Towards Robust Numerical Claim Verification
Organizations: University of Stavanger · Factiverse AI and University of Stavanger
Abstract
Large language models (LLMs) are widely used for claim verification, yet remain brittle for numerical reasoning: even small changes in value can sharply degrade accuracy. We show that this brittleness persists in frontier LLMs, but can be mitigated through adversarial fine-tuning on numerically perturbed examples. Using parameter-efficient fine-tuning, small Qwen3 models (0.6B8B) reach 98.7% accuracy on label-flipping perturbations, outperforming larger zero-shot models and frontier systems (GPT-5.4 Pro (74.0%) and Gemini 2.5 Flash (73.9%)). The gains generalise to unseen perturbation types, indicating robust numerical decision boundaries rather than memorised edits. Robustness also transfers without target-domain data, significantly improving cross-lingual performance in Spanish. We further show that the same fine-tuning recipe confers robustness to evidence-side perturbations, using the VitaminC dataset.
Figures & tables
| Category | T T | T F | F F | Total |
|---|---|---|---|---|
| Numeration | 216 | 216 | 1002 | 1434 |
| Approximation | 139 | 139 | 784 | 1062 |
| Range | 190 | 190 | 843 | 1223 |
| Masked | ✗ | 216 | 501 | 717 |
| Random | ✗ | 216 | 501 | 717 |
| Negative | ✗ | 52 | 91 | 143 |
| Model | Orig. | Approx. | Num. | Range | Neg. | Mask. | Rand. | M. Avg. | |
|---|---|---|---|---|---|---|---|---|---|
| \Block 6-1 \rotate Base | 78.12 | 92.70 +14.58 | 86.06 +7.94 | 93.44 +15.32 | 39.22 -38.90 | 17.00 -61.12 | 90.14 +12.02 | 73.96 -4.16 | |
| 74.71 | 91.97 +17.26 | 86.05 +11.34 | 92.43 +17.72 | 53.85 -20.86 | 19.62 -55.09 | 92.06 +17.35 | 73.91 -0.80 | ||
| 86.35 | 85.05 -1.30 | 69.59 -16.76 | 82.35 -4.00 | 27.27 -59.08 | 8.87 -77.48 | 86.98 +0.63 | 62.80 -23.55 | ||
| 81.96 | 88.72 +6.76 | 73.21 -8.75 | 84.78 +2.82 | 28.85 -53.11 | 12.44 -69.52 | 90.61 +8.65 | 66.10 -15.86 | ||
| 85.55 | 88.64 +3.09 | 78.89 -6.66 | 86.67 +1.12 | 36.00 -49.55 | 16.19 -69.36 | 86.41 +0.86 | 67.89 -17.66 | ||
| 95.83 | 8.63 -87.20 | 7.41 -88.42 | 9.47 -86.36 | 7.69 -88.14 | 5.56 -90.27 | 12.50 -83.33 | 8.65 -87.18 |
| Model | Orig. | Approx. | Num. | Range | Neg. | Mask. | Rand. | M. Avg. | |
|---|---|---|---|---|---|---|---|---|---|
| \Block 6-1 \rotate Base | 95.33 | 95.84 +0.51 | 96.51 +1.18 | 94.65 -0.68 | 92.22 -3.11 | 96.69 +1.36 | 97.75 +2.42 | 96.03 +0.70 | |
| 91.48 | 90.77 -0.71 | 90.87 -0.61 | 89.61 -1.87 | 90.00 -1.48 | 88.55 -2.93 | 96.77 +5.29 | 91.35 -0.13 | ||
