Deciphering and integrating invariants for neural operator learning with various physical mechanisms

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose Physical Invariant Attention Neural Operator (PIANO) to decipher and integrate the physical invariants (PI) for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional layers. Compared to existing techniques, PIANO can reduce the relative error by 13.6\%-82.2\% on PDE forecasting tasks across varying coefficients, forces, or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO. The source code will be publicly available at: https://github.com/optray/PIANO.

DocMath-Eval: Evaluating Numerical Reasoning Capabilities of LLMs in Understanding Long Documents with Tabular Data

Recent LLMs have demonstrated remarkable performance in solving exam-like math word problems. However, the degree to which these numerical reasoning skills are effective in real-world scenarios, particularly in expert domains, is still largely unexplored. This paper introduces DocMath-Eval, a comprehensive benchmark specifically designed to evaluate the numerical reasoning and problem-solving capabilities of LLMs in the context of understanding and analyzing financial documents containing both text and tables. We evaluate a wide spectrum of 19 LLMs, including those specialized in coding and finance. We also incorporate different prompting strategies (i.e., Chain-of-Thoughts and Program-of-Thoughts) to comprehensively assess the capabilities and limitations of existing LLMs in DocMath-Eval. We found that, although the current best-performing system (i.e., GPT-4), can perform well on simple problems such as calculating the rate of increase in a financial metric within a short document context, it significantly lags behind human experts in more complex problems grounded in longer contexts. We believe DocMath-Eval can be used as a valuable benchmark to evaluate LLMs' capabilities to solve challenging numerical reasoning problems in expert domains. We will release the benchmark and code at https://github.com/yale-nlp/DocMath-Eval.

KnowledgeMath: Knowledge-Intensive Math Word Problem Solving in Finance Domains

We introduce KnowledgeMath, a novel benchmark designed to evaluate LLMs' capabilities in applying financial knowledge to solve complex math word problems. Compared to prior works, this study features three core advancements. First, KnowledgeMath includes 1,259 problems with a hybrid of textual and tabular content and require college-level knowledge in the finance domain for effective resolution. Second, we provide expert-annotated, detailed solution references in Python program format, ensuring a high-quality benchmark for LLM assessment. Finally, we evaluate a wide spectrum of 14 LLMs with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. The current best-performing system (i.e., GPT-4 with Program-of-Thoughts) achieves only 45.4% accuracy, leaving substantial room for improvement. While knowledge-augmented LLMs can improve the performance (e.g., from 23.9% to 32.0% for GPT-3.5), it is still significantly lower the estimated human expert performance of 94%. We believe that KnowledgeMath can facilitate future research on domain-specific knowledge retrieval and augmentation into the math word problem-solving process. We will release the benchmark and code at https://github.com/yale-nlp/KnowledgeMath.

Fair Abstractive Summarization of Diverse Perspectives

People from different social and demographic groups express diverse perspectives and conflicting opinions on a broad set of topics such as product reviews, healthcare, law, and politics. A fair summary should provide a comprehensive coverage of diverse perspectives without underrepresenting certain groups. However, current work in summarization metrics and Large Language Models (LLMs) evaluation has not explored fair abstractive summarization. In this paper, we systematically investigate fair abstractive summarization for user-generated data. We first formally define fairness in abstractive summarization as not underrepresenting perspectives of any groups of people and propose four reference-free automatic metrics measuring the differences between target and source perspectives. We evaluate five LLMs, including three GPT models, Alpaca, and Claude, on six datasets collected from social media, online reviews, and recorded transcripts. Experiments show that both the model-generated and the human-written reference summaries suffer from low fairness. We conduct a comprehensive analysis of the common factors influencing fairness and propose three simple but effective methods to alleviate unfair summarization. Our dataset and code are available at https://github.com/psunlpgroup/FairSumm.

FaMeSumm: Investigating and Improving Faithfulness of Medical Summarization

Summaries of medical text shall be faithful by being consistent and factual with source inputs, which is an important but understudied topic for safety and efficiency in healthcare. In this paper, we investigate and improve faithfulness in summarization on a broad range of medical summarization tasks. Our investigation reveals that current summarization models often produce unfaithful outputs for medical input text. We then introduce FaMeSumm, a framework to improve faithfulness by fine-tuning pre-trained language models based on medical knowledge. FaMeSumm performs contrastive learning on designed sets of faithful and unfaithful summaries, and it incorporates medical terms and their contexts to encourage faithful generation of medical terms. We conduct comprehensive experiments on three datasets in two languages: health question and radiology report summarization datasets in English, and a patient-doctor dialogue dataset in Chinese. Results demonstrate that FaMeSumm is flexible and effective by delivering consistent improvements over mainstream language models such as BART, T5, mT5, and PEGASUS, yielding state-of-the-art performances on metrics for faithfulness and general quality. Human evaluation by doctors also shows that FaMeSumm generates more faithful outputs. Our code is available at https://github.com/psunlpgroup/FaMeSumm .

