Exponential Scaling of Factual Inconsistency in Data-to-Text Generation with Fine-Tuned LLMs
Authors: Joy Mahapatra
Soumyajit Roy
Utpal Garain
Venue: Accepted by TMLR ()

Abstract: Data-to-text (D2T) generation is a core task in text generation that involves converting semi-structured data (e.g., tables, graphs) into text. Recent advances in large language models (LLMs) have led to significant improvements in D2T. Despite these gains, factual inconsistency remains a persistent issue in LLMs for D2T. Understanding how such inconsistencies scale with factors like model size, compute (FLOPs), and data size is crucial for building trustworthy systems. While prior scaling studies focus on generalization error via power law scaling, the impact of these factors on factual inconsistency in D2T remains unexplored. This paper addresses the gap by empirically investigating how factual inconsistency scales with various scaling factors. Unlike prior studies that focus solely on power law scaling, we also examine exponential scaling. To rigorously compare these models, we introduce \textit{VaCScal}, a three-stage statistical validation framework: (1) predictive performance estimation, (2) goodness-of-fit assessment, and (3) comparative analysis. Experiments are conducted across six diverse LLM families and five D2T datasets. Factual inconsistency is inversely measured using four state-of-the-art consistency metrics, including human evaluation. We employ QLoRA, Prefix-Tuning, and full fine-tuning to fine-tune the LLMs. Our analysis, validated through the \textit{VaCScal} framework, consistently shows that factual inconsistency in D2T generation follows exponential scaling with respect to model (LLM) size, compute (FLOPs), and fine-tuning data size---challenging the prevailing assumption of power law scaling. To support this finding, a mathematical rationale is also provided, demonstrating why exponential scaling behavior is expected in factual inconsistency under typical D2T conditions.

Published in Transactions on Machine Learning Research (10/2025)
Exponential Scaling of Factual Inconsistency in Data-to-Text Generation with Tuned LLMs
Joy Mahapatra Indian Statistical Institute Kolkata
joymahopotrs390@@maa..ll
Soumyajit Roy Indian Statistical Institute Kolkata
bommygstrog2233544mmaaa...o
Utpal Garain
uttpll.garriin@gmail.com
Indian Statistical Institute Kolkata
Reviewed on OpenReview: https: // // openreview..ee.... net/ forum? id PdodPPP655
Abstract
Data-to-text (D2T) generation is core task in text generation that involves converting semi- structured data (o.g., tables, graphs) into text. Recent advances in large language models (LLMs) have led to significant improvements in D2T. Despite these gains, factual inconsis- tency remains a persistent issue in LLMs for D2T. Understanding how such inconsistencies scale with factors like model size, compute (FLOPs), and data size is crucial for building trustworthy systems. While prior scaling studies focus on generalization error via power law scaling, the impact of these factors factual inconsistency in D2T remains unexplored. This paper addresses the gap by empirically investigating how factual inconsistency scales with various scaling factors. Unlike prior studies that focus solely power law scaling, also examine exponential scaling. To rigorously compare these models, we introduce VaC- Seal, a three-stage statistical validation framework: (1) predictive performance estimation, (2) goodness-of-itt assessment, and (3) comparative analysis. Experiments are conducted across six diverse LLM families and five D2T datasets. Factual inconsistency is inversely measured using four state-of-the-arr consistency metries, including human evaluation. We employ QLoRA, Prefix-Tuning and full fine-tuning to fine-tune the LLMs. Our analysis, validated through the VaCScal framework, consistently shows that factual inconsistency in D2T generation follows exponential scaling with respect to model (LLM) size, compute (FLOPs), and fine-tuning data size challenging the prevailing assumption of power law scaling. To support this finding, a mathematical rationale is also provided, demonstrating why exponential scaling behavior expected in factual inconsistency under typical D2T conditions.
1 Introduction
Data-to-text (D2T) generation (Lin et al. 2024b Li al. 2024) involves converting semi-structured data (e.g., tables, graphs) into natural language, with applications in dialogue systems, automated journalism, and beyond. LLMs have achieved strong performance D2T tasks, particularly in coherence and informa- tiveness [Loaandi & Belz 2024). However, factual inconsistency-wiii where the generated text fails to faithfully reflect. the input data remains a major challenge [Li et al. 2022 Huang el al. 2023), often diminishing trust in LLM- based D2T systems (Fiuuee Ip. To build reliable models, it crucial to understand how fac- tual inconsistency scales with key factors such as model size, compute (FI.Oss), and training (fine-tuning) data. Nonetheless, existing scaling analyses in D2T focus almost entirely on generalization errors or test perplexity, especially under power law scaling (Kaplan et al. 2020 Hoffmann et al. 2022). while overlooking

---

Published in Transactions on Machine Learning Research (10/2025)
how factual inconsistency behaves under similar scaling. Bridging this gap is essential for advancing both research understanding and the practical development, of more trustworthy D2T systems.
John Buscema won the Eisner Award.
True reference
(John Buscema, AWARD, Eisner Award)
Source (triplet) data
John Buscema received the Eisner Award for his work Close Ahm
Delta.
LLM
Factuallly inconsistent generation
An example from the DART Nan el al. 2021 dalasel demonstrating factually inconsistent output generated by an LLM (Pythia-I.4B) The generated text contains unsupported content- work on Close to Ahm Delta" " which not grounded in the source data.
Figure 1:
In this paper, we address a critical research gap by examining how factual inconsistency scales in D2T generation. Unlike prior work focused solely on power law scaling (Kaplan et al. 2020 Hoffmann et al. 2022 Brandfonbrener et al.J 2025), we also explore exponential scaling using VaCScal three-stage statistical validation framework consisting of: (1) predictive performance estimation, (2) goodness-of-ft assessment, and (3) comparative analysis. VaCSoal enables rigorous and principled comparison between power law and exponential scaling behaviours. Our study covers three major LLM architectures (decoder-only, encoder- decoder, and state-space), evaluating six LLM familie-BLLOO FLAN-T5, Mamba, OPT, Pythia, and Qwen2.5 across five D2T datasets: E2E, ViGGO, WebNLG, DART, and Texi Models are fine- tuned using QLoRA (Dettmers et al. 2023) and Prefix- Tunnn- (Li & Liang 2021p. To ensure broader adoption, we complement these fine-tuning approaches with experiments involving full fine-tuning, which updates all trainable model parameters. For robustness toward decoding. we report results using both greedy and nucleus sampling decoding strategies. Factual inconsistency is defined the inverse of factual consistency and measured using four automatic metrics: ALIGNSCORE, QAFACTEVAL, SUMMAC-CONV and UNIEVAL-FACT, along with human amnotations. Our findings, validated through VaCScal, reveal that factual inconsistency exhibits exponential scaling across multiple factors- such as model size, compute, and fino-tuning data challengnnggg the dominant assumption of power law scaling. To support these empirical results, we also provide a mathematical rationale showing that factual inconsistency is expected to scale exponentially with LLM size under typical D2T conditions.
2 Related Work
Data-to-text generation (D2T) and factual inconsistency. Data-to-text (D2T) generation (Lin et al.
2024b involves generating natural language from structured inputs such as graphs (Gardent et al. 2017 Nan et al.] 2021). ) tables [Boo al. 2018 , and meaning representations (slot-value pairs) (Novikova et al. 2017
Juraska et al. 2019). These three representation forms constitute the main categories of D2I; graph-to-text
table-to-text. and MR-to-text Recently, LLMs have become central to D2T due to their large-scale pretrain-
ing (Zhang et al. 2022). scalability (Scao et al. 2022), and compatibility with efficient fine-tuning (Dettmers)
ct al. 2023) and prompt-based lcarning [Lester et al. 2021). These models often outperform traditional
approaches in coherence and informativeness (Ge et al. 2023). However, factual inconsistency where gen-
erated text fails to reflect input data accurately remains a persistent challenge (Fabbri et al.) 2022 Zha
ct al.
2023 lcading hallucinations and reduced trustworthiness. Prior work attributes this misalign-
ment between source data and references (Dhingra al. 2019 ul Islam al.) 2023). LLM biases (Zhang
et al.
2023 and exposure bias (Hang et al. 2023). While human evaluation is the gold standard, recent
2

---

Published in Transactions on Machine Learning Research (10/2025)
automatic metrics (Fabbri al. 2022 Zha et al. and offer scalable alternatives.
2023
have shown strong correlation with human judgments
Scaling in LLM. In LLMs, scaling describes how LLM performance varies with scaling factors such as model size, compute, data, etc (Chung et al. 2024 Zhang et al. 2024 Brandfonbrener et al. 2025 Mayil-
vahanan et al. 2025 Hestness et al. (2017) showed that deep language models follow power law scaling, which was extended by Kaplan al. 20200) to include model size, dataset size, and compute. Subsequent works have explored scaling across tasks (Bansal et al. 2022 Kaplan al.] 2020), paradigms such as sparse modeling (Frantar et al. 2024). and parameter-effiiiet fine-tuning (Zhang et al. 2024). More recently, joint scaling such as additive and multiplicative formulations-has. garnered incrcasing attention (Hoff- mann et al. 2022 Zhang et al. 2024). Scaling plays a critical role in hyperparameter tuning (Hendrycks, forthcoming) training cost estimation (Hägele et al. 2024). and model performance prediction (Hoffmann) et al. 2022). A set of recent studies (Atanasov et al.
2024 Bahri et al. 2024 Lin et al. 2024a) has further
reinforced the theoretical foundations of scaling.
3 Desiderata: Scaling Models
Moving beyond prior work on power law scaling (Kaplan et al. 2020 Brandfonbrener al. 2025 Gadre
et al. 2025), we examine two scaling models for factual inconsistency in D2T generation with respect
LLM size: power law scaling (modeled by power law function) and exponential scaling (modcled by exponential function). The two scaling models are defined as follows:
Ar + B
x N otherwise
Power Law Scaling Model f(x) =
(1)
Ce Rr +
x x otherwise
Exponential Scaling Model f(x)
(2)
Here, A and C' are case-specific parameters, a is the power law exponent, is the exponential scaling rate, represents the scaling factor (o.g., LLM size, compute (FLOPs), etc.), and fxx) denotes the scaling objective (e.g., factual inconsistency). B and D represent the irreducible error entropy of LLM family (Brandfonbrener et al. 2025);; in other studies, they are interpreted as the performance threshold or capacity of given LLM family (Hestness et al. 2017). Following the significant work by Zhang et al. (2024). we estimate the parameters of both models via maximum likelihood estimation on the factual inconsistency data D, optimizing with the standard Huber loss (8 = 1) due robustness to outliers.
4 VaCScal: Statistical Validation Framework
Prior empirical studies on LLM scaling often assess predictive performance using held-out loss alone. How- ever, we find this insufficient for rigorously evaluating or comparing multiple scaling models. To address this, we use VaCScal (Validation and Comparison of Scaling law) structured three-stage framework compris- ing predictive performance estimation, goodness-of-fi assessment, and comparative analysis. Each stage is detailed below.
Stage I: Predictive Performance Estimation. The first stage evaluates how well the scaling models generalize in terms of their predictive ability on unseen data. To achieve this, we assess the scaling models held-out data using the Huber loss (5 1). The Huber loss is known for its robustness to outliers, making it well-suited for reliable estimation. Given the limited data availability, employ five-fold cross-validation to assess predictive performance.
Stage II: Goodness-of-fit Assessment. Predictive performance alone not sufficient to validate scaling model; assessing its goodness-of-fit. is also erucial for its acceptance. Therefore, in this
3

---

Published in Transactions on Machine Learning Research (10/2025)
Stage 1
Predictive Performance Estimation Doss car))
less value
Stage
Goodness-af-ft Essessment
RALSE
scalind
X
TRUE
Stage
Comparative Analysis
0.006
Leaning scaling
TRIL
exponential
Figure 2: All three stages of VuCScal, the statistical validation framework for scaling models. Dashed ovals indicate outputs of each stage.
stage, we assess the goodness-of-th fit the scaling models using an F-test for regression WWiisergg 2005 Siegel 2016). The test statistic for the F-test is computed as follows:
SSRA - SSRe
SSRE
Fstat
dfn - dfe
dfe
Estat ~ F-distribution(z)
Here, SSRx and SSRe represent the sum of squared residuals for the reduced and exact models, respectively. Similarly, dfx and dfe denote the degrees of freedom for the reduced and exact models, respectively. We consider both of our scaling models as exact models, while the redueed model is represented by a simple mean-response model. Since the F-test applies only to linear regression models, we use a log transformation to convert our scaling models into their linear forms. We perform the F-test with a significance level of p < 0.05, which commonly considered a moderate threshold. If scaling model fails to achieve p-value below 0.05 the goodness-of-fit assessment, do not consider it feasible for modeling scaling behavior.
Stage III: Comparative analysis. In this final stage of validation, we compare the two scaling models through hypothesis testing to determine which better explains the data. Since power law and exponential scaling models are not nested hypotheses, the standard likelihood-ratio test is not applicable. Instead, we employ Vuong's likelihood-ratio test (Vuong 1989) for comparison. The test statistic for Vuong's likelihood-ratio test is computed as follows:
Vatat Vn- mean(d)
(3)
VVr((d)
Vatas normal(0,
(4)
Where represents the sample size, and d denotes the n-sized sample of the log-likelihood differences between the two scaling models. We conduct Vuong's likelihood ratio test at a stringent significance level of p < 0.005 to provide highly compelling evidence for our conclusion.
Normality Assumptions Verification. In Stage II and III of our validation framework, we incorporate the F-test and Vuong's likelihood-ratio test. Both tests rely, directly or indirectly, on the assumption that the residuals of our scaling models follow a normal distribution. Therefore, validating this assumption essential. To assess the normality of residuals for both scaling models, we employ the Shapiro -hipiro-Wilk test (Shaphiro & (with p < 0.05) throughout all of our experiments.
Wilk 1965)
4

---

Published in Transactions on Machine Learning Research (10/2025)
5
Experiment Setup
We provide brief details about the LLM families, D2T datasets, and metrics used to measure factual in- consistency. For additional information on settings and other critical implementation details, please see Appendix All code used in our scaling experiments is provided in the Supplementary Material.
5.1 D2T Datasets and LLM Families
Our experiments incorporate five widely used D2T datasets, covering three major D2T generation types: DART NNan et al, 2 and WebNLG (Gardent al. 2017) for graph-to-text, WikiTableTText (Bao et al. 2018 for table-to-text, and E2E (Dusck et al. 2018) and ViGGO (Juraska et al. 2018) for MR-to-text. Among these five D2T datasets, DART (represents diverse knowledge triples), WebNLG (extracted from DBpedia), and WikiTableText. (extracted from Wikipedia) are open-domain datasets that capt.ure broad knowledge, whereas E2E (restaurant domain) and ViGGO (video game domain) are closed-domain datasets that represent consistent, domain-specific knowledge. Additional details about these datasets are provided in Appendix A.1 We also evaluate six prominent LLM families spanning three architectural paradigms: dccoder-only, cncoder-dccoder, and stato-space. These include BLOOM (5 models) (Scao et al., 2022). FLAN-1 T5 (5 models) (Chung el al.
2024), OPT (6 models) (Zhang et al. 2022), Pythia (8 models) (Biderman) et al. 2023). Mamba (5 models) Gu & Dao 2024), and Qwen2.5 (7 models) (Yang et al. 2024 Further
details are available in Appendix
A.2 All datasets and model variants are sourced from the Hugging Face
hub (Wolf et al. 2020 summary of the LLM families is presented Table
Family
Model Paradigm
Model Counts
Parameters of Each Models
BLOOM
decoder-only
560M, 1.1B, 1.7B, 3B, 7B 77M, 248M, 783M, 2.85B, 11.3B
FLAN-T5
decoderr
5
Mamba
state-space model
5
130M, 370M, 790M, L.4B, 2.8B
OPT
decoder-only
6
125M, 350M, 1.3B, 2.7B, 6.7B, 13B
Pythia
decoder-only
8
70M, 160M, 410M, 1B, 1.4B, 2.8B, 6.9B, 12B
Qwen2.5
decoder-only
7
0.5B, 1.5B, 3B, 7B, 14B, 32B, 72B
Table 1: Overview of the five LLM families, their architectural paradigms, and model sizes (M million, B billion parameters).
5.2 Settings
Input Lincarisation, Prompt Structure, Fine-tuning, and Decoding Strategies. In D2T tasks, input linearisation involves transforming semi-structured data into a sequential representation before feeding it into an LLM. We consider two forms of linearisation: (1) lists of slot-value pairs and (2) lists of relat ional triples, as detailed in Appendix A.5 For supervised fine-tuning across all our experiments, we employ a description-guided prompt structure, also provided in Appendix A.5) We use two parametor-cfficient fine- luning strategies QLoRA (Dettmers et al. 2023) and Prefix-Tuning (Li & Liang 2021 -o fine-tune all LLMs on each D2T dataset. Alongside these two parameter-efficient fine-tuning methods, we also perform full fine-tuning to broaden the reach of our results. For more details on the fine-tuning setup, please see Appendix A.3 For decoding, we consider both greedy decoding and nucleus sampling. For further training settings and library details, please refer to Appendix A.4
Quantification for Factual Inconsistency. We define factual inconsistency the inverse of factual consistency, computed as (1 1-22 2), where z is the factual consistency score ranging from 0 to 1. To evaluate factual inconsistency in LLMs for D2T lasks, we employ four stale-of-the-arl automatic metrics that exhibit strong correlations with human judgments: ALIGNSCORE, which measures consistency through information alignment (Zha al.] 2023); QAFACTEVAL, which assesses consistency via question generation and an- swering (Fabbri et al.) )022); SUNMAC-CONV, which leverages natural language inference techniques (Laban) lt al. 2022); and UNIEAAL-PACT, which utilizes a unified evaluation framework based multi-task train-
5

---

Published in Transactions on Machine Learning Research (10/2025)
ing (Zhong et al. 2022). In addition to these automatic metries, we also conduct human evaluation, wherein
factual consistency is manually annotated by human annotators.
6 Results
This section presents the plots and VaCScal results for factual inconsistency scaling (measure using ALIGN- ScoRE and QAFACTEVAL) in D2T with respect to two scaling factor model size and compute (FLOPs), based on two scaling models- pooser law and exponential. All results this study are based on text generated using greedy decoding.
6.1 Scaling Behavior Based on Model Size of
(QLoRA) LLM Families
Here, we present the scaling behavior of factual inconsistency in D2T with respect to model size for LLM familics fine-tuned using QLoRA. Here, we present results for four LLM Families-FLAN-TS Mamba, Pythia, and Qwen2.5. Results for the other two families, BLOOO and OPT, are provided Appendix [ For results using SUMMAC-CONY and UNIEVAL-FACT as factual inconsistency metrics, please refer Appendix
Exponential scaling
Margin of error (esponential scaling)
Power law scaling
Margin of error (power law scaling)
Famil))
Family)
Family)
Farnly)
Puctull bove sieety Auatodiisio. Petus Iecosataaryy Ausraitoooe Pooua fecovlnaryy Au0r00i1i4
0.35
0.50
0.00
0.30
0.45
0:35
0.20
0.25
0.15
0.35
0.25
0.40
0.30
0:25
0:00
3:30
0.40
0.42
0.10
0.15
0.20
0.15
0.24
1.20
5.25
11:30
1.20
1.20
372
0.5
8.77
11:30
11.30
3.20
372
025
Prorene [Biiced)
Prowetes (Rllvee)
Pranete (Rllas)
Paceettes (RBkvv))
DART (w/ Mambe Fastlyl
EIE (w) Manba Fumily)
VIGGO (w/ Marba Farill))
WasNIGG (w/ Mambe Panily)
WidTabkeTeet (w) Manba Farily)
0.3
0.50
0.54
0.26
0.32
0.50
0.20
0.76
0.28
0.25
0.40
0.20
0.1-
0.20
0.22
9.08
0.43
1.0
2,02
220
2.80
220
2.00
0.40
3.00
180
0440
1.00
1.00
2.20
2.00
1.02
220
2.82
Paaneett Farrly)
Pydtia Paisly)
(w/ Famity)
Pythle
Pystu Famnty)
0.90
0.50
0.70
0.50
0.60
0.50
0.40
0.30
0.40
0.50
0.00
0.30
0.20
0.00
1.20
5.25
0.5 2.52 12.00
2.25 5,25 0.55
2.32 12.00
1.25 305 6.3 9.12 11.00
1.25
305
5,53
8.32
11:03
1.26
3.55
5.03
9.32
12:52
Promettes (Bllion))
(BBloon)
(Bi8ced)
Phanitee [0l
DART (w) Qum17 Famrly)
F3E (w/ Quieo Fastly)
ViGed (w/ Qam?755 5 Faril))
WHeNLG (w/ QueeD. Fanily)
Was Toeee (w/ Quent Famdly)
0.42
0.71
0.20
0:27
0.6
0.19
0.25
2:43
0.30
0.70
0.28
0.11
0.2
2:43
Perancior (Billono)...
Parametors (Bilon))
Parmeters (Bilionn)
Paramdoors (Bilier))..
Parametera (Billon))
Figure 3: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by ALIGNSCORE, plotted against model size across different LLM families.
6

