Quantities are distinct and critical components of texts that characterize
the magnitude properties of entities, providing a precise perspective for the
understanding of natural language, especially for reasoning tasks. In recent
years, there has been a flurry of research on reasoning tasks based on large
language models (LLMs), most of which solely focus on numerical values,
neglecting the dimensional concept of quantities with units despite its
importance. We argue that the concept of dimension is essential for precisely
understanding quantities and of great significance for LLMs to perform
quantitative reasoning. However, the lack of dimension knowledge and
quantity-related benchmarks has resulted in low performance of LLMs. Hence, we
present a framework to enhance the quantitative reasoning ability of language
models based on dimension perception. We first construct a dimensional unit
knowledge base (DimUnitKB) to address the knowledge gap in this area. We
propose a benchmark DimEval consisting of seven tasks of three categories to
probe and enhance the dimension perception skills of LLMs. To evaluate the
effectiveness of our methods, we propose a quantitative reasoning task and
conduct experiments. The experimental results show that our dimension
perception method dramatically improves accuracy (43.55%->50.67%) on
quantitative reasoning tasks compared to GPT-4.

该研究论文提出了一个基于维度感知的框架来增强语言模型的定量推理能力，并通过实验证明该方法在定量推理任务上比 GPT-4 模型提高了准确性（从 43.55% 提高到 50.67%）。

通过维度感知提升大型语言模型的量化推理能力

Enhancing Quantitative Reasoning Skills of Large Language Models through  Dimension Perception

This work focuses on the conservation of quantities such as Hamiltonians,
mass, and momentum when solution fields of partial differential equations are
approximated with nonlinear parametrizations such as deep networks. The
proposed approach builds on Neural Galerkin schemes that are based on the
Dirac--Frenkel variational principle to train nonlinear parametrizations
sequentially in time. We first show that only adding constraints that aim to
conserve quantities in continuous time can be insufficient because the
nonlinear dependence on the parameters implies that even quantities that are
linear in the solution fields become nonlinear in the parameters and thus are
challenging to discretize in time. Instead, we propose Neural Galerkin schemes
that compute at each time step an explicit embedding onto the manifold of
nonlinearly parametrized solution fields to guarantee conservation of
quantities. The embeddings can be combined with standard explicit and implicit
time integration schemes. Numerical experiments demonstrate that the proposed
approach conserves quantities up to machine precision.

该研究论文关注利用深度网络等非线性参数化近似解偏微分方程时，保持如 Hamiltonians、质量和动量等数量的守恒。研究提出的方法基于基于 Dirac-Frenkel 变分原理的神经 Galerkin 方案，在时间上逐步训练非线性参数化。论文首先表明仅添加连续时间内旨在保持数量守恒的约束可能不足够，因为参数的非线性依赖意味着即使对解场线性的数量在参数上也变为非线性，因此在时间上离散化变得困难。相反，论文提出了神经 Galerkin 方案，它在每个时间步计算出非线性参数化解场在流形上的显式嵌入，以确保数量的守恒。这些嵌入可以与标准的显式和隐式时间积分方案相结合。数值实验表明，所提出的方法可以保持数量守恒直至机器精度。

用神经伽辽金方案嵌入以保持哈密顿量和其他数量的非线性

Nonlinear embeddings for conserving Hamiltonians and other quantities  with Neural Galerkin schemes

Despite significant progress in neural abstractive summarization, recent
studies have shown that the current models are prone to generating summaries
that are unfaithful to the original context. To address the issue, we study
contrast candidate generation and selection as a model-agnostic post-processing
technique to correct the extrinsic hallucinations (i.e. information not present
in the source text) in unfaithful summaries. We learn a discriminative
correction model by generating alternative candidate summaries where named
entities and quantities in the generated summary are replaced with ones with
compatible semantic types from the source document. This model is then used to
select the best candidate as the final output summary. Our experiments and
analysis across a number of neural summarization systems show that our proposed
method is effective in identifying and correcting extrinsic hallucinations. We
analyze the typical hallucination phenomenon by different types of neural
summarization systems, in hope to provide insights for future work on the
direction.

通过对替身候选生成和选择的研究，我们提出了一个模型无关的后处理技术来修正当前神经抽象摘要生成模型中常见的不忠于原始内容的摘要幻觉现象，我们学习了一个判别式修正模型并证明，通过替代抽象式中的具名实体和数量标识来代替同源文本中语义相似类型的实体可以有效识别和修正这些不符合原文本实质的幻觉，希望此方法可以为未来的神经抽象摘要生成方向的研究提供新的思路。