arXiv subjects

Krishnamurthy Dvijotham

Publications and source records attributed to Krishnamurthy Dvijotham.

At least 37 records · Page 2Linked to original sources

arXiv2023

IBP Regularization for Verified Adversarial Robustness via Branch-and-Bound

Recent works have tried to increase the verifiability of adversarially trained networks by running the attacks over domains larger than the original perturbations and adding various regularization terms to the objective. However, these algorithms either underperform or require complex and expensive stage-wise training procedures, hindering their practical applicability. We present IBP-R, a novel verified training algorithm that is both simple and effective. IBP-R induces network verifiability by coupling adversarial attacks on enlarged domains with a regularization term, based on inexpensive interval bound propagation, that minimizes the gap between the non-convex verification problem and its approximations. By leveraging recent branch-and-bound frameworks, we show that IBP-R obtains state-of-the-art verified robustness-accuracy trade-offs for small perturbations on CIFAR-10 while training significantly faster than relevant previous work. Additionally, we present UPB, a novel branching strategy that, relying on a simple heuristic based on $β$-CROWN, reduces the cost of state-of-the-art branching algorithms while yielding splits of comparable quality.

cs.LG↗

arXiv2023

Training Private Models That Know What They Don't Know

Training reliable deep learning models which avoid making overconfident but incorrect predictions is a longstanding challenge. This challenge is further exacerbated when learning has to be differentially private: protection provided to sensitive data comes at the price of injecting additional randomness into the learning process. In this work, we conduct a thorough empirical investigation of selective classifiers -- that can abstain when they are unsure -- under a differential privacy constraint. We find that several popular selective prediction approaches are ineffective in a differentially private setting as they increase the risk of privacy leakage. At the same time, we identify that a recent approach that only uses checkpoints produced by an off-the-shelf private learning algorithm stands out as particularly suitable under DP. Further, we show that differential privacy does not just harm utility but also degrades selective classification performance. To analyze this effect across privacy levels, we propose a novel evaluation mechanism which isolate selective prediction performance across model utility levels. Our experimental results show that recovering the performance level attainable by non-private models is possible but comes at a considerable coverage cost as the privacy budget decreases.

cs.LG↗

arXiv2023

Robust Feasibility of Systems of Quadratic Equations Using Topological Degree Theory

We consider the problem of measuring the margin of robust feasibility of solutions to a system of nonlinear equations. We study the special case of a system of quadratic equations, which shows up in many practical applications such as the power grid and other infrastructure networks. This problem is a generalization of quadratically constrained quadratic programming (QCQP), which is NP-Hard in the general setting. We develop approaches based on topological degree theory to estimate bounds on the robustness margin of such systems. Our methods use tools from convex analysis and optimization theory to cast the problems of checking the conditions for robust feasibility as a nonlinear optimization problem. We then develop inner bound and outer bound procedures for this optimization problem, which could be solved efficiently to derive lower and upper bounds, respectively, for the margin of robust feasibility. We evaluate our approach numerically on standard instances taken from the MATPOWER and NESTA databases of AC power flow equations that describe the steady state of the power grid. The results demonstrate that our approach can produce tight lower and upper bounds on the margin of robust feasibility for such instances.

math.OC↗

arXiv2023

Interactive Concept Bottleneck Models

Concept bottleneck models (CBMs) are interpretable neural networks that first predict labels for human-interpretable concepts relevant to the prediction task, and then predict the final label based on the concept label predictions. We extend CBMs to interactive prediction settings where the model can query a human collaborator for the label to some concepts. We develop an interaction policy that, at prediction time, chooses which concepts to request a label for so as to maximally improve the final prediction. We demonstrate that a simple policy combining concept prediction uncertainty and influence of the concept on the final prediction achieves strong performance and outperforms static approaches as well as active feature acquisition methods proposed in the literature. We show that the interactive CBM can achieve accuracy gains of 5-10% with only 5 interactions over competitive baselines on the Caltech-UCSD Birds, CheXpert and OAI datasets.

