An Efficient Unsupervised Framework for Convex Quadratic Programs via Deep Unrolling

Quadratic programs (QPs) arise in various domains such as machine learning, finance, and control. Recently, learning-enhanced primal-dual hybrid gradient (PDHG) methods have shown great potential in addressing large-scale linear programs; however, this approach has not been extended to QPs. In this work, we focus on unrolling "PDQP", a PDHG algorithm specialized for convex QPs. Specifically, we propose a neural network model called "PDQP-net" to learn optimal QP solutions. Theoretically, we demonstrate that a PDQP-net of polynomial size can align with the PDQP algorithm, returning optimal primal-dual solution pairs. We propose an unsupervised method that incorporates KKT conditions into the loss function. Unlike the standard learning-to-optimize framework that requires optimization solutions generated by solvers, our unsupervised method adjusts the network weights directly from the evaluation of the primal-dual gap. This method has two benefits over supervised learning: first, it helps generate better primal-dual gap since the primal-dual gap is in the objective function; second, it does not require solvers. We show that PDQP-net trained in this unsupervised manner can effectively approximate optimal QP solutions. Extensive numerical experiments confirm our findings, indicating that using PDQP-net predictions to warm-start PDQP can achieve up to 45% acceleration on QP instances. Moreover, it achieves 14% to 31% acceleration on out-of-distribution instances.

One Model for One Graph: A New Perspective for Pretraining with Cross-domain Graphs

Graph Neural Networks (GNNs) have emerged as a powerful tool to capture intricate network patterns, achieving success across different domains. However, existing GNNs require careful domain-specific architecture designs and training from scratch on each dataset, leading to an expertise-intensive process with difficulty in generalizing across graphs from different domains. Therefore, it can be hard for practitioners to infer which GNN model can generalize well to graphs from their domains. To address this challenge, we propose a novel cross-domain pretraining framework, "one model for one graph," which overcomes the limitations of previous approaches that failed to use a single GNN to capture diverse graph patterns across domains with significant gaps. Specifically, we pretrain a bank of expert models, with each one corresponding to a specific dataset. When inferring to a new graph, gating functions choose a subset of experts to effectively integrate prior model knowledge while avoiding negative transfer. Extensive experiments consistently demonstrate the superiority of our proposed method on both link prediction and node classification tasks.

Towards Knowledge Checking in Retrieval-augmented Generation: A Representation Perspective

Retrieval-Augmented Generation (RAG) systems have shown promise in enhancing the performance of Large Language Models (LLMs). However, these systems face challenges in effectively integrating external knowledge with the LLM's internal knowledge, often leading to issues with misleading or unhelpful information. This work aims to provide a systematic study on knowledge checking in RAG systems. We conduct a comprehensive analysis of LLM representation behaviors and demonstrate the significance of using representations in knowledge checking. Motivated by the findings, we further develop representation-based classifiers for knowledge filtering. We show substantial improvements in RAG performance, even when dealing with noisy knowledge databases. Our study provides new insights into leveraging LLM representations for enhancing the reliability and effectiveness of RAG systems.

Learning with Less: Knowledge Distillation from Large Language Models via Unlabeled Data

In real-world NLP applications, Large Language Models (LLMs) offer promising solutions due to their extensive training on vast datasets. However, the large size and high computation demands of LLMs limit their practicality in many applications, especially when further fine-tuning is required. To address these limitations, smaller models are typically preferred for deployment. However, their training is hindered by the scarcity of labeled data. In contrast, unlabeled data is often readily which can be leveraged by using LLMs to generate pseudo-labels for training smaller models. This enables the smaller models (student) to acquire knowledge from LLMs(teacher) while reducing computational costs. This process introduces challenges, such as potential noisy pseudo-labels. Selecting high-quality and informative data is therefore critical to enhance model performance while improving the efficiency of data utilization. To address this, we propose LLKD that enables Learning with Less computational resources and less data for Knowledge Distillation from LLMs. LLKD is an adaptive sample selection method that incorporates signals from both the teacher and student. Specifically, it prioritizes samples where the teacher demonstrates high confidence in its labeling, indicating reliable labels, and where the student exhibits a high information need, identifying challenging samples that require further learning. Our comprehensive experiments show that LLKD achieves superior performance across various datasets with higher data efficiency.

