Maximilian Nickel

Yaron Lipman, Ricky T. Q. Chen, Heli Ben-Hamu et al. · meta-ai

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Heli Ben-Hamu, Samuel Cohen, Joey Bose et al. · meta-ai

Continuous Normalizing Flows (CNFs) are a class of generative models that transform a prior distribution to a model distribution by solving an ordinary differential equation (ODE). We propose to train CNFs on manifolds by minimizing probability path divergence (PPD), a novel family of divergences between the probability density path generated by the CNF and a target probability density path. PPD is formulated using a logarithmic mass conservation formula which is a linear first order partial differential equation relating the log target probabilities and the CNF's defining vector field. PPD has several key benefits over existing methods: it sidesteps the need to solve an ODE per iteration, readily applies to manifold data, scales to high dimensions, and is compatible with a large family of target paths interpolating pure noise and data in finite time. Theoretically, PPD is shown to bound classical probability divergences. Empirically, we show that CNFs learned by minimizing PPD achieve state-of-the-art results in likelihoods and sample quality on existing low-dimensional manifold benchmarks, and is the first example of a generative model to scale to moderately high dimensional manifolds.

Karan Desai, Maximilian Nickel, Tanmay Rajpurohit et al.

Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept "dog" entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text datasets. Our results show that MERU learns a highly interpretable and structured representation space while being competitive with CLIP's performance on standard multi-modal tasks like image classification and image-text retrieval. Our code and models are available at https://www.github.com/facebookresearch/meru

Guan-Horng Liu, Yaron Lipman, Maximilian Nickel et al.

Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution matching setup, where these marginals are only implicitly described as a solution to some task-specific objective function. The problem setup, known as the Generalized Schrödinger Bridge (GSB), appears prevalently in many scientific areas both within and without machine learning. We propose Generalized Schrödinger Bridge Matching (GSBM), a new matching algorithm inspired by recent advances, generalizing them beyond kinetic energy minimization and to account for task-specific state costs. We show that such a generalization can be cast as solving conditional stochastic optimal control, for which efficient variational approximations can be used, and further debiased with the aid of path integral theory. Compared to prior methods for solving GSB problems, our GSBM algorithm better preserves a feasible transport map between the boundary distributions throughout training, thereby enabling stable convergence and significantly improved scalability. We empirically validate our claims on an extensive suite of experimental setups, including crowd navigation, opinion depolarization, LiDAR manifolds, and image domain transfer. Our work brings new algorithmic opportunities for training diffusion models enhanced with task-specific optimality structures. Code available at https://github.com/facebookresearch/generalized-schrodinger-bridge-matching

Dhananjay Bhaskar, Xingzhi Sun, Yanlei Zhang et al.

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

Neta Shaul, Ricky T. Q. Chen, Maximilian Nickel et al.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the \emph{data separation function}. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to $1$ in the general case of arbitrary normalized dataset consisting of $n$ samples in $d$ dimension as $n/\sqrt{d}\rightarrow 0$. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes \emph{kinetic optimal} as $n/\sqrt{d}\rightarrow 0$. We further support this theory with empirical experiments on ImageNet.

Ricky T. Q. Chen, Matthew Le, Matthew Muckley et al. · meta-ai

Neural compression offers a domain-agnostic approach to creating codecs for lossy or lossless compression via deep generative models. For sequence compression, however, most deep sequence models have costs that scale with the sequence length rather than the sequence complexity. In this work, we instead treat data sequences as observations from an underlying continuous-time process and learn how to efficiently discretize while retaining information about the full sequence. As a consequence of decoupling sequential information from its temporal discretization, our approach allows for greater compression rates and smaller computational complexity. Moreover, the continuous-time approach naturally allows us to decode at different time intervals. We empirically verify our approach on multiple domains involving compression of video and motion capture sequences, showing that our approaches can automatically achieve reductions in bit rates by learning how to discretize.