cs.LG↗

arXiv2023

Human Uncertainty in Concept-Based AI Systems

Placing a human in the loop may abate the risks of deploying AI systems in safety-critical settings (e.g., a clinician working with a medical AI system). However, mitigating risks arising from human error and uncertainty within such human-AI interactions is an important and understudied issue. In this work, we study human uncertainty in the context of concept-based models, a family of AI systems that enable human feedback via concept interventions where an expert intervenes on human-interpretable concepts relevant to the task. Prior work in this space often assumes that humans are oracles who are always certain and correct. Yet, real-world decision-making by humans is prone to occasional mistakes and uncertainty. We study how existing concept-based models deal with uncertain interventions from humans using two novel datasets: UMNIST, a visual dataset with controlled simulated uncertainty based on the MNIST dataset, and CUB-S, a relabeling of the popular CUB concept dataset with rich, densely-annotated soft labels from humans. We show that training with uncertain concept labels may help mitigate weaknesses of concept-based systems when handling uncertain interventions. These results allow us to identify several open challenges, which we argue can be tackled through future multidisciplinary research on building interactive uncertainty-aware systems. To facilitate further research, we release a new elicitation platform, UElic, to collect uncertain feedback from humans in collaborative prediction tasks.

cs.HC↗

arXiv2022

Role of Human-AI Interaction in Selective Prediction

Recent work has shown the potential benefit of selective prediction systems that can learn to defer to a human when the predictions of the AI are unreliable, particularly to improve the reliability of AI systems in high-stakes applications like healthcare or conservation. However, most prior work assumes that human behavior remains unchanged when they solve a prediction task as part of a human-AI team as opposed to by themselves. We show that this is not the case by performing experiments to quantify human-AI interaction in the context of selective prediction. In particular, we study the impact of communicating different types of information to humans about the AI system's decision to defer. Using real-world conservation data and a selective prediction system that improves expected accuracy over that of the human or AI system working individually, we show that this messaging has a significant impact on the accuracy of human judgements. Our results study two components of the messaging strategy: 1) Whether humans are informed about the prediction of the AI system and 2) Whether they are informed about the decision of the selective prediction system to defer. By manipulating these messaging components, we show that it is possible to significantly boost human performance by informing the human of the decision to defer, but not revealing the prediction of the AI. We therefore show that it is vital to consider how the decision to defer is communicated to a human when designing selective prediction systems, and that the composite accuracy of a human-AI team must be carefully evaluated using a human-in-the-loop framework.

cs.AI↗

arXiv2021

A Fine-Grained Analysis on Distribution Shift

Robustness to distribution shifts is critical for deploying machine learning models in the real world. Despite this necessity, there has been little work in defining the underlying mechanisms that cause these shifts and evaluating the robustness of algorithms across multiple, different distribution shifts. To this end, we introduce a framework that enables fine-grained analysis of various distribution shifts. We provide a holistic analysis of current state-of-the-art methods by evaluating 19 distinct methods grouped into five categories across both synthetic and real-world datasets. Overall, we train more than 85K models. Our experimental framework can be easily extended to include new methods, shifts, and datasets. We find, unlike previous work~\citep{Gulrajani20}, that progress has been made over a standard ERM baseline; in particular, pretraining and augmentations (learned or heuristic) offer large gains in many cases. However, the best methods are not consistent over different datasets and shifts.

cs.LG↗

arXiv2021

Make Sure You're Unsure: A Framework for Verifying Probabilistic Specifications

Most real world applications require dealing with stochasticity like sensor noise or predictive uncertainty, where formal specifications of desired behavior are inherently probabilistic. Despite the promise of formal verification in ensuring the reliability of neural networks, progress in the direction of probabilistic specifications has been limited. In this direction, we first introduce a general formulation of probabilistic specifications for neural networks, which captures both probabilistic networks (e.g., Bayesian neural networks, MC-Dropout networks) and uncertain inputs (distributions over inputs arising from sensor noise or other perturbations). We then propose a general technique to verify such specifications by generalizing the notion of Lagrangian duality, replacing standard Lagrangian multipliers with "functional multipliers" that can be arbitrary functions of the activations at a given layer. We show that an optimal choice of functional multipliers leads to exact verification (i.e., sound and complete verification), and for specific forms of multipliers, we develop tractable practical verification algorithms. We empirically validate our algorithms by applying them to Bayesian Neural Networks (BNNs) and MC Dropout Networks, and certifying properties such as adversarial robustness and robust detection of out-of-distribution (OOD) data. On these tasks we are able to provide significantly stronger guarantees when compared to prior work -- for instance, for a VGG-64 MC-Dropout CNN trained on CIFAR-10, we improve the certified AUC (a verified lower bound on the true AUC) for robust OOD detection (on CIFAR-100) from $0\% \rightarrow 29\%$. Similarly, for a BNN trained on MNIST, we improve on the robust accuracy from $60.2\% \rightarrow 74.6\%$. Further, on a novel specification -- distributionally robust OOD detection -- we improve the certified AUC from $5\% \rightarrow 23\%$.

