pith. machine review for the scientific record. sign in

arxiv: 2604.21495 · v1 · submitted 2026-04-23 · 💻 cs.LG · cs.AI· cs.CL

Recognition: unknown

Generalizing Numerical Reasoning in Table Data through Operation Sketches and Self-Supervised Learning

Hanjun Cho , Gahyun Yoo , Hanseong Kim , Jay-Yoon Lee
Authors on Pith no claims yet

Pith reviewed 2026-05-09 21:49 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.CL
keywords numerical reasoningtable dataself-supervised learningoperation sketchesdomain generalizationheader anonymizationFinQAcontinual pre-training
0
0 comments X

The pith

TaNOS decouples table headers from numerical operations using anonymization, sketches, and program-first self-supervision to improve cross-domain generalization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to demonstrate that supervised fine-tuning on table-based numerical reasoning causes models to latch onto domain-specific header shortcuts rather than learning transferable operation structures. TaNOS addresses this through header anonymization to block lexical cues, operation sketches that supply minimal structural guidance, and self-supervised generation of program-question pairs directly from tables to guarantee correctness. These steps are presented as enabling models to focus on the underlying numerical logic independent of expert-domain language. A reader would care because financial and scientific tables often require reliable reasoning that fails when data comes from new fields or with limited labeled examples.

Core claim

TaNOS is a continual pre-training framework with three components: header anonymization to reduce lexical memorization, operation sketches that provide minimal structural cues, and self-supervised pretraining that constructs correctness-guaranteed program-question pairs from given tables in a program-first manner. By decoupling domain semantics and numerical operation structure, TaNOS improves the transferability of numerical reasoning. Applied to an 8B instruction-tuned model, TaNOS achieves 80.13% execution accuracy on FinQA with only 10% train data, outperforming SFT baseline (73.97%) with full train data and proprietary models such as GPT-5, Gemini-2.5-Pro. In domain-shift experiments,Ta

What carries the argument

TaNOS continual pre-training that uses header anonymization, operation sketches for structural cues, and program-first self-supervised pair construction to enforce operation-focused reasoning.

Load-bearing premise

Header anonymization combined with operation sketches and program-first self-supervision will force models to learn general numerical structures instead of discovering new domain-specific shortcuts.

What would settle it

A TaNOS-trained model that still shows accuracy drops above 10 percentage points on domain-shifted tables or relies on header cues in controlled ablations would falsify the decoupling claim.

read the original abstract

Numerical reasoning over expert-domain tables often exhibits high in-domain accuracy but limited robustness to domain shift. Models trained with supervised fine-tuning (SFT) on specific datasets tend to rely on header-operation shortcuts rather than structural reasoning. We introduce TaNOS, a continual pre-training framework comprising three components: (i) header anonymization to reduce lexical memorization, (ii) operation sketches that provide minimal structural cues, and (iii) self-supervised pretraining that constructs correctness-guaranteed program-question pairs from given tables in a program-first manner. By decoupling domain semantics and numerical operation structure, TaNOS improves the transferability of numerical reasoning. Applied to an 8B instruction-tuned model, TaNOS achieves 80.13% execution accuracy on FinQA with only 10% train data, outperforming SFT baseline (73.97%) with full train data and proprietary models such as GPT-5, Gemini-2.5-Pro. Furthermore, in the domain-shift experiments, TaNOS displays nearly-negligible cross-domain gap (<2pp) when standard SFT shows over 10pp gap. These results suggest that structural guidance with operation sketches, header-agnostic representations, and correctness-guaranteed self-supervision can improve the robustness of numerical reasoning across diverse expert-domain tables.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces TaNOS, a continual pre-training framework for numerical reasoning over table data. It comprises header anonymization to reduce lexical shortcuts, operation sketches providing minimal structural cues, and self-supervised pre-training that constructs correctness-guaranteed question-program pairs in a program-first manner from tables. Applied to an 8B instruction-tuned model, TaNOS reports 80.13% execution accuracy on FinQA using only 10% of the training data (outperforming full-data SFT at 73.97% and certain proprietary models), along with a cross-domain gap of <2pp versus >10pp for standard SFT.

