Sequential models that encode user activity for next action prediction have become a popular design choice for building web-scale personalized recommendation systems. Traditional methods of sequential recommendation either utilize end-to-end learning on realtime user actions, or learn user representations separately in an offline batch-generated manner. This paper (1) presents Pinterest's ranking architecture for Homefeed, our personalized recommendation product and the largest engagement surface; (2) proposes TransAct, a sequential model that extracts users' short-term preferences from their realtime activities; (3) describes our hybrid approach to ranking, which combines end-to-end sequential modeling via TransAct with batch-generated user embeddings. The hybrid approach allows us to combine the advantages of responsiveness from learning directly on realtime user activity with the cost-effectiveness of batch user representations learned over a longer time period. We describe the results of ablation studies, the challenges we faced during productionization, and the outcome of an online A/B experiment, which validates the effectiveness of our hybrid ranking model. We further demonstrate the effectiveness of TransAct on other surfaces such as contextual recommendations and search. Our model has been deployed to production in Homefeed, Related Pins, Notifications, and Search at Pinterest.

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.

Integrating logical reasoning within deep learning architectures has been a major goal of modern AI systems. In this paper, we propose a new direction toward this goal by introducing a differentiable (smoothed) maximum satisfiability (MAXSAT) solver that can be integrated into the loop of larger deep learning systems. Our (approximate) solver is based upon a fast coordinate descent approach to solving the semidefinite program (SDP) associated with the MAXSAT problem. We show how to analytically differentiate through the solution to this SDP and efficiently solve the associated backward pass. We demonstrate that by integrating this solver into end-to-end learning systems, we can learn the logical structure of challenging problems in a minimally supervised fashion. In particular, we show that we can learn the parity function using single-bit supervision (a traditionally hard task for deep networks) and learn how to play 9x9 Sudoku solely from examples. We also solve a "visual Sudok" problem that maps images of Sudoku puzzles to their associated logical solutions by combining our MAXSAT solver with a traditional convolutional architecture. Our approach thus shows promise in integrating logical structures within deep learning.

This paper proposes a new algorithm for solving MAX2SAT problems based on combining search methods with semidefinite programming approaches. Semidefinite programming techniques are well-known as a theoretical tool for approximating maximum satisfiability problems, but their application has traditionally been very limited by their speed and randomized nature. Our approach overcomes this difficult by using a recent approach to low-rank semidefinite programming, specialized to work in an incremental fashion suitable for use in an exact search algorithm. The method can be used both within complete or incomplete solver, and we demonstrate on a variety of problems from recent competitions. Our experiments show that the approach is faster (sometimes by orders of magnitude) than existing state-of-the-art complete and incomplete solvers, representing a substantial advance in search methods specialized for MAX2SAT problems.

In this paper, we propose a coordinate descent approach to low-rank structured semidefinite programming. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and typically attains an order of magnitude or better improvement in optimization performance over the current state of the art. We show that for certain problems, the method is strictly decreasing and guaranteed to converge to a critical point. We then apply the algorithm to three separate domains: solving the maximum cut semidefinite relaxation, solving a (novel) maximum satisfiability relaxation, and solving the GloVe word embedding optimization problem. In all settings, we demonstrate improvement over the existing state of the art along various dimensions. In total, this work substantially expands the scope and scale of problems that can be solved using semidefinite programming methods.

Matrix factorization is a core technique in many machine learning problems, yet also presents a nonconvex and often difficult-to-optimize problem. In this paper we present an approach based upon polynomial optimization techniques that both improves the convergence time of matrix factorization algorithms and helps them escape from local optima. Our method is based on the realization that given a joint search direction in a matrix factorization task, we can solve the ``subspace search'' problem (the task of jointly finding the steps to take in each direction) by solving a bivariate quartic polynomial optimization problem. We derive two methods for solving this problem based upon sum of squares moment relaxations and the Durand-Kerner method, then apply these techniques on matrix factorization to derive a direct coordinate descent approach and a method for speeding up existing approaches. On three benchmark datasets we show the method substantially improves convergence speed over state-of-the-art approaches, while also attaining lower objective value.