Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. Finally, we train EBMs on tabular data sets with applications in synthetic data generation and calibrated classification.

Mutual Information Multinomial Estimation

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data distribution can dramatically help estimate. This preliminary estimate serves as a bridge between the joint and the marginal distribution, and by comparing with this bridge distribution we can easily obtain the true difference between the joint distributions and the marginal distributions. Experiments on diverse tasks including non-Gaussian synthetic problems with known ground-truth and real-world applications demonstrate the advantages of our method.

Entropy-Based Decoding for Retrieval-Augmented Large Language Models

Augmenting Large Language Models (LLMs) with retrieved external knowledge has proven effective for improving the factual accuracy of generated responses. Despite their success, retrieval-augmented LLMs still face the distractibility issue, where the generated responses are negatively influenced by noise from both external and internal knowledge sources. In this paper, we introduce a novel, training-free decoding method guided by entropy considerations to mitigate this issue. Our approach utilizes entropy-based document-parallel ensemble decoding to prioritize low-entropy distributions from retrieved documents, thereby enhancing the extraction of relevant information of context. Additionally, it incorporates a contrastive decoding mechanism that contrasts the obtained low-entropy ensemble distribution with the high-entropy distribution derived from the model's internal knowledge across layers, which ensures a greater emphasis on reliable external information. Extensive experiments on open-domain question answering datasets demonstrate the superiority of our method.

Diffusion Model With Optimal Covariance Matching

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed full covariance moment matching technique and introduce a novel method for learning covariances. Unlike traditional data-driven covariance approximation approaches, our method involves directly regressing the optimal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency of both Markovian (DDPM) and non-Markovian (DDIM) diffusion model families.

Training Discrete Energy-Based Models with Energy Discrepancy

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only requires the evaluation of the energy function at data points and their perturbed counter parts, thus not relying on sampling strategies like Markov chain Monte Carlo (MCMC). Energy discrepancy offers theoretical guarantees for a broad class of perturbation processes of which we investigate three types: perturbations based on Bernoulli noise, based on deterministic transforms, and based on neighbourhood structures. We demonstrate their relative performance on lattice Ising models, binary synthetic data, and discrete image data sets.

Energy Discrepancies: A Score-Independent Loss for Energy-Based Models

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that ED approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum ED estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.

Modeling Semantic Composition with Syntactic Hypergraph for Video Question Answering

A key challenge in video question answering is how to realize the cross-modal semantic alignment between textual concepts and corresponding visual objects. Existing methods mostly seek to align the word representations with the video regions. However, word representations are often not able to convey a complete description of textual concepts, which are in general described by the compositions of certain words. To address this issue, we propose to first build a syntactic dependency tree for each question with an off-the-shelf tool and use it to guide the extraction of meaningful word compositions. Based on the extracted compositions, a hypergraph is further built by viewing the words as nodes and the compositions as hyperedges. Hypergraph convolutional networks (HCN) are then employed to learn the initial representations of word compositions. Afterwards, an optimal transport based method is proposed to perform cross-modal semantic alignment for the textual and visual semantic space. To reflect the cross-modal influences, the cross-modal information is incorporated into the initial representations, leading to a model named cross-modality-aware syntactic HCN. Experimental results on three benchmarks show that our method outperforms all strong baselines. Further analyses demonstrate the effectiveness of each component, and show that our model is good at modeling different levels of semantic compositions and filtering out irrelevant information.

Learning Set Functions Under the Optimal Subset Oracle via Equivariant Variational Inference

Learning set functions becomes increasingly more important in many applications like product recommendation and compound selection in AI-aided drug discovery. The majority of existing works study methodologies of set function learning under the function value oracle, which, however, requires expensive supervision signals. This renders it impractical for applications with only weak supervisions under the Optimal Subset (OS) oracle, the study of which is surprisingly overlooked. In this work, we present a principled yet practical maximum likelihood learning framework, termed as EquiVSet, that simultaneously meets the following desiderata of learning set functions under the OS oracle: i) permutation invariance of the set mass function being modeled; ii) permission of varying ground set; iii) fully differentiability; iv) minimum prior; and v) scalability. The main components of our framework involve: an energy-based treatment of the set mass function, DeepSet-style architectures to handle permutation invariance, mean-field variational inference, and its amortized variants. Although the framework is embarrassingly simple, empirical studies on three real-world applications (including Amazon product recommendation, set anomaly detection and compound selection for virtual screening) demonstrate that EquiVSet outperforms the baselines by a large margin.

Tell Me How to Survey: Literature Review Made Simple with Automatic Reading Path Generation

Recent years have witnessed the dramatic growth of paper volumes with plenty of new research papers published every day, especially in the area of computer science. How to glean papers worth reading from the massive literature to do a quick survey or keep up with the latest advancement about a specific research topic has become a challenging task. Existing academic search engines such as Google Scholar return relevant papers by individually calculating the relevance between each paper and query. However, such systems usually omit the prerequisite chains of a research topic and cannot form a meaningful reading path. In this paper, we introduce a new task named Reading Path Generation (RPG) which aims at automatically producing a path of papers to read for a given query. To serve as a research benchmark, we further propose SurveyBank, a dataset consisting of large quantities of survey papers in the field of computer science as well as their citation relationships. Each survey paper contains key phrases extracted from its title and multi-level reading lists inferred from its references. Furthermore, we propose a graph-optimization-based approach for reading path generation which takes the relationship between papers into account. Extensive evaluations demonstrate that our approach outperforms other baselines. A Real-time Reading Path Generation System (RePaGer) has been also implemented with our designed model. To the best of our knowledge, we are the first to target this important research problem. Our source code of RePaGer system and SurveyBank dataset can be found on here.

Refining BERT Embeddings for Document Hashing via Mutual Information Maximization

Existing unsupervised document hashing methods are mostly established on generative models. Due to the difficulties of capturing long dependency structures, these methods rarely model the raw documents directly, but instead to model the features extracted from them (e.g. bag-of-words (BOW), TFIDF). In this paper, we propose to learn hash codes from BERT embeddings after observing their tremendous successes on downstream tasks. As a first try, we modify existing generative hashing models to accommodate the BERT embeddings. However, little improvement is observed over the codes learned from the old BOW or TFIDF features. We attribute this to the reconstruction requirement in the generative hashing, which will enforce irrelevant information that is abundant in the BERT embeddings also compressed into the codes. To remedy this issue, a new unsupervised hashing paradigm is further proposed based on the mutual information (MI) maximization principle. Specifically, the method first constructs appropriate global and local codes from the documents and then seeks to maximize their mutual information. Experimental results on three benchmark datasets demonstrate that the proposed method is able to generate hash codes that outperform existing ones learned from BOW features by a substantial margin.