Structure First, Reason Next: Enhancing a Large Language Model using Knowledge Graph for Numerical Reasoning in Financial Documents

Numerical reasoning is an important task in the analysis of financial documents. It helps in understanding and performing numerical predictions with logical conclusions for the given query seeking answers from financial texts. Recently, Large Language Models (LLMs) have shown promising results in multiple Question-Answering (Q-A) systems with the capability of logical reasoning. As documents related to finance often consist of long and complex financial contexts, LLMs appear well-suited for building high-quality automated financial question-answering systems. However, LLMs often face challenges in accurately processing the various numbers within financial reports. Extracting numerical data from unstructured text and semi-structured tables, and reliably performing accurate calculations, remains a significant bottleneck for numerical reasoning in most state-of-the-art LLMs. Recent studies have shown that structured data augmentations, such as Knowledge Graphs (KGs), have notably improved the predictions of LLMs along with logical explanations. Thus, it is an important requirement to consider inherent structured information in financial reports while using LLMs for various financial analytics. This paper proposes a framework to incorporate structured information using KGs along with LLM predictions for numerical reasoning tasks. The KGs are extracted using a proposed schema inherently from the document under processing. We evaluated our proposed framework over the benchmark data FinQA, using an open-source LLM, namely Llama 3.1 8B Instruct. We observed that the proposed framework improved execution accuracy by approximately 12% relative to the vanilla LLM.

Schreier-Coset Graph Propagation

Graph Neural Networks (GNNs) offer a principled framework for learning over graph-structured data, yet their expressive capacity is often hindered by over-squashing, wherein information from distant nodes is compressed into fixed-size vectors. Existing solutions, including graph rewiring and bottleneck-resistant architectures such as Cayley and expander graphs, avoid this problem but introduce scalability bottlenecks. In particular, the Cayley graphs constructed over $SL(2,\mathbb{Z}_n)$ exhibit strong theoretical properties, yet suffer from cubic node growth $O(n^3)$, leading to high memory usage. To address this, this work introduces Schrier-Coset Graph Propagation (SCGP), a group-theoretic augmentation method that enriches node features through Schreier-coset embeddings without altering the input graph topology. SCGP embeds bottleneck-free connectivity patterns into a compact feature space, improving long-range message passing while maintaining computational efficiency. Empirical evaluations across standard node and graph classification benchmarks demonstrate that SCGP achieves performance comparable to, or exceeding, expander graph and rewired GNN baselines. Furthermore, SCGP exhibits particular advantages in processing hierarchical and modular graph structures, offering reduced inference latency, improved scalability, and a low memory footprint, making it suitable for real-time and resource-constrained applications.