---

Published in Transactions on Machine Learning Research (10/2025)
6.1.1 Factual Inconsistency Measured via AlignScore
Figure 3 shows the fitted curves for the power law and exponential scaling models, along with 95% confidence intervals derived from residual error. Anomalies are particularly observed in the F2E dataset for the Mamba family, where factual inconsistency unexpectedly increases with model size. A possible hypothesis for this aberrant behavior is discussed in Appendix ![ In sporadic exceptional cases involving the E2E and ViGGO datasets, both scaling models exhibit higher margins of error (MoE), although the exponential model consis- tently shows lower MoE than the power law. Outside these exceptions, exponential scaling generally yiclds much narrower MoEs, indicating more stable and reliable fits in terms of uncertainty. [Table 2 summarizes the outcomes of the VaCleal framework. Exponential scaling consistently outperforms the power law across all three validation stages: in Stage 1, it achieves lower held-out loss; in Stage I1, it passes the F-test more froquently (V); and in Stage III, Vuong's test favors exponential scaling in most cases (highlighted in bluc). In several scenarios, power law scaling found to be infeasible. Although in multiple cases for Qwen2.5 both scaling models fail to pass the Stage II feasibility test of VaCScol (i.e., meeting the minimum p-value for goodness-of-fit), exponential scaling still achieves lower comparable held-out loss (Stage I) in most sce- narios. Despite few exceptions (e.g., E2E), VaCScal results indicate that exponential scaling more reliably models factual mecosssteenyymmssurr via ALIGNSCORF-in D2T generation.
Takeaway. Exponential scaling models more accurately capture factual inconsistency (measured via ALIGN- SCORe) with respect to LLM model size in D2T, exhibiting lower error and stronger statistical fit compared to power low scaling, despile a few oulliers.
LLM Banily
Sealing
DART
E2E
VIGGO
WOONGG
WikTTabeeTst
PLAN-TS
Exponential
4.15--0//
860E-04/
2
Power Law
147B-06/
3.11E-05/
7.80E-01 X
6.16E-0//
L.5E-01/
Marnia
Exponential
Power Taw
3.77F:-05; X
2.14E 05 W
1.99 X
L.3E-04/
L08F+10777 X
3. 5.50-01/
1-22++33
3.0E-00/
Pythia
Exponential
2038-05
2.185-08/
2.901-02/W
3.315-00/
Power Law
Le8E+11
1.24E O2
1.92 02/2
1.71E+11/M
1.96-+04/2
Qwee2.
Exponestial
L.00 05 /
2:00E 04/2
3.98E 02, X
3.4LE 01/2
Law
4.79E-01/M
2008-115
6.81E-44
2.718-11
2.00--13
Table 2: Results from VaCScal corresponding to F Figure 3 Numerical values, along with (V/**) and blue/red highlights, indicate the outcomes of Stages 1, 11, and III of VaCSeal.
6.1.2 Factual Inconsistency Measured via QAFactEval
Figure shoows the fitted power law and exponential scaling curves, along with 95% MoE, using QAFACTE- VAL as the inconsistency metric. Similar to ALIGNSCORE, notable anomalies are -iserved-especialll for the E2E dataset, where all LLM families (except Pythia) exhibit increasing inconsistency with model size. Aside from a few exceptions in E2E and ViGGO, where both scaling models show higher MoE, exponential scaling generally yields narrower MoF. than power law scaling, indicating more stable fits with lower uncer- tainty. Table 3 summarizes the corresponding results under the VaCScal framework. In most Stage I results, exponential models consistently achieve lower or comparable held-out loss. For Stage II, they pass the F-test (V) more reliably than power law models, which often fail (*). Overall, Stage III also favors exponential scaling, with numerous significant Vuong test results (highlighted in blue). In two rare cases casos-DARF and WebNLG with the FLAN-T5
power law scaling outperforms exponential models. We hypothesize that FLAN-T5, having been pre-trained on graph-to-text formats, may exhibit divergence from exponential scaling in these cases due to prior alignment with power law behavior. In Qwen2.5, apart from ViGGO, all other datascts show significantly lower held-out loss (Stage I) for exponential scaling. Overall, aside from these few rare exceptions, exponential scaling emerges as a more robust and statistically valid model of factual inconsistency in D2T when measured with QAFACTEVAL.
Takeaway. Compared power law scaling, exponential scaling more effectively captures the relationship be- tween factual inconsistency (measured via QAFACTEVAL) and model size D2T across most LLM families, despite some anomalies (e.g., F2F, ViGGO).

---

Published in Transactions on Machine Learning Research (10/2025)
Exponential scaling
Margin of (exponential scaling)
Power scaling
Margin of enrer (power law scaling)
DART (w/ FLANITS Fardy))
E25 (w/ FLAN TS Fovil))
Vi660 FLAM Family
WANNLG FLAN TS
WalTweeTee (w/ FLAMISS Fannly)
Exrta Iree MESAAAA QAAPACTTI Pamual IncosAtbric wo QA07t:/ooo Dutua Ixcenbbeeey Ry QUPPeeRoo Penual Incretionc QAPAA-TTOO
0.40
0.55
0.35
0.40
0
0.50
0.54
0.14
0.46
0.30
0.45
0
0.40
0.15
0.35
0.30
1.00
322
1.20
Paramca [Biliora) +>
Paramctera (Bilbrn)
Paramderr (Billon)
Paramecoo (Bil
Paramstera (Blian))
DART (w/ Mantaa Eaidly)
E2E (w/ Marna
VIGGn Maniaa Fanell))
WHANLE (wc Moriaa Favily)
WaiTaikiTir Maenoo Farilyy)
0.58
0.33
0.52
0.18
0.34
0.50
0.36
0.30
0.40
0:26
Paramcians [Bi Icra]
Paramdoo (Bilion)) -4
Panamsters (8 lirm))
Purmecter (Bilion)
Peramcian (81 locol
DART (w/ Pytti Faiily
EIE [w/ Pyskis Fanily)
VIGGO (w) Pythis Farrlly)
WeBNLG Pytlia Farrlty)
WieTatleTeor (w/ Pybtis Fanily)
1.00
1.00
0.
0.85
0.70
0.00
0.82
0.70
0.70
0.60
0.40
0.60
0.60
0.52
0.00
0.30
0.50
0.20
0.50
0.30
0.20
0.00
0.20
0.00
1.30
3.55
12.00
1.25
3.05
6.93
9:32
Paramatera (Sil)on)
Paramoou (Billera)
Parametera (8illon))
Paramsters (Bllics))
Parammtaa [Bil))
DART Qwnn7.5 Favil))
E3E Queee Favsl))
VIG00 (4/ Qam2755 Fovily)
WWNNIG Qweed.
WalTaikeTee Quert.5 Farsly)
0.00
0.34
0.44
0.45
0.25
0.24
2:45
0.30
0.43
0.21
0.20
0.10
0.50
0:30
23.90
Paramsttrr (Billoro]-. +
Parambter (Bilioni)
Parametors (Billorn)
Paramiton (Billora) -4
Panametera (Billon))
Figure 4: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by QAFACTEVAL, plotted against model size across different LLM families.
LLM Family
Scaling
DART
E2E
VIGGO
WolNLG
WikTD
FLAN T5
Exponestial
3.37E-13. /
G.00E-166/
4.84E-00, V
2.38E-00.W
Power Law
22222022 W
7.08E 0 X
LJME AA) V
2.5TE
4.57E.04 03) K
Expemential
3.749-04/W
75FF-05
01
4.38F-55
5/88-06
Power Law
4.01E 05,
177 05/M
4.33 01/2
2663+06 X
9.08E-20) X
Pythis
Exponeetial
3.99E /
T.4TE 02/W
3.85IE 0
4.50 02/0
3.24E 01 /
Power Law
LONE
2.86E-412
2.09E
9.44E+
1.74E-02
Qwen2.5
Exponestial
7220-005/
2.00E-16
2.88E-04
Power Lawe
1.66-01.W
14F-03
*
3.63R-02
2.91F-04/
6.27F/ 16,
Table 3: Results from VaCScal corresponding to Figure 4 Numerical values, along with (V/*3) and blue/red highlights, indicate the outcomes of Stages I, II, and III of VaCSoal.
6.2 Scaling Behaviour Based on FLOPs of Fine- Tuned (QLoRA) LLM Families
Estimating compute budget is central to LLM scaling research (Kaplan el al. 2020 Chung el al. 2024). with several early works linking generalization error to FLOPs soaating-pontt operations). This section examines the scaling behavior of LLM factual inconsistency in D2T with respect to FLOPs. We evaluate LLM families across five D2T datasets using two automatic metrics ALIGNSCORE and QAFACTEVAL. Here, we present results for four I.I.M families-FL.L. FL.AN-T5, Mamba, Pythia, and Qwen2.5. Results for the other two families,
8

---

Published in Transactions on Machine Learning Research (10/2025)
BLOOM and OPT, are provided in Appendix C fine-tuned using QLoRA.
FLOPs are computed using calflops
| and all models are
Exponential scaling
Margin error (exponential scaling)
Power scaling
Margin enrer (power law scaling)
DART (w/ FLAN-TS Famil)
Eit (w/ FLAN-TS Family)
VIGGO (w/ FLAN-TS Funnly)
WASNLGG (w/ FLAN- Famil))
WaiTedee Fost (wy/ FLAN-TS Famely)
Pactal Ron My Aattodiiaee Paoted Inceeuttaaoo Armentoone Plotud bocaeoitee wy Auatoeiooeee Faouel Iodeeitaaooo A1R0000114
0.35
0.20
0.19
0.45
0:00
8.17
8.17
8.18
8.18
0.50
0.35
0.45
2.40
0.64
0/42
0.10
0.10
8.16-
116
0.25
0:20-
0:15
0.15
0.10
7.06
6-45
10 15 19
0.07
161
2:75 366 407
0:01
0.04
0.07
0.10
0:13
0.66
3.06
3:47
4:87
6:77
0.05
0.18
0.15
0.2
0.54
1x:10")
FLOPs (x110"))
FLOPs (H100*)
FLOPs (1
(w/ Farsl))
(w) Faeslt)
Faeelly)
(w/ Farily)
WaiTaaatTet Farslyy
0.32
0.95
0.52
0.32
0.20
0.30
0.45
0.24
0.78
0.16-
0.26
9:46
0.77
0.20
0.22
0.34
0.44
PLOP Da 10
PLOPs (X110")
(L1Ps(x166))
PLOPs (x 71
FLO% Ex 10"
DART (w) Pytiia Farilyy
E2E (w/ Pyttia Faiily)
VIGGO (w/ Pytii Fartly)
WHONGG (w/ Pytti Family)
WilTaseeTar (w/ Pyttia Farily)
1.00
0.80
0.80
0.70
0.70
0.40
0.10
0.50
0.20
2
0.40
0.30
0.20
0.00
40.00
0.30
3.00
9:99 15 37 28.50
0.74
7:36
3.77
5.00 7.19
5:07
0.56
0 014 c.1
0.58 310 521 7:0 6:45
0.6
0.5
0.0
577
FLOP Eo (CPP))
FLOP% (x11PP)
FLOPs (x19P8) -
FLOR [x
(w/ Family)
Q Fandg)
Fairly)
(w/ QueeD. Farily)
Farsly)
0.20
0.17
0.05
0.35
0.1
0.54
0.20
0.24
0.27
0.25
0.25
0.22
0:13
0.13
0.20
0:39
0:30
0.25
(x16%))
FLOP& (1:10"1
PLOPs (x 11
FLOPS| (x.10")) -
FLOP% (x16
Figure 5: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, mcasured by ALIGNSCORE, plotted against FLOPs across different LLM families.
Family
Scaling
VIGGO
WebNLG
WikdTable
FLAN-TS
Exponeezial
L52E 0//
4.82E
04/
3,29E-03/1 03E-00//
LIBE DL/
JUSSE
Power Law
6.148-00,
6.15E-03
3477-001 *
2.365-05/ A
1.33E-04 V
Marniu
Exponcezial
1,22 05/W
2,3R 04/
392E 05/W
4.5RE *
Power Law
4.51 46,600668
1.47E-00
1071-17677
100
4.4E 13/
Pythia
Exponcatial
1/2E-00/W
4.22
W
Poner Taw
1966- 1
2.56F-02
245R-00
00/
1.774 11
1-37 03
Qwes22
Expomertial
Power Law
L.5R 03/
0,978-05/4
1.408-04)
1.708-04/
3/11--1//
4.51F-03
2.168-03
5.53F-04 *
Table 4: Results from VaCScal corresponding to Figure Numerical values, along with (V/*) and bluc/rod highlights, indicate the outcomes of Stages I, II, and III of VaCSoal.
6.2.1 Factual Inconsistency Measured via AlignScore
F Figure 6
illustrates how factual inconsistency- via ALIGNSCORF: scales with FLOPss across LLM families under both power law and exponential models, along with 95% confidence margins. As with the
http:///gthaaacc/////////llaleee
9

---

Published in Transactions on Machine Learning Research (10/2025)
model size results, similar anomalies persist in FLOP- scaling -partiuulally in the E2E dataset (notably with the Mamba family), where inconsistency increases with FI,OPs. Similar to the model size-based findings, Appendix Deatiiixxprree provides a plausible explanation for this aberrant behavior. In Figure 5| E2E also exhibits higher MoE across both scaling models and most LLM familics. Outside these exceptions, exponential scaling consistently yields narrower MoEs, indicating more stable fits with lower residual uncertainty. [Table 4 summarizes the VaCSeal evaluation for this FLOP-based analysis. In Stage I, exponential models consistently achieve lower held-out loss. While Stage II includes a few infeasible cases (e.g., E2E and ViGGO with Qwen2.5), exponential scaling is statistically preferred in most model-dataset pairs, indicated by the frequent blue marks showing significant Vuong test outcomes in Stage III. Here, Qwen2.5 shows conclusions similar to its model size based scaling behavior for factual inconsistency measured via ALIGNSCORE. Overall, the VaCSeal results indicate that exponential scaling provides a more robust and reliable model for capluring how factual inconsistency in D2T generation decreases with increasing compute offering actionable insights for compatc-budget planning with fine-tuned LLMs.
Takeaway. Exponential scaling model better captures how factual inconsistency (via ALIGNSCORE) de- creases with FLOPs across LLM families, offering a more stable and practical scaling model than power law scaling.
Exponential scaling
Margin of error (exponential scaling)
Power law scaling
Margin of error (power law scaling)
DART (w/ FLAN T6 Faneky)
E26 (+/ FLAN- T5 Fannly
Vi6G0 (w/ FLAN Favily)
WeANLG (w/ FLAN TS Fandy)
WaiTatee Fext (w/ FLAN T5 Faseky)
FAORL HOC/Attano//// QAEAeEEo Pactull Incoe E00000 ae: QAEaeeoo Paoted Indeeiitaaoo me/ QAATSiMRoss Facmel Wook 0iec0 00/ QA77ntt F101
0.55
0.57
0.40
0.50
0.35
0.50
0.25
0.45
0.20
0.00
0.15
0.35
0:37
0:10
0.30
5:4
10.04 12 19.01
0.52
1
2.75
030
0.24
0.07
030
0.13
0.60
2.00
3.47
6.27
0.00
0.33
0.30
0.2
0.54
OP.. 1x 100
T1OP% 102
FLOPX [x [x10pt)
F1.P%
DART (wr/ Mambe Farely)
(w/ Marba Funily)
VIGGO (w/ Mamba Family)
WasNLG (w/ Mambe Farrly)
WilTaakkeeett (w) Manta Funily)
0.30
0.35
0.44
0:40
0.50
0.15
0.42
0.15
0.34
0.25
0.34
0.32
0.28
0.54
0.90
0.32
0:38
2.40
3.92
5.92
0.25
1.36
1.73
0.01
0.02
0.00
0.32
0.01
130
2.8
0.5
0.32
FLOPs 20
(X1101)
FLOPs (x16P))
FLOP& O110 20)
DART (w/ Pythi Famnly)
E2E (w/ Pythis Farnls)
VIGGO (w/ Pythi Furely)
WANNGG (w/ Pylhu Family)
Tubll Fert (w/ Patlia Furnl))
1.000
1.50
1.00
0.00
1.00
1.10
1.00
0.50
0.80
0.70
0.20
0.60
0.00
0.50
0:30
0.40
0.50
0.30
-0.0
0.20
0.20
15
38.90
0.74 3:35 3.47 7.19
0.00
0.06
0.00
031
2:93
3.0
1.11 7:3 1/6
0.00 035 0.0 0.00 037
(x166"))
FLOPs 10
FLOPs (X10Pt)
FLOP 11
(x166P)
DART (w/ Qwes2.5 Parily)
EZE (w/ Owen2. Fandy)
VIGGO (w/ Owed25 Family)
WAANLG (w/ Qwee2.5 Farrly)
WilTaakkTTst (w) Qwi12.5 Famnl)
0:45
0.25
0.22
0.30
0.32
0.40
0.20
0.35
0.39
0.59
0.37
13.57 57.01 1514 251/2.92
4.33 25.0
0.12
0:35
0.00
030
3.09
5r.36
FLOPs (x10P))
(x -
FLOP/
(x
FLOPs (x:20")
FLOPa (x10P))
Figure 6: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual
inconsistency, measured by QAFACTEVAL, plotted against FLOPs across different LLM families.
10

---

Published in Transactions on Machine Learning Research (10/2025)
6.2.2 Factual Inconsistency Measured via QAFactEval
Figure 6 displays fitted power law and exponential scaling curves with 95% confidence intervals (MoE), showing how factual
seeeiisttey--mssuune using QAFACTEVAI.- varies with FLOPs. Again, certain anomalics persist; for instance, factual inconsistency increases with compute for the E2E dataset under the FLAN-T5 and Mamba families. The E2E dataset (within FLAN-T5 and Mamba families) often exhibits large MoEs, indicating high uncertainty. Nevertheless, exponential scaling consistently delivers narrower confidence bounds than power law fits, suggesting more reliable and stable modeling. The associated VaCScal outcomes, summarized in [Tall 5| reinforce this conclusion: most model dataset pairs show a clear preference for exponential scaling, as indicated by the frequent blue-highlighted Vuong Lest results, with only a few exceptions (in DART and WebNLG with FLAN-T5). While a few configurations such as E2E are deemed infcasible Stage II, the broader pattern of VaCScal results affirms exponential scaling as the superior framework for capturing how factual inconsistency declines with increasing compulational effort.
LLM Family
Scaling
DART
E2E
VIGGO
WelNLG
WikTTablText
FLAN-TS
Exponectial
2.37E BFE--3.
G.L.E-16
2.MEE V
2.3 OL/V
Power Law
5.02F-06/
3.73K-00
6
364E-D4
Mannho
Exparetial
17766-06
3.728-66
L
Power Law
6.31E+08/ X
2600-04/
7 5.E6-OL
7.464+06 M
2.66E-21/
Pythia
Exponential
281E:005.
2.32--02/
0/22
5,871:01 /V
7.35
Power Law
8.29 02/W
10015+15/4
4.99E-12/
Quen2.5
Expomentaal
3 /
7/23F-05/W/
3.4 3.41
1.91F-04/
6.13F-01/X X
Power Law
40 01/1
1.58E
LSSE 01
1.705-04
4.00E
Table 5: Results from VaCScal corresponding to F Figure 6 Numerical values, along with (V/*) and blue/red highlights, indicate the outcomes of Stages I, II, and III of VaCSoal.
Takeaway. Compared to power law scaling, the exponential model more effectively captures the relationship between FLOPs and factual inconsistency (measured via QAFACTEVAL),, exhibiting greater stability across LLM families.
7 Discussion
Our findings consistently demonstrate that exponential scaling provides more accurate and statistically grounded explanation of factual inconsistency in D2T generation, compared to power law scaling. This conclusion holds across multiple evaluation metrics, scaling factors, and experimental setups. In the main results (section 6), exponential scaling outperformed power law scaling in modeling factual inconsistency, as measured by ALIGNSCORE and QAFACTEVAL, with respect to both model size and compute budget (FLOPs). This trend persists even when alternative factual consistency metrics are used such as SUMMAC- CONY and UNIFVALL-PACT (Appendix D) and when evaluated against human annotations (Appendix B further reinforcing the robustness of the observed scaling behavior. Moreover, exponential scaling remains dominant when other scaling factors are considered, such as the size of the fine-tuning dataset (Appendix G To ensure that our conclusions are not dependent additional experiments using Prefix- Prefix-Tuiing (Appendix F) and nucleus sampling (Appendix D Furthermore, to more comprehensively capture the scaling behavior of factual inconsistency in LLMs for D2T, we also include a full fine-tuning approach, where all trainable model parameters are updated (Appendix H In all these cases, exponential scaling consistently showed superior performance. Although a few exceptions were observed particularly with the E2E and ViGGO datasets these anomalies are limited in scope and do not undermine the broader empirical trend. We hypothesize that this aberrant behavior in E2E and ViGGO stems from two factors: their lower lexical diversity and their closed-domain nature. These characteristics likely make them more prone to overfitting in larger LLMs, leading to the obscrved inconsistencies. In contrast, the other three D2T datasets, being more diverse and open-domain, mitigate such effects. In Appendix[] we provide a critical analysis the aberrant behavior exhibited by these two datasets in details. A key enabler of our analysis is the proposod framework VaCScal, which offers statistically rigorous validation of scaling models beyond conventional measures such as margin of error (MoE) or held-out loss. While MoE is helpful for visualizing uncertainty, it does not assess the statistical plausibility of model. In several cases,
specific fine-tuning or decoding st.rategy, we conducted
11

