Knowledge tracing (KT) is a popular approach for modeling students' learning progress over time, which can enable more personalized and adaptive learning. However, existing KT approaches face two major limitations: (1) they rely heavily on expert-defined knowledge concepts (KCs) in questions, which is time-consuming and prone to errors; and (2) KT methods tend to overlook the semantics of both questions and the given KCs. In this work, we address these challenges and present KCQRL, a framework for automated knowledge concept annotation and question representation learning that can improve the effectiveness of any existing KT model. First, we propose an automated KC annotation process using large language models (LLMs), which generates question solutions and then annotates KCs in each solution step of the questions. Second, we introduce a contrastive learning approach to generate semantically rich embeddings for questions and solution steps, aligning them with their associated KCs via a tailored false negative elimination approach. These embeddings can be readily integrated into existing KT models, replacing their randomly initialized embeddings. We demonstrate the effectiveness of KCQRL across 15 KT algorithms on two large real-world Math learning datasets, where we achieve consistent performance improvements.
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The goal of multi-objective optimization (MOO) is to learn under multiple, potentially conflicting, objectives. One widely used technique to tackle MOO is through linear scalarization, where one fixed preference vector is used to combine the objectives into a single scalar value for optimization. However, recent work (Hu et al., 2024) has shown linear scalarization often fails to capture the non-convex regions of the Pareto Front, failing to recover the complete set of Pareto optimal solutions. In light of the above limitations, this paper focuses on Tchebycheff scalarization that optimizes for the worst-case objective. In particular, we propose an online mirror descent algorithm for Tchebycheff scalarization, which we call OMD-TCH. We show that OMD-TCH enjoys a convergence rate of $O(\sqrt{\log m/T})$ where $m$ is the number of objectives and $T$ is the number of iteration rounds. We also propose a novel adaptive online-to-batch conversion scheme that significantly improves the practical performance of OMD-TCH while maintaining the same convergence guarantees. We demonstrate the effectiveness of OMD-TCH and the adaptive conversion scheme on both synthetic problems and federated learning tasks under fairness constraints, showing state-of-the-art performance.
The rapid advancement of machine learning has unlocked numerous opportunities for materials science, particularly in accelerating the design and analysis of materials. However, a significant challenge lies in the scarcity and high cost of obtaining high-quality materials datasets. In other fields, such as natural language processing, foundation models pre-trained on large datasets have achieved exceptional success in transfer learning, effectively leveraging latent features to achieve high performance on tasks with limited data. Despite this progress, the concept of foundation models remains underexplored in materials science. Here, we present a foundation model specifically designed for composite materials. Our model is pre-trained on a dataset of short-fiber composites to learn robust latent features. During transfer learning, the MMAE accurately predicts homogenized stiffness, with an R2 score reaching as high as 0.959 and consistently exceeding 0.91, even when trained on limited data. These findings validate the feasibility and effectiveness of foundation models in composite materials. We anticipate extending this approach to more complex three-dimensional composite materials, polycrystalline materials, and beyond. Moreover, this framework enables high-accuracy predictions even when experimental data are scarce, paving the way for more efficient and cost-effective materials design and analysis.
Equivariant Imaging (EI) regularization has become the de-facto technique for unsupervised training of deep imaging networks, without any need of ground-truth data. Observing that the EI-based unsupervised training paradigm currently has significant computational redundancy leading to inefficiency in high-dimensional applications, we propose a sketched EI regularization which leverages the randomized sketching techniques for acceleration. We then extend our sketched EI regularization to develop an accelerated deep internal learning framework -- Sketched Equivariant Deep Image Prior (Sk.EI-DIP), which can be efficiently applied for single-image and task-adapted reconstruction. Our numerical study on X-ray CT image reconstruction tasks demonstrate that our approach can achieve order-of-magnitude computational acceleration over standard EI-based counterpart in single-input setting, and network adaptation at test time.
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.
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.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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