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We consider the problem of estimating the parameters of a Markov Random Field with hard-constraints using a single sample. As our main running examples, we use the $k$-SAT and the proper coloring models, as well as general $H$-coloring models; for all of these we obtain both positive and negative results. In contrast to the soft-constrained case, we show in particular that single-sample estimation is not always possible, and that the existence of an estimator is related to the existence of non-satisfiable instances. Our algorithms are based on the pseudo-likelihood estimator. We show variance bounds for this estimator using coupling techniques inspired, in the case of $k$-SAT, by Moitra's sampling algorithm (JACM, 2019); our positive results for colorings build on this new coupling approach. For $q$-colorings on graphs with maximum degree $d$, we give a linear-time estimator when $q>d+1$, whereas the problem is non-identifiable when $q\leq d+1$. For general $H$-colorings, we show that standard conditions that guarantee sampling, such as Dobrushin's condition, are insufficient for one-sample learning; on the positive side, we provide a general condition that is sufficient to guarantee linear-time learning and obtain applications for proper colorings and permissive models. For the $k$-SAT model on formulas with maximum degree $d$, we provide a linear-time estimator when $k\gtrsim 6.45\log d$, whereas the problem becomes non-identifiable when $k\lesssim \log d$.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Recent neural compression methods have been based on the popular hyperprior framework. It relies on Scalar Quantization and offers a very strong compression performance. This contrasts from recent advances in image generation and representation learning, where Vector Quantization is more commonly employed. In this work, we attempt to bring these lines of research closer by revisiting vector quantization for image compression. We build upon the VQ-VAE framework and introduce several modifications. First, we replace the vanilla vector quantizer by a product quantizer. This intermediate solution between vector and scalar quantization allows for a much wider set of rate-distortion points: It implicitly defines high-quality quantizers that would otherwise require intractably large codebooks. Second, inspired by the success of Masked Image Modeling (MIM) in the context of self-supervised learning and generative image models, we propose a novel conditional entropy model which improves entropy coding by modelling the co-dependencies of the quantized latent codes. The resulting PQ-MIM model is surprisingly effective: its compression performance on par with recent hyperprior methods. It also outperforms HiFiC in terms of FID and KID metrics when optimized with perceptual losses (e.g. adversarial). Finally, since PQ-MIM is compatible with image generation frameworks, we show qualitatively that it can operate under a hybrid mode between compression and generation, with no further training or finetuning. As a result, we explore the extreme compression regime where an image is compressed into 200 bytes, i.e., less than a tweet.

A novel hack involving Large Language Models (LLMs) has emerged, leveraging adversarial suffixes to trick models into generating perilous responses. This method has garnered considerable attention from reputable media outlets such as the New York Times and Wired, thereby influencing public perception regarding the security and safety of LLMs. In this study, we advocate the utilization of perplexity as one of the means to recognize such potential attacks. The underlying concept behind these hacks revolves around appending an unusually constructed string of text to a harmful query that would otherwise be blocked. This maneuver confuses the protective mechanisms and tricks the model into generating a forbidden response. Such scenarios could result in providing detailed instructions to a malicious user for constructing explosives or orchestrating a bank heist. Our investigation demonstrates the feasibility of employing perplexity, a prevalent natural language processing metric, to detect these adversarial tactics before generating a forbidden response. By evaluating the perplexity of queries with and without such adversarial suffixes using an open-source LLM, we discovered that nearly 90 percent were above a perplexity of 1000. This contrast underscores the efficacy of perplexity for detecting this type of exploit.

Deep image denoising models often rely on large amount of training data for the high quality performance. However, it is challenging to obtain sufficient amount of data under real-world scenarios for the supervised training. As such, synthesizing realistic noise becomes an important solution. However, existing techniques have limitations in modeling complex noise distributions, resulting in residual noise and edge artifacts in denoising methods relying on synthetic data. To overcome these challenges, we propose a novel method that synthesizes realistic noise using diffusion models, namely Realistic Noise Synthesize Diffusor (RNSD). In particular, the proposed time-aware controlling module can simulate various environmental conditions under given camera settings. RNSD can incorporate guided multiscale content, such that more realistic noise with spatial correlations can be generated at multiple frequencies. In addition, we construct an inversion mechanism to predict the unknown camera setting, which enables the extension of RNSD to datasets without setting information. Extensive experiments demonstrate that our RNSD method significantly outperforms the existing methods not only in the synthesized noise under multiple realism metrics, but also in the single image denoising performances.

Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.

Recently, contrastive learning (CL) has emerged as a successful method for unsupervised graph representation learning. Most graph CL methods first perform stochastic augmentation on the input graph to obtain two graph views and maximize the agreement of representations in the two views. Despite the prosperous development of graph CL methods, the design of graph augmentation schemes -- a crucial component in CL -- remains rarely explored. We argue that the data augmentation schemes should preserve intrinsic structures and attributes of graphs, which will force the model to learn representations that are insensitive to perturbation on unimportant nodes and edges. However, most existing methods adopt uniform data augmentation schemes, like uniformly dropping edges and uniformly shuffling features, leading to suboptimal performance. In this paper, we propose a novel graph contrastive representation learning method with adaptive augmentation that incorporates various priors for topological and semantic aspects of the graph. Specifically, on the topology level, we design augmentation schemes based on node centrality measures to highlight important connective structures. On the node attribute level, we corrupt node features by adding more noise to unimportant node features, to enforce the model to recognize underlying semantic information. We perform extensive experiments of node classification on a variety of real-world datasets. Experimental results demonstrate that our proposed method consistently outperforms existing state-of-the-art baselines and even surpasses some supervised counterparts, which validates the effectiveness of the proposed contrastive framework with adaptive augmentation.

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.

Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.

We introduce an effective model to overcome the problem of mode collapse when training Generative Adversarial Networks (GAN). Firstly, we propose a new generator objective that finds it better to tackle mode collapse. And, we apply an independent Autoencoders (AE) to constrain the generator and consider its reconstructed samples as "real" samples to slow down the convergence of discriminator that enables to reduce the gradient vanishing problem and stabilize the model. Secondly, from mappings between latent and data spaces provided by AE, we further regularize AE by the relative distance between the latent and data samples to explicitly prevent the generator falling into mode collapse setting. This idea comes when we find a new way to visualize the mode collapse on MNIST dataset. To the best of our knowledge, our method is the first to propose and apply successfully the relative distance of latent and data samples for stabilizing GAN. Thirdly, our proposed model, namely Generative Adversarial Autoencoder Networks (GAAN), is stable and has suffered from neither gradient vanishing nor mode collapse issues, as empirically demonstrated on synthetic, MNIST, MNIST-1K, CelebA and CIFAR-10 datasets. Experimental results show that our method can approximate well multi-modal distribution and achieve better results than state-of-the-art methods on these benchmark datasets. Our model implementation is published here: //github.com/tntrung/gaan