---

Published in Transactions on Machine Learning Research (10/2025)
models with low MoE failed Stage II of VaCScal, due to high p-values, indicating that visually good fit may not always be statistically valid. Furthermore, Stage III of VaCScal provides principled mechanism for comparing competing scaling models, often yielding strong evidence in favor of exponential scaling when both models pass feasibility checks in Stage II. Interestingly, Stage of VaCScal also reveals that exponential scaling lends to achieve lower held-out, loss even settings where neither model passes Stage leasibility, suggesting its robustness in practice. In summary, our comprchensive evaluation s multiple metrics, datasets, scaling factors, and validation strategies empirically substantiates the superiority of exponential scaling over power law scaling for capturing factual inconsistency in D2T generation with fine-tuned LLMs.
8 Theoretical Implications of Exponential Scaling for Factual Inconsistency in D2T
We aim to provide mathematical rationale for why factual inconsistency in D2T lasks is expected to follow exponential scaling pattern with respect to LLM size. We posit that seurcc-reference divergence plays central role in the emergence of factual inconsistency in LLM outputs. Source-reference divergence (Dhingra let al. 2019 Ji et al., 2023) refers to the deviation between the structured input data and the reference text in the training corpus. Such divergence is prevalent in D2T datasets due to heuristic data collection methods, data noise, and the influence of annotators' prior knowledge. Training on these divergent datasets often induces factual inconsistency in model outputs. We further assume that factual inconsistency can be represented through relative measure of perplexity, which allows ground its behavior in formal scaling law.
Theoritical Implication 8.1. Assume a D2T dataset exhibiting source-reference divergence, and let factual inconsistency be quantified using the relative perplecity of an LLM trained on this dulasel. Then,
Factual Inconsistency & c E(()
(5)
where E(N) is linear or sub-linear function of the model (LLM) size N.
A detailed mathematical interpretation of this thcoretical implication is provided in Appendix J
9 Conclusion
This work presents a comprehensive scaling analysis of factual inconsistency in D2T generation with respect to model size, compute (FLOPs), and fine-tuning data size. Contrary to prior studics favoring power law behavior, our experiments across diverse LLM families, datasets, and evaluation metrics consistently reveal that factual inconsistency follows exponential scaling. To rigorously compare scaling models, we introduce VaCSoal, a three-stage statistical framework that evaluates predictive performance, goodness-of- fit, and model comparison. Exponential scaling outperforms power law across all stages and remains robust across different tuning and decoding strategies. Finally, to reinforce our empirical findings, we provide a mathematical rationale showing that under typical D2T conditions involving source-reference divergence, factual inconsistency is expected to scale exponentially with LLM size. Together, these results establish exponential scaling more accurate and theoretically grounded model of factual inconsistency in D2T generation with fine-tuned LLMs.
Limitation and Future Scope
While our study offers promising insights into the scaling behavior of factual inconsistency in D2T generation, several limitations remain. First, we did not examine the transfcrability of scaling models across different LLM families or datasets, which could be an important avenue for future work. Second, our analysis is restricted to the D2T task due to computational constraints; extending the framework to other conditional generation tasks such as summarization or dialogue could test its broader applicability. Finally, we focus solely on fine-tuning strategics, leaving out alternative approaches like in-context learning or cfain-of-thought prompting both of which offer interesting directions for future research.
12

---

Published in Transactions on Machine Learning Research (10/2025)
Broader Impact Statement
This work highlights that factual incousistency in LLM-based data-to-text generation exhibits exponential scaling with respect model size, compute (FI.Oss), and fine-tuning data volume. By introducing the VaC- Scal framework for statistically grounded model validation and comparison, this study lays the foundation for future efforts in designing more factually consistent and rosourco-cfficeet language systems. The accom- panying mathematical perspective further deepens understanding of scaling dynamics, offering a principled basis for guiding the development of next-generation LLMs across diverse generation tasks.
Acknowledgments
This research is partially supported by the Indo-French Centre for the Promotion of Advanced Research (ECCPARCCEFIPRA) through CSRP Project No. 6702-2.
References
Alexander B. Atanasov, Jacob A. Zavatone- Veth, and Cengiz Pehlevan. Scaling and renormalization in high- dimensional regression. CoRR, 0bs/2405.00592, 2024. URL https://doo..rg// wwwp:0/4040/////.......
00592
Yasaman Bahri, Ethan Dyer, Jared Kaplan, Jachoon Lee, and Utkarsh Sharma. Explaining neural scaling laws. Proceedings of the National Academy of Sciences, 121((7) 2024. httph://t////
pnas. org/
10as/pnas..... 2311878121
Yamini Bansal, Behrooz Ghorbani, Ankush Garg, Biao Zhang, Colin Cherry, Behnam Neyshabur, and Orhan Firat. Data scaling laws in NMT: the effect of noise and architecture. In ICML, volume 162, pp. 2022. URL htttps://proceeddngg http:/gs.w.rrrrrsr/eeeee
mlr. press/ http//v122//aaa// wttp//aasaaaa.....aaaaaaa html
Junwei Bao, Duyu Tang, Nan Duan, Zhao Yan, Yuanhua Lv, Ming Zhou, and Tiejun Zhao. Table-to-text: Describing table region with natural language. In Proceedings of the AAAL, pp. 5020 5027, 2018. URL
https://doi. w0. 1609/ v32i1. 11944
Stella Biderman, Hailey Schoelkopf, Quentin Gregory Anthony, Herbie Bradley, Kyle O'Brien, Eric Hallahan, Mohammad Aflah Khan, Shivanshu Purohit, USVSN Sai Prashanth, Edward Raff, Aviya Skowron, Lintang Sutawika, and Oskar van der Wal. Pythia: A suite for analyzing large language models across training and scaling. In ICML, volume 202, pp. 2397-2430, 2023. URL httpps mmliiinng.m........mmmmmm..m.... httpiissswrrr...ss//11em press/v202/ biderman23a.14 html
David Brandfonbrener, Nikhil Anand, Nikhil Vyas, Eran Malach, and Sham M. Kakade. Loss-to-loss pre- diction: Scaling laws for all datasets. Transactions on Machine Learning Research, 2025. ISSN 2835-8856.
URL httpp:://pperreiieee www.:neeteeeeee net:/forummidd11v44411.
Featured Certification.
Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert- Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Fric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, llya Sutskever, and Dario Amodei. Language models are few-shot learners. In Procoedings of the NcurIPS, 2020. URL http/ttt///pocceednggs heg.rocceedngg...uu........ neurips. htappp//222000/aa///////c6e66660
Hyung Won Chung, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Yunxuan Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, et. al. Scaling instructionn-fietuueed language mod- els. Journal of Machine Learning Research, 25(70): 53, 2024. URL http:://jaarr.orr/ppprres 23-0870 html
Tim Dettmers, Artidoro Pagnoni, Ari Holtzman, and Luke Zettlemoyer. Qlora: Efficient finctuning of quantized 1lms. In Proceedings of the NeurIPS, 2023. URL http::/papers...tttt hatpsecccpppp_fiieee ffles/ html
13

---

Published in Transactions on Machine Learning Research (10/2025)
Bhuwan Dhingra, Manaal Faruqui, Ankur P. Parikh, Ming-Wa Wei Chang, Dipanjan Das, and William W. Cohen. Handling divergent reference texts when evaluating table-to-text generation. In Proceedings of the ACL, pp. 4884 4895, 2019. URL
Ondrej Dusek, Jekaterina Novikova, and Verena Rieser. Findings of the E2E NLG challenge. In Proceedings of the INLG, pp. 322-328, 2018. URL
Alexander R. Fabbri, Chien-Sheng Wu, Wenhao Liu, and Caiming Xiong. Qafacteval: Improved qa-based factual consistency evaluation for summarizaaion. In Procoedings of the NAACI-HILT, pp. 2587-2601, 2022. URL https://doi. http://dooooo////////// /
connected foundation models. In ICLR, 2024. URL mww.-2mmn......m....n.... 187
Elias Frantar, Carlos Riquelme Ruiz, Neil Houlsby, Dan Alistarh, and Utku Evci. Scaling laws for sparsely- htt.://wwwwetoorroooooddd9-/a21.
Samir Yitzhak Gadre, Georgios Smyrnis, Vaishaal Shankar, Suchin Gururangan, Mitchell Wortsman, Rulin Shao, Jean Mercat, Alex Fang, Jeffrey Li, Sedrick Kch, Rui Xin, Marianna Nezhurina, Igor Vasiljevic, Luca Soldaini, Jenia Jitsev, Alex Dimakis, Gabriel Ilbarco, Pang Wei Koh, Shuran Song, Thomas Kollar, and et al. Language models scale reliably with over-vvvinnee training and on downstream tasks. In ICLR, 2025. URL httts::/opennrviieg www.:neetfforree Ad=
Leo Gao, Stella Biderman, Sid Black, Laurence Golding, Travis Hoppe, Charles Foster, Jason Phang. Horace He, Anish Thite, Noa Nabeshima, Shawn Presser, and Connor Leahy. The Pile: An 800gb dataset of diverse text for language modeling. arXiv preprint arXiv:2101 .00027, 2020.
Claire Gardent, Anastasia Shimorina, Shashi Narayan, and Laura Perez- Beltraeetraciii. The webnlg challenge: Generating text from RDF data. In Proccedings of the INLG, pp. 124-133, 2017. URL https://doi. prg/10.18653/v11/
Yinggiang Ge, Wenyue Hua, Kai Mei, Jianchao Ji, Juntao Tan, Shuyuan Xu, Zelong L., and Yongfeng Zhang. Openagi: When LLM moets domain experts. In Proceodings of the NeurIPS, 2023. URL http:///:: nips. httpc//pppeeeeleeepeeeeeeeeeeeee
Albert Gu and Tri Dao. Mamba: Linear-time sequence modeling with selective state spaces. In Proceedings of the COLM, 2024. URL http:///t..aapttto///o/////////a
and Benchmarks......... html
Alexander Hägele, Elie Bakouch, Atli Kosson, Loubna Ben Allal, Leandro von Werra, and Martin Jaggi. Scaling laws and compute-optimal training beyond fixed training durations. CoRR, abs/2405.18832. 2024.
URL http::://doi.orr/11 4ati///rraa55//......... ww...ii..245.... $405.18397
Dan Hendrycks. Introduction to ai safety, ethics, and society. Taylor & Francis, forthcoming. URL www.
aisafetybook. com
Joel Hestness, Sharan Narang, Newsha Ardalani, Gregory F. Diamos, Heewoo Jun, Hassan Kianinejad, Md. Mostofa Ali Patwary, Yang Yang, and Yanqi Zhou. Deep learning scaling is predictable, empirically. CoRR, abs/1712.00409, 2017. URL http:://axxi: wttp///////...///////1///
Jordan Hoffmann, Sebastian Borgeaud, Arthur Mensch, Elena Buchatskaya, Trevor Cai, Eliza Rutherford, Diego de Las Casas, Lisa Anne Hendricks, Johannes Welbl, Aidan Clark, Tom Hennigan, Eric Noland, Katie Millican, George van den Driessche, Bogdan Damoe, Aurclia Guy, Simon Osindero, Karen Simonyan, Erich Elsen, Jack W. Rae, Oriol Vinyals, and Laurent Sifre. Training compute-optimal large language models. CoRR, 22222.115556 2022. URL https:://oo: /tttp:::/doi.org/1.... htt.://orrg/....5///rr/////
2203. 15556
Lei Huang, Weijiang Yu, Weitao Ma, Weihong Zhong, Zhangyin Feng, Haotian Wang, Qianglong Chen, Weihna Peng, Xiaocheng Feng, Bing Qin, and Ting Liu. A survey on hallucination in large language models: Principles, taxonomy, challenges, and open questions. CoRR, //////311005222 2023. URL https: 7/doi. org/ 4855//000.855/////
48550/ att.///..vv..../ 2311.05232
14

---

Published in Transactions on Machine Learning Research (10/2025)
Ziwei Ji, Naycon Lee, Rita Frieske, Tiezheng Yu, Dan Su, Yan Xu, Etsuko Ishii, Yejin Bang, Andrea Madotto, and Pascale Fung. Survey of hallucination in natural language generation. ACM Computing Surveys, 55 (12):248:1 248:38, 2023. URL htttp:://doi.org//// httpg///......./..... 1145/3571730
Juraj Juraska, Panagiotis Karagiannis, Kevin Bowden, and Marilyn A. Walker. A deep ensemble model with slot alignment for sequence-to-sequenne natural language generation. In Proceedings the NATCL-HLT, pp. 152-162, 2018. URL httpp:::/dc...or///////// 1ttp///...16/////11/.1
Juraj Juraska, Kevin Bowden, and Marilyn A. Walker. Viggo: A video game corpus for data-to- text generation in open-domain conversation. In Proceedings of the INLG, pp. 164 172, 2019. URL http://claaaaolllloooog/////////
Jared Kaplan, Sam McCandlish, Tom Henighan, Tom B. Brown, Benjamin Chess, Rewon Child, Scott Gray, Alec Radford, Jeffrey Wu, and Dario Amodei. Scaling laws for neural language models. CoRR, ab8/2000.08361, 2020. URL https:///axxiii https:://axxivoor//aaaaa wttp://a/aaaa..../aa///
Zdenek Kasner, Ekaterina Garanina, Ondrej Plátek, and Ondrej Dusek. Tabgenie: A toolkit for table-to-lext generation. In Proceedings of the ACL, pp.
2023. URL Utt.:rp:///011..gg//0./888////// 1rt../0011..885//1/2/222..
acl-demo. 42.
Philippe Laban, Tobias Schnabel, Paul N. Bennctt, and Marti A. Hcarst. Summac: Ro-visiting nli-basod models for inconsistency detection in summarization. Transactions of the Association for Computational Linguistics, 10:163-177 177, 2022. URL https:://bl..rg/// http///o...rr//...1116/t//aa.aaa 1112/tacc11attcc.c... __ac_____0553
Brian Lester, Rami Al-Rfou, and Noah Constant. The power of scale for parametee--fficiee prompt tun- ing. In Proccedings of the EMNLP, pp. 3045-3059, 2021. URL https:://oi. http://...0rr//001166//////1///0
emnlp-main. 243
Shujie Li, Liang Li, Ruiying Geng, Min Yang, Binhua Li, Guanghu Yuan, Wanwei He, Shao Yuan, Can Ma, Fei Huang, et al. Unifying structured data as graph for data-to-text pre-training. Transactions of the Association for Computational Linguistios, 12:210 228, 2024. ISSN 2307-387X. URL https: 7/direct. mit, wtt.aa//d//.aeee.araa..ppp//////
Wei Li, Wenhao Wu, Moye Chen, Jiachen Liu, Xinyan Xiao, and Hua Wu. Faithfulness in natural language generation: A systematic survey of analysis, evaluation and optimization methods. CoRR, abs/2203.000 2022. URL https: htRLsttps://///
org/ arg/10 10. 48550/arXiv 220. 05227
Xiang Lisa Li and Percy Liang. Prefix-tuning: Optimizing continuous prompts for generation. In Proceedings of the ACL/IJCNLP, pp. 4582 4597, 2021. URL https://ddi.org: 10. 118.1311112222111... acl -ong. 353
Licong Lin, Jingfeng Wu, Sham M. Kakade, Peter L. Bartlett, and Jason D. Lee. Scal- ing laws in linear regression: Compute, parameters, and data. In Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, Ulrich Paquet, Jakub M. Tomezak, and Cheng Zhang (eds.), NeurIPS, 2024a. URL htttp://papers. nips wwps.cc//apet.eeee html
Yupian Lin, Tong Ruan, Jingping Liu, and Haofen Wang. A survey neural data-to-text generation. IEEE Transactions on Knowledge and Data Engineering, 36(4):1431-1449, 2024b. URL https::/doi. org/10.
1109/TKDE.20% 2023 3304385
Yinhan Liu, Myle Out, Naman Goyal, Jingfei Du, Mandar Joshi, Danqi Chen, Omer Levy, Mike Lewis, Luke Zettlemoyer, and Veselin Stoyanov. Roberta: robustly optimized BERT pretraining approach. CoRR, abs/1907.11692, 2019. URL http::///axxi..orr/ab/////0///
Michela Lorandi and Anya Belz. High-quality data-to-text generation for severely under-resoureed languages with out-of-the-bor box large language models. In Proceedings of the EACL Findings, pp. 1451-1461, 2024. URL http:p:://accclaaooooooooo//////
seaddingg-eac..90 eac1.98.
15

