Generating accurate step-by-step reasoning is essential for Large Language Models (LLMs) to address complex problems and enhance robustness and interpretability. Despite the flux of research on developing advanced reasoning approaches, systematically analyzing the diverse LLMs and reasoning strategies in generating reasoning chains remains a significant challenge. The difficulties stem from the lack of two key elements: (1) an automatic method for evaluating the generated reasoning chains on different tasks, and (2) a unified formalism and implementation of the diverse reasoning approaches for systematic comparison. This paper aims to close the gap: (1) We introduce AutoRace for fully automated reasoning chain evaluation. Existing metrics rely on expensive human annotations or pre-defined LLM prompts not adaptable to different tasks. In contrast, AutoRace automatically creates detailed evaluation criteria tailored for each task, and uses GPT-4 for accurate evaluation following the criteria. (2) We develop LLM Reasoners, a library for standardized modular implementation of existing and new reasoning algorithms, under a unified formulation of the search, reward, and world model components. With the new evaluation and library, (3) we conduct extensive study of different reasoning approaches (e.g., CoT, ToT, RAP). The analysis reveals interesting findings about different factors contributing to reasoning, including the reward-guidance, breadth-vs-depth in search, world model, and prompt formats, etc.

Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization constraints. GNMF has demonstrated exceptional performance in clustering and dimensionality reduction, effectively discovering inherent low-dimensional structures embedded within high-dimensional spaces. However, the sensitivity of GNMF to noise limits its stability and robustness in practical applications. In order to enhance feature sparsity and mitigate the impact of noise while mining row sparsity patterns in the data for effective feature selection, we introduce the $\ell_{2,0}$-norm constraint as the sparsity constraints for GNMF. We propose an unsupervised feature learning framework based on GNMF\_$\ell_{20}$ and devise an algorithm based on PALM and its accelerated version to address this problem. Additionally, we establish the convergence of the proposed algorithms and validate the efficacy and superiority of our approach through experiments conducted on both simulated and real image data.

Recent studies have demonstrated Large Language Models (LLMs) can extend their zero-shot generalization capabilities to multimodal learning through instruction tuning. As more modalities and downstream tasks are introduced, negative conflicts and interference may have a worse impact on performance. While this phenomenon has been overlooked in previous work, we propose a novel and extensible framework, called Octavius, for comprehensive studies and experimentation on multimodal learning with Multimodal Large Language Models (MLLMs). Specifically, we combine the well-known Mixture-of-Experts (MoE) and one of the representative PEFT techniques, i.e., LoRA, designing a novel LLM-based decoder, called LoRA-MoE, for multimodal learning. To the best of our knowledge, we are one of the pioneering efforts to introduce MoE into MLLMs to address this problem. The experimental results (about 20% improvement) have shown the effectiveness and versatility of our design in various 2D and 3D downstream tasks. Code and datasets are available at https://openlamm.github.io/paper Multimodal Large Language Models (MLLMs) (Alayrac et al., 2022; Huang et al., 2023; Liu et al., 2023; Li et al., 2023a; Zhu et al., 2023) have been considered as promising general-purpose interfaces that can perform various multimodal tasks under few-/zero-shot settings. Apart from leveraging the powerful Large Language Models (LLMs) (OpenAI, 2023; Touvron et al., 2023a) as the universal interfaces that unify the responses to different types of tasks as task-specified textual sequences, the keys to the success of MLLMs are to reliably perceive more modalities and be efficiently fine-tuned to adapt more downstream tasks. To achieve this goal, MLLMs rely on the instruction-tuning scheme (Ouyang et al., 2022) where the model is fine-tuned based on multimodal instruction-following dialogues orchestrated from various multimodal tasks. Moreover, thanks to the Parameter-Efficient Fine-Tuning (PEFT) techniques (e.g., LoRA (Hu et al., 2021) and Adapter (Houlsby et al., 2019)) where only small trainable components are injected in the model and updated during fine-tuning, recent MLLMs (Zhang et al., 2023; Yin et al., 2023; Ye et al., 2023) can efficiently learn to solve downstream tasks with a small scale of annotated data, while preserve the language proficiency and generalizability to novel situations. Remarkably, these models achieve comparable performance at low costs in comparison to LLaVA (Liu et al., 2023), KOSMOS series (Huang et al., 2023; Peng et al., 2023) and Shikra (Chen et al., 2023), which are learned by full model fine-tuning with a large amount of multimodal data. Q1: What is this object? R1: There is a monitor in the image.

Source detection in graphs has demonstrated robust efficacy in the domain of rumor source identification. Although recent solutions have enhanced performance by leveraging deep neural networks, they often require complete user data. In this paper, we address a more challenging task, rumor source detection with incomplete user data, and propose a novel framework, i.e., Source Detection in Graphs with Incomplete Nodes via Positional Encoding and Attentive Fusion (GIN-SD), to tackle this challenge. Specifically, our approach utilizes a positional embedding module to distinguish nodes that are incomplete and employs a self-attention mechanism to focus on nodes with greater information transmission capacity. To mitigate the prediction bias caused by the significant disparity between the numbers of source and non-source nodes, we also introduce a class-balancing mechanism.

Social dilemmas (SDs, e.g., prisoner's dilemma), spanning various domains including environmental pollution, public health crises, and resource management, present a fundamental conflict between personal interests and the common good [Nowak, 2006]. While cooperation is beneficial for the collective, individuals are tempted to exploit or free-ride others' efforts, potentially leading to a tragedy of the commons. Historically rooted in the study of biological altruism [Smith, 1982], the traditional research on cooperation in SDs has unveiled the pivotal roles of reciprocity and social preferences in fostering cooperative behaviors in human societies [Fehr et al., 2002; Rand and Nowak, 2013]. Recently, propelled by advances in artificial intelligence (AI), this field has been undergoing a profound transformation--as AI agents now increasingly represent and engage with humans, our understanding of how cooperation emerges, evolves, and sustains in SDs is being significantly reshaped. This is particularly evident in two lines of research: multi-agent cooperation, where AI agents interact with each other in SDs, and human-agent cooperation, which examines the intricacies of human interactions with AI agents in SDs.

