Scaling Laws, Tabular Data and Actuarial Ratemaking Models

Paper: arXiv 2609.03106

Authors: Ronald Richman

Abstract

Scaling laws in modern deep learning describe how held-out loss improves as model capacity, training data, and compute increase, often following power-law trends. We investigate whether analogous scaling regularities arise in actuarial ratemaking, where data are tabular, heterogeneous, and noisy, and where classical models such as GLMs remain strong baselines. Using a real-world motor insurance portfolio, we train models from different families across increasing fractions of the training data and multiple random seeds, evaluating out-of-sample Poisson deviance, a likelihood-based loss for Poisson count predictions in which lower values indicate better held-out fit. We find that all model families improve with additional data, but scaling exponents differ substantially: TabM exhibits markedly stronger data scaling than purely supervised tabular Transformers and standard MLP baselines. Transformer variants show weak parameter scaling unless augmented with additional inductive biases (TabM-style adaptation or self-supervision). These results provide quantitative guidance on model selection by data regime and suggest that effective scaling on actuarial tabular tasks depends on architecture and loss function objective design, with simple increases in Transformer size providing limited gains.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous empirical investigation into scaling laws in actuarial ratemaking, a novel application of deep learning scaling concepts to tabular insurance data. It uses a real-world dataset and robust statistical methods, making it highly relevant for practical applications. The clarity of writing and the structured approach contribute to its overall strength.

Research Flowchart

  flowchart TD
    A[Research Goal: Do Scaling Regularities Exist in Actuarial Ratemaking?] --> B{Methodology: Investigate Scaling Laws in Actuarial Models};
    B --> C[Data: Real-World Motor Insurance Portfolio];
    C --> D{Computational Process: Train Models Across Data Fractions & Seeds};
    D --> E[Evaluation: Out-of-Sample Poisson Deviance];
    E --> F[Key Finding 1: All Models Improve with More Data, but Scaling Exponents Differ];
    F --> G[Key Finding 2: TabM Shows Stronger Data Scaling than Transformers/MLPs];
    G --> H[Key Finding 3: Transformer Scaling Weak Without Inductive Biases (TabM/Self-Supervision)];
    H --> I[Outcome: Quantitative Guidance for Model Selection & Architecture Design for Actuarial Tasks];

Cited References (72)

1. Attention is all you need (2017)
2. BERT : Pre-training of deep bidirectional transformers for language understanding (2018) — link
3. Scaling laws for neural language models (2020) — link
4. Training compute-optimal large language models (2022) — link
5. Emergent abilities of large language models (2022)
6. AI in actuarial science - a review of recent advances - part 1 (2020) — link
7. Reflections on deep learning and the actuarial profession(al) (2024) — link
8. Mind the gap - safely incorporating deep learning models into the actuarial toolkit (2021) — link

2 of 72 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.