Law of the Weakest Link: Cross Capabilities of Large Language Models

The development and evaluation of Large Language Models (LLMs) have largely focused on individual capabilities. However, this overlooks the intersection of multiple abilities across different types of expertise that are often required for real-world tasks, which we term cross capabilities. To systematically explore this concept, we first define seven core individual capabilities and then pair them to form seven common cross capabilities, each supported by a manually constructed taxonomy. Building on these definitions, we introduce CrossEval, a benchmark comprising 1,400 human-annotated prompts, with 100 prompts for each individual and cross capability. To ensure reliable evaluation, we involve expert annotators to assess 4,200 model responses, gathering 8,400 human ratings with detailed explanations to serve as reference examples. Our findings reveal that, in both static evaluations and attempts to enhance specific abilities, current LLMs consistently exhibit the "Law of the Weakest Link," where cross-capability performance is significantly constrained by the weakest component. Specifically, across 58 cross-capability scores from 17 models, 38 scores are lower than all individual capabilities, while 20 fall between strong and weak, but closer to the weaker ability. These results highlight the under-performance of LLMs in cross-capability tasks, making the identification and improvement of the weakest capabilities a critical priority for future research to optimize performance in complex, multi-dimensional scenarios.

Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations

We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Specifically, the IINN framework consists of two subnetworks, one of which is used to fit a given initial value, and the other incorporates physical information and continues training on the basis of the first subnetwork. Importantly, the IINN method does not require any additional data information including boundary conditions, apart from the given initial value. Corresponding theoretical guarantees are provided to demonstrate the effectiveness of our IINN method. The proposed IINN method is efficiently applied to learn some types of solutions in different nonlinear wave equations, including the one-dimensional (1D) nonlinear Schr\"odinger equations (NLS) equation (with and without potentials), the 1D saturable NLS equation with PT -symmetric optical lattices, the 1D focusing-defocusing coupled NLS equations, the KdV equation, the two-dimensional (2D) NLS equation with potentials, the 2D amended GP equation with a potential, the (2+1)-dimensional KP equation, and the 3D NLS equation with a potential. These applications serve as evidence for the efficacy of our method. Finally, by comparing with the traditional methods, we demonstrate the advantages of the proposed IINN method.

See What LLMs Cannot Answer: A Self-Challenge Framework for Uncovering LLM Weaknesses

The impressive performance of Large Language Models (LLMs) has consistently surpassed numerous human-designed benchmarks, presenting new challenges in assessing the shortcomings of LLMs. Designing tasks and finding LLMs' limitations are becoming increasingly important. In this paper, we investigate the question of whether an LLM can discover its own limitations from the errors it makes. To this end, we propose a Self-Challenge evaluation framework with human-in-the-loop. Starting from seed instances that GPT-4 fails to answer, we prompt GPT-4 to summarize error patterns that can be used to generate new instances and incorporate human feedback on them to refine these patterns for generating more challenging data, iteratively. We end up with 8 diverse patterns, such as text manipulation and questions with assumptions. We then build a benchmark, SC-G4, consisting of 1,835 instances generated by GPT-4 using these patterns, with human-annotated gold responses. The SC-G4 serves as a challenging benchmark that allows for a detailed assessment of LLMs' abilities. Our results show that only 44.96\% of instances in SC-G4 can be answered correctly by GPT-4. Interestingly, our pilot study indicates that these error patterns also challenge other LLMs, such as Claude-3 and Llama-3, and cannot be fully resolved through fine-tuning. Our work takes the first step to demonstrate that LLMs can autonomously identify their inherent flaws and provide insights for future dynamic and automatic evaluation.

Investigating Instruction Tuning Large Language Models on Graphs

Inspired by the recent advancements of Large Language Models (LLMs) in NLP tasks, there's growing interest in applying LLMs to graph-related tasks. This study delves into the capabilities of instruction-following LLMs for engaging with real-world graphs, aiming to offer empirical insights into how LLMs can effectively interact with graphs and generalize across graph tasks. We begin by constructing a dataset designed for instruction tuning, which comprises a diverse collection of 79 graph-related tasks from academic and e-commerce domains, featuring 44,240 training instances and 18,960 test samples. Utilizing this benchmark, our initial investigation focuses on identifying the optimal graph representation that serves as a conduit for LLMs to understand complex graph structures. Our findings indicate that JSON format for graph representation consistently outperforms natural language and code formats across various LLMs and graph types. Furthermore, we examine the key factors that influence the generalization abilities of instruction-tuned LLMs by evaluating their performance on both in-domain and out-of-domain graph tasks.

