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This paper claims that modern text embedding models, which power semantic search and retrieval-augmented generation, do not reliably preserve numerical details in the text they encode: on a new 1,000-question financial benchmark, 13 models

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2026-08-05 05:09 UTC pith:4P6UIM7D

load-bearing objection The near-chance numeracy result is probably real, but the minimal-pair assumption and an impossible Adjusted R2 need fixing before I'd trust the fine-grained claims. the 1 major comments →

arxiv 2509.05691 v1 pith:4P6UIM7D submitted 2025-09-06 cs.CL cs.AI

Revealing the Numeracy Gap: An Empirical Investigation of Text Embedding Models

Ningyuan Deng , Hanyu Duan , Yixuan Tang , Yi Yang This is my paper
classification cs.CL cs.AI
keywords text embedding modelsnumeracynumerical reasoningretrievalbenchmark evaluationfinancial NLP
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that modern text embedding models—the systems that turn sentences into vectors for search and retrieval—do not reliably preserve the numerical details of the text they encode. To test this, it introduces EmbedNum-1K, a set of 1,000 financial question-answer triples where the correct and incorrect answers are identical except for the number. Across 13 widely used embedding models, retrieval accuracy averages 0.54, barely above random guessing, and the best numeric format (decimal values like 0.8) reaches only 0.62 while four-digit integers fall to 0.50. The paper also finds that LLM-based embeddings outperform encoder-based ones by about five points, but that domain-specific financial fine-tuning does not improve numeracy, and that more context dilutes the numerical signal. If this holds, applications in finance and healthcare that rely on embeddings to compare numbers in text could be making errors at scale.

Core claim

The paper's central claim is that numeracy is a distinct capability that current text embedding models lack, and that this gap is masked by standard benchmarks. On EmbedNum-1K, a synthetic retrieval task constructed so that the correct answer and its distractor differ only in numeric value, the 13 evaluated models achieve an average accuracy of 0.54, with the original integer format at 0.519 and no format reaching 0.62. The authors interpret this as evidence that embeddings encode overall semantics while dropping the fine-grained numeric facts that determine whether an answer satisfies a question such as "Who owns over 15% of the company?" Additional experiments show the failure is not fixed

What carries the argument

EmbedNum-1K, a synthetic benchmark of 1,000 question-answer triples generated from financial text-to-SQL queries and augmented with seventeen numeric-format variants. For each triple, the correct answer (A+) and the incorrect answer (A−) are constructed to be identical in wording except for the number, so a model that retrieves A+ over A− must have encoded that a 20% stake satisfies "over 15%" while a 5% stake does not. The dataset isolates numeracy from semantics: cosine-similarity ranking on this task measures whether numeric detail is preserved in the embedding, and variations across formats, context length, and number length let the authors attribute failures to specific mechanisms such

Load-bearing premise

The benchmark assumes that each generated pair of candidate answers differs only in the numeric value, and the paper does not verify that this holds across all 1,000 triples; if the pairs differ in wording, specificity, or sentiment, the accuracy figures measure something other than numeracy.

