Soham Mukherjee

Simon Zhang, Soham Mukherjee, Tamal K. Dey

Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable. We use a link-cut tree data structure and parallelism to lower the complexity of computing extended persistence, obtaining a speedup of more than 60x over the state-of-the-art for extended persistence computation. This makes extended persistence feasible for machine learning. We show that, under certain conditions, extended persistence surpasses both the WL[1] graph isomorphism test and 0-dimensional barcodes in terms of expressivity because it adds more global (topological) information. In particular, arbitrarily long cycles can be represented, which is difficult for finite receptive field message passing graph neural networks. Furthermore, we show the effectiveness of our method on real world datasets compared to many existing recent graph representation learning methods.

Ashutosh Bhown, Soham Mukherjee, Sean Yang et al.

Lossy image compression has been studied extensively in the context of typical loss functions such as RMSE, MS-SSIM, etc. However, compression at low bitrates generally produces unsatisfying results. Furthermore, the availability of massive public image datasets appears to have hardly been exploited in image compression. Here, we present a paradigm for eliciting human image reconstruction in order to perform lossy image compression. In this paradigm, one human describes images to a second human, whose task is to reconstruct the target image using publicly available images and text instructions. The resulting reconstructions are then evaluated by human raters on the Amazon Mechanical Turk platform and compared to reconstructions obtained using state-of-the-art compressor WebP. Our results suggest that prioritizing semantic visual elements may be key to achieving significant improvements in image compression, and that our paradigm can be used to develop a more human-centric loss function. The images, results and additional data are available at https://compression.stanford.edu/human-compression