Exploring the Alignment Landscape: LLMs and Geometric Deep Models in Protein Representation

Latent representation alignment has become a foundational technique for constructing multimodal large language models (MLLM) by mapping embeddings from different modalities into a shared space, often aligned with the embedding space of large language models (LLMs) to enable effective cross-modal understanding. While preliminary protein-focused MLLMs have emerged, they have predominantly relied on heuristic approaches, lacking a fundamental understanding of optimal alignment practices across representations. In this study, we explore the alignment of multimodal representations between LLMs and Geometric Deep Models (GDMs) in the protein domain. We comprehensively evaluate three state-of-the-art LLMs (Gemma2-2B, LLaMa3.1-8B, and LLaMa3.1-70B) with four protein-specialized GDMs (GearNet, GVP, ScanNet, GAT). Our work examines alignment factors from both model and protein perspectives, identifying challenges in current alignment methodologies and proposing strategies to improve the alignment process. Our key findings reveal that GDMs incorporating both graph and 3D structural information align better with LLMs, larger LLMs demonstrate improved alignment capabilities, and protein rarity significantly impacts alignment performance. We also find that increasing GDM embedding dimensions, using two-layer projection heads, and fine-tuning LLMs on protein-specific data substantially enhance alignment quality. These strategies offer potential enhancements to the performance of protein-related multimodal models. Our code and data are available at https://github.com/Tizzzzy/LLM-GDM-alignment.

A Theoretical Understanding of Chain-of-Thought: Coherent Reasoning and Error-Aware Demonstration

Few-shot Chain-of-Thought (CoT) prompting has demonstrated strong performance in improving the reasoning capabilities of large language models (LLMs). While theoretical investigations have been conducted to understand CoT, the underlying transformer used in these studies isolates the CoT reasoning process into separated in-context learning steps (Stepwise ICL). In this work, we theoretically show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps (Coherent CoT) is integrated. Given that this coherent reasoning changes the behavior of the transformer, we further investigate the sensitivity of the transformer with Coherent CoT when the demonstration examples are corrupted at the inference stage. Our theoretical results indicate that the transformer is more sensitive to errors in intermediate reasoning steps than the final outcome. Building upon this observation, we propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration. Our experiments validate the effectiveness of the proposed approach.

Make LLMs better zero-shot reasoners: Structure-orientated autonomous reasoning

Zero-shot reasoning methods with Large Language Models (LLMs) offer significant advantages including great generalization to novel tasks and reduced dependency on human-crafted examples. However, the current zero-shot methods still have limitations in complex tasks, e.g., answering questions that require multi-step reasoning. In this paper, we address this limitation by introducing a novel structure-oriented analysis method to help LLMs better understand the question and guide the problem-solving process of LLMs. We first demonstrate how the existing reasoning strategies, Chain-of-Thought and ReAct, can benefit from our structure-oriented analysis. In addition to empirical investigations, we leverage the probabilistic graphical model to theoretically explain why our structure-oriented analysis can improve the LLM reasoning process. To further improve the reliability in complex question-answering tasks, we propose a multi-agent reasoning system, Structure-oriented Autonomous Reasoning Agents (SARA), that can better enforce the reasoning process following our structure-oriented analysis by refinement techniques and is equipped with external knowledge retrieval capability to reduce factual errors. Extensive experiments verify the effectiveness of the proposed reasoning system. Surprisingly, in some cases, the system even surpasses few-shot methods. Finally, the system not only improves reasoning accuracy in complex tasks but also demonstrates robustness against potential attacks that corrupt the reasoning process.