---

Published in Transactions on Machine Learning Research (10/2025)
Prasanna Mayilvahanan, Thaddäus Wiedemer, Sayak Mallick, Matthias Bethge, and Wieland Brendel. Llms on the line: Data determines loss-to-loss scaling laws. CoRR, abs/2502.12122) 2025. URL http/tt/t://d.. prg/10.400 1rg/10..8550//r/ 488500/rxa/ii 2502.12120
Linyong Nan, Dragomir R. Radev, Rui Zhang, Amrit Rau, Abhinand Sivaprasad, Chiachun Hsieh, Xian- gru Tang, Aadit Vyas, Neha Verma, Pranav Krishna, Yangxiaokang Liu, Nadia Irwanto, Jessica Pan, Faiaz Rahman, Ahmad Zaidi, Mutethia Mutuma, Yasin Tarabar, Ankit Gupta, Tao Yu, Yi Chern Tan, Xi Victoria Lin, Caiming Xiong, Richard Socher, and Nazneen Fatema Rajani. DART: open-domain structured data record to text generation. In Proceedings of the NAACL-HLT, pp. 432 447, 2021. URL https://doi.org// 10. 11t.11886//122222 100.0/0/0001011116//////202002 naacl -main.31 37
Jekaterina Novikova, Ondrej Dusek, and Verena Rieser. The E2E dataset: New challenges for end-to-end generation. In Proceedings of the SIGDIAL, pp. 201-206 2017. URL httt::://oii.ogg/0.1188888 w17-5525
Teven Le Scao, Angela Fan, Christopher Akiki, Ellie Pavlick, Suzana 1ice, Daniel Hesslow, Roman Castagné, Alexandra Sasha Luccioni, François Yvon, Matthias Gallé, Jonathan Tow, Alexander M. Rush, Stella Biderman, Albert Webson, Pawan Sasanka Ammanamanchi, Thomas Wang, Benoît Sagot, Niklas Muen- nighoff, Albert Villanova del Moral, Olatunji Ruwase, Rachel Bawden, Stas Bekman, Angelina McMillan- Major, Iz Beltagy, Huu Nguyen, Lucile Saulnier, Samson Tan, Pedro Ortiz Suarez, Victor Sanh, Hugo Laurençon, Yacine Jernite, Julien Launay, Margaret Mitchell, Colin Raffel, Aaron Gokaslan, Adi Simhi, Aitor Soroa, Alham Fikri Aji, Amit Alfassy, Anna Rogers, Ariel Kreisberg Nitzav, Canwen Xu, Chenghao Mou, Chris Emezue, Christopher Klamm, Colin Leong, Daniel van Strien, David Ifeoluwa Adelani, and al. BLOOM: A parameerr open-access multilingual language model. CoRR, abs/2211.051000, 2022. URL https: org/10 10. 48550/arXiv 2211.05110011
S Shaphiro and MBJB Wilk, An analysis of variance test for normality. Biometrika, 52(3):5911 611, 1965.
Utkarsh Sharma and Jared Kaplan. Scaling laws from the data manifold dimension. Journal of Machine Learning Research, 23:9:1-966 -9:34, 2022. URL https:// http:///wmmm.ooo/ppprrs///////// atggppapers/23322-1111 htmll
Andrew F Siegel. Practical Business Statistics. 2016.
Saad Obaid ul Islam, Iza Skrjanee, Ondrej Dusek, and Vera Demberg. Tackling hallucinations in neural chart summarization. In Proceedings of the INLG, pp. 414-423, 2023. URL https::///o...... wrw.r...g.......o... 18653330..66111111111
122g.inlg-man 30
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention all you need. In Proceedings of the NeurIPS, pp. 5998 6008, 2017. URL https://proceeddngs seaeeediingnneuiiips. newrips. https//s///apppe///////aaa/////
Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Ev- geni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Breut Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Fric Jones, Robert Kern, Eric Larson, C Carcy, Îlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fun- damental Algorithms for Scientific Computing in Python. Nature Methods, 17:261-272, 2020.
Quang H Vuong. Likelihood ratio tests for model selection and non non-nested hypotheses. Econometrica: journal of the Econometric Socicty, pp. 307-333, 1989.
S Weisberg. Applied Linear Regression. 2005.
Thomas Wolf, Lysandre Debut, Victor Sanh, Julien Chaumond, Clement Delangue, Anthony Moi, Pier- ric Cistac, Tim Rault, Rémi Louf, Morgan Funtowicz, Joe Davison, Sam Shleifer, Patrick von Platen, Clara Ma, Yacine Jernite, Julien Plu, Canwen Xu, Teven Le Scao, Sylvain Gugger, Mariama Drame,
16

---

Published in Transactions on Machine Learning Research (10/2025)
Quentin Lhoest, and Alexander M. Rush. Transformers: State-of-the-art natural language processing. In Proceedings of the EMNLP, pp. 45,45, 2020.
6
An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, Haoran Wei, Huan Lin, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Yang, Jiaxi Yang, Jingren Zhou, Junyang Lin, Kai Dang, Keming Lu, Keqin Bao, Kexin Yang, Le Yu, Mei Li, Mingleng Xue, Pei Zhang, Qin Zhu, Rui Men, Runji Lin, Tianhao Li, Tingyu Xia, Xingzhang Ren, Xuancheng Ren, Yang Fan, Yang Su, Yichang Zhang, Yu Wan, Yugiong Liu, Zeyu Cui, Zhenru Zhang, and Zihan Qiu. Qwen2.5 technical report. CoRR, abs/ Aus/2412.15115, 2024. URL httts:://dde /ttp:////oooooo/.....oo org/10.48550.
2412 15115
Yuheng Zha, Yichi Yang, Ruichen Li, and Zhiting Hu. Alignscore: Evaluating factual consistency with A unified alignment function. In Proceedings of the ACL, pp. 11328 11348, 2023. URL https://doi.org
10. 1...1853/vvv http//11222222 www.:220...111ommo acc-llog..ee 634
Biao Zhang, Zhongtao Liu, Colin Cherry, and Orhan Firat. When scaling meets LLM finetuning: The effect of data, model and finetuning method. In ICLR, 2024. URL http:://ppprrrvvieen.nffoooo net/formm?d-
5HCnKDeTws
Susan Zhang, Stephen Roller, Naman Goyal, Mikel Artetxe, Moya Chen, Shuohui Chen, Christopher Dewan, Mona T. Diab, Xian Li, Xi Victoria Lin, Todor Mihaylov, Myle Ott, Sam Shleifer, Kurt Shuster, Daniel Simig, Punit Singh Koura, Anjali Sridhar, Tianlu Wang, and Luke Zettlemoyer. OPT: open pre-trained transformer language models. CoRR, abs/2205.01068. 2022. URL hattps://dol fttp:::/ddoioor/1000 11tg/00.45550 118500/arXiv. 2205. 01068
Yue Zhang, Yafu Li, Leyang Cui, Deng Cai, Lemao Liu, Tingchen Fu, Xinting Huang, Enbo Zhao, Yu Zhang, Yulong Chen, Longyue Wang, Anh Tuan Luu, Wei Bi, Freda Shi, and Shuming Shi. Siren's 's song in the AI ocean: A survey hallucination in large language models. CoRR, abs/ abss/2309.01299, 2023. URL https://aoi.org 0ttp:////0i..rr/10.4455/5///////
48550/ 2wt.:/485////vv...88 2309901219 01219
Ming Zhong, Yang Liu, Da Yin, Yuning Mao, Yizhu Jiao, Pengfei Liu, Chenguang Zhu, Heng Ji, and Jiawei Han. Towards a unified multi-dimensional evaluator for text generation. In Proccodings of the EMNLP, pp. 2023 2038, 2022. URL https: org/ 18613.11/2113332
eetp::2mmmmmpmmma.mmmmmmmm 131
A Experiment Setup
A.1 D2T Dataset
F2F Novikova et al. 2017 Dusek et al. 2018) is an MR-to-text dataset from the restaurant domain, containing over 37K instances with an average text length of 21 words. ViGGO (Juraska et al., 2018). another MR-to-text dattase,, comprises 7K instances across nine dialogue acts in the video game domain, averaging 14 words per text. Both E2E and ViGGO closed-domain datasets. WikiTableTest (Bao ct al. 2018) is open-domain table-to-texs text dataset with around 13K pairs derived from Wikipedia tables. DART (Nan et al.] 2021) includes nearly 70K knowledge graph triples with an average output length of 34 words. WebNL.G (Gardent et al. 2017) is a graph-to-text dataset focused on RDF-to-text generation, containing approximately 38K samples with an average of 30 words per output. Both DART and WebNLG are open-domain datasets. All datasots are sourced from (Kasner al. 2023 and (Wolf al. 2020). Key
statistics for all datasets shown in Table 6
A.2 LLM Families
We consider six prominent LLM families in our study, spanning three distinct architectural paradigms: dccoder-only, encoder-docoder, and stato-space model. BLOOM (Scao et al. 2022) is docoder-only language model trained on the multilingual ROOT dataset. We include five BLOOM variants in our experiments. FLAN-T5 CChung et al. 2024) is encoder-decoder model family. Unlike decoder-only models, FLANN-55
17

---

Published in Transactions on Machine Learning Research (10/2025)
Dataset
D2T Types
Domain Type
Dataset Size
Source Data
Reference Unique Tokoss
Averaaee length
Unique Tokens
Total Tokens
Average length
Total Tokens
E2E
MR-to-tent
closed
36,856
27.3
125
1M
20.8
4.5K
885K
VIGGo MR-to-text
elosed
6,500
29.9
618
200K
.5
4.4K
148K
WikTTableToxt
Table-to-texi
open
13,318
35.2
29K
169K
13.9
24K
185K
DART
groph-to-text
open
70.324
34.8
44K
2.5M
19.3
45K
1.5M
WoeNLG
graphetto-est
open
38,872
30.4
7K
1.2M
20.1
19K
905K
Table 6: Summary of key statistics, D2T lypes, and domains for the five incorporated datasets. The table presents average length (number of tokens in text), unique tokens, and total tokens for both sources data (lincarized to text) and references.
processes input prompts primarily through its encoder. We incorporate five models of varying sizes from this family. OPT (Zhang et al.) 2022) consists of decoder-only transformer models ranging from 130M to 13B parameters. OPT family are trained on mixture of datasets including Roddit, the Pile Gao et al., 2020), and RoBERTa {Liu al.) 2019) pretraining corpora, following the setup of Brown et al. (2020). We use six OPT models in our experiments. Pythia (Biderman et al., 2023 is collection of eight decoder-only, GPT-style autoregressive models (70M-12B parameters) employing flash attention. All Pythia models are trained on the Pile dataset using a consistent data ordering scheme. In contrast to these attention- models, recent work in NLP has explored state-space models as a scalable alternative for modeling long-range dependencies with linear-time inference. To include this model paradigm, we include Mamba (Gu & Dao 2024), a stato-of-tte stato-of-the-art state-space language model, and evaluate five different model sizes. Qwen2.5 Yang et al. 2024) decoder-only LLM family built on the Transformer architecture (Vaswani et al. 2017 Our experiments use seven models from this family, covering wide range of sizes from 0.5B to 72B parameters. The models are pre-trained on an extensive corpus of 18 trillion tokens and further enhanced through post-training techniques, including supervised fine-tuning on over 1 million examples, resulting in strong language understanding and generation capabilities. Qwen2.5 exhibits advanced reasoning skills (e.g., in mathematics and programming) and robust commonsense knowledge. Given its training on structured data such as tables and JSON, we hypothesize that Qwen2.5 can significantly enhance D2T task performance and provide valuable insights into scaling behavior.
A.3 Fine-tuning and Decoding Strategies
All LLMs are primarily fine-tuned separately on each of the five D2T datascts using two parameter-cfficient fine-tuning strategies: QLoRA (Dettmers et al. 2023) (Quantized Low-Rank Adapter) and Prefix- Trefx-TTnning (Li & Liang 2021). J. In the QLoRA setup, we use a reduced rank (r = 16), applied primarily to the attention and feedforward modules of the LLMs. For Prefix-Tuning we use a virtual prefix of 32 tokens. Prefix-Tuning is widely regarded as one of the most effective soft prompt-tuning methods. Prefix- Prefix-Tuning is applied all considered LLM families except Mamba, due to unstable initialization issues for virtual tokens in the state-space architecture. For both fine-tuning methods, parameters. Full fine-tuning (i.e., updating all trainable parameters) is often regarded essential for accu- rately capturing scaling behavior. For full fine-tuning, we use a learning rate of 5.00e-05. Given the critical role of decoding strategies in D2T, we evaluate both deterministic (greedy decoding) and stochastic (nucleus sampling) approaches to provide a comprehensive analysis. For nucleus sampling, we set the nucleus size to 0.95. Most of the results in this paper are based on text generated through greedy decoding.
fix the learning rate 1.00e-04 for trainable
A.4 Training Setting and Libraries
In all of our experiments, use the SciPy library (Virtanen et al. 2020 to train both scaling models (power law and exponential) on factual inconsistency results. Along with plotting the scaling models, we include the margin of error (MoE) on residual deviation with a 95% confidence interval, as a measure of the uncertainty in fitting these models. We also use the same SciPy library for all hypothesis testing. Vuong's Python. For all fino-tuning and model quantization tasks involving the LLM families, we make extensive use of the transformers library (Wolf al.) (220)) from HuggingFace. Fine-tuning and evaluation are conducted separately on each D2T dataset, using their respective training
likelihodd-ratio test is implemented
18

---

Published in Transactions on Machine Learning Research (10/2025)
and testing splits. All experiments were conducted using single NVIDIA A6000 GPU (48 GB) and single NVIDIA A100 GPU (80 GB). The cumulative computational time across both devices was approximately 22.5 days. Throughout the entire training process, no catastrophic failures or system instabilities were encountered.
A.5 Input Linearisation and Prompt Structure
Input lincarisation and prompt structure are essential components of D2T generation, influencing both language model fine-tuning and inference.
Input Linearisation. Linearisation refers to the process transforming semi-structured input data into sequential format suitable for LLM-based generation. As discussed earlier, we consider three types of D2T tasks: MR-to-text (E2E and ViGGO), table-to-text (WikiTableTTxt)) and graph-to-text (DART and WebNLG). For MR-to-text and table-to-text generation, inputs are linearised sequences of slot-value pairs in the following format:
[(S1otNamel, Value1), (SlotName2, Value2), ValueN)]
(SlotNameN,
For graph-to-text generation, inputs are linearised as lists relational triplets the following format:
[(EntityA1, Relationi, EntityB1), (Entity42, Relation2, EntityB2), (EntityAN, RelationN, EntityBN)]
Prompt Structure. Prompt design plays a crucial role in both supervised fine-tuning (and other post- training methods) and inference for D2T tasks. For our experiments, we use the following unified prompt template for both supervised fine-tuning ZZhng et al. 2022 Yang et al. 2024 and inference:
Instruction: Please generate textual description ('Output') from the provided structured data (' ('Input'). Input: [linearised input data] Output: [reference tent]
19

---

Published in Transactions on Machine Learning Research (10/2025)
B Scaling Behaviour Based on Model Size of Fine- Tuned (QLoRA) LLM Families With Human Evaluation
Although automatic metrics for evaluating factual consistency have improved in recent years, they still fall short compared to human-based evaluations. To strengthen the validity of exponential scaling for modeling factual inconsistency in D2T, we conducted human evaluation involving five university student annotators from diverse academic backgrounds. This voluntary task was performed on outputs generated by four LLM Familie-FLLANTTS, Mamba, OPT, and Qwen2.5. Importantly, this evaluation was limited to QLoRA-fine- tuned versions of these LLM families. Prior to the anmotation process, each annotator participated in & brief training session that included five example instances, along with corresponding source data and reference texts. Factual inconsistency was assessod on Likert scale ranging from 5 (completely inconsistent) to 0 (fully consistent). In addition assigning scores, annotators were required to justify inconsistencies using one or more of the following categories: (1) missing facl, (2) sabricaled fact, and (3) irrelevanl facl. A gold-labeled reference set provided to guide the evaluation process (TTbble 7j. Each annotator independently evaluated 30 generated outputs across five D2T datasets, without consulting others or using external resources. Inter- annotator agreement was high, with Fleiss' kappa coefficient of 0.79, indicating strong reliability.
label (Likert Scale
SONIOOO
reference
genersted text
5, with reasons)
MotorSport Vision located Fowkhum.
(incomslatent:
( (MotorSport Vision', 'eity", 'Fukkhumm)
Fawkhhmn is in the UK.
inreevant fact))
(suubjittle' 'If' tizana"), ). (ssbbjsahritle', 'presidents history"), ('name', 'uuti mari"). ('from-tod (1988-997)
lutfi muri president of lff tiraua during 1998- 99
Junfi muri president of lef
(consistent)
tirana who took office 1998-99
(Csubjtätle" "aachen'), ), ('subjsubrttle' "demographhic"), ("yoar,, 2015"), ) ("popalation', '245,885")
the population of anchen 245,885 in 2015
245,885 people in aachen lived in 2015
(consistent)
(Usubjtitle', 'fe rubin kozan") ('subjoubüitle", "average attendance") ). ('yoar,, "2011"), ("rog- sosson', ; '16,380")
the average attendance fe rubin lazzmin 2011 I 16,380
To rubin keasn got 16,380 attendenees in 2011
1 (slmost consistent:
missing 'uverage')
(('mame', "Clowns)), Typat 'pub'), ("uewr' 'The Sorrento"))
Close The Sorrento you find Clowns pub.
Clowns pub serves food for under (220
(incomsistent:: fabricated fact
and is located near The Sorrento.
Table The five short sample given to each annotators for training before annotation task.
Figure 7 presents the fitted power law and exponential scaling curves, along with 95% confidence intervals (MoE), based on human-annotale annotated assessments of factual inconsistency across varying model sizes (in terms of parameter count). Across all D2T datasets, exponential scaling consistently exhibits lower MoEs than power law scaling, indicating greater stability and confidence undor human evaluation. The corresponding VaCSool results are shown in Table 8) where, in almost all dalasets (except E2E), the LLM families favor exponential scaling. This is evidenced by the blue-highlighted cells denoting strong statistical preference for exponential scaling in Stage III of the Vuong test. While some exceptions are observed in the E2E dataset, even in these cases, exponential scaling achieves lower held-out error in Stage I compared to power law iealing-indicatinng superior predictive performance. Although in two rare cases, where power law scaling outperforms exponential scaling for the DART and WebNLG datasets with FLAN-T5 models, exponential scaling remains competitive in Stages I and II of the VaCScal framework. Except for these rare cases, all other consistent. VaCSoal outcomes further support the suitability of exponential scaling for modeling the relationship between model size and factual inconsistency in D2T generation.
In human evaluations across the FLAN-T5, Mamba, OPT, and Qwen2.5 LLM famálies, expo- nential scaling shows stronger acceptance in capturing the decrease of factual inconsistency with increasing model size, offering more slable and praclically reliable model than power law scaling.
Takeaway.
20

---

Published in Transactions on Machine Learning Research (10/2025)
Expanential scaling
Margin (exponential scaling)
Power scaling
Margin (power law scaling)
DMIT (w/ FLAK TS Farby)
ECE (w/ FLAM-TS Farby)
VIDEO (er FLAN T5 Fanky)
WeaNLG (w/ FLAN TS Famby
WaiThbeeee (v) TLAM Tarb)
0.38
0.40
846
0.00
0.55
0:30
6:30
0.15
6.00
0:100
0:40
646
0.60
6:38
8.42
0.30
0.33
6:30
0.5
142
1.0 1:0 500 2.0
3:42 1:30 100 35t
1:00 106 232 2:00
0.43
1.00
166 333 2:00
1:0
300
Pinmster (B8)m))
Peonster (81l
Peomstur (8il)o0))
Promoin Bang)
Phrseeto Bong
DART (w) OPT Fiesh)
F0e (w) OPT Fundly
Va50 (wr OPT Roeis)
WeAkED (wr DPT Roeks)
Walitaa Tral (o) Fowely)
01:00
0.50
08:00
0.50
0.00
0.53
0.65
0.43
0.30
0.25
0228
0.25
025
10:10 13:00
1.41
11:00
1A1
10:00
Prorstes Boit
Parratee (50 (0l
Paareter
Paramatn (8) Band
Prcamotex Sacis)
Foeily)
Feeey)
Faeb))
Fanis)
0.50
C42
0.32
0:50-
242
0.40
0.55
0.54
2.7L 22.00 48:21
2004 72.70
23.06 43211 DEAS 72.00
23.56 40.21 5544 72.70
7.72 23 40.2 52.4
2.71
23.06 42.21
3646
72.0
Paranstar (28
Proestust (D
(Dlllone)
Faramate (18
Figure 7: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, based on HUMAN evaluation, plotted against model size for QLoRA fine-tuned FLAN- T5, Mamba, OPT, and Qwen2.5 LLM families.
LLM Family
Sculing
DART
E2C
VIGGO
WobNLG
Tiki
Exponential
1.14F-04/v
4.31F-05/
L.5E-03
2.48-038/ A
4.35R+00/V
FLAN-TS
Power Law
L
7.06E-04/K
8.62E-05/ V
5.05E-04,
6.02E-04/v
Exponential
3.28F. 06/V
8.17E. 05,
L.9E. 04/W
2.84F. 04/W
6.68E *
Mamba
Power Law
4.51F+H0,/ X
1.47F-03
2.58E 177
5.66F-01 X
8.87F+13// x
Exponeutial
1 1.25--03 /
4.29E-01/V /V
4.13E-03/v V
2.541--44 /
2.84I-03/v
OPT
Power Law
7.00E+01,18 x
1.26E 00/ *
6.51E x
1,58E+ 10 //D
2.03E-03/ *
Exponeutial
4 4/1
1.26E-04/
4 4-05E+00/4
6.08E-05/ /
7.98E-05/v
Qwen2.5
Power Law
3.88E+00/ V
6.44E 04/
1.03E 04/ *
9.36E x
4.05E-01/K
Table 8: Results from VaCScal corresponding to Figure 7
Numerical values, along with (V/*) and blue/red
highlights, indicate the outcomes of Stages I, II, and III of VaCScal.
21

