In the article, within the framework of the Boolean Satisfiability problem (SAT), the problem of estimating the hardness of specific Boolean formulas w.r.t. a specific complete SAT solving algorithm is considered. Based on the well-known Strong Backdoor Set (SBS) concept, we introduce the notion of decomposition hardness (d-hardness). If $B$ is an arbitrary subset of the set of variables occurring in a SAT formula $C$, and $A$ is an arbitrary complete SAT solver , then the d-hardness expresses an estimate of the hardness of $C$ w.r.t. $A$ and $B$. We show that the d-hardness of $C$ w.r.t. a particular $B$ can be expressed in terms of the expected value of a special random variable associated with $A$, $B$, and $C$. For its computational evaluation, algorithms based on the Monte Carlo method can be used. The problem of finding $B$ with the minimum value of d-hardness is formulated as an optimization problem for a pseudo-Boolean function whose values are calculated as a result of a probabilistic experiment. To minimize this function, we use evolutionary algorithms. In the experimental part, we demonstrate the applicability of the concept of d-hardness and the methods of its estimation to solving hard unsatisfiable SAT instances.
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Despite significant strides in multimodal tasks, Multimodal Large Language Models (MLLMs) are plagued by the critical issue of hallucination. The reliable detection of such hallucinations in MLLMs has, therefore, become a vital aspect of model evaluation and the safeguarding of practical application deployment. Prior research in this domain has been constrained by a narrow focus on singular tasks, an inadequate range of hallucination categories addressed, and a lack of detailed granularity. In response to these challenges, our work expands the investigative horizons of hallucination detection. We present a novel meta-evaluation benchmark, MHaluBench, meticulously crafted to facilitate the evaluation of advancements in hallucination detection methods. Additionally, we unveil a novel unified multimodal hallucination detection framework, UNIHD, which leverages a suite of auxiliary tools to validate the occurrence of hallucinations robustly. We demonstrate the effectiveness of UNIHD through meticulous evaluation and comprehensive analysis. We also provide strategic insights on the application of specific tools for addressing various categories of hallucinations.
The sequential recommendation problem has attracted considerable research attention in the past few years, leading to the rise of numerous recommendation models. In this work, we explore how Large Language Models (LLMs), which are nowadays introducing disruptive effects in many AI-based applications, can be used to build or improve sequential recommendation approaches. Specifically, we design three orthogonal approaches and hybrids of those to leverage the power of LLMs in different ways. In addition, we investigate the potential of each approach by focusing on its comprising technical aspects and determining an array of alternative choices for each one. We conduct extensive experiments on three datasets and explore a large variety of configurations, including different language models and baseline recommendation models, to obtain a comprehensive picture of the performance of each approach. Among other observations, we highlight that initializing state-of-the-art sequential recommendation models such as BERT4Rec or SASRec with embeddings obtained from an LLM can lead to substantial performance gains in terms of accuracy. Furthermore, we find that fine-tuning an LLM for recommendation tasks enables it to learn not only the tasks, but also concepts of a domain to some extent. We also show that fine-tuning OpenAI GPT leads to considerably better performance than fine-tuning Google PaLM 2. Overall, our extensive experiments indicate a huge potential value of leveraging LLMs in future recommendation approaches. We publicly share the code and data of our experiments to ensure reproducibility.
Modeling the correlations among errors is closely associated with how accurately the model can quantify predictive uncertainty in probabilistic time series forecasting. Recent multivariate models have made significant progress in accounting for contemporaneous correlations among errors, while a common assumption on these errors is that they are temporally independent for the sake of statistical simplicity. However, real-world observations often deviate from this assumption, since errors usually exhibit substantial autocorrelation due to various factors such as the exclusion of temporally correlated covariates. In this work, we propose an efficient method, based on a low-rank-plus-diagonal parameterization of the covariance matrix, which can effectively characterize the autocorrelation of errors. The proposed method possesses several desirable properties: the complexity does not scale with the number of time series, the resulting covariance can be used for calibrating predictions, and it can seamlessly integrate with any model with Gaussian-distributed errors. We empirically demonstrate these properties using two distinct neural forecasting models -- GPVar and Transformer. Our experimental results confirm the effectiveness of our method in enhancing predictive accuracy and the quality of uncertainty quantification on multiple real-world datasets.
Spiking Neural Networks (SNNs), providing more realistic neuronal dynamics, have shown to achieve performance comparable to Artificial Neural Networks (ANNs) in several machine learning tasks. Information is processed as spikes within SNNs in an event-based mechanism that significantly reduces energy consumption. However, training SNNs is challenging due to the non-differentiable nature of the spiking mechanism. Traditional approaches, such as Backpropagation Through Time (BPTT), have shown effectiveness but comes with additional computational and memory costs and are biologically implausible. In contrast, recent works propose alternative learning methods with varying degrees of locality, demonstrating success in classification tasks. In this work, we show that these methods share similarities during the training process, while they present a trade-off between biological plausibility and performance. Further, this research examines the implicitly recurrent nature of SNNs and investigates the influence of addition of explicit recurrence to SNNs. We experimentally prove that the addition of explicit recurrent weights enhances the robustness of SNNs. We also investigate the performance of local learning methods under gradient and non-gradient based adversarial attacks.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
We consider the problem of explaining the predictions of graph neural networks (GNNs), which otherwise are considered as black boxes. Existing methods invariably focus on explaining the importance of graph nodes or edges but ignore the substructures of graphs, which are more intuitive and human-intelligible. In this work, we propose a novel method, known as SubgraphX, to explain GNNs by identifying important subgraphs. Given a trained GNN model and an input graph, our SubgraphX explains its predictions by efficiently exploring different subgraphs with Monte Carlo tree search. To make the tree search more effective, we propose to use Shapley values as a measure of subgraph importance, which can also capture the interactions among different subgraphs. To expedite computations, we propose efficient approximation schemes to compute Shapley values for graph data. Our work represents the first attempt to explain GNNs via identifying subgraphs explicitly and directly. Experimental results show that our SubgraphX achieves significantly improved explanations, while keeping computations at a reasonable level.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.
We study the problem of textual relation embedding with distant supervision. To combat the wrong labeling problem of distant supervision, we propose to embed textual relations with global statistics of relations, i.e., the co-occurrence statistics of textual and knowledge base relations collected from the entire corpus. This approach turns out to be more robust to the training noise introduced by distant supervision. On a popular relation extraction dataset, we show that the learned textual relation embedding can be used to augment existing relation extraction models and significantly improve their performance. Most remarkably, for the top 1,000 relational facts discovered by the best existing model, the precision can be improved from 83.9% to 89.3%.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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