skip to main content


The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Thursday, June 13 until 2:00 AM ET on Friday, June 14 due to maintenance. We apologize for the inconvenience.

Title: Adversarial Examples for k-Nearest Neighbor Classifiers Based on Higher-Order Voronoi Diagrams
Adversarial examples are a widely studied phenomenon in machine learning models. While most of the attention has been focused on neural networks, other practical models also suffer from this issue. In this work, we propose an algorithm for evaluating the adversarial robustness of k-nearest neighbor classification, i.e., finding a minimum-norm adversarial example. Diverging from previous proposals, we propose the first geometric approach by performing a search that expands outwards from a given input point. On a high level, the search radius expands to the nearby higher-order Voronoi cells until we find a cell that classifies differently from the input point. To scale the algorithm to a large k, we introduce approximation steps that find perturbation with smaller norm, compared to the baselines, in a variety of datasets. Furthermore, we analyze the structural properties of a dataset where our approach outperforms the competition.  more » « less
Award ID(s):
Author(s) / Creator(s):
; ; ;
Ranzato, M.; Beygelzimer, A.; Dauphin, Y; Liang, P. S.; Wortman Vaughan, J.
Date Published:
Journal Name:
Advances in Neural Information Processing Systems 34 (NeurIPS 2021)
Page Range / eLocation ID:
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive performance and reduced memory consumption. However, they can remain brittle with respect to input adversarial perturbations. This paper proposes a theoretical and computational framework for robustness verification of implicit neural networks; our framework blends together mixed monotone systems theory and contraction theory. First, given an implicit neural network, we introduce a related embedded network and show that, given an infinity-norm box constraint on the input, the embedded network provides an infinity-norm box overapproximation for the output of the original network. Second, using infinity-matrix measures, we propose sufficient conditions for well-posedness of both the original and embedded system and design an iterative algorithm to compute the infinity-norm box robustness margins for reachability and classification problems. Third, of independent value, we show that employing a suitable relative classifier variable in our analysis will lead to tighter bounds on the certified adversarial robustness in classification problems. Finally, we perform numerical simulations on a Non-Euclidean Monotone Operator Network (NEMON) trained on the MNIST dataset. In these simulations, we compare the accuracy and run time of our mixed monotone contractive approach with the existing robustness verification approaches in the literature for estimating the certified adversarial robustness. 
    more » « less
  2. null (Ed.)
    Differentiable Neural Architecture Search (DNAS) has demonstrated great success in designing state-of-the-art, efficient neural networks. However, DARTS-based DNAS's search space is small when compared to other search methods', since all candidate network layers must be explicitly instantiated in memory. To address this bottleneck, we propose a memory and computationally efficient DNAS variant: DMaskingNAS. This algorithm expands the search space by up to 10^14x over conventional DNAS, supporting searches over spatial and channel dimensions that are otherwise prohibitively expensive: input resolution and number of filters. We propose a masking mechanism for feature map reuse, so that memory and computational costs stay nearly constant as the search space expands. Furthermore, we employ effective shape propagation to maximize per-FLOP or per-parameter accuracy. The searched FBNetV2s yield state-of-the-art performance when compared with all previous architectures. With up to 421x less search cost, DMaskingNAS finds models with 0.9% higher accuracy, 15% fewer FLOPs than MobileNetV3-Small; and with similar accuracy but 20% fewer FLOPs than Efficient-B0. Furthermore, our FBNetV2 outperforms MobileNetV3 by 2.6% in accuracy, with equivalent model size. FBNetV2 models are open-sourced at 
    more » « less
  3. Skyline queries are used to find the Pareto optimal solution from datasets containing multi-dimensional data points. In this paper, we propose a new type of skyline queries whose evaluation is constrained by a multi-cost transportation network (MCTN) and whose answers are off the network. This type of skyline queries is useful in many applications. For example, a person wants to find an apartment by considering not only the price and the surrounding area of the apartment, but also the transportation cost, time, and distance between the apartment and his/her work place. Most existing works that evaluate skyline queries on multi-cost networks (MCNs), which are either MCTNs or road networks, find interesting objects that locate on edges of the networks. Formally, our new type of skyline queries takes as input an MCTN, a query point q, and a set of objects of interest D with spatial information, where q and the objects in D are off the network. The answers to such queries are objects in D that are not dominated by other D objects when considering the multiple attributes of these objects and the multiple network cost from q to the solution objects. To evaluate such queries, we propose an exact search algorithm and its improved version by implementing several properties. The space of the exact skyline solutions is huge and can easily reach the order of thousands and incur long evaluation time. We further design much more efficient heuristic methods to find approximate solutions. We run extensive experiments using both real and synthetic datasets to test the effectiveness and efficiency of our proposed approaches. The results show that the exact search algorithm can be dramatically improved by utilizing several properties. The heuristic approaches to find approximate answers can largely reduce the query time and retrieve results that are comparable to the exact solutions. 
    more » « less
  4. Dataset search is emerging as a critical capability in both research and industry: it has spurred many novel applications, ranging from the enrichment of analyses of real-world phenomena to the improvement of machine learning models. Recent research in this field has explored a new class of data-driven queries: queries consist of datasets and retrieve, from a large collection, related datasets. In this paper, we study a specific type of data-driven query that supports relational data augmentation through numerical data relationships: given an input query table, find the top-k tables that are both joinable with it and contain columns that are correlated with a column in the query. We propose a novel hashing scheme that allows the construction of a sketch-based index to support efficient correlated table search. We show that our proposed approach is effective and efficient, and achieves better trade-offs that significantly improve both the ranking accuracy and recall compared to the state-of-the-art solutions. 
    more » « less
  5. Neural networks can learn complex, non-convex functions, and it is challenging to guarantee their correct behavior in safety-critical contexts. Many approaches exist to find failures in networks (e.g., adversarial examples), but these cannot guarantee the absence of failures. Verification algorithms address this need and provide formal guarantees about a neural network by answering "yes or no" questions. For example, they can answer whether a violation exists within certain bounds. However, individual "yes or no" questions cannot answer qualitative questions such as “what is the largest error within these bounds”; the answers to these lie in the domain of optimization. Therefore, we propose strategies to extend existing verifiers to perform optimization and find: (i) the most extreme failure in a given input region and (ii) the minimum input perturbation required to cause a failure. A naive approach using a bisection search with an off-the-shelf verifier results in many expensive and overlapping calls to the verifier. Instead, we propose an approach that tightly integrates the optimization process into the verification procedure, achieving better runtime performance than the naive approach. We evaluate our approach implemented as an extension of Marabou, a state-of-the-art neural network verifier, and compare its performance with the bisection approach and MIPVerify, an optimization-based verifier. We observe complementary performance between our extension of Marabou and MIPVerify 
    more » « less