Oluwadamilola Fasina, Guillaume Huguet, Alexander Tong et al. · mila

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

Ricky T. Q. Chen, Brandon Amos, Maximilian Nickel

Mapping between discrete and continuous distributions is a difficult task and many have had to resort to heuristical approaches. We propose a tessellation-based approach that directly learns quantization boundaries in a continuous space, complete with exact likelihood evaluations. This is done through constructing normalizing flows on convex polytopes parameterized using a simple homeomorphism with an efficient log determinant Jacobian. We explore this approach in two application settings, mapping from discrete to continuous and vice versa. Firstly, a Voronoi dequantization allows automatically learning quantization boundaries in a multidimensional space. The location of boundaries and distances between regions can encode useful structural relations between the quantized discrete values. Secondly, a Voronoi mixture model has near-constant computation cost for likelihood evaluation regardless of the number of mixture components. Empirically, we show improvements over existing methods across a range of structured data modalities.

Arjun Subramonian, Adina Williams, Maximilian Nickel et al. · meta-ai

The expressive power of graph neural networks is usually measured by comparing how many pairs of graphs or nodes an architecture can possibly distinguish as non-isomorphic to those distinguishable by the $k$-dimensional Weisfeiler-Leman ($k$-WL) test. In this paper, we uncover misalignments between graph machine learning practitioners' conceptualizations of expressive power and $k$-WL through a systematic analysis of the reliability and validity of $k$-WL. We conduct a survey ($n = 18$) of practitioners to surface their conceptualizations of expressive power and their assumptions about $k$-WL. In contrast to practitioners' beliefs, our analysis (which draws from graph theory and benchmark auditing) reveals that $k$-WL does not guarantee isometry, can be irrelevant to real-world graph tasks, and may not promote generalization or trustworthiness. We argue for extensional definitions and measurement of expressive power based on benchmarks. We further contribute guiding questions for constructing such benchmarks, which is critical for graph machine learning practitioners to develop and transparently communicate our understandings of expressive power.

Tyler L. Hayes, Maximilian Nickel, Christopher Kanan et al.

There has been significant progress in creating machine learning models that identify objects in scenes along with their associated attributes and relationships; however, there is a large gap between the best models and human capabilities. One of the major reasons for this gap is the difficulty in collecting sufficient amounts of annotated relations and attributes for training these systems. While some attributes and relations are abundant, the distribution in the natural world and existing datasets is long tailed. In this paper, we address this problem by introducing a novel incremental active learning framework that asks for attributes and relations in visual scenes. While conventional active learning methods ask for labels of specific examples, we flip this framing to allow agents to ask for examples from specific categories. Using this framing, we introduce an active sampling method that asks for examples from the tail of the data distribution and show that it outperforms classical active learning methods on Visual Genome.

Ramakrishnan Krishnamurthy, Arpit Agarwal, Lakshminarayanan Subramanian et al.

User interactions in online recommendation platforms create interdependencies among content creators: feedback on one creator's content influences the system's learning and, in turn, the exposure of other creators' contents. To analyze incentives in such settings, we model collaboration as a multi-agent stochastic linear bandit problem with a transferable utility (TU) cooperative game formulation, where a coalition's value equals the negative sum of its members' cumulative regrets. We show that, for identical (homogenous) agents with fixed action sets, the induced TU game is convex under mild algorithmic conditions, implying a non-empty core that contains the Shapley value and ensures both stability and fairness. For heterogeneous agents, the game still admits a non-empty core, though convexity and Shapley value core-membership are no longer guaranteed. To address this, we propose a simple regret-based payout rule that satisfies three out of the four Shapley axioms and also lies in the core. Experiments on MovieLens-100k dataset illustrate when the empirical payout aligns with -- and diverges from -- the Shapley fairness across different settings and algorithms.

Danqi Liao, Chen Liu, Benjamin W. Christensen et al.

