[Paper Review] Document-Level Tabular Numerical Cross-Checking: A Coarse-to-Fine Approach

Pang, C., Cao, Y., Zhou, G., Li, H., & Luo, P. (2025). Document-Level Tabular Numerical Cross-Checking: A Coarse-to-Fine Approach. http://arxiv.org/abs/2506.13328

---

This paper addresses a challenging document-level fact-checking problem: verifying numerical consistency across tables in disclosure documents.

The numerical cross-checking process can be decomposed into two sequential tasks:

• Numerical Semantic Matching: identifies all semantically equivalent numerical mention pairs within a document.
• Numerical Comparison: determines whether two semantically equivalent numerical mentions are numerically equal.

To address this task, the paper propeses CoFiTCheck, a novel Coarse-to-Fine Tabular Numerical Cross-Checking framework, which operates through two sequential stages:

Coarse-to-fine: 복잡한 문제를 해결할 때 넓고 대략적인 단계에서 시작해 점차 좁고 정밀한 단계로 구체화해 나가는 계층적 문제 해결방식

1) Embedding-Based Filtering

Efficiently reduces the large candidate space by encoding numerical mentions as dense embeddings and filtering candidate pairs based on embedding similarity.

2) Discriminative Classification

Performs fine-grained classification on the remaining candidate pairs to determine whether the numerical mentions are semantically equivalent.

---

[Method]

• To prevent cross-contamination between numerical mentions after the prompt, a specialized attention mask is applied.

  여러 숫자 $v_1, v_2, … ,v_n$을 한번에 EmbLLM에 넣으면, 뒤에 있는 숫자가 앞 숫자의 정보를 볼 수 있음 → 각 숫자의 embedding이 섞임 → attention mask와 positional encoding으로 해결

• For numerical mention $v_i$, consisting of $N_i$ tokens $\{t_{i,1},…,t_{i,Ni}\}$, the attention mask is defined as:
  • $M[t_{i,m}, t'] = \begin{cases} 1, & \text{if } t' \in T(c) \cup T(p_{\mathrm{emb}}) \cup \{t_{i,1}, \ldots, t_{i,m}\} \\ 0, & \text{otherwise} \end{cases}$

    > 현재 Numerical mention의 특정 token이 어떤 token들을 볼 수 있는지
    > 
    - This ensures that tokens within a numerical mention can attend only to:
        - the table context $c$
        - the prompt $p_{emb}$
        - preceding tokens within the same numerical mention
    - and not to other numerical mentions

• The position indices of numerical mention tokens are reset to start after the end of the prompt regardless of their absolute position in the sequence:
  • $Position_{(ti,m)}=∣T(c)∪T(p_{emb})∣+m−1$

    Numerical mention의 Positional index를 Prompt 직후부터 독립적으로 다시 시작하여, mention간 순서정보가 섞이지 않도록 함

• These adjustments preserve contextual understanding while isolating the representations of individual numerical mentions.

Pruning: 딥러닝 인공지능 모델에서 중요도가 낮은 가중치나 뉴런을 제거하여 모델의 크기와 연산량을 줄이는 경량화 기법

• After obtaining embeddings for all numerical mentions $E=\{e_K\}^{|V|}_{k=1}$, candidate pairs retained only when their embedding similarity exceeds a threshold t: $P_{cand}=\{(i,j)|cos(e_i,e_j)>t,(v_i,v_j)∈V_i×V_j,i \neq j\}$
• To efficiently identify candidate pairs at scale, the authors use the HNSW algorithm implemented in the FAISS library for approximate nearest-neighbor search.

> FAISS의 HNSW(Hierarchical Navigable Small World)
수많은 dense vector 중에서 query vector와 가장 비슷한 vector를 빠르게 찾기 위한 그래프 기반 Approximate Nearest Neighbor (ANN) 알고리즘
> 

• The computational complexity of constructing $P_{cand}$: $O(|E|^2)$ → $O(|E|log|E|)$

• To train EmbLM, the paper proposed a decoupled InfoNCE objective utilizing in-batch negatives.

  InfoNCE(Information Noise-Contrastive Estimation): Self-Supervised Learning에서 Positive Sample과 Negative Sample을 비교해 유용한 특징 표현을 학습하도록 돕는 핵심 손실 함수

• For each mention $i$: $P(i)$ denotes the set of indices of mentions that are semantically equivalent to $i$, while the remaining mentions are treated as negatives.
• The paper identifies two characteristics that distinguish numerical semantic matching from traditional retrieval:
  1. Mentions serve as both queries and passages
  2. Most mentions are isolated without semantic equivalents
• Accordingly:

  • $N_n$: set of non-isolated numerical mentions

  • $N_i$: set of isolated numerical mentions

    are treated separately.

  • $\mathcal{L}n = -\frac{1}{|N_n|} \sum{i=1}^{|N_n|} \log \frac{ \sum_{j \in P(i)} \exp\left(\operatorname{sim}(e_i,e_j)/\tau\right) }{ \sum_{k \in N_n} \exp\left(\operatorname{sim}(e_i,e_k)/\tau\right) }$

  • $\mathcal{L}i = -\log \frac{ \epsilon }{ \epsilon + \sum{\substack{(t,q) \in N_i \times N_i \\ t \ne q}} \exp\left(\operatorname{sim}(e_t,e_q)/\tau\right) }$
    - $sim( , )$: cosine similarity
    - $τ$: temperature parameter
    - $ϵ$: small constant

• $\mathcal{L}_n$ encourges semantically equivalent mentions to have similar representations while pushing apart non-equivalent pairs, whereas $\mathcal{L}_i$ explicitly enforces dissimilarity between isolated numerical mentions.
• The final training objective is: $\mathcal{L} = \alpha_1 \mathcal{L}_n + \alpha_2 \mathcal{L}_i$

※ 앞으로 더 추가 예정!