Self-Comparison for Dataset-Level Membership Inference in Large (Vision-)Language Models

Large Language Models (LLMs) and Vision-Language Models (VLMs) have made significant advancements in a wide range of natural language processing and vision-language tasks. Access to large web-scale datasets has been a key factor in their success. However, concerns have been raised about the unauthorized use of copyrighted materials and potential copyright infringement. Existing methods, such as sample-level Membership Inference Attacks (MIA) and distribution-based dataset inference, distinguish member data (data used for training) and non-member data by leveraging the common observation that models tend to memorize and show greater confidence in member data. Nevertheless, these methods face challenges when applied to LLMs and VLMs, such as the requirement for ground-truth member data or non-member data that shares the same distribution as the test data. In this paper, we propose a novel dataset-level membership inference method based on Self-Comparison. We find that a member prefix followed by a non-member suffix (paraphrased from a member suffix) can further trigger the model's memorization on training data. Instead of directly comparing member and non-member data, we introduce paraphrasing to the second half of the sequence and evaluate how the likelihood changes before and after paraphrasing. Unlike prior approaches, our method does not require access to ground-truth member data or non-member data in identical distribution, making it more practical. Extensive experiments demonstrate that our proposed method outperforms traditional MIA and dataset inference techniques across various datasets and models, including including public models, fine-tuned models, and API-based commercial models.

Towards the Effect of Examples on In-Context Learning: A Theoretical Case Study

In-context learning (ICL) has emerged as a powerful capability for large language models (LLMs) to adapt to downstream tasks by leveraging a few (demonstration) examples. Despite its effectiveness, the mechanism behind ICL remains underexplored. To better understand how ICL integrates the examples with the knowledge learned by the LLM during pre-training (i.e., pre-training knowledge) and how the examples impact ICL, this paper conducts a theoretical study in binary classification tasks. In particular, we introduce a probabilistic model extending from the Gaussian mixture model to exactly quantify the impact of pre-training knowledge, label frequency, and label noise on the prediction accuracy. Based on our analysis, when the pre-training knowledge contradicts the knowledge in the examples, whether ICL prediction relies more on the pre-training knowledge or the examples depends on the number of examples. In addition, the label frequency and label noise of the examples both affect the accuracy of the ICL prediction, where the minor class has a lower accuracy, and how the label noise impacts the accuracy is determined by the specific noise level of the two classes. Extensive simulations are conducted to verify the correctness of the theoretical results, and real-data experiments also align with the theoretical insights. Our work reveals the role of pre-training knowledge and examples in ICL, offering a deeper understanding of LLMs' behaviors in classification tasks.

How Do Large Language Models Understand Graph Patterns? A Benchmark for Graph Pattern Comprehension

Benchmarking the capabilities and limitations of large language models (LLMs) in graph-related tasks is becoming an increasingly popular and crucial area of research. Recent studies have shown that LLMs exhibit a preliminary ability to understand graph structures and node features. However, the potential of LLMs in graph pattern mining remains largely unexplored. This is a key component in fields such as computational chemistry, biology, and social network analysis. To bridge this gap, this work introduces a comprehensive benchmark to assess LLMs' capabilities in graph pattern tasks. We have developed a benchmark that evaluates whether LLMs can understand graph patterns based on either terminological or topological descriptions. Additionally, our benchmark tests the LLMs' capacity to autonomously discover graph patterns from data. The benchmark encompasses both synthetic and real datasets, and a variety of models, with a total of 11 tasks and 7 models. Our experimental framework is designed for easy expansion to accommodate new models and datasets. Our findings reveal that: (1) LLMs have preliminary abilities to understand graph patterns, with O1-mini outperforming in the majority of tasks; (2) Formatting input data to align with the knowledge acquired during pretraining can enhance performance; (3) The strategies employed by LLMs may differ from those used in conventional algorithms.