Overcoming the Paradox of Certified Training with Gaussian Smoothing

Training neural networks with high certified accuracy against adversarial examples remains an open problem despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation, in training, these methods perform worse than looser relaxations. Prior work hypothesized that this is caused by the discontinuity and perturbation sensitivity of the loss surface induced by these tighter relaxations. In this work, we show theoretically that Gaussian Loss Smoothing can alleviate both of these issues. We confirm this empirically by proposing a certified training method combining PGPE, an algorithm computing gradients of a smoothed loss, with different convex relaxations. When using this training method, we observe that tighter bounds indeed lead to strictly better networks that can outperform state-of-the-art methods on the same network. While scaling PGPE-based training remains challenging due to high computational cost, our results clearly demonstrate the promise of Gaussian Loss Smoothing for training certifiably robust neural networks.

Expressivity of ReLU-Networks under Convex Relaxations

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.

Understanding Certified Training with Interval Bound Propagation

As robustness verification methods are becoming more precise, training certifiably robust neural networks is becoming ever more relevant. To this end, certified training methods compute and then optimize an upper bound on the worst-case loss over a robustness specification. Curiously, training methods based on the imprecise interval bound propagation (IBP) consistently outperform those leveraging more precise bounding methods. Still, we lack an understanding of the mechanisms making IBP so successful. In this work, we thoroughly investigate these mechanisms by leveraging a novel metric measuring the tightness of IBP bounds. We first show theoretically that, for deep linear models, tightness decreases with width and depth at initialization, but improves with IBP training, given sufficient network width. We, then, derive sufficient and necessary conditions on weight matrices for IBP bounds to become exact and demonstrate that these impose strong regularization, explaining the empirically observed trade-off between robustness and accuracy in certified training. Our extensive experimental evaluation validates our theoretical predictions for ReLU networks, including that wider networks improve performance, yielding state-of-the-art results. Interestingly, we observe that while all IBP-based training methods lead to high tightness, this is neither sufficient nor necessary to achieve high certifiable robustness. This hints at the existence of new training methods that do not induce the strong regularization required for tight IBP bounds, leading to improved robustness and standard accuracy.

SMAP: A Novel Heterogeneous Information Framework for Scenario-based Optimal Model Assignment

The increasing maturity of big data applications has led to a proliferation of models targeting the same objectives within the same scenarios and datasets. However, selecting the most suitable model that considers model's features while taking specific requirements and constraints into account still poses a significant challenge. Existing methods have focused on worker-task assignments based on crowdsourcing, they neglect the scenario-dataset-model assignment problem. To address this challenge, a new problem named the Scenario-based Optimal Model Assignment (SOMA) problem is introduced and a novel framework entitled Scenario and Model Associative percepts (SMAP) is developed. SMAP is a heterogeneous information framework that can integrate various types of information to intelligently select a suitable dataset and allocate the optimal model for a specific scenario. To comprehensively evaluate models, a new score function that utilizes multi-head attention mechanisms is proposed. Moreover, a novel memory mechanism named the mnemonic center is developed to store the matched heterogeneous information and prevent duplicate matching. Six popular traffic scenarios are selected as study cases and extensive experiments are conducted on a dataset to verify the effectiveness and efficiency of SMAP and the score function.

TAPS: Connecting Certified and Adversarial Training

Training certifiably robust neural networks remains a notoriously hard problem. On one side, adversarial training optimizes under-approximations of the worst-case loss, which leads to insufficient regularization for certification, while on the other, sound certified training methods optimize loose over-approximations, leading to over-regularization and poor (standard) accuracy. In this work we propose TAPS, an (unsound) certified training method that combines IBP and PGD training to yield precise, although not necessarily sound, worst-case loss approximations, reducing over-regularization and increasing certified and standard accuracies. Empirically, TAPS achieves a new state-of-the-art in many settings, e.g., reaching a certified accuracy of $22\%$ on TinyImageNet for $\ell_\infty$-perturbations with radius $\epsilon=1/255$.