---

Published in Transactions on Machine Learning Research (10/2025)
C Result: Scaling Behavior Based on Model Size and FLOPs for Fine- Tuned (QLoRA) BLOOM and OPT Families
Here, we present the scaling behavior of fine-tuned (QLoRA) BLOOM and OPT families with respect to factual inconsistency, measured using ALIGNSCORE and QAFACTÉVAL. Figure and Figure 9 illustrate the fitted power law and exponential scaling models for both familles, based on model size and FLOPs, respectively. We find that scaling trends based model size and FLOPs are largely consistent with each other. Similar to the other four LLM families, exponential scaling generally provides a better fit than power law scaling, particularly for the OPT family, as indicated by narrower margins of error (MoE). Although BLOOM exhibits relatively higher MoEs, exponential scaling still consistently achieves lower MoEs compared to power law scaling. Despite the aberrant scaling behavior observed for the E2E and ViGGO datasets (Appendix D the corresponding VaCScal results in Table 9 and Table 10 strongly support the superiority of exponential scaling over power law scaling across all three validation stages.
Exponential scaling
Margin of orror (esponential scaling)
Power law scaling
Mangin of error (power law scaling)
DART (w BLOOM Pariil
EIE (w) BLOOM Pendly)
ViDGO (w) BLOOM Fendly)
Wesht (wy BLOOM Purelyy
Wes Tabll Text (er BLOOM Party)
0:42
0.42
0.40
8:22
0.25
0:38
0.30
5:34
Pronatare Bona)
Taraneu (Slllem))
Panasstrr (BB
Peomann lore
ViD0O
0.50
0:00
0.35
2.43
0.55
0.30
3.3
0.28
0.25
16100
731
DART Owy BLOOM Fanily
CIE BLOOM Funnly)
ViGGo (w) BLOOM Fannly)
WNENLG (w) BLOOM Fartly)
Wart Text SLOOM Fundy)
0:50-
E.24
0.40
8.22
8:25
0.42
2:4
041
612 2.10
1.21
2.09
4.16
7:0
121
268
542
1.10
4.10
Proeectr (B Bore)
Paemern (50lkes))
Poraecter vr)
Pereetoo (Rilkens)
Piramitoo (18ime))
DART (w/ OPT Feeeb))
CX (w/ GPT Fandly
ViGGO (w/ OPT Fardy)
WANNGG (er OPT Kueel!
WalTaal Text dey OPT Fastly
0.53
0.40
0.500
0.3
0.52
0.54
0.50
0.32
042
602
0.20
3443 431 723 10:10 13.00
L41
4.3
7.21 50.00 13.00
3
4.1
1.2 10:00 13.00
144
30.30 13:00 Tarmmoson (5) Bonioo
4.31
7:2
1.1 4:2 7.21 10.10 11:22
Dirnnou (8 (D
Parmens (Sillon))
Paransttrs (BRimn)
Phoomtte (101loe))
Figure 8: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by QAFACTEVAL, plotted against model size across different LLM families.
Takeaway: In D&T, exponential scaling demontrate the factual inconsistency (measured by ALIGNSCORE and QAFACTEVAL) with increasing model size and FLOPs more reliably than power law scaling across BLOOM and OPT families, excepl a few minor exceplion.
22

---

Published in Transactions on Machine Learning Research (10/2025)
family
Sraling
DART
VIGGO
WirThaaeee
BLOOM
Exponcerial
1.80-000
6.802/104
3:300-011
(-50-A0)
AUGISCORE
OFT
Expoueecial
Power Low
2,562.002
1.150000
8.7284511
1.776000
MINE
1.0E-003
REDOM
Repcrnecial
Poweer Law
20/8-80
L400 01,
7.11E-01
8.56E 04
R.1.8-10)
3.26E-01,
4.41--06/ X
QAPACTEEAA
OPT
Reponnectal
Power Lov
2 200E-401
5 2688-00 X
8.51B-02.
L/65E-02/ 21
1-367-10/
5.60E-A0/ P
Table 9: Results from VaCSeal corresponding Figure 8) Numerical values, along with (V/*) and blue/rod
highlights, indicate the outcomes of Stages I, II, and III of VaCSool.
Exponential scaling
Margin error (esponential scaling)
Power scaling
Margin enror (power scaling)
Fank))
Fank))
faeeg)
Taeb)
0.4
320
0.30
0.37
0:1--
924
11.0% 16:96
0311
222 174 6:24
00F 525 000 0:0 617
100
0.51
FLUP (xt0Pl))
FLOT (X30P))
PLOPs (458P))
DART (w/ feesh)
206 (w/ OPT Reedly)
V400 (w/ OPT fanh))
Ve4 (ed OPT Back)
WalTee-Tow (w] hack)
0.42
0-66
0.70
0.64
011
3.35
0.30
0.0
0.20
0:37
014
FLOP Ex (x1)P))
FL07 1=100
FLOP%
DART BLOOM Famky)
SLOOM Fanky)
VIGGO (w) BLOUM Fundly)
WARLD (w/ BLOOK Famnh)
WilTineston (er BLOON Famil)
0.42
2.44
0.41
6.14
014
532
0.2
323
3.0
324
0.27
0.30
0.39
322
7.44 11:55 U60 11:77
031
139
270
376
4.24
0.0
025
0.00 6.12
100
2.3
155
4.1
500
0.00
121
0.20
144
P1.P
Tunil)
Fandlyy
Tamih))
0.13
0.53
0.40
01:00
0.45
0.3
033
350
0.30
0.22
632
044
0.22
0:58
0.16
152 19
17.0 0N 12
332
501
4.66
6.0
6.0
0/0
2.0
01
616
0.0
1.2
242
3.33
0:30
0.00
(x
Figure 9: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by ALIGNSCORE, plotted against FLOPs across different LLM familics.
Metries
LLM Femily
Sealing
DAKI
VIKJU
WeINIGG
BLOOM
Eeponrzzial
Tower
181E-1
1.50E-000
1.36-020
LUSE--G
2808-198
201E-00 *
2.228-002
1.38-00
AuceS
OPT
Expancctial
LABE-
17718-04/1
2.28
BLOOM
Repeorntall
Power Lone
75R-22
6.23--66
1333--11
4.18--1. 30
2888-000
Q QARAE
OPT
Peponerzial
Power Lawe
7,500 -100
851 10/
2000--00 IM
6.37--01 M
1 -0
1.22-100)
Table 10: Results from VaClcal corresponding to Figure Numerical values, along with (</*) and blue/red highlights, indicate the outcomes of Stages I, II, and III of VaCScal.
23

---

Published in Transactions on Machine Learning Research (10/2025)
D Result: Scaling Behavior Based on Model Size of Fine-Tuned Tuned (QLoRA) LLM Families
D.1 Factual Inconsistency Measured via SummaC-conv
Figure 10 presents fitted power law and exponential scaling curves (with 95% confidence intervals) for factual inconsistency measured via SUMMAC-CONY plotted against model size across all six LLM familiess. Although some anomalies appear hypear--paticularrly in the E2E dataset with BLOOM BLOOM-exponentann scaling consistently yields lower MoE and lower held-out loss. Table 11 shows corresponding VaCScal results, where exponential models pass statistical tests more frequently and are preferred by Vuong's test in most settings. These measured
VaCScal results support the robustness of exponential scaling in modeling factual via SUMMAC-CONV with respect to LLM model size across families.
Exponential scaling captures better the decline of factual inconsistency (measured by SUMMAC- CONV) with increasing model size more reliably than power law scaling across L.L.M families, supported by tighter confidence margins and stronger statistical validation from VaCScal.
Takeaway:
LLM Family
Scaling
DART
F2F
VIGGO
WebNLG
WikiTableTet
Exponential
1.79E-04
2.39E-+02
2.45E-04/ X
5.40E-04/* x
2.20E-05
BLOOM
Power Law
2.72F-02
2.98E-02, *
2.11E-04/#
7.8GE-03/
9.19E-03
Exponential
6. 6.46E-04/v
9.07E-06/ *
2.39E-D4/V
2
+013
FLAN-15
Power Law
2.12E-03/ /
1.35E-05/ *
2.43E+01/
2.96E-04/
4.74E-05
Exponential
7 7888--05 V
1.76E-06 *
1.88E 01/ x
L.52E-0//
3.04E-04 V
Mamba
Power Law
8.26E-06/
1.00E-04/ *
LOSE++168 X
L.4E-04/x
5.13E+11 *
Exponential
-2F--04/v
2.85F-01 x
6.21FF04/ *
3.4
O.75F-04/V
OPT
Power Law
3.91E-01 *
8.17E+80/2 x
1.42E-04/ x
6.67E+10/ *
5.98E+04/
Exponential
1 1388-03/ V
1.05E-03V /
8.16E-04/V V
5.51E-03/
4.07E-04/4 V
Pythia
Power Law
5.21E-03/ x
1.25E-02/v /
3.14E-03/# x
L.42E 09/
7.34E-03/ X
Exponential
4 4.96F-04/v
1.15F-04/v
1.21FF03// *
2.12F-04/
2.52F.04/8
Qwen2.5
Power Law
1388-033 /
3.70E-03/ *
3.08E-04/ x
1.57E-02 *
7.73E-03/ x
Table 11: Results from VaCScal corresponding to Figure 10
Numerical values, along with (</x)) and
blue/red highlights, indicate the outcomes of Stages I, I1, and III of VaCSool.
24

---

Published in Transactions on Machine Learning Research (10/2025)
Exponential scaling
Margin of error (exponential scaling)
Power law scaling
Margin of error (power law scaling)
DART (we BLOOM Fasbl
EIE (w) BLOOM Foedl))
ViGGO (w/ BLOOM Fuei))
WNANLE (w) BLOOM Fueely)
Waraaa Text (o) BLOOM Fasee)
0:58
0.33
8.22
0.0
091
2.5
6:48
0.11
244
0.59
0.50
2:43
Fasky)
Fack))
(w/ (wf Fach)
0.40
253
0.04
3.47
2.5
2.40
6.75 977 11:30
120
527
6:55 8TT 11.30
577
837 11.30
1.00
6:55
577 11:30
577 975 13:33
(2Blom)
Panrstux Bond)
(Dillea)
Paanntur (Billon)
DART te/ Membe Tamhy)
EZE (w/ Mambe Tamby)
VIGGO Manbs Panday)
WeRRLG (w/ Mambe Tumnl
VndmaleeTon (w/ Membe Fumb)))
0:51
0:51
0:50
0.000
1422 1.00
1.00 225 2.0
242 1.30
1.00 325 100
2.43
1.30
1.60 122 2.0
0.40
1,00
3 123 2.00
0.40
1.00
3.5
230
2.30
Paraeater (28
Parosttrs (B8
Pronstur (B
Paometin (B Bond)
Paramoon (8 Bond)
DART (w/ OFT Seeib)
CI (w/ GPT Fuedl)
VIGGO (w/ OPT Faedl)
WARLG (e/ OPT Foeeb!
Wal.aale Teat (e) GPT Fueiol
0.54
0.50
0:43
442
0.51
031
0:08
252
0.50
5.31
15.00
1.01 431 721 1506
1441
611 121 1610 13
231
1:21 T21
Promiou (3 Bonae-
Parmen (50 lone)n)
Phrsestes (BRim))
Thrmmon (5) Bonei
DAIT (w/ Pyttes Fandy)
EZE (w/ Pysta foreh)
VIDEU le/ Pytes Pandly
WesMLG (w) Pythis Tamdy)
WisTaaeeTestt (m) Pytte Porth!
3.50
3.0
0.75
0.50
3.30
122
932 12.00
3.28
640 922
1
6,0
2122
105 653
12:00
335
12.00
(Bikae)
Pasentis (B.8.n)
(Raim))
DART (wd Owedd55 Fuedly
(w/ Quaid5 Fandy)
VIGGO [w| Qves25 Faci))
WAnK&G iw/ Ques25 Facily
Will TalleTtt (w] Quee25 Fanil
0.47
0.52
0110-
352
0.41
0.51
Figure 10: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, mcasured by SUMMAC-CONV, plotted against model size across different LLM families.
D.2 Factual Inconsistency Measured via UniEval-fact
F Figure 11 shows the fitted power law and exponential scaling curves with 95% confidence intervals (MoE) for factual inconsistency measured by UNIEVAL-FACT. As with other metrics (ALIGNSCORE, QAFACTEVAL, SUMMAC-CONV), anomalics persist- most notably in the E2E datasct and BLOOM family, which exhibit increasing inconsistency or large MoEs. Despite these outliers, exponential scaling consistently yields sub- stantially lower MoEs across all cases compared to power law scaling, indicating reduced uncertainty in
25

---

Published in Transactions on Machine Learning Research (10/2025)
estimation. The corresponding VaCScal results (Table 12) scaling achieves significantly lower held-out loss in Stage I. In Stages II and III, exponential models also demonstrate greater statistical feasibility (marked with V) and receive more support from Vuong's test (highlighted in blue) than their power law counterparts. Overall, VaCScal results affirm that exponential scaling more effectively captures how factual inconsistency varies with model size in D2T generation under UNIEVAL-PACT.
further support this observation: exponential
Takeaway. Exponential scaling more reliably models the relalionship belween model size of LLMs and factual inconsistency in D2T tasks, measured by UNIEVAL-FACT, outperforming power law scaling despite few dalaset-specife anomalies.
LLM Family
Sealing
DART
E2E
VIGGO
WebNLG
WikiTahleTest
Exponential
3.07E-04/v V
1.39E-04/ *
6.31E-04/ X
4.78E-06/V /V
3.45E-04/V /V
BLOOM
Power Law
3.25E.02/ *
8.95E-03// *
1.49E-04/ X
1.06E-02 x
1.30E-04
Exponential
2.15F.04/v
5.01F-05/1 *
8.94F.04/
1.26F-03/
7.04F-01
PLAN-TS
Power Law
2.64E-04/v
4.26E+00// 00/
1.74E-03/
1.74E-03/
8.80F-05/
Exponential
4. 1.890-05/ V
1.22E-04/# *
1.98E
02/ V
4. 4.13E-05/4 /
2.920-04/
Mamba
Power Law
3.56E | 06/
1.18E-04/K *
4.22E
170
3.91E-04/X x
1.00E-03/
Exponential
1. 13EE-03/v /
8.96E-05 *
2.81E-03/V
5,28E-01
/V
L.33-D1/V
OPT
Power Law
3. 3.08E+02/*
5.89E-02/5 *
6.76E-04//
1.20++87/ *
0.6
Exponential
1.06F-02/v
026E-02/V
7.3/
6.82F-03/1
4.14F-02/v
Pythia
Power Law
1.36F+05/
1.0/F+13/v
2.11R+03/8
4.45F+10
4.23E+00/ x
Exponential
E-51
1.26E-04/W
4.05E F00
6.08E-05/
7.98D-05/
Qweu2.5
Power Law
3.88E
00/
6.4-E-04/x
1.03-00/ *
9.36E-05
4.05E-01/W
Table 12: Results from VaCScal corresponding to Figure 11. Numerical values, along with (</*)) and blue/red highlights, indicate the outcomes of Stages I, II, and III of VaCSoal.
26

---

Published in Transactions on Machine Learning Research (10/2025)
Exponential scaling
Margin of error (exponertial scaling)
Power law scaling
Margin of error (power law scaling)
DART (ey BLOOM Fandyl
EIE (w) BLOOM Fandg))
VIDGO (w) BLOOM funeh)
WNENLG ow BLOOM Famdly)
Toxt SLOOM Fandy)
0.27
8:23
0:34
0:23
220
0.34
8:20
0.51
135
0.05
8.30
277
0.20
2.38
2.00
5.2
6:4
2.09
4.16
2.00
121
5.22
DART (w/ PLAK Fandy)
200 (w) FLAM Packy)
VI000 (e/ PLAK: TS Paniy)
WAAEDD (w/ FLAN TS Faniy))
WaiTTakk/Ted (v) Fl FLAM Fach))
0:55
0.75
0.22
124
0.52
0.10
223
(5 (Bloora
(381km))
(50
DART (e/ Membe Tamky)
EZE (e/ Mambe Tanky)
VIGGO Manbo Peedin)
WeaBLG (w// Membe Furnhy
WidTaleTTon (m] Mente Famb))
0.34
8.53
0:28
0.24
8:06
0.40
142 1.0
1.00 225 200
242 1.30 1 225 100
2.4
1.30
140 122 100
0.40
1,00
186 122 2.00
0.40
1.00
1
220
2.30
Promuter (28cm))
Paonsttrs (B8 pna)
Pronstoo (B()
Prometin (B Bond)
Phrseetn ID Bone)
Faeih)
(w/ Fuedy)
0
0.22
11
0.25
0.12
T21
DART (w/ Pytaa Favdl)
136 (w/ Pyskia Keeeh)
VISGO (e| Pylka Fuedly)
WASMEG (ef Patio Fandy)
WiSTa (m/ Pylte Rooely
6.00
330
0.3
6:30
3.30
032
225 595 1:1 9.0 12.00
322
535
663 932 12.00
1.26
355
6,55
132 32533
1.36
1.5
555
1.2 12.00
1.3
395
113 0.2 12.00
Pacamoun (Di (Dilonn)
Phorstes (B:8ca)
Planstes (B8lzu)
Pararacc (00
Paramatnn (5i Bond)
327
0.31
0.30
0.54
0.59
0330
0.53
0.10
0.27
0.22
0.24
0.22
0:2
0.10
0.00
0:51
0:50
7.21 25.90 48:21
Stu 12.70
7.71
43.21 56 72.70 Plaarettr (BBlcw)
20.6
23.59 40.21 45 T2.TE
7312 23 40.22
59.45 12.32
7.71
23.96 42.21
36465 72.00
(Siliee)
Paurettrr (BiSann)
(Bilkon))
Paranita (BBlced)
Figure 11: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by UNIEVAL-PACT, plotted against model size across different LLM families.
27

---

Published in Transactions on Machine Learning Research (10/2025)
E Resulls: Scaling Behavior Based on Model Size of Fine-Tuned Tuned (QLoRA) LLM Families with Nucleus Sampling
all prior results were based on greedy decoding. However, decoding strategy siguificantly influences the factual inconsistency of LLM outputs. To evaluate the robustness of our find- ings favoring exponential scaling over power law scaling, we conduct additional experiments using mucleus sampling (with a nucleus probability of 0.95) a widely used stochastic decoding method. For this setup, five LLM families (BLOOM, FLAN-T5, Mamba, OPT, and Pythia) are fine-tuned on the five D2T datascts using QLORA, and factual inconsistency is assessed using ALIGNSCORE and QAPACTEVAL.
As discussed in Section 7,
Exponential scaling
Margin of crror (exponertial scaling)
Power law scaling
Margin of crror (power law scaling)
DART BLOOM Faniby
EIE BLOOM Fandly))
ViGGo (w) BLOOM Funely)
WAENLG BLOOM
WaiThale Text SLOOM Fandl)
0,50
8:35
0:50
0.60-
2.55
8:50
8:28
2.45
0.50
0.48
2.9
436 583 7:0
1.21
2.00
435 5:5 1:2
322
237
4.15 163 7:0
1.2
240
435 545 130
322 200 435 555 732
Prorster (1 Bonn)
Parseoon (50kees)
Porautters (m8)
Perreion (iikke))
Plramdton (18
DAIT (w/ TLAN- Fanky)
(w/ FLAN-T5 Famby)
VIGGO (e: FLAN- ranty)
WeaNLG (w/ FLAN-TS Farky)
Waraaatt (w) TL64-T3 Famey)
0:50
0.10
8.7
6.5 11:0
372
837
1.30
372
DART (e/ Monda Favi))
E3E (e/ Marto Fank))
VIGGO (w) Maska Foeey)
DHARLG (wr Moeda Fanily)
WisTabbeion [mc Moeda Facb))
0.00
0:50
0.62
0.40
8.58
8.58
6:55
8.54
1.0
220 280
242
100 228
1.30
1/0
121 2.0
0.40
1.00
1.6
223 2.00
0.40
1.00
230
Posae (Billo))
Paueein boy (Bila))
Pavee (8 (BiBee))
Pavestion (8 (Bikan))
Faeeh)
Fandal
Fanil)
Faeeb)
0.75
0.70
0.50
0.50
0:44
0.5
0.55
01:00
0.55
840
0.45
2.45
0.30
7,21
DAIT (w/ Pybta Tamby)
rysia Tanal)
VIGCO (w/ Pytta Fandly)
WaNNLG Pyblas Tank))
WiiTaakTee (w/ Tyska Fanely
1.00
3.0
0.50
3.0
2.40
-25 236
0,20
12:00
1.26
2.05
663
9.22
12.00
1.55
3.05
820
12.33
1.35
3.00
642
6:22
11.00
100 CC3 0.32 Paecetoon Bolees)
12.00
Pareetom (Bilern)
Prssecters (Bi8oo))
Porender (14imm))
Poraedter (50 (ellee))
Figure 12: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by ALIGNSCORE, plotted against model size across different LLM families. Here we have considered nucleus sampling for text generation.
Figure 12 and Figure 13 show fitted power law and exponential scaling curves (with 95% confidence intervals) for factual inconsistency measured by ALIGNScore and QAFACTEVAL- -nderrddrrrrrr under nucleus sampling (p = 0.95). The trends largely mirror those from greedy decoding: exponential scaling yields consistently lower MoEs, indicating greater stability. Exceptions such as the E2E dataset and the BLOOM family persist, with large uncertainties and irregular patterns. VaCScal results in Table 13 and
Table 14 reaffirm exponential
28

