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Paper · 2404.09586 · ICLR · 2024

Mitigating the Curse of Dimensionality for Certified Robustness via Dual Randomized Smoothing

Yi Yu, Song Xia, Xudong Jiang

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 10 functions out of this paper's own repositories and ran 7 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
xiasong0501/DRS canonical 6 of 9
xiasong0501/drs canonical 1 of 1
FunctionStatusWhere it lives
conv3x3 Ran xiasong0501/DRS/archs/cifar_resnet.py
pointer only (licence: NONE) · get_code("fac5364e2f53c6db")
entropy Ran xiasong0501/DRS/imagenet_train_lowres_2.py
pointer only (licence: NONE) · get_code("23f822c3d6d64a12")
get_low_res_data Ran xiasong0501/drs/DDS/imagenet/DRM.py
pointer only (licence: NONE) · get_code("a16b11c89a38dfca")
get_low_res_data Ran xiasong0501/DRS/core1_lowres_2.py
pointer only (licence: NONE) · get_code("966d9e557ce5aa94")
get_low_res_data Ran xiasong0501/DRS/imagenet_train_lowres_2.py
pointer only (licence: NONE) · get_code("4d4b1a4a3fc08e85")
get_upper_res_data Ran xiasong0501/DRS/core1_lowres_2.py
pointer only (licence: NONE) · get_code("3cd8ab8f4217978f")
kl_div Ran xiasong0501/DRS/imagenet_train_lowres_2.py
pointer only (licence: NONE) · get_code("74325f9c5d49ca67")
dali_data Not yet run xiasong0501/DRS/imagenet_model_lower_2.py
pointer only (licence: NONE) · get_code("54e10cf0f3dd3389")
get_imagenet_iter_torch Not yet run xiasong0501/DRS/imagenet_dali.py
pointer only (licence: NONE) · get_code("6ddacd69764c3835")
get_low_res_data_mn Not yet run xiasong0501/DRS/core1_lowres_2.py
pointer only (licence: NONE) · get_code("a1abf4153e3f406a")

Repositories linked to this paper

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Abstract

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of ℓ 2 certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/ √ d. This paper explores the feasibility of providing ℓ 2 certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight ℓ 2 certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the ℓ 2 robustness radius, which decreases proportionally at a rate of Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and ℓ 2 certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

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