A Poisson GLM beat TabPFN, a model pretrained on millions of synthetic tables, on claim frequency in both motor portfolios that researchers at KU Leuven and the University of Antwerp tested, with a deviance of 0.296 against TabPFN's best of 0.343 on French data.
The result is in the third version of "Is TabPFN the Silver Bullet for Insurance Pricing?", which Bruno Deprez, Wouter Verbeke and Tim Verdonck posted on October 9. It is one of four papers since June that set pretrained "foundation" models, or neural networks trained from scratch, against the GLM on motor data. All four are arXiv preprints, not peer-reviewed journal articles.
The tests follow a 2025 Nature paper reporting that TabPFN with default settings on average outperformed tuned tabular models. Deprez and his co-authors wrote that those benchmarks "provide no evidence on its suitability for insurance pricing."
Key Takeaways
- TabPFN had the lowest deviance in one of four comparisons, Belgian claim severity, at 2.041 against the GLM's 2.046.
- Language-model embeddings used as GLM covariates led the hand-built GLM by about 2% of test deviance at 50,000 policies, down from a far wider gap at 500.
- Adding "Policyholder height: 175 cm" to each policy's text description raised the embedding model's mean predicted frequency by 20.9%, more than adding a race label did.
- On one insurer's 4.5 million records, the GLM beat TabM, a neural network of several linked sub-models, on frequency deviance at 202,000 rows and trailed it by 1.1% at 4 million.
TabPFN on French and Belgian motor data
Deprez and colleagues ran TabPFN-v2.6 and TabPFN-v3 against a GLM and XGBoost on the public freMTPL2 (about 678,000 policies) and beMTPL97 (about 163,000) datasets. TabPFN has no fitted parameters: the training rows are passed through the network as "context" with the rows being scored.
That context is capped at 100,000 rows for v2.6 and 1,000,000 for v3. The authors tested contexts from 2,000 policies up to the full French training fold of about 542,400. The GLM and XGBoost used the full fold every time.
On French frequency the GLM's Poisson deviance was 0.296 and XGBoost's 0.344. TabPFN-v3 improved from 0.363 at 2,000 policies to 0.343 on the full fold. TabPFN-v2.6 went the other way, from 0.356 at 2,000 to 0.383 at 10,000. On Belgian frequency the GLM scored 0.551, TabPFN-v2.6 0.563 at its best, XGBoost 0.583 and TabPFN-v3 0.626.
TabPFN "supports neither an offset nor observation weights," the authors wrote, so exposure went in as an ordinary feature and the model had to learn its effect from the data.
Severity has far fewer rows, 24,944 French and 18,276 Belgian policies with a claim, and the order changed. On French data XGBoost had the lowest gamma deviance at 1.598, then TabPFN-v2.6 at 1.654, with the GLM last at 1.755. On Belgian data TabPFN-v3 led at 2.041 against the GLM's 2.046. Fold-to-fold standard deviation for the French GLM was 0.263. The May 25 version had put TabPFN's French severity deviance at 2.656 and said TabPFN was never best; the October version fits it on log claim amounts.
Scoring a fold took "several minutes at the model's capacity limit" on an NVIDIA A100 GPU, more than the GLM and XGBoost needed to train and predict. The v2.6 and v3 weights carry Prior Labs' non-commercial licences, so production use needs a commercial one. "TabPFN cannot yet replace established actuarial methods for claim frequency," the authors wrote.
Embeddings in a GLM and the size of a small book
Christopher Blier-Wong and Derek Kusmenko of the University of Toronto took a different route in "Semantic insurance pricing with large language models", posted June 28. Each policy's nine rating variables are written out as text, a language model turns the text into a vector, and 12, 48 or 192 principal components of that vector become the covariates of a Poisson GLM with an exposure offset.
They used the French data again: 676,782 policies after cleaning and 35,976 claims. The benchmark, a 48-covariate GLM with hand-built interactions from a Wüthrich and Merz textbook, kept all 48 covariates at every sample size.
With 500 training policies the benchmark's test deviance was 1.208 and the best embedding GLM's 0.359. At 10,000 policies the figures were 0.3371 and 0.3180; at 50,000, 0.3218 and 0.3153; at 500,000, 0.3211 and 0.3120. The portfolio averages about 0.53 exposure-years a policy, so 10,000 policies is roughly 5,300 car-years and 530 claims. The embedding lead works out to 5.7% at that size and 2.0% at 50,000 policies. The authors wrote that reductions "on the order of 1%" may be financially substantial across a large portfolio.
At 500,000 policies the small Qwen model with 48 components scored 0.3258, worse than the benchmark, and XGBoost on the raw features reached 0.3145.