What would settle it

Run a lexical-overlap baseline on EmbedNum-1K that scores each candidate answer by the length of the digit substring it shares with the question; if that baseline reaches or exceeds the reported 0.54 average accuracy, the claim that models are essentially at chance would be undermined because the task is solvable by surface pattern matching rather than numeracy.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Retrieval-augmented systems that rely on embedding similarity in financial or clinical domains will frequently return answers whose numeric detail is wrong, even when the overall meaning matches the query.
  • Scores on standard embedding benchmarks such as MTEB-style tasks should not be interpreted as evidence of numeric competence; a separate numeracy evaluation like EmbedNum-1K is necessary.
  • Adjusting tokenization so that numbers are kept intact, for instance avoiding comma-driven splits, may reduce some of the gap, but the paper's results on written-out numbers indicate this will not fully solve the problem.
  • Context-rich embeddings trade off semantic fidelity for fine detail: adding surrounding context weakens the numeric signal, so applications may need hybrid retrieval that explicitly checks numeric constraints outside the embedding comparison.
  • Domain-specific fine-tuning on financial text does not automatically confer numeracy, so future training should include explicit objectives that treat numbers as content-bearing tokens rather than ordinary words.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A natural testable extension is to add a token-overlap baseline: if a matcher that scores candidate answers by shared digit substrings with the question exceeds the reported 0.54 average on EmbedNum-1K, the 'barely above chance' headline would need qualification as a property of embedding models rather than of the task's surface difficulty.
  • The greater-than versus less-than performance asymmetry could be probed beyond embeddings: running the same 1,000 triples through an LLM in a direct question-answering setting would cheaply test whether the bias is a retrieval artifact or a deeper numerical-reasoning bias.
  • The significant-figure finding suggests a monotone numeracy difficulty curve; an extension would predict that all embedding models, regardless of architecture, will show the same ordering across formats, which could be checked with a larger format grid.
  • The probing result—encoder embeddings decode numbers more easily yet retrieve worse—implies that linear accessibility of a number in the embedding space is not sufficient for relational use; a possible test is to train a nonlinear probe or a probe that predicts the ordering relation rather than the magnitude.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. The paper introduces EmbedNum-1K, a synthetic financial-domain dataset of 1,000 ⟨Q, A+, A−⟩ triples in which, by construction, the two answer candidates are claimed to differ only in their numeric values and the retrieval task is to choose the answer satisfying a greater-than/less-than condition. The authors evaluate 13 text embedding models (encoder-based, LLM-based, and commercial) on the original integer format and 17 numeric-format variants. The main empirical claim is that embedding models generally fail to capture numerical details: average retrieval accuracy is 0.54, only slightly above random, with LLM-based models outperforming encoder-based ones (0.56 vs. 0.51). Additional analyses examine format-dependent performance, greater-than/less-than asymmetry, written vs. digit number forms, token frequency, context effects, and probing-based predictability.

Significance. If the dataset construction is sound, the paper fills a real gap in embedding evaluation, because existing benchmarks such as MTEB and FinMTEB are largely insensitive to exact numeric content. The negative result across 13 diverse models, including recent LLM-based embedders, would be a useful caution for RAG and domain-specific applications. The paper also includes a deliberate design to vary numeric formats and to study context effects, which could inform future numeracy-aware embedding training. However, the central claim rests entirely on the assumption that A+ and A− differ only in numeric value and that lexical overlap does not already solve the task; neither is currently demonstrated. The probing analysis in §5.5 is also compromised by impossible Adjusted R² values.

major comments (1)
  1. [Table 3, §5.5] Table 3 reports Adjusted R² values greater than 1 (e.g., MiniLM-L6: 4.98, RoBERTa: 1.25, finance-embeddings: 1.99). Adjusted R² cannot exceed 1; such values indicate a computation or reporting error, likely in the regression or the adjusted-R² formula. This invalidates the quantitative ranking in §5.5 and the conclusion that encoder-based models yield higher Adjusted R² than LLM-based models. Recompute the probing results and report correct Adjusted R² values (or another metric). If the corrected ranking changes, revise the corresponding text and conclusion.
minor comments (5)
  1. [Section 2.2] The example 'Stock A roseby 2%' and 'Stock A fell by 2%' appears to contain a formatting typo ('Arose' should be 'A rose'), which slightly obscures the intended contrast.
  2. [Table 2 / §4.2] The claim that average accuracy is 'slightly above random guessing' is made without confidence intervals or significance tests. Given 1,000 samples, the standard error is about 1.6 percentage points under independence; adding per-model binomial CIs and a sign test or paired test across models would strengthen the interpretation.
  3. [§5.4, Figure 8] The 'context-reduced' version replaces rich financial questions with 'Which number is above 200?' and answers like '220' and '180'. This is a substantially different task (bare number comparison), so the comparison with the main dataset should be interpreted as an ablation of context length, not as evidence that the original dataset is easier. Consider adding a more controlled context-reduced variant that preserves the original sentence frame while dropping only the surrounding clauses.
  4. [§5.2, Figure 4] The written-form evaluation covers integers up to four digits (e.g., 'six thousand seven hundred and eighty-nine'), but it is unclear whether the written forms were generated automatically and whether they were checked for grammaticality. A short note on the generation and validation procedure would improve reproducibility.
  5. [Section 3, Step 4] The 17 variant formats are described in Table 1, but the mapping from each format to the exact transformation of numeric values is not formally defined. For example, the 'scaled down' and 'scaled up' rows preserve the significant digits but change the numerical value (e.g., 8 → 0.8). State explicitly how the numeric values are transformed and how the question threshold is adjusted (if at all) for these variants.

