# Fast Amortized Inference and Learning in Log-linear Models with Randomly Perturbed Nearest Neighbor Search Source: [Fast Amortized Inference and Learning in Log-linear Models with Randomly Perturbed Nearest Neighbor Search]() Collection index: [llms.txt]() Data updated: 2025-10-25T20:43:17.087Z Authors: Stephen Mussmann, Daniel Levy, Stefano Ermon Published: 2017-07-11T17:23:10.000Z ## Abstract Inference in log-linear models scales linearly in the size of output space in the worst-case. This is often a bottleneck in natural language processing and computer vision tasks when the output space is feasibly enumerable but very large. We propose a method to perform inference in log-linear models with sublinear amortized cost. Our idea hinges on using Gumbel random variable perturbations and a pre-computed Maximum Inner Product Search data structure to access the most-likely elements in sublinear amortized time. Our method yields provable runtime and accuracy guarantees. Further, we present empirical experiments on ImageNet and Word Embeddings showing significant speedups for sampling, inference, and learning in log-linear models. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()