Ronald Richman's "Scaling Laws, Tabular Data and Actuarial Ratemaking Models", posted September 2 and funded by the CAS, covers the other end of the size range. None of its models is pretrained. It trains a GLM, feed-forward networks, transformers and TabM on a multinational insurer's 4.5 million policy-period records, about 1 million exposure-years.
At 5% of the data, about 202,000 rows, the GLM's deviance of 0.29343 beat the feed-forward networks (0.29424) and TabM (0.29380). At the full 4.03 million rows the largest TabM-mini reached 0.28885 against the GLM's 0.29200. Richman's fitted data-scaling exponent was 0.091 for the GLM and 0.309 for TabM, or 0.409 counting the largest run, at which each doubling of data removes about 25% of TabM's remaining gap to the fitted floor. In smaller data regimes, he wrote, GLMs "remain difficult to beat."
| Paper | Model tested | Data | Where it beat the GLM | Where it did not |
|---|---|---|---|---|
| Deprez et al. (October 9) | TabPFN-v2.6 and v3 | freMTPL2 and beMTPL97, frequency and severity | Severity: 2.041 v 2.046 Belgian, 1.654 v 1.755 French | Frequency: 0.343 v 0.296 French, 0.563 v 0.551 Belgian |
| Blier-Wong and Kusmenko (June 28) | Language-model embeddings in a Poisson GLM | freMTPL2 frequency, 500 to 500,000 policies | Best embedding at every size: 0.359 v 1.208 at 500 | Qwen3-0.6B, 48 components, 500,000 policies: 0.3258 v 0.3211 |
| Richman (September 2) | Feed-forward, transformer and TabM networks | One insurer, 202,000 to 4.03 million rows | TabM-mini at full data: 0.28885 v 0.29200 | Feed-forward and TabM at 202,000 rows: 0.29424 and 0.29380 v 0.29343 |
| Blier-Wong (September 13) | Review, no experiment | None | Not tested | Not tested |
Sources: the four arXiv preprints. Figures are test deviance, model v GLM; each paper computes it differently, so levels do not compare across rows.
Reproducibility, licensing and filing
Blier-Wong and Kusmenko rest their governance case on the split between the two steps. The language model "outputs embeddings and never a premium," the extraction is a single deterministic pass, and the same description always gives the same price. The GLM on top is, they wrote, "audited with existing regulatory tools."
The components have no reading in terms of rating variables, the paper said, and the prompt template carried weight. Appending "Favourite colour: blue" to 100,000 test prompts raised mean predicted frequency 16.1%, and the height field 20.9%, against 14.6% and 12.8% for two race labels. The authors called controlled templates and perturbation audits "a governance requirement."
Deprez and colleagues listed "the absence of transparent coefficients" among TabPFN's costs. Richman noted that many US state regulators require rating models to be filed and "large-scale deep learning (and other machine learning) models may not be acceptable." The site's model risk guide covers validation by model class.
Blier-Wong's September 13 review, "Towards foundation models for insurance risk modelling", turns to vendors. A provider update creates a new embedding space, so a model fitted to the old vectors "may need to be retrained." He wrote that an insurer needs a fallback loss model that uses only its structured variables.
Every experiment in the four papers is on motor business, and both tests of pretrained models use the same French portfolio. Only Deprez and colleagues looked at severity. Richman used a random split and listed time-based splits, other lines, gradient-boosted baselines and severity as next steps. Blier-Wong proposed bodily injury reserving as a first test of pretraining, comparing reserving models with and without pretrained text features as the number of local claims varies.
Further Reading
- Model Risk Management for Actuarial Models, From GLM to LLM: validation requirements by model class.
- CAS Funds Research to Fine-Tune LLMs for P&C Actuarial Reasoning: the CAS research tracks on language models.
- SOA Study Cuts Underwriting Bias Gap to 0.071 for 0.001 of AUC: a GLM against an adversarial neural network on fairness measures.
- Senior Actuaries Tell SOA Study AI Use Is Wide, Shallow and Unguided: how actuarial leaders describe AI adoption.
Sources
- Bruno Deprez, Wouter Verbeke and Tim Verdonck, "Is TabPFN the Silver Bullet for Insurance Pricing?", arXiv:2605.22892, version 3, 9 October 2026 (version 2, 25 May 2026)
- Christopher Blier-Wong and Derek Kusmenko, "Semantic insurance pricing with large language models", arXiv:2606.29371, 28 June 2026
- Ronald Richman, "Scaling Laws, Tabular Data and Actuarial Ratemaking Models", arXiv:2609.03106, 2 September 2026
- Christopher Blier-Wong, "Towards foundation models for insurance risk modelling", arXiv:2609.14576, 13 September 2026