| 94.30 | 95.51 +1.21 | 94.65 +0.35 | 92.18 -2.12 | 93.75 -0.55 | 94.03 -0.27 | 97.70 +3.40 | 94.83 +0.53 | ||
| 95.42 | 96.43 +1.01 | 95.99 +0.57 | 95.23 -0.19 | 94.51 -0.91 | 94.37 -1.05 | 98.60 +3.18 | 96.08 +0.66 | ||
| 95.24 | 96.64 +1.40 | 95.37 +0.13 | 94.67 -0.57 | 93.33 -1.91 | 95.77 +0.53 | 97.77 +2.53 | 95.96 +0.72 | ||
| 96.75 | 97.70 +0.95 | 96.41 -0.34 | 96.92 +0.17 | 96.70 -0.05 | 96.61 -0.14 | 98.20 +1.45 | 97.13 +0.38 |
| Model | Approx. | Num. | Range | M. Avg. | |
|---|---|---|---|---|---|
| \Block 6-1 \rotate Base | 77.04 -1.08 | 81.43 +3.31 | 82.39 +4.27 | 80.28 +2.16 | |
| 70.80 -3.91 | 74.65 -0.06 | 74.33 -0.38 | 73.56 -1.15 | ||
| 80.51 -5.84 | 87.44 +1.09 | 85.29 -1.06 | 84.92 -1.43 | ||
| 73.33 -8.63 | 82.94 +0.98 | 79.56 -2.40 | 79.31 -2.65 | ||
| 77.44 -8.11 | 82.30 -3.25 | 81.01 -4.54 | 80.61 -4.94 | ||
| 96.40 +0.57 | 95.83 | 95.26 -0.57 | 95.78 -0.05 |
| Model | T1 | T2 | T3 | M. Avg |
|---|---|---|---|---|
| AVeriTeC 2.0 dev | ||||
| 95.65 | 95.09 | 96.83 | 95.31 | |
| 89.72 5.93 | 93.73 1.37 | 97.20 0.37 | 92.13 3.18 | |
| 90.12 5.53 | 95.20 0.11 | 97.20 0.37 | 93.20 2.11 | |
| CLEF 2025 Spanish | ||||
| 95.51 | 97.17 | 97.40 | 96.44 | |
| VitaminC | QuanTemp | QuanTemp by perturbation type | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Training data | Acc. | Pair | Acc. | M-F1 | Orig. | T1 | T2 | Mask | Rand |
| None ( ) | 90.96 | 84.25 | — | — | — | — | — | — | — |
| QuanTemp ( ) | 78.35 | 54.45 | 97.52 | 94.62 | 96.13 | 94.95 | 98.80 | 100.00 | 99.86 |
| VitaminC ( ) | 98.05 | 96.56 | 80.86 | 69.80 | 79.29 | 72.69 | 92.26 | 57.88 | 95.12 |
| Both ( ) | 98.25 | 97.15 | 98.20 | 96.10 | 96.36 | 96.45 | 99.45 | 100.00 | 99.72 |
Appendix figures & tables17 assets
Supplementary material from the paper’s appendix.
Appendix
| Category | T T | T F | F F | Total |
|---|---|---|---|---|
| Numeration | 775 | 775 | 3872 | 5422 |
| Approximation | 539 | 539 | 3010 | 4088 |
| Range | 931 | 931 | 4868 | 6730 |
| Masked | ✗ | 775 | 1939 | 2714 |
| Random | ✗ | 775 | 1939 | 2714 |
| Negative | ✗ | 218 | 294 | 512 |
| Category | T T | T F | F F | Total |
|---|---|---|---|---|
| Numeration | 273 | 273 | 1206 | 1752 |
| Approximation | 197 | 197 | 938 | 1332 |
| Range | 324 | 324 | 1494 | 2142 |
| Masked | ✗ | 273 | 603 | 876 |
| Random | ✗ | 273 | 603 | 876 |
| Negative | ✗ | 75 | 95 | 170 |
| Type | Label | Original claim fragment | Perturbed fragment | Variant |
|---|---|---|---|---|
| Numeration | T1 | “fell to 3.5% ” | “fell to three point five percent ” | T1 (preserving) |
| “fell to thirty-five percent ” | T2 (changing) | |||