Circularity Check

0 steps flagged

No significant circularity: the benchmark's ground truth is external arithmetic and no fitted parameter is renamed as a prediction.

full rationale

EmbedNum-1K's correctness labels come from externally defined arithmetic conditions (e.g., SQL thresholds like 'pettm > 200'), and the reported accuracies are computed from third-party embedding models or commercial APIs; no parameter is fitted to the benchmark and no 'prediction' is derived from such a fit. The paper's self-citations (Fin-E5/FinMTEB, Duan et al., Liu et al.) are used as baselines, related work, or context, and the central claim—that retrieval accuracy on this controlled numeric task is only slightly above chance—does not depend on those citations. The unverified minimal-pair assumption in Step 3 is a genuine data-validity concern (the generated A+ and A− may differ in more than the number), but it is not a circularity: the paper does not define numeracy as retrieval accuracy, nor does it fit the observed accuracy into existence. A lexical-overlap baseline would strengthen the external interpretation of the 0.54 average, but its absence does not make the derivation circular. The probing analysis in Section 5.5 also uses an independent train/test split and is not used as evidence for the main retrieval claim. Overall, the derivation chain is self-contained with respect to circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The paper relies on standard assumptions about cosine similarity and the arithmetic validity of the benchmark. The most fragile assumption is that the LLM-generated pairs differ only numerically. No new physical or conceptual entities are introduced.

axioms (4)
  • domain assumption Cosine similarity is an appropriate measure of semantic closeness for the retrieval task.
    Used in Section 4.1 without justification; standard in embedding evaluation, but not the only possible similarity metric.
  • domain assumption The correctness of A+ over A- is determined purely by the numeric comparison (greater-than/less-than), decidable arithmetically.
    Section 3; this is the ground truth that makes the benchmark objective, but it depends on the pairs differing only in the number.
  • ad hoc to paper The LLM-generated candidate pairs (A+, A-) differ only in their numeric value, as stated in Section 3 Step 3.
    This is asserted without verification. If false, the benchmark measures something other than numeracy.
  • domain assumption Token l2-norm in the embedding lookup table correlates with training frequency, as cited from Li et al. 2020 and Yu et al. 2022.
    Invoked in Section 5.3 to stratify numbers into high/low frequency groups; the cited correlation is treated as a reliable proxy.

pith-pipeline@v1.3.0-alltime-deepseek · 13912 in / 12807 out tokens · 129236 ms · 2026-08-05T05:09:57.762788+00:00 · methodology

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Cite this review

Pith. "Pith review of Revealing the Numeracy Gap: An Empirical Investigation of Text Embedding Models." pith.science (2026). https://pith.science/paper/4P6UIM7D

@misc{pith2026250905691,
  author       = {Pith},
  title        = {Pith review of: Revealing the Numeracy Gap: An Empirical Investigation of Text Embedding Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4P6UIM7D}},
  note         = {Machine review of arXiv:2509.05691}
}
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read the original abstract

Text embedding models are widely used in natural language processing applications. However, their capability is often benchmarked on tasks that do not require understanding nuanced numerical information in text. As a result, it remains unclear whether current embedding models can precisely encode numerical content, such as numbers, into embeddings. This question is critical because embedding models are increasingly applied in domains where numbers matter, such as finance and healthcare. For example, Company X's market share grew by 2\% should be interpreted very differently from Company X's market share grew by 20\%, even though both indicate growth in market share. This study aims to examine whether text embedding models can capture such nuances. Using synthetic data in a financial context, we evaluate 13 widely used text embedding models and find that they generally struggle to capture numerical details accurately. Our further analyses provide deeper insights into embedding numeracy, informing future research to strengthen embedding model-based NLP systems with improved capacity for handling numerical content.

Figures

Figures reproduced from arXiv: 2509.05691 by Hanyu Duan, Ningyuan Deng, Yixuan Tang, Yi Yang.

Figure 9
Figure 9. Figure 9: Prompt used for question augmentation. Answer Generation Please generate a financial sentence that answers the following question: Format Requirements: The sentence must include only one specific number The description must be unambiguous. Only the sentence should be provided; no additional information is needed Example: Question: Which company's profit growth exceeded 15%? Answer: Tesla's profit in the se… view at source ↗
Figure 10
Figure 10. Figure 10: Prompt used for answer generation [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗

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