Label Propagation Training Schemes for Physics-Informed Neural Networks and Gaussian Processes

This paper proposes a semi-supervised methodology for training physics-informed machine learning methods. This includes self-training of physics-informed neural networks and physics-informed Gaussian processes in isolation, and the integration of the two via co-training. We demonstrate via extensive numerical experiments how these methods can ameliorate the issue of propagating information forward in time, which is a common failure mode of physics-informed machine learning.

Multi-LoRA Composition for Image Generation

Low-Rank Adaptation (LoRA) is extensively utilized in text-to-image models for the accurate rendition of specific elements like distinct characters or unique styles in generated images. Nonetheless, existing methods face challenges in effectively composing multiple LoRAs, especially as the number of LoRAs to be integrated grows, thus hindering the creation of complex imagery. In this paper, we study multi-LoRA composition through a decoding-centric perspective. We present two training-free methods: LoRA Switch, which alternates between different LoRAs at each denoising step, and LoRA Composite, which simultaneously incorporates all LoRAs to guide more cohesive image synthesis. To evaluate the proposed approaches, we establish ComposLoRA, a new comprehensive testbed as part of this research. It features a diverse range of LoRA categories with 480 composition sets. Utilizing an evaluation framework based on GPT-4V, our findings demonstrate a clear improvement in performance with our methods over the prevalent baseline, particularly evident when increasing the number of LoRAs in a composition.

Investigating Data Contamination for Pre-training Language Models

Language models pre-trained on web-scale corpora demonstrate impressive capabilities on diverse downstream tasks. However, there is increasing concern whether such capabilities might arise from evaluation datasets being included in the pre-training corpus -- a phenomenon known as \textit{data contamination} -- in a manner that artificially increases performance. There has been little understanding of how this potential contamination might influence LMs' performance on downstream tasks. In this paper, we explore the impact of data contamination at the pre-training stage by pre-training a series of GPT-2 models \textit{from scratch}. We highlight the effect of both text contamination (\textit{i.e.}\ input text of the evaluation samples) and ground-truth contamination (\textit{i.e.}\ the prompts asked on the input and the desired outputs) from evaluation data. We also investigate the effects of repeating contamination for various downstream tasks. Additionally, we examine the prevailing n-gram-based definitions of contamination within current LLM reports, pinpointing their limitations and inadequacy. Our findings offer new insights into data contamination's effects on language model capabilities and underscore the need for independent, comprehensive contamination assessments in LLM studies.

PINNs-Based Uncertainty Quantification for Transient Stability Analysis

This paper addresses the challenge of transient stability in power systems with missing parameters and uncertainty propagation in swing equations. We introduce a novel application of Physics-Informed Neural Networks (PINNs), specifically an Ensemble of PINNs (E-PINNs), to estimate critical parameters like rotor angle and inertia coefficient with enhanced accuracy and reduced computational load. E-PINNs capitalize on the underlying physical principles of swing equations to provide a robust solution. Our approach not only facilitates efficient parameter estimation but also quantifies uncertainties, delivering probabilistic insights into the system behavior. The efficacy of E-PINNs is demonstrated through the analysis of $1$-bus and $2$-bus systems, highlighting the model's ability to handle parameter variability and data scarcity. The study advances the application of machine learning in power system stability, paving the way for reliable and computationally efficient transient stability analysis.

Learning Collective Behaviors from Observation

We present a review of a series of learning methods used to identify the structure of dynamical systems, aiming to understand emergent behaviors in complex systems of interacting agents. These methods not only offer theoretical guarantees of convergence but also demonstrate computational efficiency in handling high-dimensional observational data. They can manage observation data from both first- and second-order dynamical systems, accounting for observation/stochastic noise, complex interaction rules, missing interaction features, and real-world observations of interacting agent systems. The essence of developing such a series of learning methods lies in designing appropriate loss functions using the variational inverse problem approach, which inherently provides dimension reduction capabilities to our learning methods.

Instruct and Extract: Instruction Tuning for On-Demand Information Extraction

Large language models with instruction-following capabilities open the door to a wider group of users. However, when it comes to information extraction - a classic task in natural language processing - most task-specific systems cannot align well with long-tail ad hoc extraction use cases for non-expert users. To address this, we propose a novel paradigm, termed On-Demand Information Extraction, to fulfill the personalized demands of real-world users. Our task aims to follow the instructions to extract the desired content from the associated text and present it in a structured tabular format. The table headers can either be user-specified or inferred contextually by the model. To facilitate research in this emerging area, we present a benchmark named InstructIE, inclusive of both automatically generated training data, as well as the human-annotated test set. Building on InstructIE, we further develop an On-Demand Information Extractor, ODIE. Comprehensive evaluations on our benchmark reveal that ODIE substantially outperforms the existing open-source models of similar size. Our code and dataset are released on https://github.com/yzjiao/On-Demand-IE.