Significance. If the causal mechanism holds, the work offers a promising route to more robust, data-efficient numerical reasoning in LLMs for expert-domain tables. The program-first self-supervision with guaranteed correctness and the reported low-data + near-zero domain-shift results are strengths that could influence future table-reasoning pipelines in finance and similar fields.

major comments (2)
  1. [§3 (TaNOS framework) and §4 (Experiments)] The central claim that header anonymization, operation sketches, and program-first self-supervision cause models to rely on structural numerical operations rather than header-operation shortcuts is load-bearing but unsupported by direct evidence. No ablations isolate each component's contribution, nor are shortcut-usage diagnostics (e.g., header-swap or lexical perturbation tests) reported; performance gains could stem from increased data volume alone.
  2. [§4.2 (Domain-shift experiments)] Domain-shift results claim a <2pp gap for TaNOS versus >10pp for SFT, but the manuscript does not specify the exact source/target domains, data-split sizes, number of runs, or statistical tests. This detail is required to substantiate the generalization claim.
minor comments (2)
  1. [Abstract and §4.1] Clarify the exact prompting and version details used when comparing against GPT-5 and Gemini-2.5-Pro in the abstract and results tables.
  2. [§3.2 and §3.3] Provide additional concrete examples of operation sketches and the program-first pair construction process in the main text or appendix to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of TaNOS's potential. We address each major comment below with clarifications and commitments to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§3 (TaNOS framework) and §4 (Experiments)] The central claim that header anonymization, operation sketches, and program-first self-supervision cause models to rely on structural numerical operations rather than header-operation shortcuts is load-bearing but unsupported by direct evidence. No ablations isolate each component's contribution, nor are shortcut-usage diagnostics (e.g., header-swap or lexical perturbation tests) reported; performance gains could stem from increased data volume alone.

    Authors: We agree that component-wise ablations and shortcut diagnostics would provide stronger causal evidence. However, the reported results already indicate benefits beyond data volume: TaNOS with only 10% training data achieves 80.13% accuracy, outperforming full-data SFT at 73.97%. The program-first self-supervision generates correctness-guaranteed pairs without relying on lexical cues from headers. We will add ablations removing each component individually and include header-swap/lexical perturbation tests in the revised manuscript to directly isolate contributions. revision: yes

  2. Referee: [§4.2 (Domain-shift experiments)] Domain-shift results claim a <2pp gap for TaNOS versus >10pp for SFT, but the manuscript does not specify the exact source/target domains, data-split sizes, number of runs, or statistical tests. This detail is required to substantiate the generalization claim.

    Authors: We apologize for the omission of these specifics. We will revise §4.2 to explicitly detail the source and target domains (e.g., financial tables to general table benchmarks), exact data-split sizes, number of runs with reported variance, and statistical tests (such as t-tests) to confirm the significance of the <2pp gap versus >10pp for SFT. revision: yes

Circularity Check

0 steps flagged

Empirical framework with no derivation chain or self-referential reduction

full rationale

The paper describes an empirical continual pre-training framework (TaNOS) consisting of header anonymization, operation sketches, and program-first self-supervised pair construction, then reports benchmark results on FinQA execution accuracy and domain-shift gaps. No mathematical derivations, equations, or first-principles predictions are present that could reduce to fitted inputs or self-citations by construction. Claims rest on experimental outcomes rather than tautological definitions or load-bearing self-references, making the work self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 2 invented entities

The central claim rests on the unverified premise that the three introduced components successfully decouple semantics from numerical structure; no independent evidence for this decoupling is supplied in the abstract.

axioms (3)
  • domain assumption Header anonymization reduces lexical memorization of column names
    Invoked to prevent models from relying on specific header-operation shortcuts.
  • domain assumption Operation sketches supply sufficient structural cues for numerical reasoning without domain semantics
    Core premise of the framework.
  • ad hoc to paper Program-first construction of question-program pairs guarantees correctness for self-supervision
    Method-specific assumption enabling the self-supervised stage.
invented entities (2)
  • Operation sketches no independent evidence
    purpose: Minimal structural cues that guide numerical operations independently of headers
    New representational device introduced by the paper.
  • TaNOS continual pre-training framework no independent evidence
    purpose: Combine anonymization, sketches, and self-supervision to improve transferability
    Newly proposed system whose effectiveness is the central claim.

pith-pipeline@v0.9.0 · 5542 in / 1745 out tokens · 51154 ms · 2026-05-09T21:49:03.308497+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