Graph Neural Networks (GNNs) have gained considerable traction for their capability to effectively process topological data, yet their interpretability remains a critical concern. Current interpretation methods are dominated by post-hoc explanations to provide a transparent and intuitive understanding of GNNs. However, they have limited performance in interpreting complicated subgraphs and can't utilize the explanation to advance GNN predictions. On the other hand, transparent GNN models are proposed to capture critical subgraphs. While such methods could improve GNN predictions, they usually don't perform well on explanations. Thus, it is desired for a new strategy to better couple GNN explanation and prediction. In this study, we have developed a novel interpretable causal GNN framework that incorporates retrieval-based causal learning with Graph Information Bottleneck (GIB) theory. The framework could semi-parametrically retrieve crucial subgraphs detected by GIB and compress the explanatory subgraphs via a causal module. The framework was demonstrated to consistently outperform state-of-the-art methods, and to achieve 32.71\% higher precision on real-world explanation scenarios with diverse explanation types. More importantly, the learned explanations were shown able to also improve GNN prediction performance.

This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task of exactly completing the rating matrix -- the task is achievable when the sample probability is above the threshold, and is impossible otherwise -- demonstrating a phase transition phenomenon. The threshold can be expressed as a function of the ``quality'' of hypergraphs, enabling us to \emph{quantify} the amount of reduction in sample probability due to the exploitation of hypergraphs. This also highlights the usefulness of hypergraphs in the matrix completion problem. En route to discovering the sharp threshold, we develop a computationally efficient matrix completion algorithm that effectively exploits the observed graphs and hypergraphs. Theoretical analyses show that our algorithm succeeds with high probability as long as the sample probability exceeds the aforementioned threshold, and this theoretical result is further validated by synthetic experiments. Moreover, our experiments on a real social network dataset (with both graphs and hypergraphs) show that our algorithm outperforms other state-of-the-art matrix completion algorithms.

Learning neural operators for solving partial differential equations (PDEs) has attracted great attention due to its high inference efficiency. However, training such operators requires generating a substantial amount of labeled data, i.e., PDE problems together with their solutions. The data generation process is exceptionally time-consuming, as it involves solving numerous systems of linear equations to obtain numerical solutions to the PDEs. Many existing methods solve these systems independently without considering their inherent similarities, resulting in extremely redundant computations. To tackle this problem, we propose a novel method, namely Sorting Krylov Recycling (SKR), to boost the efficiency of solving these systems, thus significantly accelerating data generation for neural operators training. To the best of our knowledge, SKR is the first attempt to address the time-consuming nature of data generation for learning neural operators. The working horse of SKR is Krylov subspace recycling, a powerful technique for solving a series of interrelated systems by leveraging their inherent similarities. Specifically, SKR employs a sorting algorithm to arrange these systems in a sequence, where adjacent systems exhibit high similarities. Then it equips a solver with Krylov subspace recycling to solve the systems sequentially instead of independently, thus effectively enhancing the solving efficiency. Both theoretical analysis and extensive experiments demonstrate that SKR can significantly accelerate neural operator data generation, achieving a remarkable speedup of up to 13.9 times.

This paper considers the problem of community detection on multiple potentially correlated graphs from an information-theoretical perspective. We first put forth a random graph model, called the multi-view stochastic block model (MVSBM), designed to generate correlated graphs on the same set of nodes (with cardinality $n$). The $n$ nodes are partitioned into two disjoint communities of equal size. The presence or absence of edges in the graphs for each pair of nodes depends on whether the two nodes belong to the same community or not. The objective for the learner is to recover the hidden communities with observed graphs. Our technical contributions are two-fold: (i) We establish an information-theoretic upper bound (Theorem~1) showing that exact recovery of community is achievable when the model parameters of MVSBM exceed a certain threshold. (ii) Conversely, we derive an information-theoretic lower bound (Theorem~2) showing that when the model parameters of MVSBM fall below the aforementioned threshold, then for any estimator, the expected number of misclassified nodes will always be greater than one. Our results for the MVSBM recover several prior results for community detection in the standard SBM as well as in multiple independent SBMs as special cases.

Augmenting large language models (LLMs) with external tools has emerged as a promising approach to solving complex problems. However, traditional methods, which finetune LLMs with tool demonstration data, can be both costly and restricted to a predefined set of tools. Recent in-context learning paradigm alleviates these issues, but the limited context length only allows for a few shots of demonstrations, leading to suboptimal understandings of the tools. Moreover, when there are numerous tools to choose from, in-context learning could completely fail to work. In this paper, we propose an alternative approach, $\textbf{ToolkenGPT}$, which combines the benefits of both sides. Our approach represents each $\underline{tool}$ as a to$\underline{ken}$ ($\textit{toolken}$) and learns an embedding for it, enabling tool calls in the same way as generating a regular word token. Once a toolken is triggered, the LLM is prompted to complete arguments for the tool to execute. ToolkenGPT offers the flexibility to plug in an arbitrary number of tools by expanding the set of toolkens on the fly. In addition, it improves tool use by allowing extensive demonstration data for learning the toolken embeddings. In diverse domains, including numerical reasoning, knowledge-based question answering, and embodied plan generation, our approach effectively augments LLMs with tools and substantially outperforms various latest baselines. ToolkenGPT demonstrates the promising ability to use relevant tools from a large tool set in complex scenarios.