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Lily Hong Zhang, Smitha Milli, Karen Jusko et al.

How can large language models (LLMs) serve users with varying preferences that may conflict across cultural, political, or other dimensions? To advance this challenge, this paper establishes four key results. First, we demonstrate, through a large-scale multilingual human study with representative samples from five countries (N=15,000), that humans exhibit significantly more variation in preferences than the responses of 21 state-of-the-art LLMs. Second, we show that existing methods for preference dataset collection are insufficient for learning the diversity of human preferences even along two of the most salient dimensions of variability in global values, due to the underlying homogeneity of candidate responses. Third, we argue that this motivates the need for negatively-correlated sampling when generating candidate sets, and we show that simple prompt-based techniques for doing so significantly enhance the performance of alignment methods in learning heterogeneous preferences. Fourth, based on this novel candidate sampling approach, we collect and open-source Community Alignment, the largest and most representative multilingual and multi-turn preference dataset to date, featuring almost 200,000 comparisons from annotators spanning five countries. We hope that the Community Alignment dataset will be a valuable resource for improving the effectiveness of LLMs for a diverse global population.

Armand Joulin, Edouard Grave, Piotr Bojanowski et al.

This paper shows that a simple baseline based on a Bag-of-Words (BoW) representation learns surprisingly good knowledge graph embeddings. By casting knowledge base completion and question answering as supervised classification problems, we observe that modeling co-occurences of entities and relations leads to state-of-the-art performance with a training time of a few minutes using the open sourced library fastText.

Jamelle Watson-Daniels, Himaghna Bhattacharjee, Skyler Wang et al.

While many studies of Large Language Model (LLM) reasoning capabilities emphasize mathematical or technical tasks, few address reasoning about social concepts: the abstract ideas shaping social norms, culture, and institutions. This understudied capability is essential for modern models acting as social agents, yet no systematic evaluation methodology targets it. We introduce SCRuB (Social Concept Reasoning under Rubric-Based Evaluation), a framework designed for this setting of task indeterminacy. Our goal is to measure the degree to which a model reasons about social concepts with the depth and critical rigor of a human expert. SCRuB proceeds in three phases: prompt construction from established sources, response generation by experts and models, and comparative evaluation using a five-dimensional critical thinking rubric. To enable generalization of the pipeline, we introduce a Panel of Disciplinary Perspectives ensemble validated against independent expert judges. We release SCRuBEval (n=4,711 evaluation prompts) and SCRuBAnnotations (300 expert-authored responses and 150 expert comparative judgments from 45 PhD-level scholars). Our results show that frontier models consistently outperform human experts across all five rubric dimensions. Across 1,170 pairwise comparisons, expert judges ranked a model response first in 80.8% of judgments and preferred model responses overall 74.4% of the time. Ultimately, this study provides the first expert-grounded demonstration of evaluation saturation for social concept reasoning: the single-turn exam-style format has reached its ceiling for models and humans alike.

Shomik Jain, Jack Lanchantin, Maximilian Nickel et al. · meta-ai

A large language model can be less helpful if it exhibits output response homogenization. But whether two responses are considered homogeneous, and whether such homogenization is problematic, both depend on the task category. For instance, in objective math tasks, we often expect no variation in the final answer but anticipate variation in the problem-solving strategy. Whereas, for creative writing tasks, we may expect variation in key narrative components (e.g. plot, genre, setting, etc), beyond the vocabulary or embedding diversity produced by temperature-sampling. Previous work addressing output homogenization often fails to conceptualize diversity in a task-dependent way. We address this gap in the literature directly by making the following contributions. (1) We present a task taxonomy comprised of eight task categories that each have distinct conceptualizations of output homogenization. (2) We introduce task-anchored functional diversity to better evaluate output homogenization. (3) We propose a task-anchored sampling technique that increases functional diversity for task categories where homogenization is undesired, while preserving homogenization where it is desired. (4) We challenge the perceived existence of a diversity-quality trade-off by increasing functional diversity while maintaining response quality. Overall, we demonstrate how task dependence improves the evaluation and mitigation of output homogenization.