---

Published in Transactions on Machine Learning Research (10/2025)
LLM Family
Scaling
DART
E2E
VIGGO
WebNLG
WilaTableTent
Expoucntial
2.99E-04/
1.43E-03/
L62E-03/
2.60E-04/V
2.03E-03/
BLOOM
Power Law
02
2.82E-04/
3.81E-01/4
2.68E-03/ *
5.65E-01
Exponential
2.59E-04/1 V
5,44E-04
7.12E-03/4
2.59E-04/V
9.13E-05/ V
FLAN-T5
Power Law
2.26E-03/1 V
5,46E-06/ x
2.55E-01/ x
4.34E 08/*
5.38E I 14/V
Exponential
1011-033
5.39F-05
1.39.-03/
4.22F.04/v
1.977-04/
Mamba
Power Taw
0.8 *
1.05FF-33/
6.78E+05/
2.51R+02/
5.08F+03 X
Exponential
9.81E-04/ V
8.72E-01/
3.64E-04/v
2.68E-01/V
3.99E-03/
OPT
Power Law
9.50E 03/ *
1,86 79/ *
2.37E 03/ *
7.56E-03/ *
151E-03/# *
Exponential
5.34E-03//
3.06E-01/
0/
5.82E-03/v
1.26E-03/v
Pythia
Power Law
05
1.97F-02/
2.17E+03/4
8.13E+04/4
1.24
Table 13: Results from VaCScal corresponding to Figure 12. Numerical values, along with (v/*) and blue/red highlights, indicate the outcomes of Stages I, I1, and III of VaCSoal.
scaling as the preferred model across most celaase-mooke combinations. These findings confirm that our conclusions hold under stochastic decoding, consistent with the results obtained using greedy decoding across all our experiments.
Takeaway: Exponential scaling remains the more robust and statistically valid model for capturing factual inconsistency in D2T generation even under stochastic decoding with nucleus sampling further validating the generalizability of our findings across decoding strategies.
LLM Family
Scaling
DART
E2E
VIGGO
WebNLG
WikITable
Exponential
5.01F-03/
7.46F=01
4.92F-03/ *
2376F.03/v
1.49F-03/ x
BLOOM
Power Law
4.35E+00,
5.92E-04/
9.12E-03/ *
2.51E-03/
2.84E
Exponential
2. 2.80-004/
6.21E-05 x
1.377-00// *
3.01E-04// 04/0//
3.11E:03
FLAN-T5
Power Law
5.65E+05 V
1.12E-03/ /
8.98E-02/ *
5.46E-03 *
1881+07 V
Exponential
3.32E-01/
3.82E-05
9.18E+01/
L85E-D4/V
3.01E-01/V
Mamba
Power Law
2.233-03 *
2.81E-06/
7.28E-04/ *
1.74E+01
1.37-004
Exponential
2.83E-03/
L58
2.14E-03/
03/V
1.13E-03/V
2.64E-02/v
OPT
Power Law
2.31E 01
6.34E-01/% x
1.02E +8/
3.28E + 05
1.24E 08/
Exponential
1330-03// /
2.67E-03/V
3.60E-03/v
7.31E-03/v
6.69E-01/v
Pythia
Power Law
4.16E.088/
4.99E+07/v
2.04E+02/x
2.90E-02/
*
4.00E+10/$
Table 14: Results from VaCSoal corresponding to Figure 13
Numerical values, along with (</*) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCScol.
29

---

Published in Transactions on Machine Learning Research (10/2025)
Exponential scaling
Margin error (ecponential scaling)
Power scaling
Margin error (power law staling)
BART BLOOM Parbhl
ESE BLO0M Feedin)
VI50O (w) BLOOM Fereh)
WeeRLD BLOOM Purtin)
Wartible Text BLOOM Fundy)
3.50
8:50
3.58
8:54
0.50
8.
0.45
0.40
5.1 710
1.1
3.9
616
710
171
5,5 110
Pronuttor (8 Bonei-
Tarmpee (56 (ellee)
Pionsters (58
Phomebu (Dilere lont)
DART (w/ TLAN-T Tarby)
CI (w) TLAN-T5 Tarby)
VIGEO (er TLAN-T5 Tanky)
WNBNLG (w/ FLAN-TS Tamb))
WaIThbeTTe (V) TLANTS Tumb))
0.85
2.5
0.40
0.00
8.40-
0.20
335
0.15
0.30
123
B37
13.3
372
837 12.30
1.20
1133
(3Blcm)
Paorstas Bond)
Para (S8ise))
Paarster (B)
Pareratan (06 (orr))
DART te/ Mambe Faxb))
EZE le/ Marbe Famby)
VIGOO (w) Marbo Fanday)
WeaRLG te/ Meebe Furely
WirTaaeTTer (m/ Menbe Farb/
0:50
6.5
0.60
0.40
6.50
0.6
833
Permmtte (BBlma)
Phomuttr ona)
Phrmetter (Billon))
Prossttn Bona)
Pirametton Bone)
DART (w/ DPT foesh)
E36 (w/ OPT Fuedy)
VIGGO (w/ OPT fooil)
WhoKLD (wr) DPT Roebl)
WalTtak Trai (w) DPT Foodly
0.75
0.50
010
0.70
0.85
0.5
0.55
0..00
255
0.500
8:5
0.50
6:28-
0.50
2.45
022
144
1530 33.00
144 30.00
3
16:10
7.21
Prorstus (8 Boal
Patantter (B
Paranoon (B) (and
Prcurater (Bilce))
DART (wy Pytte Fank))
EZE (e/ Pytte Fondly)
VICGO (w/ Pyytas Fendyy)
WNsMLG (v) Pytblc Fast))
WarTandeTier (mc Pyyda Fandin)
Tactes 00030000
350
330
0.50
620
0.00
3.40
5:0
313 12.00
325 12:00
126
325
932 12.00
1
232
1.29 513 Passsaes (80
Rasesann (86 Ran))
Pasceliss (B Ban)
Posentos (BB8a))
Pasanean (R2 km))
Figure 13: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by QAFACTEVAL, plotted against model size across different LLM families. Here we have considered mucleus sampling for text generation.
30

---

Published in Transactions on Machine Learning Research (10/2025)
F Result: Scaling Behavior Based on Model Size of Fine- Tuned (Prefix-Tunin LLM Families
In this section, we report results from experiments where LLM families (BLOOM, FLAN-T5, OPT, and Pythia) were fine-tuned using Prefix-Tuming, to verify the robustness of our conclusions across different fine-tuning strategies. We compare these results against the previously used QLoRA setup. Factual incon- sistency is evaluated using ALIGNSCORF and GAFATEEVAL, as these metries were sufficient to generalize the trends under QLoRA. Note that Prefix-Tuning Tuning was not applied to the Mamba family due to stability issues encountered during fine-tuning.
F.1 Factual Inconsistency Measured via AlignScore and QAFactEval.
Here we present experimental results using Tuning as an alternative fine-tuning strategy to the pre- viously employed QLoRA. This comparison aims to assess the robustness of our findings across different fine-tuning approaches. We evaluate factual inconsistency using two representative automatic metrics ALIGNSCORE and QAFACTEVAL- have consistently captured key trends and are sufficient to support our conclusions. Note that the Mamba family was excluded from this setup due to instability encountered during Prefix-Tuning.
Expanential staling
Margin (esponential szaling) ViCGO (w) BLOOM Fardhy)
Power scaling
Mangin (power law scaling)
DART (e BLOOM Parehl
EI bw BLOOM Pandly)
WNeNLG (w BLOOM Fardly
Wa Text (N! BLOOM Party)
0.70
0.55
0.50
0:50
0.50
8:2
0.90
0
1:32
2.00
0.40
7:0
1.21
Berm)
DART (w/ Fasi))
E05 (w/ FLAM Fank))
VAGO FLAK To
WNBRLG (w/ FLAN
WalTTse Fext (w/ FLAM TE Fasi))
0.00
0.00
0.70
0.0
1.6
0.50
0.0
133
130
6:10
1.20
0.20
0.00
1.30
372
6.25 877 11.00
122 372 625 877 11:0
L30 372
4.5 837 11.00
1.20
372
625
877 11:00
128 372 425 L.7 1133
Resedden (Rilm]]
Peoreins (R.ke))
Paxeston (R2im)
Reaectos (R.ken)
Paverion, (Roke))
DART (w/ OPT faesl))
CC dw/ OPT Fandy)
VIGGO (w/ OPT Fanily
WoaNLG (wr) OPT Fueeb)
WalTaal Text (w) OPT Fanily
0.75
0.70
0.40
0.50
0.50
0.25
0.7
8:5
0.55
3.03
6:0
0.35
0.50
2.45
2.43
4.1
10:00 13.00
L41
4:33 7.21 13.00
3
431
10:0
141
7:2
1.1
7.21
Parmato (50 (Slller))
Phraneter (8film)
Tesmesu (51 Bonn)))
Prromster (Bilkem)
Tamky)
Pysta Tareh))
Fandly)
Pyblas
WhiTaasTes Tyska
0.95
0.90
0.50
0.55
6700
3.00
040
370
3.00
0.50
0.50
0.2 15:00
122
9.22
120
12.23
1.05
3/6 0.22
12.00
(Bilonno
Pacanatonn (DiGeeo
Figure 14: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by ALIGNSCORE, plotted against model size across different LLM families. Here we consider Tannx--Tuinng for fine-tuning all LLM families.
Figure 14 and Figure 15 present the fitted power law and exponential scaling curves with 95% confidence intervals (MoE) for factual inconsistency, measured using ALIGNSCORE and QAFACTEVAL, plotted against model size (in terms of parameter count). For ALIGNSCORE, both the FLAN-T5 and Pythia families exhibit
31

---

Published in Transactions on Machine Learning Research (10/2025)
LLM Family
Scaling
DART
E2E
VIGGO
WebNLG
WinTTable
Exponential
2.14E-04/v
1.16E-02/4
4.73E 00/0
2.78E-05/V
3,00E 03/V
BLOOM
Power Law
1.31E+05/
6.16E-03/
3.25E-03/
108E-033/ *
+
Exponential
1.09E-02 *
3.01E-02/ x
5.14E-03/ *
3. 3.88E-02/ *
3.08E-03/
FLAN-T5
Power Law
1.49E-01/ *
8,41E-02/ *
6,03E-04/ 98
8.07E-03/ *
8,31E-04/ *
Exponential
7.88E-04/
4.38E-03/
5.62E-03/ X
3. 3.40E-03//
6.92E-01/
OPT
Power Law
1.75F++09/
4.30B-56/v /
1.92F++01/
02//
1377+003
Exponeutial
2. 2.49E-02// *
1882E-02/
6.60E-02/ *
8.25E-03/ *
2.65E-03/V
Pythia
Power Law
4.80E-02/1 *
2.07E-02
1.84E-02/ *
2.04E-022/ *
9-41--2/VV
Table 15: Results from VaCScal corresponding to Figure 14.
Numerical values, along with (V/*) and
blue/red highlights, indicate the outcomes of Stages I, II, and ITT of VaCSool.
unusually large MoEs under both scaling models; similarly, for QAFACTEVAL, the Pythia family shows high uncertainty. We hypothesize that this arises from the uniform addition of 32 virtual tokens during Prefix-Tuning across all models within family. This fixed augmentation likely benefits smaller models disproportionatell,, while offering diminishing returns for larger ones, thereby limiting their improvement in factual consistency. Despite these anomalies, exponential scaling generally results in tighter MoEs than power law scaling, indicating more stable and confident. fits. The corresponding VaCSoal results, shown in Table 15) and Table 16 reveal that although many model-dataset combinations fail fcasibility in Stage II, exponential scaling consistently achieves lower held-out loss (Stage I) compared to power law scaling. Moreover, in all feasible cases, exponential scaling outperforms power law scaling in capturing the relationship between factual inconsistency and model size.
Takeaway. Exponential scaling remains more stable and accurate than power law scaling in modeling fac- tual inconsistency under Penfin-Tunnng, despite some anomalies caused by uniformly applied virtual tokens especially in smaller models like FLAN-TT T5 and Pythia. Even when feasibility is limited, exponentiol scoling consistently yields lower held-out loss and better fits in all valid cases.
LLM Family
Sealing
DART
E2E
VIGGO
WeeNLG
WikiTableText
Exponential
2. 2.99E-04/ /
1.171/-02/ *
1.01E-03/
9.22E-04/V
3.07E-03
BLOOM
Power Law
6.86E-01/1 x
8.30E-02/ x
1.05E-03/4 /
2.33E-01/8 *
7.28E-02/ V
Exponcutial
1.13E 00 *
1.77E-02,
2.36E-04 x
1.42E-05 V
7.38E-04/V /
FLAN-T5
Power Law
9.30E 95, *
1.52E-01,
1.11E-02/ *
1.55E (02
7.74E-D4
Exponential
7.88E-01/V V
4.38E-03/V
G.62E-03/ x
3.
3.40E-0//
6.92E-01/
OPT
Power Law
1.75E+09, *
4.30B+56/v
+01 x
1.82E+02/ 02/V
1.77+03/
Exponential
1.51E-02 x
2 2.06E-02/* x
9.79E-05/ *
2.04E-02/* *
2.93E-03/2
Pythia
Power Law
1.46F+51
3.66F-02 x
4.51F+07/ *
1800-02/K
109F+550
Numerical values, along with (V/*) and blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCScal.
Table 16: Results from VaCScal corresponding to Figure 15.
32

---

Published in Transactions on Machine Learning Research (10/2025)
Exponential scaling
Margin of crror (exponential scaling)
Power law scaling
Mangin of crror (power law scaling)
DART BLOON Fanky
E2E SLOOM Fanky)
(w: BLOOM Fandly)
WABLLG ELOON Fambyy
Win TeltTatseer (m/ CLOOM Fanb))
0.50
0.66
0.00
0.70
6.5
020
0.50
Fark))
Fack))
250
0.50
0.50
260
135
0.50
0.40
0.00
0.30
0.00
210
0.00
1.30
6.25
8.7
625
13:00
130
372
1.7 11.00
1.20
6.5
8.7
3/2
11:3
Parmsttr
DMRT
V8500
WeeNED OPT
0.75
0.70
0:5
0:35
0.50
2.03
370
0.53
670
6:15
0.7
0.30
0.40
01:00
0.50
0.35
0.0
0.0
10:10 11:00
L40
1A1
10:00
23: 20.00
7.11 1010
Fanky)
Pyska fareh)
Fandly
Pytlis
Pydla
1.10
1.25
1.00
01:00
0.30
0.00
3.20
0.57
0.05
0.70
3.00
0.50
0.55
610
0.5
0.2
696
12
(Bikae)
Figure 15: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, mcasured by QAFACTEVAL, plotted against model size across different LLM familics. Here we consider Prefix-Tuning for fine-tuning all LLM families.
33

---

Published in Transactions on Machine Learning Research (10/2025)
G
Result: Scaling Behavior Based on Fine-tune Data Size
Data size is a fundamental factor in understanding scaling behavior. To investigate its effect on factual inconsisteney in D2T tasks with LLMs, we analyze how varying the amount of fine-tuning data influences factual inconsistency outcomes. Here, "fine-tuning data" refers to different proportions of the original training set speesficcllllly 10%, 20%, 40%, 60%, and 100% used during fine-tuning with the QLoRA technique. This experiment is conducted on three representative D2T datascts: DART (graph-to-text), E2E (MR- to-text), and WikiTabbeText (lable-to-text), with factual inconsistency measured using ALIGNSCORE and QAFACTEVAL. We use the largest variants from each of the five incorporated LLM families (BLOOM, FLAN-T5, Mamba, OPT, and Pythia). Fiiure 16 and Figure 17 show the fitted power law and exponential scaling curves along with 95% confidence intervals (MoE), derived from residual-based estimation. Across both metrics and all model families, the F2E dataset consistently exhibits aberrant behavior behavior characterized by wide confidence bands and unstable scaling patterns likely due to its inherent characteristics, which we discuss in more detail in Appendix | DART also shows elevated MoEs, especially under ALIGNSCORE, whereas WikiTableText demonstrates relatively stable scaling behavior, with low Možs under both models. The corresponding VaCScal rosults, presented in Table 17 and Table 18] support these observations. For the E2E dataset, neither scaling model yields feasible fitss, indicaling unreliable scaling behavior. However, DART (particularly under QAFACTEVAL) and WikiTableText show stronger support for exponential scaling, A few exceptions persist for instance, the FLANN-55 model on Wiki'Table Text favors power law scaling, as indicated by a red-marked cell. In summary, while fine-tuning data size does not lead to universally consistent scaling across all settings, the results broadly support exponential ial scaling as the more robust and reliable model for capturing the relationship between factual inconsistency and data size across LLMs.
Takeaway. Faponential scaling generally serves a more robust and reliable model than power law scaling for predicting how factual inconsistency in D2T tasks decreases with increasing fine-tuning data size, despite some datasets (e.g., E2E) exhibiting aberrant or unstable behavior.
Exponential staling
Margin (esponential scaling)
Power scaling
Margin (power law scaling)
DART Iw/ BLOOM Fardly)
DART der FLAN T5 Faedyl
DART Dw) Marka Funeb)
DART (w] OFT Fani))
DART (w/ Pydkk Faneby
DAT
2.5
0.60-
6:20
0.46
0.05
042
0.25
3.30
0.45
3.63
100
0.10
0.40 1.00
0.10
Pasotam Data Six (50
Tineoure Deta Ste (h)
Fieetoss Date 3 (5)
Thneouee Oeta Stee (%)
Piesuces Unn Soe 1%3
(w/ BLOOM Fannly)
(w/ FLAN-T3 Pardly)
(w) Mambe Famil))
EZE (v) OFF Fandy)
EZE (N/ rysta Fueeh)
0.20
0.43
0.27
8:25
0:37
335
8.24
0:20
(1))
Deta
Sin (%)
176
WilTabeTes (v/ BL00M
WWaTaaeTar RuM TE Fave)))
WarfiaiTee (e/ Marka
WolTlaaTTe OPT Feeel))
Wdu TolTTaoToutt Pyrla
0140-
0.70
0.50
0.5
0.55
0.50
0'90
0.90
0.45
0.55
0.45
0.40
0.90
0:00
1:0
0.90
0:30
100
010
0.39
0.00
0:00
0.10 5.15
1000
1.00 011
5:38
0.00
Flae-tre Data Siz
Tlaetane Stm
(7))
Sam (7))
Figure 16: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by ALIGNSCORE, plotted against fine-tune data size across three datasets Gatasets-DARTT E2E and WikiTableText.
34