| Approximation | T1 | “matched 50 years ” | “matched about 50 years ” | T1 (preserving) |
| “matched about 5 years ” | T2 (changing) | |||
| Range | T1 | “over 30 million filed” | “over 25–35 million filed” | T1 (preserving) |
| “over 10–15 million filed” | T2 (changing) |
| AVeriTeC 2.0 dev | CLEF 2025 Spanish | |||
|---|---|---|---|---|
| Category | True | False | True | False |
| Num. | 74 | 124 | 328 | 3,614 |
| Approx. | 64 | 90 | 322 | 3,470 |
| Range | 64 | 94 | 317 | 3,397 |
| Rand. | 45 | 62 | 164 | 1,807 |
| Neg. | 5 | 9 | 70 | 338 |
| Hyperparameter | Value |
|---|---|
| Epochs | 2 |
| Batch size (per device) | 5 |
| Gradient accumulation | 1 |
| Learning rate | |
| LR scheduler | Cosine |
| Warmup steps | 50 |
| Model | T F | T T | F F |
|---|---|---|---|
| Gemini | 14.38 | 16.19 | 6.64 |
| GPT-5.4 | 3.00 | 4.00 | 2.50 |
| Quantised (Q4_K_M) | |||
| 17.90 | 10.30 | 11.90 | |
| 2.40 | 2.80 | 0.50 | |
| 4.40 | 3.70 | 1.30 | |
| Column | Strict | Relaxed | |
| T F | |||
| Orig. | 76.16 | 73.93 | 2.23 |
| Approx. | 89.66 | 94.93 | 5.27 |
| Num. | 81.00 | 85.92 | 4.92 |
| Range | 87.23 | 91.94 | 4.71 |
| Neg. | 47.83 | 72.55 | 24.72 |
| Dataset | Protocol | (pp) | 95% CI (pp) | McNemar | ||
|---|---|---|---|---|---|---|
| CLEF Spanish | Parseable-only (reported) | 96.44 | 97.36 | 0.93 | — | |
| Paired ( ) | 96.44 | 98.77 | 2.33 | |||
| Failures as errors | 53.26 | 97.36 | 44.11 | |||
| AVeriTeC | Parseable-only (reported) | 95.31 | 93.20 | 2.11 | — | |
| Paired ( ) | 95.31 | 94.24 | 1.07 | |||
| Failures as errors | 59.60 | 93.20 | 33.60 |
| True | False | ||||||
|---|---|---|---|---|---|---|---|
| Model | P | R | F1 | P | R | F1 | M-F1 |
| 42.4 | 80.9 | 55.6 | 99.4 | 96.9 | 98.1 | 76.88 | |
| 65.7 | 82.5 | 73.1 | 99.2 | 98.1 | 98.7 | 85.89 | |
| 64.4 | 81.6 | 72.0 | 99.2 | 98.0 | 98.6 | 85.31 | |
| Model | Approx. | Num. | Range | Neg. | Rand. | M. Avg. |
|---|---|---|---|---|---|---|
| T F (label-flipping) | ||||||
| 72.97 | 80.00 | 82.50 | 35.29 | 76.09 | 73.71 | |
| 98.76 25.78 | 97.56 17.56 | 95.57 13.07 | 100.00 64.71 | 96.95 20.86 | 97.49 23.78 | |
| 98.14 25.16 | 96.34 16.34 | 96.20 13.70 | 100.00 64.71 | 96.34 20.25 | 97.07 23.36 | |
| (n) | 161 | 164 | 158 | 70 | 164 | 717 |
| T T (label-preserving) | ||||||
| Relative distance | ||||
|---|---|---|---|---|
| 0 (value preserved) | 1,373 | 90.17 | 96.07 | 5.90 |
| 399 | 87.99 | 95.49 | 7.50 | |
| 345 | 90.11 | 98.55 | 8.44 | |
| 661 | 94.14 | 99.39 | 5.26 | |
| 513 | 94.06 | 98.83 | 4.77 | |
| 503 | 96.69 | 99.60 | 2.91 |
| Per instance | Per pair | Pair error mode | |||||