Maximilian Nickel

Rapid model validation via the train-test paradigm has been a key driver for the breathtaking progress in machine learning and AI. However, modern AI systems often depend on a combination of tasks and data collection practices that violate all assumptions ensuring test validity. Yet, without rigorous model validation we cannot ensure the intended outcomes of deployed AI systems, including positive social impact, nor continue to advance AI research in a scientifically sound way. In this paper, I will show that for widely considered inference settings in complex social systems the train-test paradigm does not only lack a justification but is indeed invalid for any risk estimator, including counterfactual and causal estimators, with high probability. These formal impossibility results highlight a fundamental epistemic issue, i.e., that for key tasks in modern AI we cannot know whether models are valid under current data collection practices. Importantly, this includes variants of both recommender systems and reasoning via large language models, and neither naïve scaling nor limited benchmarks are suited to address this issue. I am illustrating these results via the widely used MovieLens benchmark and conclude by discussing the implications of these results for AI in social systems, including possible remedies such as participatory data curation and open science.

Noam Rozen, Aditya Grover, Maximilian Nickel et al.

We are interested in learning generative models for complex geometries described via manifolds, such as spheres, tori, and other implicit surfaces. Current extensions of existing (Euclidean) generative models are restricted to specific geometries and typically suffer from high computational costs. We introduce Moser Flow (MF), a new class of generative models within the family of continuous normalizing flows (CNF). MF also produces a CNF via a solution to the change-of-variable formula, however differently from other CNF methods, its model (learned) density is parameterized as the source (prior) density minus the divergence of a neural network (NN). The divergence is a local, linear differential operator, easy to approximate and calculate on manifolds. Therefore, unlike other CNFs, MF does not require invoking or backpropagating through an ODE solver during training. Furthermore, representing the model density explicitly as the divergence of a NN rather than as a solution of an ODE facilitates learning high fidelity densities. Theoretically, we prove that MF constitutes a universal density approximator under suitable assumptions. Empirically, we demonstrate for the first time the use of flow models for sampling from general curved surfaces and achieve significant improvements in density estimation, sample quality, and training complexity over existing CNFs on challenging synthetic geometries and real-world benchmarks from the earth and climate sciences.

Ricky T. Q. Chen, Brandon Amos, Maximilian Nickel

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.

Ricky T. Q. Chen, Brandon Amos, Maximilian Nickel

The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and differentiated through. Neural Event ODEs are capable of modeling discrete and instantaneous changes in a continuous-time system, without prior knowledge of when these changes should occur or how many such changes should exist. We test our approach in modeling hybrid discrete- and continuous- systems such as switching dynamical systems and collision in multi-body systems, and we propose simulation-based training of point processes with applications in discrete control.

Ramakrishna Vedantam, Arthur Szlam, Maximilian Nickel et al.

Humans can learn and reason under substantial uncertainty in a space of infinitely many concepts, including structured relational concepts ("a scene with objects that have the same color") and ad-hoc categories defined through goals ("objects that could fall on one's head"). In contrast, standard classification benchmarks: 1) consider only a fixed set of category labels, 2) do not evaluate compositional concept learning and 3) do not explicitly capture a notion of reasoning under uncertainty. We introduce a new few-shot, meta-learning benchmark, Compositional Reasoning Under Uncertainty (CURI) to bridge this gap. CURI evaluates different aspects of productive and systematic generalization, including abstract understandings of disentangling, productive generalization, learning boolean operations, variable binding, etc. Importantly, it also defines a model-independent "compositionality gap" to evaluate the difficulty of generalizing out-of-distribution along each of these axes. Extensive evaluations across a range of modeling choices spanning different modalities (image, schemas, and sounds), splits, privileged auxiliary concept information, and choices of negatives reveal substantial scope for modeling advances on the proposed task. All code and datasets will be available online.

