Learning Latent Permutations with Gumbel-Sinkhorn Networks

Permutations and matchings are core building blocks in a variety of latent variable models, as they allow us to align, canonicalize, and sort data. Learning in such models is difficult, however, because exact marginalization over these combinatorial objects is intractable. In response, this paper introduces a collection of new methods for end-to-end learning in such models that approximate discrete maximum-weight matching using the continuous Sinkhorn operator. Sinkhorn iteration is attractive because it functions as a simple, easy-to-implement analog of the softmax operator. With this, we can define the Gumbel-Sinkhorn method, an extension of the Gumbel-Softmax method (Jang et al. 2016, Maddison2016 et al. 2016) to distributions over latent matchings. We demonstrate the effectiveness of our method by outperforming competitive baselines on a range of qualitatively different tasks: sorting numbers, solving jigsaw puzzles, and identifying neural signals in worms

Modeling Orders of User Behaviors via Differentiable Sorting: A Multi-task Framework to Predicting User Post-click Conversion

User post-click conversion prediction is of high interest to researchers and developers. Recent studies employ multi-task learning to tackle the selection bias and data sparsity problem, two severe challenges in post-click behavior prediction, by incorporating click data. However, prior works mainly focused on pointwise learning and the orders of labels (i.e., click and post-click) are not well explored, which naturally poses a listwise learning problem. Inspired by recent advances on differentiable sorting, in this paper, we propose a novel multi-task framework that leverages orders of user behaviors to predict user post-click conversion in an end-to-end approach. Specifically, we define an aggregation operator to combine predicted outputs of different tasks to a unified score, then we use the computed scores to model the label relations via differentiable sorting. Extensive experiments on public and industrial datasets show the superiority of our proposed model against competitive baselines.Comment: The paper is accepted as a short research paper by SIGIR 202

Sinkhorn Transformations for Single-Query Postprocessing in Text-Video Retrieval

A recent trend in multimodal retrieval is related to postprocessing test set results via the dual-softmax loss (DSL). While this approach can bring significant improvements, it usually presumes that an entire matrix of test samples is available as DSL input. This work introduces a new postprocessing approach based on Sinkhorn transformations that outperforms DSL. Further, we propose a new postprocessing setting that does not require access to multiple test queries. We show that our approach can significantly improve the results of state of the art models such as CLIP4Clip, BLIP, X-CLIP, and DRL, thus achieving a new state-of-the-art on several standard text-video retrieval datasets both with access to the entire test set and in the single-query setting.Comment: SIGIR 202

Sinkhorn-Flow: Predicting Probability Mass Flow in Dynamical Systems Using Optimal Transport

Predicting how distributions over discrete variables vary over time is a common task in time series forecasting. But whereas most approaches focus on merely predicting the distribution at subsequent time steps, a crucial piece of information in many settings is to determine how this probability mass flows between the different elements over time. We propose a new approach to predicting such mass flow over time using optimal transport. Specifically, we propose a generic approach to predicting transport matrices in end-to-end deep learning systems, replacing the standard softmax operation with Sinkhorn iterations. We apply our approach to the task of predicting how communities will evolve over time in social network settings, and show that the approach improves substantially over alternative prediction methods. We specifically highlight results on the task of predicting faction evolution in Ukrainian parliamentary voting.Comment: A prior version of the work appeared in the Optimal Transport Workshop at NeurIPS 201

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets