Signal recovery from Pooling Representations

Authors: Joan Bruna Estrach, Arthur Szlam, Yann LeCun

ICML 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression. 3. Numerical Experiments Our main goal in this section is to experimentally compare the invertibility of ℓp pooling for p {1, 2, }, with and without rectification.
Researcher Affiliation Academia Joan Bruna, Courant Institute, New York University BRUNA@CIMS.NYU.EDU Arthur Szlam, The City College of New York, CUNY ASZLAM@CCNY.CUNY.EDU Yann Le Cun, Courant Institute, New York Unversity YANN@CS.NYU.EDU
Pseudocode Yes Starting with an initial signal x0, update Ik = (Pp(x))k Fkx(n) ||Fkx(n)||p , k = 1 . . . K, 2. x(n+1) = F( 1)y(n).
Open Source Code No The paper does not provide an explicit statement or link for open-source code for the described methodology.
Open Datasets Yes For MNIST, we use the standard training set projected to R100 via PCA, and we let the number of dictionary elements range from 60 to 600 (that is, 30 to 300 measurements). ... We draw approximately 5 million 16 16 grayscale image patches from the PASCAL VOC data set; these are sorted by variance, and the largest variance 1 million are kept.
Dataset Splits No The paper mentions 'training set' and 'test set' but does not explicitly provide details for a 'validation' split or a 3-way split with specific percentages or counts.
Hardware Specification No The paper does not explicitly describe the hardware used for running its experiments, such as specific GPU or CPU models.
Software Dependencies No The paper mentions using 'the fast neighbor searcher from (Vedaldi and Fulkerson, 2008)' which refers to VLFeat, but does not provide a specific version number for this or any other software dependency.
Experiment Setup Yes Fix a number of neighbors q (in the experiments below we use q = 10, and suppose X is the training set). The basic setup of the experiments in each case is the same: we vary the number of measurements (that is, number of pools) over some range, and attempt to recover the original signal from the ℓp pooled measurements, using various methods. We record the average angle between the recovered signal r and the original x, that is, we use |r T x|2/(||r||2||x||2) as the measure of success in recovery.