---

Published in Transactions on Machine Learning Research (10/2025)
Dataset
Scaling
BLOOM
FLAN-T5
Mamba
OPT
Pythia
Exponcntial
4.17E 00
2.00E-04/X *
1,20E 02/V
2.95E-04/ *
1.39E-03/ *
DART
Power Law
7.72E+144/
1.24E-04/ X
0.9 x
3.16E.00/ x
4.60E-03/ x
Exponential
1.20E-04//
5.14E-006/
4. 4.61E-05// *
6.41E+001
1.56E5033/
E2E
Power Law
1.48E-+00%
2.49E-05/
6.86E-04/
4.24E-02/4
2.25E-03/
Expoucutial
7,02B-04/* *
1.35E-03/
1.64E-03/ V
1.32E-04/ *
1. 1800-04// /
WikiTableeext
Power Law
1. 1.89E-01/x
*
8.59E-05/ /
6.68E 00/ x
4.95E-03/ *
3. 1,100-22/ x
Table 17: Results from VaCScal corresponding to Figure 16. Numerical values, along with (</*) and
blue/red highlights, indicate the outcomes of Stages I, II, and III of VaCSoll.
Exponential scaling
Margin error (exponential scaling)
Power scaling
Margin crror (power law scaling)
BARl (w/ RLOOM Furely
DART (wf FLaN TO Fueey)
DART (w) Marku Rewb))
DART (m] OPT Fenk))
BART (e/ Pylks Foeel)
0:51
0:78-
0,42
0.55
225
4.45
0.40
8:44
6:24
0.5
0.51
0.33
0.42
0.10
3.00
0.00
1.30
332
0.3
0.50 630 1.00
0.10
0.3
E40
183 1.0
233 3.31 0.00 0.30 1.00
0.59
0.30
0.0
280
200
Tate See
Fir Data Ste (%)
Fax lear Tate Sie (8)
Tate Six (%)
Fax
See [h)
ba/ BLOOM Famil))
E2E FLAN-TS Fartly)
(w/ Marbo Famib)
EZE (u/ OPT Fanky)
Pysta Faeel)
8:28
0.20
0.32
834
0.22
0.27
0.32
0.2
0.35
634
634
0.5
622
0.24
0.10
833
0.3
1.00
332
0.39
020
3.00
0.19
122
1.30
532
0.00
0.00
1.00
0.59
0.00
8.2
Dat 3TN
Drta Stn
Data 3
Wil.Tse BLOOM WhuTaleTat FLNN TE
Whitide Teal (e/ Marku
WOUTL OPT
USu Pyrla
0.53
0.54
0.50
0.55
0.50
0.50
0.400
0.50
0.42
112 333 0:00 1.00
0:15
0.90 0:00 1:0
010
0:39
0.0 0.0
0.15 135 3.00
0.15
0:35
383
0.00 1.00
Tiaetrr Data Sia
Tiaetane Ste
(21)
Sax (5)
Fintams Data Six
Figure 17: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency, measured by QAFACTEVAL, plotted against fine-tune data size across three datasets DART, E2E and WikiTableeText.
Dataset
Scaling
BLOOM
FLAN-T5
Momba
OPT
Pythia
Exponential
5.83F-04 x
1.53F-05/ V
7.41E+01 /V
6.25F
1.52F++01
DART
Power Law
1.74E+1147 *
2.87E-03/ *
6.66E 163/*
5.70E-04 *
1.23E-02 *
Exponential
3.40F-05/
3.38E+00/
9.86E+00/4 *
1.54E+01/ /
5.85E-04/ *
F2F
Power Law
2.00F++04/
3.47F-05/ *
4.59F+05/8 *
4.32F.04/ *
6.65F-03/ *
Exponential
3.72E-04/
4.82E-04/V
2.220-03/V V
4.03B-04// x
6.34E-04/V
Tok
Power Law
8.04E-04/*
3.13E-01/v
2.13E-04/* *
6.11E-02/ *
1.41E-02/K *
Table 18: Results from VaCl corresponding to
Figure 17
Numerical values, along with (</*)) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCSoal.
35

---

Published in Transactions on Machine Learning Research (10/2025)
H Scaling Experiments with Full Fine-tuning
Unlike parameter-effiient fine-tuning methods such as QLoRA and prefix-tuning, full fine-tuning updates all model parameters, offering greater flexibility at the cost of substantially higher computational demands. Due to resource constraints, we perform full fine-tuning experiments on four LLM families FLAN-T3, Mamba, Pythia, and Qwen2.5--cros lamily, we consider only five models ranging from 0.5B to 14B parameters, as full fine-tuning of Qwen2.5-328 and Qwen2. 5-72B exceeds our computational resource limits. We investigate scaling behavior with respect to both model size and computational budget (measured in FLOPs). For all outputs generated in these full fine-tuning experiments, we employ greedy decoding.
three D2T datasets: DART, E2E, and WikiTableText. Within the Qwen2.5
Exponential scaling
Margin error (esponential scaling)
Power scaling
Margin error (power law scaling)
FLAN Family)
DART (w/ Mamba Famils)
DART (w/ Family)
DART (w/ Qwen2.5 Family
Factual Incosinessyy w/ A3iovScco
0.55
0.58
0.50
0.50
0.40
0.56
0.56
0.45
0.52
0.20
0.35
0.50
0.48
0.60
0.34
0.35
0.45
0.50
0.44
0.42
0.40
0.30
0.40
0.30
1.20
2.20
1.91
Paramcters (Biliion)
Paramctess (Bilions)
Paramotirr (Bilians)
Paranctes (Billios)
ESE (w/ FLAN- T5 Familyy
E2E (w/ Mamnhs Family)
E2E (w/ Pythis Family)
E2E (w/ Qwee2. 5 Family)
Faciual Incondaiiing w/ Au0orocmms Factual Irom Slancy w/ Aucon Scott
0.27
024
0.50
0.10
0.26
0.80
0.70
0.2
0.25
0.60
0.30
0.24
0.23
0.30
0.40
0:30
020
0.10
0.15
0.29
0.20
0.10
0.17
0.00
220
125
Parsmbeer (Billone
Parameten (Billions
Parammtere (Billone) -
Porameters (Billion)) -+
WitTabkTeet (w/ FLAN-TS Famil)
Wik WWw.eakeeett.cc (w/ Mamba Family)
WilTTbbcTest (w/ Pythia Family)
WikTableTest (w/ Qwen2.5 Family)
0:40
0.40
0.44
0.38
0.50
0.54
0.32
0.50
0.75
0.45
0.70
0.60
0.40
0.60
3.55
D44
0.60
0.40
0.45
0.40
0.45
0.40
0.48
0.35
0.34
0.50
0.32
0.48
0.25
1.20
3.72
6:2
B.7
11.30
0.40
1.00
1.60
2:20
2:00
1.25
3.00
5,55
9.32
$2.00
1.91
5:11
8.5L
11.30 (Bilione)
14.10
(Billoon)
(Biloons
(fillione)
Figure 18: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, measured by ALIGNSCORE, plotted against model size across full fine-tuned FLAN- T5, Mamba, Pythia and Qwen2.5 LLM families.
H.1 Scaling Behavior Based on Model Size of Full Fine- Tuned LLM Families
The scaling results based on all four automatic
ALIGNSCORE, QAFACTEVAL, SUMMAC-CONV, and UNIEVAL-PACT-ADE across four LLM families (FLAN-T5, MAMBA, PYTHIA, and QWEN2.5) are shown in Figure 18 Figure 19. Figure 20] and Figure 21 These results (especially in DART and Tiki)ableText) consistently demonstrate that exponential scaling outperforms power law scaling when model size is used the scaling factor, as evidenced by its lower margin of error (MoF.), indicating more stable and reliable fits to factual inconsistency trends in D2T tasks. This superiority is further substantiated by the outputs of the VaCScal framework (Table 19 Table 20 [Table 21 and Table 22), which consistently favor exponential scaling over power law scaling across all metrics. Similar to our findings with QLoRA, exponential scaling under full fine-tuning also exhibits strong support in Stage IIT of VaCScal (highlighted in blue), suggesting better empirical consistency. Compared to trnii,,tunin, full fine-tuning shows greater alignment with
36

---

Published in Transactions on Machine Learning Research (10/2025)
exponential scaling. Although full fine-tuning yields fewer accepted fits in Stages II and III of VaCScal compared to QIoRA-exponeen exponential scaling still achieves significantly lower predictive error (Stage T) than power law scaling, reaffirming its superior predictive performance.
Dataset
Scaling
FLAN-T5
Mamba
Pythia
Qwen2.5
Exponential
3.63E-08/ x
4.08E+01//
2.28E-02/ x
4.44E-04/ /
DART
Power Law
3.61E+11/ x
2.25E-04/v
3.08E+02/ x
1.46E+17/v /V
Exponential
6.22E-04/ x
2.28E+011/5 x
6.29E-04/e /
1.46E-05/ /
E2E
Power Law
1.2612-03/# x
2.94E-04/ x
3.64E++05/ x
1.30E-05// /
Exponential
1.22E-+00/ /
2.61 x
6.12E-03/ /
9.80F=06/ x
WikiTableText
Power Law
1.21 x
5.18E *
8.45E++09// x
2.43E.4-22/4
Table 19: Results from VaCScal corresponding to Figure 18
along with (V/x) and blue/red highlights,
indicate the outcomes of Stages I, II, and III of VaCScol.
Takeaway. In the full fine-tuning setting, across all four state-of-the-art automatic metrics and LLM families (FLAN-T5, T5, Mamba, Pythia, and Qwen2.5), erponential scaling consistently demonstrates better agreement with how factual inconsistency decreases with model size, offering a more stable and practically reliable scaling model than power law scaling.
Exponential scaling
Margin of errar (exponential scaling)
Power law scaling
Margin of error (power law scaling)
DART (w/ FLAN-TS Family
DART (w/ Mamba Fanily)
DART (w/ Pythia Family)
DART (w/ Quen2 5 Famiy)
Festral Inansstunn QAPATTEOAL Factual Incosktancy w/ QAFACTENAL Factall Inconsieen QABume
0.60
1.10
0.55
1:00
0:35
0.58
0.80
0.35
0.54
0.00
0.50
0:50
0.48
0.40
0.30
0:30
1.20
3.72
6.25
8.77 11.30
0:40
1.00
1.60
2.20 2:30
1.25
5.05
5.63
0.32
12.00
1.01
5.11
5.51
11.50 14./0
(fillion)
(Billons)
(Billion))
(Billoon)
EZE (w/ FLAN-TS Family)
EZE (w/ Mamba Family)
EZE (w/ Pythia Family)
EZE (w/ Owes2.5 Family)
0.15
1:00
0.14
0.19
0.60
0.14
0:17
0.12
0:15
0.20
0.14
0:13
0.00
0.15
0.15
1.20
372
6.75
8.77 11:30
1.00
1.60
2:30
2.80
1.5
3.05
661
9.37 12.00
1.91 5.11
8.31
14.70
Parsmaters (Bilions)
Parametan (Bilions)
Paramater (Billoms) -
Paramatera (Billion)) -+
(w/ TS Famil)
(w) Fanily)
Pythia Fanil))
(w/ Qwend.5 Family)
0.44
0:40
0.52
0.43
0.44
0.50
0.43
0.42
0.40
0.46
0.44
0:42
0.37
0.40
1.20
6.5
1,00
2.20 2.90
9.32
191
8.3 Parameter (Bilions) -*
Parametera (Billiom) -+
Parametera (Bilions)
-+
Parametera (Billios)
Figure 19: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, measured by QAFACTEVAL, plotted against model size across full fine-tuned FLAN- T5, Mamba, Pythia and Qwen2.5 LLM families.
37

---

Published in Transactions on Machine Learning Research (10/2025)
Dataset
Scaling
FLAN-T5
Mamba
Pythia
Qwen2.5
Exponential
1.12E-03/ *
1.05E-03/
2.02E-02 *
5.48E-04/
DART
Power Law
7.57E++19/ x
1.48E-03/ *
2.71E-02/ x
3.05E-04/ /
Exponential
1.60F-05// x
6.69F-03/
3.63F-04/v V
1.38FF005/
F2E
Power Law
3.76F--01/ x
3.23F2+26 *
1.55E-02/ x
2.19F-01/ x
Exponential
9.30E-04/
(.43E-04/ V
2.46E-02/
1.51E+01 /V
WikiTTalleText
Power Law
1.68E-03/2
x
9.86E-06/ x
5.40E+09/ x
3.13E-05/ /V
Table 20: Results from VaCScal corresponding to Figure 19
Numerical values, along with (</x) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCScal.
Expomential staling
Margin of erior (eeponential scaling)
Powver law scaling
Margin of error (power law scaling)
DART FLAN Family)
DART (w/ Mambaa Family)
DART (w/ Family)
DART (w/ Qwen2.5 Famil)
Factual Incondating Wy S.unuaC.ssee Factual Inarsaterny w/ Suamic - Factual haresteng StowrrC..com
0.68
0.
0.55
0.87
0.80
0.00
0.54
0.25
0.52
0.55
0.52
0.70
0.51
0.53
0.00
0.50
0.48
0.58
0:55
0:48
0.56
0.50
Parameters (Billins)
Parameters (Bilions)
Paramatora (Bilions)
Paranctes (Billors)
E2E (w/ FLAN-TS Family)
E2E (w/ Mamba Family)
E2E (w/ Pythia Family)
E2E (w/ Qwes2. 5 Fanily)
0.41
0.41
0.46
0.46
0.80
0.45
0.43
0.45
0.41
0.45
0.60
0.50
0.40
0.43
0.45
0.30
1.30
3.2
6.25 8.77 11:30
0:40
1.00
1.60
2:20
2:80
125
5.5
585
9.32
12.00
1.91
5.11
5.51
11.50 14./0
(filloon)
(Rilloos)
(filloon)
(Rillion)
WiiT (w/ FLAN-TS Family
WWTT (w/ Mamba Family)
WilITatieTest Pythia Family)
WilTTateeTsst (w/ Qwer2.5 Family)
0.60
0.50
0.58
0.54
0.60
0.50
0.75
0.70
0.51
0.52
0.5
0.5
0.37
0.50
0.55
05:
0.38
2.50
0.50
0.45
0.46
0.54
0.40
1.30
3.72
625
8.77
11.30
0.40
1.00
1.60
2.20
2.00
125
3.05
6.63
9.32 12.00
1901
5.11
831
11.50
1470
Paramoters (Biliiom) -+
Paramotera (B lioona) +
Paramotera (Bilions)
Parameters (Bilions)
Figure 20: Filted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, measured by SUMMAC-CONV, plotted against model size across full fine-tuned FLAN- T5, Mamba, Pythia and Qwen2.5 LLM families.
Dataset
Scaling
FLAN-T5
Mamba
Pythia
Qwen2.5
Exponential
1. 1.19F-03// /
6.45E-04/* x
5.15E-03/ x
1.18E+02, /V
DART
Power Law
1.23F-03// x
4.38E-04/ x
1.38F+000 *
6.58E-05/ /
Exponential
2.03E-05/ x
3.17E+011
1.08F-03// /
2.07E-04/
E2E
Power Law
2.76F-06/ x
5.18E-01/ x
9.26E.+01 x
8.35E-03// x
Exponential
3.79E-05// /
1.34E-03/ V
3.26E-03/ /
01/V
WikiTableText
Power Law
1.26E-02/ *
8.00E 14/ x
6.00E x
1.0EE04// x
Table 21: Results from VaCScal corresponding to Figure 20,
Numerical values, along with (</x) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCScal.
38

---

Published in Transactions on Machine Learning Research (10/2025)
Expanential
Mangin (eeponential scaling)
Power scaling
Mangin (power law scaling)
DART FLAN Famil))
(w/ Mamba Famils)
DART (w/ Family)
(w/ Qwen2.5 Famiy)
Fattial Inorssians w/ USbSaL- SXRT Inconsasercy wt UnIEVLL--OO Incosiesrnyy W/ USIENALEAATT
0.50
0.50
1:00
0.50
0.34
0.48
0.70
0:42
0.30
0.40
0.50
0.25
0.38
0.25
0.36
0.30
0.20
11.30
2.20
1.25
1.81
8.1 Parameter (Billoos)
Parameters (Bilions)
Parameters (Bilions)
Parametora (Bilionm)
FLAN Family)
EZE (w/ Mamba Family)
E2E
Family)
(w/ Owee2.5 Family)
0.31
0.70
0.80
0:31
0:32
0.60
0.30
0:30
0.40
0.30
0.30
0.20
Parameters (Bilions)
Parametars (Bilions)
Parameters (Biliom)
Paramaters (Billion)
WeaT (w/ FLAN-TS Family)
That (w/ Mamba Family)
WiiTaatieTest (w/ Pythi Family)
WibTTatinTest (w/ Quen2.5 Family)
0.80
DS3
0.58
0:53
0.50
0.70
0.52
0.58
0.56
0.36
0.50
0.34
0.32
0.48
0.46
0.50
0.30
0.52
0.50
0.51
0.:
1.50
372
625
8.77
11.30
0.40
1.00
1.60
2.20
2:00
1.25
3.05
6.63
9.32
12.00
1.91
5:11
8.1
11.50
34.70
Paremctass (Biliona)
Paramcter (Bliima)
Paramdion (Bilions)
Paramciors (Biliers)
Figure 21: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, measured by UNIEVAL-FACT, plotted against model size across full fine-tuned FLAN- T5, Mamba, Pythia and Qwen2.5 LLM families.
Dataset
Scaling
FLAN-T5
Mamba
Pythia
Qwen2.5
Exponential
1.17E-03/ /
2.49E=01/
6.10E-02/
2.45E 04/v
DART
Power Law
2.40E+199 19/ x
3.64E-03// V
4.99E+889 x
2.03E-04/e V
Exponential
1.43E-04/
9.19E-05/ x
1.79E-03/ /
1.06E-05 05/4
E2E
Power Law
1.02E-03// x
1.36E-03/ x
5.24E 136 x
3.18E-05/ /
Exponential
1.28E-04/1 /V
9.08E-04/8
3.63E-04/
1.02E-+011
WikiTableText
Power Law
1.32E-04/V /v
1.13E-03/ x
1.38E-03/ /V
3.04E+ 134/*
Table 22: Results from VaCSoal corresponding to Figure 21
Numerical values, along with (</*) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCSoa..
39

---

Published in Transactions on Machine Learning Research (10/2025)
H.2 Scaling Behavior Based on FLOPs of Full Fine- Tuned LLM Families
We present the scaling behavior of four LLM families Bamilies-FLLAN-E FLAN-T5, Mamba, Pythia, and Qwen2.5 on three D2T datasets (DART, E2E, and WikiTableleett) based on model size, using two automatic factual consis- teney metrics: ALIGNSCORE and QA Our analysis reveals that the scaling behavior with respoct to FLOPs under full fine-tuning closely mirrors the trends observed with model size. As shown in Figure 22 and Figure 23, exponential scaling consistently outperforms power law scaling across all four L.M families in terms of lower margin of error (MoE), indicating more stable and reliable fits. The outcomes from the VaCScal framework (Table 23 and Table 24) further reinforce the superiority of exponential scaling, offering strong empirical support when FL.OPs are considered as the scaling factor.
Exponential scaling
Margin (exponential scaling)
Power scaling
Margin crror (power law scaling)
DART (w/ FLAN-TS Famiy)
DART (w/ Mamba Family)
DART (w/ Pythis Family)
DART (w/ Quen2.5 5 Famiy)
Factual Incomiitunng w/ AurosScom Factual hoareaaancy w) ALEONS.COE:
1.00
0.35
0.20
0.36
0.70
0.40
0.60
0.35
0.32
0.30
0:30
0.25
0.30
4:33
12.90 21 68 1045 30.22
1998 1.97 7.97 10.90 13:95
6.00
96
31, 10.90 96 07 93
8.53
23,04 58.35
53.00 07.77
FLOP (x110") -+
FLOP (x:10") -
FL.OFs (x
FLOPx (x100))
EZE (w/ FLAN TS Family)
E2E (w/ Mamba Family)
EZE (w/ Pythia Family)
E2E (w/ Qwes2.5 Family)
0.20
1:00
0.25
0.25
0.38
0.25
0.2
0.17
0.34
0.30
0.16
0.23
0.30
0.40
0.18
0.29
0.20
0.17
0.21
0.10
1.05
5.49
9.04
1.23
2.2
11.16 14.38
2.19
5.81
9.42 16.64
FLOPs (x110"))
FLOPs (XC10P)
FLOP (x
FLOPs (x10P)
WilTabtiTTxxt (w/ FLAN- Family)
WilTableTen Text (w/ Mamba Fanily)
WiiTabicTox (w/ Pythia Family)
WaiTabecess (w/ Qwen2.5 Family)
Facioal Inconslanngg AttosSoont
0.48
0.56
0:41
0:
0.42
0.32
0.00
0.40
0.50
0.36
0.35
0:00
0:34
0.46
0.30
0.25
0.59
0.11
0:3b
0.60
0.44
1.00
0.35
0.21
0.29
0.16
0.30
0.85
1.39
1:53
0.25
0.56
2.00
1.4g
1.00
FLOPs
(x10P9)
FLOP, (Xx30P))
FLOPs
(x162")
FLOPs (x (x)1P')
Figure 22: Fitted power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, measured by ALIGNSCORF, plotted against FLOOPs across full fine-tuned FLAN-T5. Mamba, Pythia and Qwen2.5 LLM families.
Dataset
Scaling
FLAN-T5
Mamba
Pythia
Qwen2.5
Exponential
3.36E-03/ *
1.96E-04/4 /
8.98E+01, x
4.58E-05// /
DART
Power Law
3.30E+11/8 *
8.52E-04/V /
4.16E-01/ x
4.65E-05
Exponential
2.42E-05/ x
1.15E+01/ x
2.87E-03// /
1.19E-05//
E2E
Power Law
2.27E-044/ x
5,22E-04/X x
1.71E+137 x
1,13E-05 /
Exponential
3.39E 339E++00) +00/ V
3.06E-04/x x
6.08E-03/ /
8,81E-05/ x
WikllableTextt
Power Law
1.23E-02//8 x
6.19E+03// x
4.2815+07 *
7.24E+22/ x
Table 23: Results from VaCScal corresponding to Figure 22
Numerical values, along with (V/*) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCScal.
Takeaway. In the full fine-turêng setting, across all four otate-of-the-att the-ort automatic metrics and LLM fam- ilies (PLAN-T5, Mamba, Pylhia, and Qwen2.5), exponential scaling shows stronger acceplance in modeling
40