Emile Mathieu, Maximilian Nickel

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic spaces, most normalizing flows implicitly assume a flat geometry, making them either misspecified or ill-suited in these situations. To overcome this problem, we introduce Riemannian continuous normalizing flows, a model which admits the parametrization of flexible probability measures on smooth manifolds by defining flows as the solution to ordinary differential equations. We show that this approach can lead to substantial improvements on both synthetic and real-world data when compared to standard flows or previously introduced projected flows.

Maximilian Nickel, Matthew Le

Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal dependencies, MHPs have proven to be notoriously difficult to scale, what has limited their applications to relatively small domains. In this work, we propose a novel model and computational approach to overcome this important limitation. By exploiting a characteristic sparsity pattern in real-world diffusion processes, we show that our approach allows to compute the exact likelihood and gradients of an MHP -- independently of the ambient dimensions of the underlying network. We show on synthetic and real-world datasets that our model does not only achieve state-of-the-art predictive results, but also improves runtime performance by multiple orders of magnitude compared to standard methods on sparse event sequences. In combination with easily interpretable latent variables and influence structures, this allows us to analyze diffusion processes at previously unattainable scale.

Qi Liu, Maximilian Nickel, Douwe Kiela

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we propose a novel GNN architecture for learning representations on Riemannian manifolds with differentiable exponential and logarithmic maps. We develop a scalable algorithm for modeling the structural properties of graphs, comparing Euclidean and hyperbolic geometry. In our experiments, we show that hyperbolic GNNs can lead to substantial improvements on various benchmark datasets.

Senthil Purushwalkam, Maximilian Nickel, Abhinav Gupta et al.

One of the hallmarks of human intelligence is the ability to compose learned knowledge into novel concepts which can be recognized without a single training example. In contrast, current state-of-the-art methods require hundreds of training examples for each possible category to build reliable and accurate classifiers. To alleviate this striking difference in efficiency, we propose a task-driven modular architecture for compositional reasoning and sample efficient learning. Our architecture consists of a set of neural network modules, which are small fully connected layers operating in semantic concept space. These modules are configured through a gating function conditioned on the task to produce features representing the compatibility between the input image and the concept under consideration. This enables us to express tasks as a combination of sub-tasks and to generalize to unseen categories by reweighting a set of small modules. Furthermore, the network can be trained efficiently as it is fully differentiable and its modules operate on small sub-spaces. We focus our study on the problem of compositional zero-shot classification of object-attribute categories. We show in our experiments that current evaluation metrics are flawed as they only consider unseen object-attribute pairs. When extending the evaluation to the generalized setting which accounts also for pairs seen during training, we discover that naive baseline methods perform similarly or better than current approaches. However, our modular network is able to outperform all existing approaches on two widely-used benchmark datasets.

Matt Le, Stephen Roller, Laetitia Papaxanthos et al.

We consider the task of inferring is-a relationships from large text corpora. For this purpose, we propose a new method combining hyperbolic embeddings and Hearst patterns. This approach allows us to set appropriate constraints for inferring concept hierarchies from distributional contexts while also being able to predict missing is-a relationships and to correct wrong extractions. Moreover -- and in contrast with other methods -- the hierarchical nature of hyperbolic space allows us to learn highly efficient representations and to improve the taxonomic consistency of the inferred hierarchies. Experimentally, we show that our approach achieves state-of-the-art performance on several commonly-used benchmarks.

Maximilian Nickel, Douwe Kiela

We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is substantially more efficient than in the Poincaré-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincaré embeddings, especially in low dimensions. Lastly, we apply our model to discover hierarchies in two real-world datasets: we show that an embedding in hyperbolic space can reveal important aspects of a company's organizational structure as well as reveal historical relationships between language families.