"Is your explanation stable?": A Robustness Evaluation Framework for Feature Attribution

Understanding the decision process of neural networks is hard. One vital method for explanation is to attribute its decision to pivotal features. Although many algorithms are proposed, most of them solely improve the faithfulness to the model. However, the real environment contains many random noises, which may leads to great fluctuations in the explanations. More seriously, recent works show that explanation algorithms are vulnerable to adversarial attacks. All of these make the explanation hard to trust in real scenarios. To bridge this gap, we propose a model-agnostic method \emph{Median Test for Feature Attribution} (MeTFA) to quantify the uncertainty and increase the stability of explanation algorithms with theoretical guarantees. MeTFA has the following two functions: (1) examine whether one feature is significantly important or unimportant and generate a MeTFA-significant map to visualize the results; (2) compute the confidence interval of a feature attribution score and generate a MeTFA-smoothed map to increase the stability of the explanation. Experiments show that MeTFA improves the visual quality of explanations and significantly reduces the instability while maintaining the faithfulness. To quantitatively evaluate the faithfulness of an explanation under different noise settings, we further propose several robust faithfulness metrics. Experiment results show that the MeTFA-smoothed explanation can significantly increase the robust faithfulness. In addition, we use two scenarios to show MeTFA's potential in the applications. First, when applied to the SOTA explanation method to locate context bias for semantic segmentation models, MeTFA-significant explanations use far smaller regions to maintain 99\%+ faithfulness. Second, when tested with different explanation-oriented attacks, MeTFA can help defend vanilla, as well as adaptive, adversarial attacks against explanations.

Transfer Attacks Revisited: A Large-Scale Empirical Study in Real Computer Vision Settings

One intriguing property of adversarial attacks is their "transferability" -- an adversarial example crafted with respect to one deep neural network (DNN) model is often found effective against other DNNs as well. Intensive research has been conducted on this phenomenon under simplistic controlled conditions. Yet, thus far, there is still a lack of comprehensive understanding about transferability-based attacks ("transfer attacks") in real-world environments. To bridge this critical gap, we conduct the first large-scale systematic empirical study of transfer attacks against major cloud-based MLaaS platforms, taking the components of a real transfer attack into account. The study leads to a number of interesting findings which are inconsistent to the existing ones, including: (1) Simple surrogates do not necessarily improve real transfer attacks. (2) No dominant surrogate architecture is found in real transfer attacks. (3) It is the gap between posterior (output of the softmax layer) rather than the gap between logit (so-called $\kappa$ value) that increases transferability. Moreover, by comparing with prior works, we demonstrate that transfer attacks possess many previously unknown properties in real-world environments, such as (1) Model similarity is not a well-defined concept. (2) $L_2$ norm of perturbation can generate high transferability without usage of gradient and is a more powerful source than $L_\infty$ norm. We believe this work sheds light on the vulnerabilities of popular MLaaS platforms and points to a few promising research directions.

Application of Knowledge Graphs to Provide Side Information for Improved Recommendation Accuracy

Personalized recommendations are popular in these days of Internet driven activities, specifically shopping. Recommendation methods can be grouped into three major categories, content based filtering, collaborative filtering and machine learning enhanced. Information about products and preferences of different users are primarily used to infer preferences for a specific user. Inadequate information can obviously cause these methods to fail or perform poorly. The more information we provide to these methods, the more likely it is that the methods perform better. Knowledge graphs represent the current trend in recording information in the form of relations between entities, and can provide additional (side) information about products and users. Such information can be used to improve nearest neighbour search, clustering users and products, or train the neural network, when one is used. In this work, we present a new generic recommendation systems framework, that integrates knowledge graphs into the recommendation pipeline. We describe its software design and implementation, and then show through experiments, how such a framework can be specialized for a domain, say movie recommendations, and the improvements in recommendation results possible due to side information obtained from knowledge graphs representation of such information. Our framework supports different knowledge graph representation formats, and facilitates format conversion, merging and information extraction needed for training recommendation methods.