---

Published in Transactions on Machine Learning Research (10/2025)
the decline of factual inconsistency in VAl, offering a more slable and practically reliable scaling model compored to power law scaling.
respect to FLOPs-based on ALIGNSCORE and QAFACTE-
Exponential scaling
Margin (exponential scaling)
Power scaling
Margin crrer (power law scaling)
DART (w/ FLAN T5 Family)
DART (w/ Mambaa Family)
DART (w/ Pythi Famrls)
DART (w/ Qwen2.5 Family)
Facibal bromdaainng QARACTENUL Factual atureattnnn w/ QAFACTEEO Factual Incosittnnc w/ QAPACTENAL
0.62
1.10
0.40
0.55
0.00
0.50
0.50
0.45
0.40
0.56
0.50
0.50
0.60
0.20
0.34
0.50
0.48
0.40
0.30
0:30
4.13 12.90 21 68 30:45 39
1.98
4.97
7.97 10.90 13995
5.00
18 90
31, 10 04 95 57.90
8:53
23.54
38.35 53.06 07.77
FLOPs [s 10
FLOP& (x 10"
FLOPs (x:10"))
FLOPs (x100))
(w/ Family)
(w/ Mamba Family)
(w/ Pythia Familyy)
(w/ Owes2.5 Fanily)
0.20
0.80
0.14
0.14
0.14
0.18
0.17
0.36
0.40
0.12
0.15
0.20
0.13
0.12
0.34
0.00
0.13
0.15
1.05
123
272
1.40
7.04 11.16
2,10
0.42
F1.0P [x 10
GPs 10
OPs (x1020)
DP 1x10
WiiTTabeeestt (w/ FLAN T5 Famils)
Wik.Tabltesst (w/ Mamba Family)
WiiTabeeTert (w/ Pythia Family)
WikTTakeTest (w/ Qwen225 Family)
0.30
0.54
1.10
0.40
1.00
0:43
0.40
0.90
0.43
0.44
0.50
0.50
0.40
0.70
2.50
0.50
0.42
0.36
0.44
0.34
0.42
0.32
0.40
0:00
(x100)
01.0Px (X3309))
F1 F1.0P (x (x10PP)
FI (x100))
Figure 23: Filled power law and exponential scaling models (with 95% confidence intervals) for factual inconsistency in D2T, measured by QAFACTEVAL, plotted against FLOPs across full fine-tuned FLAN-T5, Mamba, Pythia and Qwen2.5 LLM families.
Dataset
Scaling
FLAN-T5
Mamba
Pythia
Qwen2.5
Exponential
3.63E-03/ x
4.82E-04/x x
1.86E-02/ x
3.23E-05/ /
DART
Power Law
1.47F-03/ x
5.92F-01/ x
2.84F-02/ x
5.59F-05 /
Exponential
2.24E-05//
x
1.54E-04/ x
1.59E+02// V
1.03E-05/* x
E2E
Power Law
3.56E-04/$ x
1.22E+27 x
3,53E+133// x
7.00E-06 x
Exponential
8.80E-05// V
3.81E-04/V
2.52E-02/v
2.63E-04/ V
Wike
Power Law
6.07E-03/ x
1.51E-01/ x
1.17E+09/
1.08E-05,
Table 24: Results from VaCScal corresponding to Figure 23
Numerical values, along with (</*)) and
blue/red highlights, indicate the outcomes of Stages I, 11, and III of VaCScal.
41

---

Published in Transactions on Machine Learning Research (10/2025)
On the Aberrant Scaling Patterns of E2E and ViGGO
Throughout our experiments, we consistently observed aberrant bchavior from the E2E datasct, and to a lesser extent, the ViGGO dataset. Specifically, factual inconsistency in these datasets tends to increase with scaling factors such as model size, FLOPs, and fine-tuning data size contrrrr to expected trends. Although we could not definitively identify the root cause of this behavior, we hypothesize that the low lexical diversity and closod-domain nature of these datasots may be contributing factors. Limited diversity can lead to overfitting during fine-tuning, resulting in degraded outpul quality and increased factual inconsistency. Additionally, the closed-domain nature of the E2E and ViGGO datasets (see Table 6) may hinder LLMs from effectively leveraging their pre-trained knowledge. To support this hypothesis, present the type-token ratio (TTR), computed using the following formula, for all five datasets used in our study:
TTR number of unique words tokens total number of words and tokens
A lower TTR indicates reduced lexical diversity. As shown in Table 25 the F2E and ViGGO datasets exhibit the lowest lexical richness both in the input source data and the corresponding references compared to the other three datasets.
DART
E2E
VIGGO
WebNLG
WikiTableTest
TTR (of source-input)
0.0178
0.0001
0.0029
0.0057 0.0209
0.0621
TTR (of reference text)
0.03
0.0058
0.0297
0.1297
Table 25: Type-Token Ratio (TTR) for all five D2T datasets, calculated separately for input source data and corresponding reference texts.
42

---

Published in Transactions on Machine Learning Research (10/2025)
J Mathematical Interpretation of Exponential Scaling in Factual Inconsistency for D2T with LLM Size
To develop an intuitive understanding of why factual inconsistency in D2T generation often exhibits expo- nential scaling with LLM size, we draw on few mathematical insights. We hypothesize that one of the primary causes of factual inconsistency in D2T tasks is sourcereference divergence discrepancy between the input source data and the reference outputs in the training (or fine-tuning) data. Such divergence intro- duces systematic biases during learning, which manifest as factual errors at inference time. Consequently, standard perplexity computed against the training reference fails to serve as a reliable indicator of factual inconsistency, since the model is trained on references that may themselves contain factual deviations. To address this limitation, we propose relative perplexity measure, which more closely (though NOT exactly) reflects the degree of factual inconsistency. Using relative perplexity instead of ordinary perplexity is mo- tivated by the need to compare how the model scores factual reference against. its own most likely (and potentially inconsistent) output. While ordinary perplexity captures the overall fluency or likelihood of a sequence, it docsn't reveal whether the model prefers hallucinated output over the truth. Formally, we define the relative perplexity R. between the input x and the true factual reference yet = y ...y. as the ratio between the perplexity of the true reference and that the model's most likely output at inference, yu = y2 ...yI,, where denotes the sequence length of both texts (Equation 6j. Note that the "true" reference here may differ from the dataset- reference; it may also incorporate information directly grounded in the input x.
vz
I. II Pr(y(") i=1
R(x, )= (erplexity(1rd))
(6)
perplexity (yxxx) imput=r
L
11 Pr(y.mxx max
imput
The relative perplexity R takes values in the range (1, where a value of indicates minimal factual inconsistency i.e, the LLM assigns maximum likelihood to the true factual reference. As R. increases (i.e., R + 20), it reflects growing factual inconsistency between the model's output and the true reference. In practice, this range may be bounded through proper calibration of the LLM.
Since most LLMs compute token probabilities via a softmax function applied over logits at inference time, we now lurn our attention to the logits underlying the tokens in Equation 6 Let gref and mmax denote the logits associated with ye and yuxx respectively.
not e
oef
R(
i i=1
c
aaax
(7)
L
(2)
input=m
fi
Imput==
input=x
In the first (1) case of Equation 7 the simplification follows directly from the observation that the softmax denominators in both the numerator and the denominator are identical and hence cancel out. It is crucial to emphasize that the terms 2/o and zmax do not denote the i-th index in the vocabulary V. Instead, they refer to the logits assigned to the i-th token in the respective sequences re and max, Interpreting Equation 7 we see that the relative perplexity R which we propose as a proxy for factual inconsistency captures the aggregate deflection of the logits assigned to the factual reference tokens from those assigned to the model's most likely output. Given that D2T datasets often exhibit sourco-reference divergence, it expected that such a mismatch between get and 2maax will frequently occur. In the following part, we mathematically analyze the nature and implications of this mismatch in greater detail.
43

---

For notational simplicity, let denote =; and 2b = where and are the indices of the corresponding tokens in the vocabulary V. Before proceeding further, make the following assumptions about the generation of logits. At time step, the logit vector is computed as = Eh, where E = R RVVx is the output embedding matrix (mapping hidden representations to vocabulary logits), and h E Rd is the hidden state of the LLM at time step t. Assune the model dimension is d, i.e., dim(h) = d. Following training and under a normalized regime, we assume that the elements of E and h are independent and Published in Transactions on Machine Learning Research (10/2025)
2 Logits
Output embebbings (E R )
h
Hidden state (h E RR)
Previous token
Figure 24: simplified systematic view of the logits output in a LLM.
identically distributed (IID) with zero mean: E.j .N(0,, (2) and h2 NO, of) for all valid indices i, and all random variables mutually independent. Under these assumptions, the logit value for the k-th token in the vocabulary is given by following Equation 8
2
En,hh
(8)
The variance of any logit can be computed using the expression for 2 from Equation 8
as follows:
var[zu] = d oo oF d. o²
(9)
Assuming 0² 07, of
(10)
It is well established in prior work scaling laws (Sharma & Kaplan 2022 model dimension d scales with the model size N according to function Φ i.c., d x Φ(N), where & is typically linear or sub-linear. Given this relationship, we now aim to estimate the expected mismatch between the logits zn and zg. To that end, we invoke Chebyshev's inequality to bound the probability of large deviations between these two logits. This provides a principled estimate the likelihood of factual inconsistency as captured by the logit-level difference 12a 2z/-
Bahri et al. 2024 that the
Var(z, - 26) E(N)²
Pr (|z - 2bl E(N)) S
(11)
In Equation 11. we define {(N) to be a lincar or sub-lincar function of the model size N. Now, let recall the basic rule for the variance of the difference between two random variables. Given independent random variables, the variance of their difference is given by:
44

---

Published in Transactions on Machine Learning Research (10/2025)
Var(za 2n) Var(za) + Var(=)) 2 Cov(Ea: 26)
(12)
We now observe that Fa E h and Eb E, h, where E., and Es., denote the a-th and b-th rows of the output embedding matrix E, respectively. Under this formulation, the covariance between &a and 2b can be expressed as:
Cov(Za: 26) =E,, Cov(h)Es, = =0h- Eg, Eb.:
(13)
(14)
An important observation here is that the term Eg, En,: corresponds to the inner product (or similarily) between the embeddings of the a-th and b-th vocabulary tokens. When the embeddings are normalized, this similarity lics in the range [-1, According to Equation 14 the variance of the logit difference can then expressed as Var(z, - =b) = O(d o²), where o² denotes the product of variances o and d x ((N) for some linear or sub-linear function & of the model size N. This variance becomes particularly large when E,, and Es,; are nearly orthogonal (i.e., dissimilar), which is frequently the case in D2T tasks involving divergent sourcc-reference training pairs-where the model must learn to associate imputs and references that contain distinct or conflicting facts. Now, applying Chebyshev's inequality from Equation 11 we obtain the upper bound Var(;,-=)). where E(N) is assumed to be linear sub-linear function of N. Since Var(z, =)) = Odd Od) the right-hand side can still be a relatively large quantity for realistic values of N and E(N). This implics that the event 12g - 2el 2 {(N) is not unlikely-in fact, it may occur with high probability under lypical D2T conditions. Consequently, the occurrence significant logit deviations between the factual reference and the likiiho output is a plausible and theoretically grounded phenomenon.
{(N)²
Recall that 2a 2re and 24 _ Therefore, the probability of observing deviation of the form ze mma 2 ((N) is also high. Substituting {(N) in place of age mmax into the expression in Equation we obtain:
-
fi (((N)
R(x, ref
E(N)
(15)
imput=r
Input=e
Hence, based on the above reasoning and Equation can conclude that the relative perplexity R which serves a proxy (NOT an exact measure) for factual inconsistency tends to scale exponentially with the size of the LLM, denoted by N. Thus, generalizing Equation 15 we obtain:
Factual Inconsistency e -S(N) input=zz
(16)
where {(N) is a linear or sub-linear function of the model size N.
This conclusion follows from Equation 16 which implies that as the LLM size N increases, the logit deviations between 2ς and z also grow. When aggregated within the relative perplexity R used here as a proxy for factual inconsistency- these deviations exhibit exponential dependence on N. Therefore, under the presence of source-reference divergence in D2T datasets, factual inconsistency expected to follow exponential scaling pattern with respect to model size.
45


Reviews:
[{"review_id": "0U5IQUkIFM", "reviewer": "Reviewer_7fDX", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "## Strengths\n\n1. **Timely Topic:** The paper addresses an important problem in data-to-text generation, especially as many real-world systems transition from entity-based responses to free-form answers. Inconsistency in generation is a critical issue for LLM applications, and understanding how it scales with model size is valuable.\n\n2. **Model Diversity:** By evaluating different model classes—transformer decoders, encoder-decoders, and state-space models—the paper provides broader insights beyond the commonly studied architectures. This sheds light on the potential of emerging LLM architectures.\n\n3. **Statistical Rigor:** The use of well-established statistical tools for evaluating scaling behavior, goodness-of-fit, and functional comparisons (e.g., power-law vs. exponential) adds rigor to the analysis and supports the credibility of the findings.\n\n---\n\n## Weaknesses\n\n1. **Outdated Model Choices:** The selected models (e.g., OPT, BLOOM, Pythia) are relatively outdated and may not reflect the behavior of current state-of-the-art LLMs. This limits the generalizability of the results.\n\n2. **Limited Model Scale:** Most of the models studied are relatively small (≤13B). In practice, larger models (e.g., 70B or more) show significantly better consistency and reliability. Thus, the practical relevance of the findings is questionable.\n\n3. **Lack of In-Depth Prompt Analysis:** Inconsistency in generation is often highly sensitive to prompt design. Many inconsistencies can be mitigated through better prompt engineering or few-shot instruction tuning. A thorough investigation into the interaction between prompting strategies and inconsistency is necessary to support the practical implications of the study's conclusions.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper investigates the scaling laws of inconsistency in data-to-text generation across three major model classes: transformer decoders, transformer encoder-decoders, and state-space models. To conduct a rigorous analysis, the authors propose a framework called VaCScal, which evaluates predictive performance, goodness-of-fit, and performs comparative analysis between power-law and exponential scaling functions. Their findings suggest that the exponential function better captures the scaling behavior of inconsistency across all model classes and fine-tuning methods.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "To strengthen the paper, I recommend that the authors to address the weakness points, specifically,\n1. extend their experiments to include more recent LLMs, and\n2. larger models at 70B or above, also comapring with closed-model for strong baseline comparisons.\nto ensure the findings are representative of current systems.\n3. Additionally, since inconsistency in generation is often highly sensitive to prompt design, a thorough analysis of prompt formulation and its impact on consistency would be essential to validate the practical relevance of the conclusions.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "hOn5u9j8Np", "reviewer": "Reviewer_jHSa", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n-----------\n* The paper is very polished and clearly written.\n* Results are presented clearly and comprehensively.\n* The extension of scaling laws with VaCScal is (to the best of my knowledge) novel, thorough, and well-motivated.\n\nWeaknesses\n--------------\n* The density of information in the results feels at times a bit overwhelming.\n* Due to the volume of results presented, other relevant parts have been relegated to the appendix.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work examines scaling laws for different kinds of datasets and model families in the area of data-to-text generation in the context of factual inconsistency.\nIn the same vein, it proposes an extended methodology to determine and validate scaling laws through a three-step procedure called VaCScal, which makes use tof the F-test to assess goodness-of-fit and Vuong's likelihood ratio test to decide whether to prefer a exponential or power law scaling model. \nThey find that exponential scaling better explains factual inconsistency as a function of model size, FLOPs and finetuning dataset set size across families and factuality metrics.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I have only very few requested changes with the structure of the paper, as I think the content itself is very good.\n\n* The scaling law figures (figure 3-6) could be a bit scaled up for readability. I acknowledge that this was probably done in order to preserve space. Therefore, I also wonder whether authors could show only some of the mentioned figures in the main paper and move figures with similar conclusions / trends to the appendix, or only show the scaling laws for some datasets in the main text. This would also decrease the amount of information a reader has to parse at once.\n* It is also apparent to me that due to giving the presentation and discussion of experimental results a lot of space, many other relevant sections had to be moved to the appendix. Sections I would personally consider relevant to the main text are for instance section A.1 that explains the kinds of dataset used, appendix F, and at least a short summary of the discussion in appendix G regarding the counter-intuitive \"anti-scaling\" results for some datasets.\n* The same holds for the derivation in Appendix H - the result could be presented in abbreviated / simplified form, with the detailed derivation in the appendix.\n\nOther minor points:\n* Missing citations for RoBERTa and Reddit / Pile datasets at the top of page 17\n* I believe the comma after \"two scaling models\" in Stage III on page 4 is redundant.", "broader_impact_concerns": "I foresee no broader impact concerns with this paper.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "Ry5cDJk3ib", "reviewer": "Reviewer_YPVG", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. The study provides a thorough empirical investigation of the relationship between factual inconsistency and LLM size across multiple datasets and models. This comprehensive approach offers valuable insights into the behavior of LLMs in D2T tasks.\n\n2. The authors employ a structured three-stage statistical validation framework, which includes predictive performance estimation, goodness-of-fit assessment, and comparative analysis.\n\n3. The research addresses a critical issue in D2T—factual inconsistency—which is highly relevant for ensuring trustworthiness in applications such as automated journalism and conversational systems. The findings that factual inconsistency scales exponentially with LLM size are novel and provide new directions for future research.\n\nWeaknesses:\n\n1. The use of QLoRA for fine-tuning LLMs may invalidate the meaning of the scaling factor  x in the scaling law. In theory, full parameter fine-tuning would better observe model performance.\n\n2. Some newer popular LLMs, such as Llama and Qwen, should be included in the experiments. These models often have stronger comprehension abilities. It remains to be seen whether stronger base models still follow exponential scaling.\n\n3. The authors primarily use automatic metrics to observe performance, which can introduce more uncertainty. Although they also include human evaluation, the scale is relatively small.\n\n4. After the model size exceeds 2 billion parameters, factual inconsistency decreases sharply, but the authors do not analyze this phenomenon.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "his paper investigates the scaling laws in the field of data-to-text generation (D2T) by examining the relationship between factual inconsistency and the size of large language models (LLMs).\n\nThe authors conduct an extensive empirical analysis to explore how factual inconsistency in D2T tasks scales with the size of LLMs. They compare two scaling laws—power law and exponential scaling—across three major LLM families (Pythia, OPT, and BLOOM) and five well-established D2T datasets (E2E, ViGGO, WebNLG, DART, and WikiTableText).\n\nThe authors introduce a structured three-stage statistical validation framework to rigorously evaluate the scaling laws:\n\n1. Predictive Performance Estimation: Assessing the predictive ability of the scaling laws on unseen data using Huber loss.\n2. Goodness-of-Fit Assessment: Evaluating how well the scaling laws fit the data using an F-test.\n3. Comparative Analysis: Comparing the power law and exponential scaling models using Vuong’s likelihood-ratio test to determine which model better explains the data.\n\nThe study reveals that factual inconsistency in D2T follows an exponential scaling with LLM size, rather than the commonly assumed power law scaling. This finding is validated through extensive empirical results and the rigorous statistical framework. The exponential scaling indicates a rapid initial decline in factual inconsistency up to approximately 3–4 billion parameters, after which it stabilizes.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "1. Conduct Experiments with Full Parameter Fine-Tuning\n\n2. Utilize Stronger Base Models like Llama or Qwen\n\n3. Perform More Extensive Experimental Analysis", "broader_impact_concerns": "No need", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)