83 research outputs found
NP-Hardness of Tensor Network Contraction Ordering
We study the optimal order (or sequence) of contracting a tensor network with
a minimal computational cost. We conclude 2 different versions of this optimal
sequence: that minimize the operation number (OMS) and that minimize the time
complexity (CMS). Existing results only shows that OMS is NP-hard, but no
conclusion on CMS problem. In this work, we firstly reduce CMS to CMS-0, which
is a sub-problem of CMS with no free indices. Then we prove that CMS is easier
than OMS, both in general and in tree cases. Last but not least, we prove that
CMS is still NP-hard. Based on our results, we have built up relationships of
hardness of different tensor network contraction problems.Comment: Jianyu Xu and Hanwen Zhang are equal contributors. 10 pages
(reference and appendix excluded), 20 pages in total, 6 figure
Exploring Adversarial Attack in Spiking Neural Networks with Spike-Compatible Gradient
Recently, backpropagation through time inspired learning algorithms are
widely introduced into SNNs to improve the performance, which brings the
possibility to attack the models accurately given Spatio-temporal gradient
maps. We propose two approaches to address the challenges of gradient input
incompatibility and gradient vanishing. Specifically, we design a gradient to
spike converter to convert continuous gradients to ternary ones compatible with
spike inputs. Then, we design a gradient trigger to construct ternary gradients
that can randomly flip the spike inputs with a controllable turnover rate, when
meeting all zero gradients. Putting these methods together, we build an
adversarial attack methodology for SNNs trained by supervised algorithms.
Moreover, we analyze the influence of the training loss function and the firing
threshold of the penultimate layer, which indicates a "trap" region under the
cross-entropy loss that can be escaped by threshold tuning. Extensive
experiments are conducted to validate the effectiveness of our solution.
Besides the quantitative analysis of the influence factors, we evidence that
SNNs are more robust against adversarial attack than ANNs. This work can help
reveal what happens in SNN attack and might stimulate more research on the
security of SNN models and neuromorphic devices
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