (SPE-FR). SPE-FR is a statistical method for evaluating the performance and algorithmic bias of face verification systems when identity labels are unavailable or incomplete. The method is based on parametric Bayesian modeling of the face embedding similarity scores. SPE-FR produces point estimates, performance curves, and confidence bands that reflect uncertainty in the estimation procedure. Focusing on the unsupervised setting wherein no identity labels are available, we validate our method through experiments on a wide range of face embedding models and two publicly available evaluation datasets. Experiments show that SPE-FR can accurately assess performance on data with no identity labels, and confidently reveal demographic biases in system performance.

Uddeshya Upadhyay, Shyamgopal Karthik, Yanbei Chen, Massimiliano Mancini, Zeynep Akata

High-quality calibrated uncertainty estimates are crucial for numerous real-world applications, especially for deep learning-based deployed ML systems. While Bayesian deep learning techniques allow uncertainty estimation, training them with large-scale datasets is an expensive process that does not always yield models competitive with non-Bayesian counterparts. Moreover, many of the high-performing deep learning models that are already trained and deployed are non-Bayesian in nature, and do not provide uncertainty estimates. To address these issues, we propose BayesCap that learns a Bayesian identity mapping for the frozen model, allowing uncertainty estimation. BayesCap is a memory-efficient method that can be trained on a small fraction of the original dataset, enhancing pretrained non-Bayesian computer vision models by providing calibrated uncertainty estimates for the predictions without (i) hampering the performance of the model and (ii) the need for expensive retraining the model from scratch. The proposed method is agnostic to various architectures and tasks. We show the efficacy of our method on a wide variety of tasks with a diverse set of architectures, including image super-resolution, deblurring, inpainting, and crucial application such as medical image translation. Moreover, we apply the derived uncertainty estimates to detect out-of-distribution samples in critical scenarios like depth estimation in autonomous driving.

Jing Bi, Jiebo Luo, Chenliang Xu

Learning new skills by observing humans' behaviors is an essential capability of AI. In this work, we leverage instructional videos to study humans' decision-making processes, focusing on learning a model to plan goal-directed actions in real-life videos. In contrast to conventional action recognition, goal-directed actions are based on expectations of their outcomes requiring causal knowledge of potential consequences of actions. Thus, integrating the environment structure with goals is critical for solving this task. Previous works learn a single world model will fail to distinguish various tasks, resulting in an ambiguous latent space; planning through it will gradually neglect the desired outcomes since the global information of the future goal degrades quickly as the procedure evolves. We address these limitations with a new formulation of procedure planning and propose novel algorithms to model human behaviors through Bayesian Inference and model-based Imitation Learning. Experiments conducted on real-world instructional videos show that our method can achieve state-of-the-art performance in reaching the indicated goals. Furthermore, the learned contextual information presents interesting features for planning in a latent space.

Ershad Banijamali, Mohsen Rohani, Elmira Amirloo, Jun Luo, Pascal Poupart

In autonomous driving (AD), accurately predicting changes in the environment can effectively improve safety and comfort. Due to complex interactions among traffic participants, however, it is very hard to achieve accurate prediction for a long horizon. To address this challenge, we propose prediction by anticipation, which views interaction in terms of a latent probabilistic generative process wherein some vehicles move partly in response to the anticipated motion of other vehicles. Under this view, consecutive data frames can be factorized into sequential samples from an action-conditional distribution that effectively generalizes to a wider range of actions and driving situations. Our proposed prediction model, variational Bayesian in nature, is trained to maximize the evidence lower bound (ELBO) of the log-likelihood of this conditional distribution. Evaluations of our approach with prominent AD datasets NGSIM I-80 and Argoverse show significant improvement over current state-of-the-art in both accuracy and generalization.

A. Braunegg, Amartya Chakraborty, Michael Krumdick, Nicole Lape, Sara Leary, Keith Manville, Elizabeth Merkhofer, Laura Strickhart, Matthew Walmer

Physical adversarial attacks threaten to fool object detection systems, but reproducible research on the real-world effectiveness of physical patches and how to defend against them requires a publicly available benchmark dataset. We present APRICOT, a collection of over 1,000 annotated photographs of printed adversarial patches in public locations. The patches target several object categories for three COCO-trained detection models, and the photos represent natural variation in position, distance, lighting conditions, and viewing angle. Our analysis suggests that maintaining adversarial robustness in uncontrolled settings is highly challenging, but it is still possible to produce targeted detections under white-box and sometimes black-box settings. We establish baselines for defending against adversarial patches through several methods, including a detector supervised with synthetic data and unsupervised methods such as kernel density estimation, Bayesian uncertainty, and reconstruction error. Our results suggest that adversarial patches can be effectively flagged, both in a high-knowledge, attack-specific scenario, and in an unsupervised setting where patches are detected as anomalies in natural images. This dataset and the described experiments provide a benchmark for future research on the effectiveness of and defenses against physical adversarial objects in the wild.

Yuming Shen, Jie Qin, Lei Huang, Li Liu, Fan Zhu, Ling Shao

Deep generative models have been successfully applied to Zero-Shot Learning (ZSL) recently. However, the underlying drawbacks of GANs and VAEs (e.g., the hardness of training with ZSL-oriented regularizers and the limited generation quality) hinder the existing generative ZSL models from fully bypassing the seen-unseen bias. To tackle the above limitations, for the first time, this work incorporates a new family of generative models (i.e., flow-based models) into ZSL. The proposed Invertible Zero-shot Flow (IZF) learns factorized data embeddings (i.e., the semantic factors and the non-semantic ones) with the forward pass of an invertible flow network, while the reverse pass generates data samples. This procedure theoretically extends conventional generative flows to a conditional scheme. To explicitly solve the bias problem, our model enlarges the seen-unseen distributional discrepancy based on negative sample-based distance measurement. Notably, IZF works flexibly with either a naive Bayesian classifier or a held-out trainable one for zero-shot recognition. Experiments on widely-adopted ZSL benchmarks demonstrate the significant performance gain of IZF over existing methods, in terms of both classic and generalized settings.