Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks

• URL: http://arxiv.org/abs/2204.00187v1
• Date: Fri, 1 Apr 2022 03:31:27 GMT
• Title: Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks
• Authors: Alexander Davydov, Saber Jafarpour, Matthew Abate, Francesco Bullo, Samuel Coogan
• Abstract summary: We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs) INNs are a class of implicit learning models that use implicit equations as layers. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs.
• Score: 64.23331120621118
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs). INNs are a class of implicit learning models that use implicit equations as layers and have been shown to exhibit several notable benefits over traditional deep neural networks. We first establish that tight inclusion functions of neural networks, which provide the tightest rectangular over-approximation of an input-output map, lead to sharper robustness guarantees than the well-studied robustness measures of local Lipschitz constants. Like Lipschitz constants, tight inclusions functions are computationally challenging to obtain, and we thus propose using mixed monotonicity and contraction theory to obtain computationally efficient estimates of tight inclusion functions for INNs. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs. We design a novel optimization problem for training robust INNs and we provide empirical evidence that suitably-trained INNs can be more robust than comparably-trained feedforward networks.

Related papers

• RSC-SNN: Exploring the Trade-off Between Adversarial Robustness and Accuracy in Spiking Neural Networks via Randomized Smoothing Coding [17.342181435229573]
  Spiking Neural Networks (SNNs) have received widespread attention due to their unique neuronal dynamics and low-power nature. Previous research empirically shows that SNNs with Poisson coding are more robust than Artificial Neural Networks (ANNs) on small-scale datasets. This work theoretically demonstrates that SNN's inherent adversarial robustness stems from its Poisson coding.
  arXiv  Detail & Related papers  (2024-07-29T15:26:15Z)
• Efficient kernel surrogates for neural network-based regression [0.8030359871216615]
  We study the performance of the Conjugate Kernel (CK), an efficient approximation to the Neural Tangent Kernel (NTK) We show that the CK performance is only marginally worse than that of the NTK and, in certain cases, is shown to be superior. In addition to providing a theoretical grounding for using CKs instead of NTKs, our framework suggests a recipe for improving DNN accuracy inexpensively.
  arXiv  Detail & Related papers  (2023-10-28T06:41:47Z)
• An Automata-Theoretic Approach to Synthesizing Binarized Neural Networks [13.271286153792058]
  Quantized neural networks (QNNs) have been developed, with binarized neural networks (BNNs) restricted to binary values as a special case. This paper presents an automata-theoretic approach to synthesizing BNNs that meet designated properties.
  arXiv  Detail & Related papers  (2023-07-29T06:27:28Z)
• Benign Overfitting in Deep Neural Networks under Lazy Training [72.28294823115502]
  We show that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification. Our results indicate that interpolating with smoother functions leads to better generalization.
  arXiv  Detail & Related papers  (2023-05-30T19:37:44Z)
• Quantization-aware Interval Bound Propagation for Training Certifiably Robust Quantized Neural Networks [58.195261590442406]
  We study the problem of training and certifying adversarially robust quantized neural networks (QNNs) Recent work has shown that floating-point neural networks that have been verified to be robust can become vulnerable to adversarial attacks after quantization. We present quantization-aware interval bound propagation (QA-IBP), a novel method for training robust QNNs.
  arXiv  Detail & Related papers  (2022-11-29T13:32:38Z)
• 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)
• Reinforcement Learning with External Knowledge by using Logical Neural Networks [67.46162586940905]
  A recent neuro-symbolic framework called the Logical Neural Networks (LNNs) can simultaneously provide key-properties of both neural networks and symbolic logic. We propose an integrated method that enables model-free reinforcement learning from external knowledge sources.
  arXiv  Detail & Related papers  (2021-03-03T12:34:59Z)
• Encoding the latent posterior of Bayesian Neural Networks for uncertainty quantification [10.727102755903616]
  We aim for efficient deep BNNs amenable to complex computer vision architectures. We achieve this by leveraging variational autoencoders (VAEs) to learn the interaction and the latent distribution of the parameters at each network layer. Our approach, Latent-Posterior BNN (LP-BNN), is compatible with the recent BatchEnsemble method, leading to highly efficient (in terms of computation and memory during both training and testing) ensembles.
  arXiv  Detail & Related papers  (2020-12-04T19:50:09Z)
• Progressive Tandem Learning for Pattern Recognition with Deep Spiking Neural Networks [80.15411508088522]
  Spiking neural networks (SNNs) have shown advantages over traditional artificial neural networks (ANNs) for low latency and high computational efficiency. We propose a novel ANN-to-SNN conversion and layer-wise learning framework for rapid and efficient pattern recognition.
  arXiv  Detail & Related papers  (2020-07-02T15:38:44Z)
• Interval Neural Networks: Uncertainty Scores [11.74565957328407]
  We propose a fast, non-Bayesian method for producing uncertainty scores in the output of pre-trained deep neural networks (DNNs) This interval neural network (INN) has interval valued parameters and propagates its input using interval arithmetic. In numerical experiments on an image reconstruction task, we demonstrate the practical utility of INNs as a proxy for the prediction error.
  arXiv  Detail & Related papers  (2020-03-25T18:03:51Z)

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.