22 extracted references · 17 canonical work pages · 3 internal anchors

  1. [1]

    arXiv preprint arXiv:2109.00122 , year=

    FinQA: A Dataset of Numerical Reasoning over Financial Data , author=. arXiv preprint arXiv:2109.00122 , year=

    work page arXiv

  2. [2]

    In Proceedings of the IEEE/CVF Confer- ence on Computer Vision and Pattern Recognition, pages 9556–9567

    TAT-QA: A question answering benchmark on a hybrid of tabular and textual content in finance , author=. arXiv preprint arXiv:2105.07624 , year=

    work page arXiv

  3. [3]

    arXiv preprint arXiv:2206.01347 , year=

    MultiHiertt: Numerical reasoning over multi hierarchical tabular and textual data , author=. arXiv preprint arXiv:2206.01347 , year=

    work page arXiv

  4. [4]

    Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4

    Evaluating the logical reasoning ability of chatgpt and gpt-4 , author=. arXiv preprint arXiv:2304.03439 , year=

    work page arXiv

  5. [5]

    Finqa: A dataset of numerical reasoning over financial data

    Convfinqa: Exploring the chain of numerical reasoning in conversational finance question answering , author=. arXiv preprint arXiv:2210.03849 , year=

    work page arXiv

  6. [6]

    BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding

    Bert: Pre-training of deep bidirectional transformers for language understanding , author=. arXiv preprint arXiv:1810.04805 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  7. [7]

    MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms

    Mathqa: Towards interpretable math word problem solving with operation-based formalisms , author=. arXiv preprint arXiv:1905.13319 , year=

    work page Pith review arXiv 1905

  8. [8]

    DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs

    DROP: A reading comprehension benchmark requiring discrete reasoning over paragraphs , author=. arXiv preprint arXiv:1903.00161 , year=

    work page Pith review arXiv 1903

  9. [9]

    Tapas: Weakly supervised table parsing via pre-training,

    TaPas: Weakly supervised table parsing via pre-training , author=. arXiv preprint arXiv:2004.02349 , year=

    work page arXiv 2004

  10. [10]

    Tabert: Pretraining for joint understanding of textual and tabular data,

    TaBERT: Pretraining for joint understanding of textual and tabular data , author=. arXiv preprint arXiv:2005.08314 , year=

    work page arXiv 2005

  11. [11]

    arXiv preprint arXiv:2004.07347 , year=

    Hybridqa: A dataset of multi-hop question answering over tabular and textual data , author=. arXiv preprint arXiv:2004.07347 , year=

    work page arXiv 2004

  12. [12]

    arXiv preprint arXiv:2210.06710 , year=

    Large language models are few (1)-shot table reasoners , author=. arXiv preprint arXiv:2210.06710 , year=

    work page arXiv

  13. [13]

    arXiv preprint arXiv:2305.05862 , year=

    Are chatgpt and gpt-4 general-purpose solvers for financial text analytics? an examination on several typical tasks , author=. arXiv preprint arXiv:2305.05862 , year=

    work page arXiv

  14. [14]

    Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

    Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks , author=. arXiv preprint arXiv:2211.12588 , year=

    work page internal anchor Pith review arXiv

  15. [15]

    arXiv preprint arXiv:2401.15555 , year=

    Augment before You Try: Knowledge-Enhanced Table Question Answering via Table Expansion , author=. arXiv preprint arXiv:2401.15555 , year=

    work page arXiv

  16. [16]

    arXiv preprint arXiv:2004.04487 , year=

    Injecting numerical reasoning skills into language models , author=. arXiv preprint arXiv:2004.04487 , year=

    work page arXiv 2004

  17. [17]

    NumNet: Machine Reading Comprehension with Numerical Reasoning , author =. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP) , year =

    2019

  18. [18]

    Zhang, Jiaxin and Moshfeghi, Yashar , booktitle =

  19. [19]

    arXiv e-prints , pages=

    The llama 3 herd of models , author=. arXiv e-prints , pages=

  20. [20]

    2025 , archivePrefix=

    Qwen2.5 Technical Report , author=. 2025 , archivePrefix=

    2025

  21. [21]

    Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities

    Gemini 2.5: Pushing the frontier with advanced reasoning, multimodality, long context, and next generation agentic capabilities , author=. arXiv preprint arXiv:2507.06261 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    Singh, Aaditya and Fry, Adam and Perelman, Adam and Tart, Adam and others , journal =