Stephen Roller, Douwe Kiela, Maximilian Nickel

Methods for unsupervised hypernym detection may broadly be categorized according to two paradigms: pattern-based and distributional methods. In this paper, we study the performance of both approaches on several hypernymy tasks and find that simple pattern-based methods consistently outperform distributional methods on common benchmark datasets. Our results show that pattern-based models provide important contextual constraints which are not yet captured in distributional methods.

Andreas Veit, Maximilian Nickel, Serge Belongie et al.

The variety, abundance, and structured nature of hashtags make them an interesting data source for training vision models. For instance, hashtags have the potential to significantly reduce the problem of manual supervision and annotation when learning vision models for a large number of concepts. However, a key challenge when learning from hashtags is that they are inherently subjective because they are provided by users as a form of self-expression. As a consequence, hashtags may have synonyms (different hashtags referring to the same visual content) and may be ambiguous (the same hashtag referring to different visual content). These challenges limit the effectiveness of approaches that simply treat hashtags as image-label pairs. This paper presents an approach that extends upon modeling simple image-label pairs by modeling the joint distribution of images, hashtags, and users. We demonstrate the efficacy of such approaches in image tagging and retrieval experiments, and show how the joint model can be used to perform user-conditional retrieval and tagging.

Douwe Kiela, Alexis Conneau, Allan Jabri et al.

We introduce a variety of models, trained on a supervised image captioning corpus to predict the image features for a given caption, to perform sentence representation grounding. We train a grounded sentence encoder that achieves good performance on COCO caption and image retrieval and subsequently show that this encoder can successfully be transferred to various NLP tasks, with improved performance over text-only models. Lastly, we analyze the contribution of grounding, and show that word embeddings learned by this system outperform non-grounded ones.

Théo Trouillon, Maximilian Nickel

Embeddings of knowledge graphs have received significant attention due to their excellent performance for tasks like link prediction and entity resolution. In this short paper, we are providing a comparison of two state-of-the-art knowledge graph embeddings for which their equivalence has recently been established, i.e., ComplEx and HolE [Nickel, Rosasco, and Poggio, 2016; Trouillon et al., 2016; Hayashi and Shimbo, 2017]. First, we briefly review both models and discuss how their scoring functions are equivalent. We then analyze the discrepancy of results reported in the original articles, and show experimentally that they are likely due to the use of different loss functions. In further experiments, we evaluate the ability of both models to embed symmetric and antisymmetric patterns. Finally, we discuss advantages and disadvantages of both models and under which conditions one would be preferable to the other.

Maximilian Nickel, Douwe Kiela

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincaré ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincaré embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Volker Tresp, Maximilian Nickel

We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational machine learning approaches. Relational models typically are based on probabilistic graphical models, e.g., Bayesian networks, Markov networks, or latent variable models. Relational models have applications in social networks analysis, the modeling of knowledge graphs, bioinformatics, recommendation systems, natural language processing, medical decision support, and linked data.

Maximilian Nickel, Lorenzo Rosasco, Tomaso Poggio

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. In extensive experiments we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction in knowledge graphs and relational learning benchmark datasets.

Maximilian Nickel, Kevin Murphy, Volker Tresp et al.

Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used to predict new facts about the world (which is equivalent to predicting new edges in the graph). In particular, we discuss two fundamentally different kinds of statistical relational models, both of which can scale to massive datasets. The first is based on latent feature models such as tensor factorization and multiway neural networks. The second is based on mining observable patterns in the graph. We also show how to combine these latent and observable models to get improved modeling power at decreased computational cost. Finally, we discuss how such statistical models of graphs can be combined with text-based information extraction methods for automatically constructing knowledge graphs from the Web. To this end, we also discuss Google's Knowledge Vault project as an example of such combination.

Maximilian Nickel, Volker Tresp

Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors. We study the improvements that can be gained via this approach on various benchmark datasets and show that the logistic extension can improve the prediction results significantly.