cs.LG↗

arXiv2021

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.

cs.LG↗

arXiv2020

Autoencoding Variational Autoencoder

Does a Variational AutoEncoder (VAE) consistently encode typical samples generated from its decoder? This paper shows that the perhaps surprising answer to this question is `No'; a (nominally trained) VAE does not necessarily amortize inference for typical samples that it is capable of generating. We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. Our approach hinges on an alternative construction of the variational approximation distribution to the true posterior of an extended VAE model with a Markov chain alternating between the encoder and the decoder. The method can be used to train a VAE model from scratch or given an already trained VAE, it can be run as a post processing step in an entirely self supervised way without access to the original training data. Our experimental analysis reveals that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks. We provide experimental results on the ColorMnist and CelebA benchmark datasets that quantify the properties of the learned representations and compare the approach with a baseline that is specifically trained for the desired property.

cs.LG↗

arXiv2020

Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming

Convex relaxations have emerged as a promising approach for verifying desirable properties of neural networks like robustness to adversarial perturbations. Widely used Linear Programming (LP) relaxations only work well when networks are trained to facilitate verification. This precludes applications that involve verification-agnostic networks, i.e., networks not specially trained for verification. On the other hand, semidefinite programming (SDP) relaxations have successfully be applied to verification-agnostic networks, but do not currently scale beyond small networks due to poor time and space asymptotics. In this work, we propose a first-order dual SDP algorithm that (1) requires memory only linear in the total number of network activations, (2) only requires a fixed number of forward/backward passes through the network per iteration. By exploiting iterative eigenvector methods, we express all solver operations in terms of forward and backward passes through the network, enabling efficient use of hardware like GPUs/TPUs. For two verification-agnostic networks on MNIST and CIFAR-10, we significantly improve L-inf verified robust accuracy from 1% to 88% and 6% to 40% respectively. We also demonstrate tight verification of a quadratic stability specification for the decoder of a variational autoencoder.

cs.LG↗

arXiv2020

Lagrangian Decomposition for Neural Network Verification

A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even further, making the bounds unnecessarily loose. We propose a novel approach based on Lagrangian Decomposition. Our formulation admits an efficient supergradient ascent algorithm, as well as an improved proximal algorithm. Both the algorithms offer three advantages: (i) they yield bounds that are provably at least as tight as previous dual algorithms relying on Lagrangian relaxations; (ii) they are based on operations analogous to forward/backward pass of neural networks layers and are therefore easily parallelizable, amenable to GPU implementation and able to take advantage of the convolutional structure of problems; and (iii) they allow for anytime stopping while still providing valid bounds. Empirically, we show that we obtain bounds comparable with off-the-shelf solvers in a fraction of their running time, and obtain tighter bounds in the same time as previous dual algorithms. This results in an overall speed-up when employing the bounds for formal verification. Code for our algorithms is available at https://github.com/oval-group/decomposition-plnn-bounds.

cs.LG↗

arXiv2020

Achieving Robustness in the Wild via Adversarial Mixing with Disentangled Representations

Recent research has made the surprising finding that state-of-the-art deep learning models sometimes fail to generalize to small variations of the input. Adversarial training has been shown to be an effective approach to overcome this problem. However, its application has been limited to enforcing invariance to analytically defined transformations like $\ell_p$-norm bounded perturbations. Such perturbations do not necessarily cover plausible real-world variations that preserve the semantics of the input (such as a change in lighting conditions). In this paper, we propose a novel approach to express and formalize robustness to these kinds of real-world transformations of the input. The two key ideas underlying our formulation are (1) leveraging disentangled representations of the input to define different factors of variations, and (2) generating new input images by adversarially composing the representations of different images. We use a StyleGAN model to demonstrate the efficacy of this framework. Specifically, we leverage the disentangled latent representations computed by a StyleGAN model to generate perturbations of an image that are similar to real-world variations (like adding make-up, or changing the skin-tone of a person) and train models to be invariant to these perturbations. Extensive experiments show that our method improves generalization and reduces the effect of spurious correlations (reducing the error rate of a "smile" detector by 21% for example).

cs.LG↗

arXiv2019

Achieving Verified Robustness to Symbol Substitutions via Interval Bound Propagation