Emergent Communication for Rules Reasoning

Research on emergent communication between deep-learning-based agents has received extensive attention due to its inspiration for linguistics and artificial intelligence. However, previous attempts have hovered around emerging communication under perception-oriented environmental settings, that forces agents to describe low-level perceptual features intra image or symbol contexts. In this work, inspired by the classic human reasoning test (namely Raven's Progressive Matrix), we propose the Reasoning Game, a cognition-oriented environment that encourages agents to reason and communicate high-level rules, rather than perceived low-level contexts. Moreover, we propose 1) an unbiased dataset (namely rule-RAVEN) as a benchmark to avoid overfitting, 2) and a two-stage curriculum agent training method as a baseline for more stable convergence in the Reasoning Game, where contexts and semantics are bilaterally drifting. Experimental results show that, in the Reasoning Game, a semantically stable and compositional language emerges to solve reasoning problems. The emerged language helps agents apply the extracted rules to the generalization of unseen context attributes, and to the transfer between different context attributes or even tasks.

Multi-Beam Forming with Movable-Antenna Array

Conventional multi-beam forming with fixed-position antenna (FPA) arrays needs to trade-off between maximizing the beamforming gain over desired directions and minimizing the interference power over undesired directions. In this letter, we study the enhanced multi-beam forming with a linear movable-antenna (MA) array by exploiting the new degrees of freedom (DoFs) via antennas' position optimization. Specifically, we jointly optimize the antenna position vector (APV) and antenna weight vector (AWV) to maximize the minimum beamforming gain over multiple desired directions, subject to a given constraint on the maximum interference power over undesired directions. We propose an efficient alternating optimization algorithm to find a suboptimal solution by iteratively optimizing one of the APV and AWV with the other being fixed. Numerical results show that the proposed multi-beam forming design with MA arrays can significantly outperform that with the traditional FPA arrays and other benchmark schemes in terms of both beamforming gain and interference suppression.

Unified Low-Resource Sequence Labeling by Sample-Aware Dynamic Sparse Finetuning

Unified Sequence Labeling that articulates different sequence labeling problems such as Named Entity Recognition, Relation Extraction, Semantic Role Labeling, etc. in a generalized sequence-to-sequence format opens up the opportunity to make the maximum utilization of large language model knowledge toward structured prediction. Unfortunately, this requires formatting them into specialized augmented format unknown to the base pretrained language model (PLMs) necessitating finetuning to the target format. This significantly bounds its usefulness in data-limited settings where finetuning large models cannot properly generalize to the target format. To address this challenge and leverage PLM knowledge effectively, we propose FISH-DIP, a sample-aware dynamic sparse finetuning strategy that selectively focuses on a fraction of parameters, informed by feedback from highly regressing examples, during the fine-tuning process. By leveraging the dynamism of sparsity, our approach mitigates the impact of well-learned samples and prioritizes underperforming instances for improvement in generalization. Across five tasks of sequence labeling, we demonstrate that FISH-DIP can smoothly optimize the model in low resource settings offering upto 40% performance improvements over full fine-tuning depending on target evaluation settings. Also, compared to in-context learning and other parameter-efficient fine-tuning approaches, FISH-DIP performs comparably or better, notably in extreme low-resource settings.

Context Shift Reduction for Offline Meta-Reinforcement Learning

Offline meta-reinforcement learning (OMRL) utilizes pre-collected offline datasets to enhance the agent's generalization ability on unseen tasks. However, the context shift problem arises due to the distribution discrepancy between the contexts used for training (from the behavior policy) and testing (from the exploration policy). The context shift problem leads to incorrect task inference and further deteriorates the generalization ability of the meta-policy. Existing OMRL methods either overlook this problem or attempt to mitigate it with additional information. In this paper, we propose a novel approach called Context Shift Reduction for OMRL (CSRO) to address the context shift problem with only offline datasets. The key insight of CSRO is to minimize the influence of policy in context during both the meta-training and meta-test phases. During meta-training, we design a max-min mutual information representation learning mechanism to diminish the impact of the behavior policy on task representation. In the meta-test phase, we introduce the non-prior context collection strategy to reduce the effect of the exploration policy. Experimental results demonstrate that CSRO significantly reduces the context shift and improves the generalization ability, surpassing previous methods across various challenging domains.