Quantum low-density parity-check (qLDPC) codes are an important component in the quest for quantum fault tolerance. Dramatic recent progress on qLDPC codes has led to constructions which are asymptotically good, and which admit linear-time decoders to correct errors affecting a constant fraction of codeword qubits. These constructions, while theoretically explicit, rely on inner codes with strong properties only shown to exist by probabilistic arguments, resulting in lengths that are too large to be practically relevant. In practice, the surface/toric codes, which are the product of two repetition codes, are still often the qLDPC codes of choice. A previous construction based on the lifted product of an expander-based classical LDPC code with a repetition code (Panteleev & Kalachev, 2020) achieved a near-linear distance (of $\Omega(N/\log N)$ where $N$ is the number of codeword qubits), and avoids the need for such intractable inner codes. Our main result is an efficient decoding algorithm for these codes that corrects $\Theta(N/\log N)$ adversarial errors. En route, we give such an algorithm for the hypergraph product version these codes, which have weaker $\Theta(\sqrt{N})$ distance (but are simpler). Our decoding algorithms leverage the fact that the codes we consider are quasi-cyclic, meaning that they respect a cyclic group symmetry. Since the repetition code is not based on expanders, previous approaches to decoding expander-based qLDPC codes, which typically worked by greedily flipping code bits to reduce some potential function, do not apply in our setting. Instead, we reduce our decoding problem (in a black-box manner) to that of decoding classical expander-based LDPC codes under noisy parity-check syndromes. For completeness, we also include a treatment of such classical noisy-syndrome decoding that is sufficient for our application to the quantum setting.
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Large Language Models (LLMs) have demonstrated remarkable capabilities on various tasks, while the further evolvement is limited to the lack of high-quality training data. In addition, traditional training approaches rely too much on expert-labeled data, setting an upper limit on the performance of LLMs. To address this issue, we propose a novel paradigm that enables LLMs to train itself by autonomously generating, cleaning, reviewing, and annotating data with preference information, named LANCE. Our approach demonstrates that LLMs can serve as continuous self-evolving data engineers, significantly reducing the time and cost of the post-training data construction process. Through iterative fine-tuning on different variants of the Qwen2, we validate the effectiveness of LANCE across various tasks, showing that it can continuously improve model performance and maintain high-quality data generation. Across eight benchmark dimensions, LANCE resulted in an average score enhancement of 3.36 for Qwen2-7B and 2.70 for Qwen2-7B-Instruct. This training paradigm with autonomous data construction not only reduces the reliance on human experts or external models but also ensures that the data aligns with human values and preferences, paving the way for the development of future superintelligent systems that can exceed human capabilities.
We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.
Photoacoustic imaging (PAI) suffers from inherent limitations that can degrade the quality of reconstructed results, such as noise, artifacts and incomplete data acquisition caused by sparse sampling or partial array detection. In this study, we proposed a new optimization method for both two-dimensional (2D) and three-dimensional (3D) PAI reconstruction results, called the regularized iteration method with shape prior. The shape prior is a probability matrix derived from the reconstruction results of multiple sets of random partial array signals in a computational imaging system using any reconstruction algorithm, such as Delay-and-Sum (DAS) and Back-Projection (BP). In the probability matrix, high-probability locations indicate high consistency among multiple reconstruction results at those positions, suggesting a high likelihood of representing the true imaging results. In contrast, low-probability locations indicate higher randomness, leaning more towards noise or artifacts. As a shape prior, this probability matrix guides the iteration and regularization of the entire array signal reconstruction results using the original reconstruction algorithm (the same algorithm for processing random partial array signals). The method takes advantage of the property that the similarity of the object to be imitated is higher than that of noise or artifact in the results reconstructed by multiple sets of random partial array signals of the entire imaging system. The probability matrix is taken as a prerequisite for improving the original reconstruction results, and the optimizer is used to further iterate the imaging results to remove noise and artifacts and improve the imaging fidelity. Especially in the case involving sparse view which brings more artifacts, the effect is remarkable. Simulation and real experiments have both demonstrated the superiority of this method.
The key challenge of image manipulation detection is how to learn generalizable features that are sensitive to manipulations in novel data, whilst specific to prevent false alarms on authentic images. Current research emphasizes the sensitivity, with the specificity overlooked. In this paper we address both aspects by multi-view feature learning and multi-scale supervision. By exploiting noise distribution and boundary artifact surrounding tampered regions, the former aims to learn semantic-agnostic and thus more generalizable features. The latter allows us to learn from authentic images which are nontrivial to be taken into account by current semantic segmentation network based methods. Our thoughts are realized by a new network which we term MVSS-Net. Extensive experiments on five benchmark sets justify the viability of MVSS-Net for both pixel-level and image-level manipulation detection.
Graph Convolutional Networks (GCNs) have received increasing attention in recent machine learning. 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 optimizing the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the GEneralized Multi-relational Graph Convolutional Networks (GEM-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge-base embedding methods, and goes beyond. Our theoretical analysis shows that GEM-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 GEM-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
Knowledge graphs (KGs) serve as useful resources for various natural language processing applications. Previous KG completion approaches require a large number of training instances (i.e., head-tail entity pairs) for every relation. The real case is that for most of the relations, very few entity pairs are available. Existing work of one-shot learning limits method generalizability for few-shot scenarios and does not fully use the supervisory information; however, few-shot KG completion has not been well studied yet. In this work, we propose a novel few-shot relation learning model (FSRL) that aims at discovering facts of new relations with few-shot references. FSRL can effectively capture knowledge from heterogeneous graph structure, aggregate representations of few-shot references, and match similar entity pairs of reference set for every relation. Extensive experiments on two public datasets demonstrate that FSRL outperforms the state-of-the-art.
Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.
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, thereby allowing manual manipulation in predicting the final answer.
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