Robustness Verifcation in Neural Networks

• URL: http://arxiv.org/abs/2403.13441v1
• Date: Wed, 20 Mar 2024 09:34:38 GMT
• Title: Robustness Verifcation in Neural Networks
• Authors: Adrian Wurm,
• Abstract summary: We investigate formal verification problems for Neural Network computations. One question is whether there do exist valid inputs such that the network computes a valid output. We show that the problems are conquerable in a semi-linear setting.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in form of Linear Programming instances, one question is whether there do exist valid inputs such that the network computes a valid output? And does this property hold for all valid inputs? Do two given networks compute the same function? Is there a smaller network computing the same function? The complexity of these questions have been investigated recently from a practical point of view and approximated by heuristic algorithms. We complement these achievements by giving a theoretical framework that enables us to interchange security and efficiency questions in neural networks and analyze their computational complexities. We show that the problems are conquerable in a semi-linear setting, meaning that for piecewise linear activation functions and when the sum- or maximum metric is used, most of them are in P or in NP at most.

Related papers

• Complexity of Deciding Injectivity and Surjectivity of ReLU Neural Networks [5.482420806459269]
  We prove coNP-completeness of deciding injectivity of a ReLU layer. We also characterize surjectivity for two-layer ReLU networks with one-dimensional output.
  arXiv  Detail & Related papers  (2024-05-30T08:14:34Z)
• The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks [59.26515696183751]
  We show that algorithm discovery in neural networks is sometimes more complex. We show that even simple learning problems can admit a surprising diversity of solutions.
  arXiv  Detail & Related papers  (2023-06-30T17:59:13Z)
• The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks [94.63547069706459]
  #DNN-Verification problem involves counting the number of input configurations of a DNN that result in a violation of a safety property. We propose a novel approach that returns the exact count of violations. We present experimental results on a set of safety-critical benchmarks.
  arXiv  Detail & Related papers  (2023-01-17T18:32:01Z)
• Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Tasks [51.8723187709964]
  We study the OOD generalization of neural algorithmic reasoning tasks. The goal is to learn an algorithm from input-output pairs using deep neural networks.
  arXiv  Detail & Related papers  (2022-11-01T18:33:20Z)
• Robust Training and Verification of Implicit Neural Networks: A Non-Euclidean Contractive Approach [64.23331120621118]
  This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks. We introduce a related embedded network and show that the embedded network can be used to provide an $ell_infty$-norm box over-approximation of the reachable sets of the original network. We apply our algorithms to train implicit neural networks on the MNIST dataset and compare the robustness of our models with the models trained via existing approaches in the literature.
  arXiv  Detail & Related papers  (2022-08-08T03:13:24Z)
• Reachability In Simple Neural Networks [2.7195102129095003]
  We show that NP-hardness already holds for restricted classes of simple specifications and neural networks. We give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.
  arXiv  Detail & Related papers  (2022-03-15T14:25:44Z)
• Neural networks with linear threshold activations: structure and algorithms [1.795561427808824]
  We show that 2 hidden layers are necessary and sufficient to represent any function representable in the class. We also give precise bounds on the sizes of the neural networks required to represent any function in the class. We propose a new class of neural networks that we call shortcut linear threshold networks.
  arXiv  Detail & Related papers  (2021-11-15T22:33:52Z)
• Reachability Is NP-Complete Even for the Simplest Neural Networks [0.0]
  It was recently claimed that the problem is NP-complete for general neural networks and conjunctive input/output specifications. We show that NP-hardness already holds for restricted classes of simple specifications and neural networks with just one layer.
  arXiv  Detail & Related papers  (2021-08-30T12:38:57Z)
• Achieving Small Test Error in Mildly Overparameterized Neural Networks [30.664282759625948]
  We show an algorithm which finds one of these points in time. In addition, we prove that for a fully connected neural net, with an additional assumption on the data distribution, there is a time algorithm.
  arXiv  Detail & Related papers  (2021-04-24T06:47:20Z)
• A Survey of Quantization Methods for Efficient Neural Network Inference [75.55159744950859]
  quantization is the problem of distributing continuous real-valued numbers over a fixed discrete set of numbers to minimize the number of bits required. It has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x.
  arXiv  Detail & Related papers  (2021-03-25T06:57:11Z)
• Efficient Integer-Arithmetic-Only Convolutional Neural Networks [87.01739569518513]
  We replace conventional ReLU with Bounded ReLU and find that the decline is due to activation quantization. Our integer networks achieve equivalent performance as the corresponding FPN networks, but have only 1/4 memory cost and run 2x faster on modern GPU.
  arXiv  Detail & Related papers  (2020-06-21T08:23:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.