ANCER: Anisotropic Certification via Sample-wise Volume Maximization

Randomized smoothing has recently emerged as an effective tool that enables certification of deep neural network classifiers at scale. All prior art on randomized smoothing has focused on isotropic $\ell_p$ certification, which has the advantage of yielding certificates that can be easily compared among isotropic methods via $\ell_p$-norm radius. However, isotropic certification limits the region that can be certified around an input to worst-case adversaries, \ie it cannot reason about other "close", potentially large, constant prediction safe regions. To alleviate this issue, (i) we theoretically extend the isotropic randomized smoothing $\ell_1$ and $\ell_2$ certificates to their generalized anisotropic counterparts following a simplified analysis. Moreover, (ii) we propose evaluation metrics allowing for the comparison of general certificates - a certificate is superior to another if it certifies a superset region - with the quantification of each certificate through the volume of the certified region. We introduce ANCER, a practical framework for obtaining anisotropic certificates for a given test set sample via volume maximization. Our empirical results demonstrate that ANCER achieves state-of-the-art $\ell_1$ and $\ell_2$ certified accuracy on both CIFAR-10 and ImageNet at multiple radii, while certifying substantially larger regions in terms of volume, thus highlighting the benefits of moving away from isotropic analysis. Code used in our experiments is available in https://github.com/MotasemAlfarra/ANCER.

Do Different Tracking Tasks Require Different Appearance Models?

Tracking objects of interest in a video is one of the most popular and widely applicable problems in computer vision. However, with the years, a Cambrian explosion of use cases and benchmarks has fragmented the problem in a multitude of different experimental setups. As a consequence, the literature has fragmented too, and now the novel approaches proposed by the community are usually specialised to fit only one specific setup. To understand to what extent this specialisation is actually necessary, in this work we present UniTrack, a unified tracking solution to address five different tasks within the same framework. UniTrack consists of a single and task-agnostic appearance model, which can be learned in a supervised or self-supervised fashion, and multiple "heads" to address individual tasks and that do not require training. We show how most tracking tasks can be solved within this framework, and that the same appearance model can be used to obtain performance that is competitive against specialised methods for all the five tasks considered. The framework also allows us to analyse appearance models obtained with the most recent self-supervised methods, thus significantly extending their evaluation and comparison to a larger variety of important problems. Code available at https://github.com/Zhongdao/UniTrack.

DeformRS: Certifying Input Deformations with Randomized Smoothing

Deep neural networks are vulnerable to input deformations in the form of vector fields of pixel displacements and to other parameterized geometric deformations e.g. translations, rotations, etc. Current input deformation certification methods either (i) do not scale to deep networks on large input datasets, or (ii) can only certify a specific class of deformations, e.g. only rotations. We reformulate certification in randomized smoothing setting for both general vector field and parameterized deformations and propose DeformRS-VF and DeformRS-Par, respectively. Our new formulation scales to large networks on large input datasets. For instance, DeformRS-Par certifies rich deformations, covering translations, rotations, scaling, affine deformations, and other visually aligned deformations such as ones parameterized by Discrete-Cosine-Transform basis. Extensive experiments on MNIST, CIFAR10 and ImageNet show that DeformRS-Par outperforms existing state-of-the-art in certified accuracy, e.g. improved certified accuracy of 6% against perturbed rotations in the set [-10,10] degrees on ImageNet.

Learning Multimodal VAEs through Mutual Supervision

Multimodal VAEs seek to model the joint distribution over heterogeneous data (e.g.\ vision, language), whilst also capturing a shared representation across such modalities. Prior work has typically combined information from the modalities by reconciling idiosyncratic representations directly in the recognition model through explicit products, mixtures, or other such factorisations. Here we introduce a novel alternative, the MEME, that avoids such explicit combinations by repurposing semi-supervised VAEs to combine information between modalities implicitly through mutual supervision. This formulation naturally allows learning from partially-observed data where some modalities can be entirely missing -- something that most existing approaches either cannot handle, or do so to a limited extent. We demonstrate that MEME outperforms baselines on standard metrics across both partial and complete observation schemes on the MNIST-SVHN (image-image) and CUB (image-text) datasets. We also contrast the quality of the representations learnt by mutual supervision against standard approaches and observe interesting trends in its ability to capture relatedness between data.

