Personalized item recommendation typically suffers from data sparsity, which is most often addressed by learning vector representations of users and items via low-rank matrix factorization. While this effectively densifies the matrix by assuming users and movies can be represented by linearly dependent latent features, it does not capture more complicated interactions. For example, vector representations struggle with set-theoretic relationships, such as negation and intersection, e.g. recommending a movie that is “comedy and action, but not romance”. In this work, we formulate the problem of personalized item recommendation as matrix completion where rows are set-theoretically dependent. To capture this set-theoretic dependence we represent each user and attribute by a hyperrectangle or box (i.e. a Cartesian product of intervals). Box embeddings can intuitively be understood as trainable Venn diagrams, and thus not only inherently represent similarity (via the Jaccard index), but also naturally and faithfully support arbitrary set-theoretic relationships. Queries involving set-theoretic constraints can be efficiently computed directly on the embedding space by performing geometric operations on the representations. We empirically demonstrate the superiority of box embeddings over vector-based neural methods on both simple and complex item recommendation queries by up to 30% overall.

Qi Cheng, Michael Boratko, Pranay Kumar Yelugam, Tim O’Gorman, Nalini Singh, Andrew McCallum, Xiang Li. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

In dense retrieval, deep encoders provide embeddings for both inputs and targets, and the softmax function is used to parameterize a distribution over a large number of candidate targets (e.g., textual passages for information retrieval). Significant challenges arise in training such encoders in the increasingly prevalent scenario of (1) a large number of targets, (2) a computationally expensive target encoder model, (3) cached target embeddings that are out-of-date due to ongoing training of target encoder parameters. This paper presents a simple and highly scalable response to these challenges by training a small parametric _corrector network_ that adjusts stale cached target embeddings, enabling an accurate softmax approximation and thereby sampling of up-to-date high scoring "hard negatives." We theoretically investigate the generalization properties of our proposed target corrector, relating the complexity of the network, staleness of cached representations, and the amount of training data. We present experimental results on large benchmark dense retrieval datasets as well as on QA with retrieval augmented language models. Our approach matches state-of-the-art results even when no target embedding updates are made during training beyond an initial cache from the unsupervised pre-trained model, providing a 4-80x reduction in re-embedding computational cost.

When training node embedding models to represent large directed graphs (digraphs), it is impossible to observe all entries of the adjacency matrix during training. As a consequence most methods employ sampling. For very large digraphs, however, this means many (most) entries may be unobserved during training. In general, observing every entry would be necessary to uniquely identify a graph, however if we know the graph has a certain property some entries can be omitted - for example, only half the entries would be required for a symmetric graph. In this work, we develop a novel framework to identify a subset of entries required to uniquely distinguish a graph among all transitively-closed DAGs. We give an explicit algorithm to compute the provably minimal set of entries, and demonstrate empirically that one can train node embedding models with greater efficiency and performance, provided the energy function has an appropriate inductive bias. We achieve robust performance on synthetic hierarchies and a larger real-world taxonomy, observing improved convergence rates in a resource-constrained setting while reducing the set of training examples by as much as 99%.

Clustering algorithms are often evaluated using metrics which compare with ground-truth cluster assignments, such as Rand index and NMI. Algorithm performance may vary widely for different hyperparameters, however, and thus model selection based on optimal performance for these metrics is discordant with how these algorithms are applied in practice, where labels are unavailable and tuning is often more art than science. It is therefore desirable to compare clustering algorithms not only on their optimally tuned performance, but also some notion of how realistic it would be to obtain this performance in practice. We propose an evaluation of clustering methods capturing this ease-of-tuning by modeling the expected best clustering score under a given computation budget. To encourage the adoption of the proposed metric alongside classic clustering evaluations, we provide an extensible benchmarking framework. We perform an extensive empirical evaluation of our proposed metric on popular clustering algorithms over a large collection of datasets from different domains, and observe that our new metric leads to several noteworthy observations.

Shib Dasgupta, Michael Boratko, Siddhartha Mishra, Shriya Atmakuri, Dhruvesh Patel, Xiang Li, Andrew McCallum. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2022.