Neural networks are part of many contemporary NLP systems, yet their empirical successes come at the price of vulnerability to adversarial attacks. Previous work has used adversarial training and data augmentation to partially mitigate such brittleness, but these are unlikely to find worst-case adversaries due to the complexity of the search space arising from discrete text perturbations. In this work, we approach the problem from the opposite direction: to formally verify a system's robustness against a predefined class of adversarial attacks. We study text classification under synonym replacements or character flip perturbations. We propose modeling these input perturbations as a simplex and then using Interval Bound Propagation -- a formal model verification method. We modify the conventional log-likelihood training objective to train models that can be efficiently verified, which would otherwise come with exponential search complexity. The resulting models show only little difference in terms of nominal accuracy, but have much improved verified accuracy under perturbations and come with an efficiently computable formal guarantee on worst case adversaries.

cs.CL↗

arXiv2019

Adversarial Robustness through Local Linearization

Adversarial training is an effective methodology for training deep neural networks that are robust against adversarial, norm-bounded perturbations. However, the computational cost of adversarial training grows prohibitively as the size of the model and number of input dimensions increase. Further, training against less expensive and therefore weaker adversaries produces models that are robust against weak attacks but break down under attacks that are stronger. This is often attributed to the phenomenon of gradient obfuscation; such models have a highly non-linear loss surface in the vicinity of training examples, making it hard for gradient-based attacks to succeed even though adversarial examples still exist. In this work, we introduce a novel regularizer that encourages the loss to behave linearly in the vicinity of the training data, thereby penalizing gradient obfuscation while encouraging robustness. We show via extensive experiments on CIFAR-10 and ImageNet, that models trained with our regularizer avoid gradient obfuscation and can be trained significantly faster than adversarial training. Using this regularizer, we exceed current state of the art and achieve 47% adversarial accuracy for ImageNet with l-infinity adversarial perturbations of radius 4/255 under an untargeted, strong, white-box attack. Additionally, we match state of the art results for CIFAR-10 at 8/255.

stat.ML↗

arXiv2019

Robust Optimization for Electricity Generation

We consider a robust optimization problem in an electric power system under uncertain demand and availability of renewable energy resources. Solving the deterministic alternating current optimal power flow (ACOPF) problem has been considered challenging since the 1960s due to its nonconvexity. Linear approximation of the AC power flow system sees pervasive use, but does not guarantee a physically feasible system configuration. In recent years, various convex relaxation schemes for the ACOPF problem have been investigated, and under some assumptions, a physically feasible solution can be recovered. Based on these convex relaxations, we construct a robust convex optimization problem with recourse to solve for optimal controllable injections (fossil fuel, nuclear, etc.) in electric power systems under uncertainty (renewable energy generation, demand fluctuation, etc.). We propose a cutting-plane method to solve this robust optimization problem, and we establish convergence and other desirable properties. Experimental results indicate that our robust convex relaxation of the ACOPF problem can provide a tight lower bound.

math.OC↗

arXiv2019

On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models

Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all possible adversarial perturbations. While these techniques show promise, they often result in difficult optimization procedures that remain hard to scale to larger networks. Through a comprehensive analysis, we show how a simple bounding technique, interval bound propagation (IBP), can be exploited to train large provably robust neural networks that beat the state-of-the-art in verified accuracy. While the upper bound computed by IBP can be quite weak for general networks, we demonstrate that an appropriate loss and clever hyper-parameter schedule allow the network to adapt such that the IBP bound is tight. This results in a fast and stable learning algorithm that outperforms more sophisticated methods and achieves state-of-the-art results on MNIST, CIFAR-10 and SVHN. It also allows us to train the largest model to be verified beyond vacuous bounds on a downscaled version of ImageNet.

cs.LG↗

arXiv2019

Knowing When to Stop: Evaluation and Verification of Conformity to Output-size Specifications

Models such as Sequence-to-Sequence and Image-to-Sequence are widely used in real world applications. While the ability of these neural architectures to produce variable-length outputs makes them extremely effective for problems like Machine Translation and Image Captioning, it also leaves them vulnerable to failures of the form where the model produces outputs of undesirable length. This behavior can have severe consequences such as usage of increased computation and induce faults in downstream modules that expect outputs of a certain length. Motivated by the need to have a better understanding of the failures of these models, this paper proposes and studies the novel output-size modulation problem and makes two key technical contributions. First, to evaluate model robustness, we develop an easy-to-compute differentiable proxy objective that can be used with gradient-based algorithms to find output-lengthening inputs. Second and more importantly, we develop a verification approach that can formally verify whether a network always produces outputs within a certain length. Experimental results on Machine Translation and Image Captioning show that our output-lengthening approach can produce outputs that are 50 times longer than the input, while our verification approach can, given a model and input domain, prove that the output length is below a certain size.

cs.LG↗