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Nonnegative Matrix Factorization (NMF) is the problem of approximating a given nonnegative matrix M through the conic combination of two nonnegative low-rank matrices W and H. Traditionally NMF is tackled by optimizing a specific objective function evaluating the quality of the approximation. This assessment is often done based on the Frobenius norm. In this study, we argue that the Frobenius norm as the "point-to-point" distance may not always be appropriate. Due to the nonnegative combination resulting in a polyhedral cone, this conic perspective of NMF may not naturally align with conventional point-to-point distance measures. Hence, a ray-to-ray chordal distance is proposed as an alternative way of measuring the discrepancy between M and WH. This measure is related to the Euclidean distance on the unit sphere, motivating us to employ nonsmooth manifold optimization approaches. We apply Riemannian optimization technique to solve chordal-NMF by casting it on a manifold. Unlike existing works on Riemannian optimization that require the manifold to be smooth, the nonnegativity in chordal-NMF is a non-differentiable manifold. We propose a Riemannian Multiplicative Update (RMU) that preserves the convergence properties of Riemannian gradient descent without breaking the smoothness condition on the manifold. We showcase the effectiveness of the Chordal-NMF on synthetic datasets as well as real-world multispectral images.

Knowledge tracing (KT), aiming to mine students' mastery of knowledge by their exercise records and predict their performance on future test questions, is a critical task in educational assessment. While researchers achieved tremendous success with the rapid development of deep learning techniques, current knowledge tracing tasks fall into the cracks from real-world teaching scenarios. Relying heavily on extensive student data and solely predicting numerical performances differs from the settings where teachers assess students' knowledge state from limited practices and provide explanatory feedback. To fill this gap, we explore a new task formulation: Explainable Few-shot Knowledge Tracing. By leveraging the powerful reasoning and generation abilities of large language models (LLMs), we then propose a cognition-guided framework that can track the student knowledge from a few student records while providing natural language explanations. Experimental results from three widely used datasets show that LLMs can perform comparable or superior to competitive deep knowledge tracing methods. We also discuss potential directions and call for future improvements in relevant topics.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.

Few-shot learning (FSL) methods typically assume clean support sets with accurately labeled samples when training on novel classes. This assumption can often be unrealistic: support sets, no matter how small, can still include mislabeled samples. Robustness to label noise is therefore essential for FSL methods to be practical, but this problem surprisingly remains largely unexplored. To address mislabeled samples in FSL settings, we make several technical contributions. (1) We offer simple, yet effective, feature aggregation methods, improving the prototypes used by ProtoNet, a popular FSL technique. (2) We describe a novel Transformer model for Noisy Few-Shot Learning (TraNFS). TraNFS leverages a transformer's attention mechanism to weigh mislabeled versus correct samples. (3) Finally, we extensively test these methods on noisy versions of MiniImageNet and TieredImageNet. Our results show that TraNFS is on-par with leading FSL methods on clean support sets, yet outperforms them, by far, in the presence of label noise.

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.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.

As a crucial component in task-oriented dialog systems, the Natural Language Generation (NLG) module converts a dialog act represented in a semantic form into a response in natural language. The success of traditional template-based or statistical models typically relies on heavily annotated data, which is infeasible for new domains. Therefore, it is pivotal for an NLG system to generalize well with limited labelled data in real applications. To this end, we present FewShotWoz, the first NLG benchmark to simulate the few-shot learning setting in task-oriented dialog systems. Further, we develop the SC-GPT model. It is pre-trained on a large set of annotated NLG corpus to acquire the controllable generation ability, and fine-tuned with only a few domain-specific labels to adapt to new domains. Experiments on FewShotWoz and the large Multi-Domain-WOZ datasets show that the proposed SC-GPT significantly outperforms existing methods, measured by various automatic metrics and human evaluations.

Automatic KB completion for commonsense knowledge graphs (e.g., ATOMIC and ConceptNet) poses unique challenges compared to the much studied conventional knowledge bases (e.g., Freebase). Commonsense knowledge graphs use free-form text to represent nodes, resulting in orders of magnitude more nodes compared to conventional KBs (18x more nodes in ATOMIC compared to Freebase (FB15K-237)). Importantly, this implies significantly sparser graph structures - a major challenge for existing KB completion methods that assume densely connected graphs over a relatively smaller set of nodes. In this paper, we present novel KB completion models that can address these challenges by exploiting the structural and semantic context of nodes. Specifically, we investigate two key ideas: (1) learning from local graph structure, using graph convolutional networks and automatic graph densification and (2) transfer learning from pre-trained language models to knowledge graphs for enhanced contextual representation of knowledge. We describe our method to incorporate information from both these sources in a joint model and provide the first empirical results for KB completion on ATOMIC and evaluation with ranking metrics on ConceptNet. Our results demonstrate the effectiveness of language model representations in boosting link prediction performance and the advantages of learning from local graph structure (+1.5 points in MRR for ConceptNet) when training on subgraphs for computational efficiency. Further analysis on model predictions shines light on the types of commonsense knowledge that language models capture well.

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.

Previous cross-lingual knowledge graph (KG) alignment studies rely on entity embeddings derived only from monolingual KG structural information, which may fail at matching entities that have different facts in two KGs. In this paper, we introduce the topic entity graph, a local sub-graph of an entity, to represent entities with their contextual information in KG. From this view, the KB-alignment task can be formulated as a graph matching problem; and we further propose a graph-attention based solution, which first matches all entities in two topic entity graphs, and then jointly model the local matching information to derive a graph-level matching vector. Experiments show that our model outperforms previous state-of-the-art methods by a large margin.