KL Guided Domain Adaptation

Domain adaptation is an important problem and often needed for real-world applications. In this problem, instead of i.i.d. datapoints, we assume that the source (training) data and the target (testing) data have different distributions. With that setting, the empirical risk minimization training procedure often does not perform well, since it does not account for the change in the distribution. A common approach in the domain adaptation literature is to learn a representation of the input that has the same distributions over the source and the target domain. However, these approaches often require additional networks and/or optimizing an adversarial (minimax) objective, which can be very expensive or unstable in practice. To tackle this problem, we first derive a generalization bound for the target loss based on the training loss and the reverse Kullback-Leibler (KL) divergence between the source and the target representation distributions. Based on this bound, we derive an algorithm that minimizes the KL term to obtain a better generalization to the target domain. We show that with a probabilistic representation network, the KL term can be estimated efficiently via minibatch samples without any additional network or a minimax objective. This leads to a theoretically sound alignment method which is also very efficient and stable in practice. Experimental results also suggest that our method outperforms other representation-alignment approaches.

You Never Cluster Alone

Recent advances in self-supervised learning with instance-level contrastive objectives facilitate unsupervised clustering. However, a standalone datum is not perceiving the context of the holistic cluster, and may undergo sub-optimal assignment. In this paper, we extend the mainstream contrastive learning paradigm to a cluster-level scheme, where all the data subjected to the same cluster contribute to a unified representation that encodes the context of each data group. Contrastive learning with this representation then rewards the assignment of each datum. To implement this vision, we propose twin-contrast clustering (TCC). We define a set of categorical variables as clustering assignment confidence, which links the instance-level learning track with the cluster-level one. On one hand, with the corresponding assignment variables being the weight, a weighted aggregation along the data points implements the set representation of a cluster. We further propose heuristic cluster augmentation equivalents to enable cluster-level contrastive learning. On the other hand, we derive the evidence lower-bound of the instance-level contrastive objective with the assignments. By reparametrizing the assignment variables, TCC is trained end-to-end, requiring no alternating steps. Extensive experiments show that TCC outperforms the state-of-the-art on challenging benchmarks.

Breaking Shortcut: Exploring Fully Convolutional Cycle-Consistency for Video Correspondence Learning

Previous cycle-consistency correspondence learning methods usually leverage image patches for training. In this paper, we present a fully convolutional method, which is simpler and more coherent to the inference process. While directly applying fully convolutional training results in model collapse, we study the underline reason behind this collapse phenomenon, indicating that the absolute positions of pixels provide a shortcut to easily accomplish cycle-consistence, which hinders the learning of meaningful visual representations. To break this absolute position shortcut, we propose to apply different crops for forward and backward frames, and adopt feature warping to establish correspondence between two crops of a same frame. The former technique enforces the corresponding pixels at forward and back tracks to have different absolute positions, and the latter effectively blocks the shortcuts going between forward and back tracks. In three label propagation benchmarks for pose tracking, face landmark tracking and video object segmentation, our method largely improves the results of vanilla fully convolutional cycle-consistency method, achieving very competitive performance compared with the self-supervised state-of-the-art approaches.

Gradient Matching for Domain Generalization

Machine learning systems typically assume that the distributions of training and test sets match closely. However, a critical requirement of such systems in the real world is their ability to generalize to unseen domains. Here, we propose an inter-domain gradient matching objective that targets domain generalization by maximizing the inner product between gradients from different domains. Since direct optimization of the gradient inner product can be computationally prohibitive -- requires computation of second-order derivatives -- we derive a simpler first-order algorithm named Fish that approximates its optimization. We demonstrate the efficacy of Fish on 6 datasets from the Wilds benchmark, which captures distribution shift across a diverse range of modalities. Our method produces competitive results on these datasets and surpasses all baselines on 4 of them. We perform experiments on both the Wilds benchmark, which captures distribution shift in the real world, as well as datasets in DomainBed benchmark that focuses more on synthetic-to-real transfer. Our method produces competitive results on both benchmarks, demonstrating its effectiveness across a wide range of domain generalization tasks.

Improved Branch and Bound for Neural Network Verification via Lagrangian Decomposition

We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. First, we propose novel bounding algorithms based on Lagrangian Decomposition. Previous works have used off-the-shelf solvers to solve relaxations at each node of the BaB tree, or constructed weaker relaxations that can be solved efficiently, but lead to unnecessarily weak bounds. Our formulation restricts the optimization to a subspace of the dual domain that is guaranteed to contain the optimum, resulting in accelerated convergence. Furthermore, it allows for a massively parallel implementation, which is amenable to GPU acceleration via modern deep learning frameworks. Second, we present a novel activation-based branching strategy. By coupling an inexpensive heuristic with fast dual bounding, our branching scheme greatly reduces the size of the BaB tree compared to previous heuristic methods. Moreover, it performs competitively with a recent strategy based on learning algorithms, without its large offline training cost. Finally, we design a BaB framework, named Branch and Dual Network Bound (BaDNB), based on our novel bounding and branching algorithms. We show that BaDNB outperforms previous complete verification systems by a large margin, cutting average verification times by factors up to 50 on adversarial robustness properties.