Abstract. In this paper, we consider the problem of calculating fast and accurate approximations to the personalized PageRank score of a webpage. We focus on techniques to improve speed by limiting the amount of web graph data we need to access.Our algorithms provide both the approximation to the personalized PageRank score as well as guidance in using only the necessary information-and therefore sensibly reduce not only the computational cost of the algorithm but also the memory and memory bandwidth requirements. We report experiments with these algorithms on web graphs of up to 118 million pages and prove a theoretical approximation bound for all. Finally, we propose a local, personalized web-search system for a future client system using our algorithms.
Instance discrimination based contrastive learning has emerged as a leading approach for self-supervised learning of visual representations. Yet, its generalization to novel tasks remains elusive when compared to representations learned with supervision, especially in the few-shot setting. We demonstrate how one can incorporate supervision in the instance discrimination based contrastive self-supervised learning framework to learn representations that generalize better to novel tasks. We call our approach CIDS (Contrastive Instance Discrimination with Supervision). CIDS performs favorably compared to existing algorithms on popular few-shot benchmarks like Mini-ImageNet or Tiered-ImageNet. We also propose a novel model selection algorithm that can be used in conjunction with a universal embedding trained using CIDS to outperform state-of-the-art algorithms on the challenging Meta-Dataset benchmark.
Classifiers that are linear in their parameters, and trained by optimizing a convex loss function, have predictable behavior with respect to changes in the training data, initial conditions, and optimization. Such desirable properties are absent in deep neural networks (DNNs), typically trained by non-linear fine-tuning of a pre-trained model. Previous attempts to linearize DNNs have led to interesting theoretical insights, but have not impacted the practice due to the substantial performance gap compared to standard non-linear optimization. We present the first method for linearizing a pre-trained model that achieves comparable performance to non-linear fine-tuning on most of real-world image classification tasks tested, thus enjoying the interpretability of linear models without incurring punishing losses in performance. LQF consists of simple modifications to the architecture, loss function and optimization typically used for classification: Leaky-ReLU instead of ReLU, mean squared loss instead of cross-entropy, and pre-conditioning using Kronecker factorization. None of these changes in isolation is sufficient to approach the performance of non-linear fine-tuning. When used in combination, they allow us to reach comparable performance, and even superior in the low-data regime, while enjoying the simplicity, robustness and interpretability of linear-quadratic optimization.
In this paper we compute the generating function for the Euler characteristic of the Deligne-Mumford compactification of the moduli space of smooth n-pointed genus 2 curves. The proof relies on quite elementary methods, such as the enumeration of the graphs involved in a suitable stratification of M 2,n .
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