| Model | Prompt | Acc. | Macro-F1 | Pair Acc. | Refutes | Confirms | PF |
| No target-domain training | |||||||
| Zero-shot | 90.96 | 90.86 | 84.25 | 8.8 | 8.4 | 704 | |
| Trained on QuanTemp claim-side perturbations | |||||||
| Zero-shot | 78.35 12.60 | 77.63 | 54.45 29.81 | 15.0 | 31.5 | 0 | |
| SCoT | 74.98 15.98 | 73.20 | 46.15 38.10 | 10.7 | 44.2 | 0 | |
| Model | Orig. | Approx. | Num. | Range | Neg. | Mask. | Rand. | Micro Avg. | |
|---|---|---|---|---|---|---|---|---|---|
| \Block 5-1 \rotate Base | 94.35 | 81.82 -12.53 | 35.94 -58.41 | 78.18 -16.17 | 3.70 -90.65 | 2.50 -91.85 | 71.43 -22.92 | 48.74 -45.61 | |
| 86.92 | 86.61 -0.31 | 62.50 -24.42 | 80.00 -6.92 | 21.74 -65.18 | 8.63 -78.29 | 84.70 -2.22 | 60.28 -26.64 | ||
| 88.24 | 85.86 -2.38 | 66.42 -21.82 | 85.34 -2.90 | 29.27 -58.97 | 7.29 -80.95 | 83.80 -4.44 | 61.90 -26.34 | ||
| 94.70 | 8.63 -86.07 | 6.94 -87.76 | 9.47 -85.23 | 7.69 -87.01 | 6.94 -87.76 | 15.28 -79.42 | 9.42 -85.28 | ||
| \Block 4-1 \rotate All Perturb | 81.06 | 93.53 +12.47 | 75.00 -6.06 | 83.68 +2.62 | 100.00 +18.94 | 99.54 +18.48 | 96.76 +15.70 | 90.09 +9.03 | |
| 85.23 | 89.93 +4.70 | 88.43 +3.20 | 88.42 +3.19 | 98.08 +12.85 | 99.54 +14.31 | 94.91 +9.68 | 92.81 +7.58 |
| Model | Orig. | Approx. | Num. | Range | Micro Avg. | |
|---|---|---|---|---|---|---|
| \Block 5-1 \rotate Base | 94.35 | 93.67 -0.68 | 97.33 +2.98 | 98.17 +3.82 | 96.69 +2.34 | |
| 86.92 | 80.83 -6.09 | 86.14 -0.78 | 89.41 +2.49 | 85.93 -0.99 | ||
| 88.24 | 89.29 +1.05 | 90.37 +2.13 | 87.84 -0.40 | 89.21 +0.97 | ||
| 94.70 | 95.68 +0.98 | 95.37 +0.67 | 94.21 -0.49 | 95.04 +0.34 | ||
| \Block 4-1 \rotate All Perturb | 81.06 | 84.17 +3.11 | 78.70 -2.36 | 87.37 +6.31 | 83.12 +2.06 | |
| 85.23 | 89.93 +4.70 | 85.65 +0.42 | 91.58 +6.35 | 88.81 +3.58 |
| Model | Orig. | Approx. | Num. | Range | Neg. | Mask. | Rand. | Micro Avg. | |
|---|---|---|---|---|---|---|---|---|---|
| \Block 5-1 \rotate Base | 91.69 | 95.73 +4.04 | 94.37 +2.68 | 86.88 -4.81 | 88.10 -3.59 | 92.52 +0.83 | 95.91 +4.22 | 92.98 +1.29 | |
| 94.95 | 96.77 +1.82 | 96.30 +1.35 | 92.31 -2.64 | 93.10 -1.85 | 93.62 -1.33 | 98.33 +3.38 | 95.42 +0.47 | ||
| 95.99 | 96.69 +0.70 | 95.87 -0.12 | 94.48 -1.51 | 93.75 -2.24 | 95.50 -0.49 | 98.21 +2.22 | 96.09 +0.10 | ||
| 97.56 | 97.45 -0.11 | 97.21 -0.35 | 96.92 -0.64 | 95.60 -1.96 | 96.81 -0.75 | 98.40 +0.84 | 97.30 -0.26 | ||
| \Block 4-1 \rotate All Perturb | 95.93 | 95.15 -0.78 | 95.41 -0.52 | 88.86 -7.07 | 100.00 +4.07 | 100.00 +4.07 | 100.00 +4.07 | 96.30 +0.37 | |
| 96.59 | 94.64 -1.95 | 95.21 -1.38 | 92.18 -4.41 | 100.00 +3.41 | 100.00 +3.41 | 99.40 +2.81 | 96.64 +0.05 |