Modeling directed graphs with differentiable representations is a fundamental requirement for performing machine learning on graph-structured data. Geometric embedding models (e.g. hyperbolic, cone, and box embeddings) excel at this task, exhibiting useful inductive biases for directed graphs. However, modeling directed graphs that both contain cycles and some element of transitivity, two properties common in real-world settings, is challenging. Box embeddings, which can be thought of as representing the graph as an intersection over some learned super-graphs, have a natural inductive bias toward modeling transitivity, but (as we prove) cannot model cycles. To this end, we propose binary code box embeddings, where a learned binary code selects a subset of graphs for intersection. We explore several variants, including global binary codes (amounting to a union over intersections) and per-vertex binary codes (allowing greater flexibility) as well as methods of regularization. Theoretical and empirical results show that the proposed models not only preserve a useful inductive bias of transitivity but also have sufficient representational capacity to model arbitrary graphs, including graphs with cycles.

Yasumasa Onoe, Michael Boratko, Andrew McCallum, Greg Durrett. Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing (Volume 1: Long Papers). 2021.

Xuelu Chen, Michael Boratko, Muhao Chen, Shib Sankar Dasgupta, Xiang Lorraine Li, Andrew McCallum. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

A wide variety of machine learning tasks such as knowledge base completion, ontology alignment, and multi-label classification can benefit from incorporating into learning differentiable representations of graphs or taxonomies. While vectors in Euclidean space can theoretically represent any graph, much recent work shows that alternatives such as complex, hyperbolic, order, or box embeddings have geometric properties better suited to modeling real-world graphs. Experimentally these gains are seen only in lower dimensions, however, with performance benefits diminishing in higher dimensions. In this work, we introduce a novel variant of box embeddings that uses a learned smoothing parameter to achieve better representational capacity than vector models in low dimensions, while also avoiding performance saturation common to other geometric models in high dimensions. Further, we present theoretical results that prove box embeddings can represent any DAG. We perform rigorous empirical evaluations of vector, hyperbolic, and region-based geometric representations on several families of synthetic and real-world directed graphs. Analysis of these results exposes correlations between different families of graphs, graph characteristics, model size, and embedding geometry, providing useful insights into the inductive biases of various differentiable graph representations.

In representation learning, capturing correlations between the represented elements is paramount. A recent line of work introduces the notion of learning region-based representations, with the objective of being able to better capture these correlations as set interactions. Box models use regions which are products of intervals on $[0,1]$ (i.e., "boxes"), representing joint probability distributions via Lebesgue measure. To mitigate issues with training, a recent work models the endpoints of these intervals using Gumbel distributions, chosen due to their min/max-stability. In this work we analyze min/max-stability on a bounded domain and provide a specific family of such distributions which, replacing Gumbel, allow for stochastic boxes embedded in a finite measure space. This allows for a latent noise model which is a probability measure. Furthermore, we demonstrate an equivalence between this region-based representation and a density representation, where intersection is given by products of densities. We compare our model to previous region-based probability models, and demonstrate it is capable of being trained effectively to modeling correlations.

Given questions regarding some prototypical situation -such as Name something that people usually do before they leave the house for work?-a human can easily answer them via acquired experiences.There can be multiple right answers for such questions, with some more common for a situation than others.This paper introduces a new question answering dataset for training and evaluating common sense reasoning capabilities of artificial intelligence systems in such prototypical situations.The training set is gathered from an existing set of questions played in a longrunning international game show -FAMILY-FEUD.The hidden evaluation set is created by gathering answers for each question from 100 crowd-workers.We also propose a generative evaluation task where a model has to output a ranked list of answers, ideally covering all prototypical answers for a question.After presenting multiple competitive baseline models, we find that human performance still exceeds model scores on all evaluation metrics with a meaningful gap, supporting the challenging nature of the task. * Equal contribution.(i) Name something that people usually do before they leave for work?Ask 100 crowd-workers + manual clustering

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly promising example of such an embedding as they are closed under intersection and their volume can be calculated easily, allowing them to naturally represent calibrated probability distributions. The benefits of geometric embeddings also introduce a problem of local identifiability, however, where whole neighborhoods of parameters result in equivalent loss which impedes learning. Prior work addressed some of these issues by using an approximation to Gaussian convolution over the box parameters, however this intersection operation also increases the sparsity of the gradient. In this work we model the box parameters with min and max Gumbel distributions, which were chosen such that the space is still closed under the operation of intersection. The calculation of the expected intersection volume involves all parameters, and we demonstrate experimentally that this drastically improves the ability of such models to learn.