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Register a new userDefence against adversarial attacks using classical and quantum-enhanced Boltzmann machines
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Added by
Alejandro Pozas-Kerstjens
Publication date
2020
fields
Physics
and research's language is
English
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We provide a robust defence to adversarial attacks on discriminative algorithms. Neural networks are naturally vulnerable to small, tailored perturbations in the input data that lead to wrong predictions. On the contrary, generative models attempt to learn the distribution underlying a dataset, making them inherently more robust to small perturbations. We use Boltzmann machines for discrimination purposes as attack-resistant classifiers, and compare them against standard state-of-the-art adversarial defences. We find improvements ranging from 5% to 72% against attacks with Boltzmann machines on the MNIST dataset. We furthermore complement the training with quantum-enhanced sampling from the D-Wave 2000Q annealer, finding results comparable with classical techniques and with marginal improvements in some cases. These results underline the relevance of probabilistic methods in constructing neural networks and highlight a novel scenario of practical relevance where quantum computers, even with limited hardware capabilites, could provide advantages over classical computers. This work is dedicated to the memory of Peter Wittek.
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The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators (OPOs) and a field programmable gate array (FPGA) circuit. The similar mathematical models were proposed three decades ago by J. J. Hopfield, et al. in the context of classical neural networks. In this article, we compare the computational performance of both models.
In this work, we consider compressed sensing reconstruction from $M$ measurements of $K$-sparse structured signals which do not possess a writable correlation model. Assuming that a generative statistical model, such as a Boltzmann machine, can be trained in an unsupervised manner on example signals, we demonstrate how this signal model can be used within a Bayesian framework of signal reconstruction. By deriving a message-passing inference for general distribution restricted Boltzmann machines, we are able to integrate these inferred signal models into approximate message passing for compressed sensing reconstruction. Finally, we show for the MNIST dataset that this approach can be very effective, even for $M < K$.
A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance-sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.
Deep learning has become an integral part of various computer vision systems in recent years due to its outstanding achievements for object recognition, facial recognition, and scene understanding. However, deep neural networks (DNNs) are susceptible to be fooled with nearly high confidence by an adversary. In practice, the vulnerability of deep learning systems against carefully perturbed images, known as adversarial examples, poses a dire security threat in the physical world applications. To address this phenomenon, we present, what to our knowledge, is the first ever image set based adversarial defence approach. Image set classification has shown an exceptional performance for object and face recognition, owing to its intrinsic property of handling appearance variability. We propose a robust deep Bayesian image set classification as a defence framework against a broad range of adversarial attacks. We extensively experiment the performance of the proposed technique with several voting strategies. We further analyse the effects of image size, perturbation magnitude, along with the ratio of perturbed images in each image set. We also evaluate our technique with the recent state-of-the-art defence methods, and single-shot recognition task. The empirical results demonstrate superior performance on CIFAR-10, MNIST, ETH-80, and Tiny ImageNet datasets.
We develop two cutting-edge approaches to construct deep neural networks representing the purified finite-temperature states of quantum many-body systems. Both methods commonly aim to represent the Gibbs state by a highly expressive neural-network wave function, exemplifying the idea of purification. The first method is an entirely deterministic approach to generate deep Boltzmann machines representing the purified Gibbs state exactly. This strongly assures the remarkable flexibility of the ansatz which can fully exploit the quantum-to-classical mapping. The second method employs stochastic sampling to optimize the network parameters such that the imaginary time evolution is well approximated within the expressibility of neural networks. Numerical demonstrations for transverse-field Ising models and Heisenberg models show that our methods are powerful enough to investigate the finite-temperature properties of strongly correlated quantum many-body systems, even when the problematic effect of frustration is present.
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