Tab-TRM: Tiny Recursive Model for Insurance Pricing on Tabular Data

TL;DR

Tab-TRM introduces a tiny recursive model tailored for tabular insurance pricing by embedding each covariate as a token and augmenting the sequence with an answer token $\mathbf{a}$ and a reasoning token $\boldsymbol{z}$. The model iteratively refines $\boldsymbol{z}$ and $\mathbf{a}$ through a compact core of two update networks, then maps the final $\mathbf{a}$ to a Poisson-mean via an exponential decoder, trained with Poisson deviance. Empirically, on the French MTPL dataset, Tab-TRM achieves competitive out-of-sample Poisson deviance with far fewer parameters than several baselines, aided by a staged, interpretable recursion that aligns with actuarial intuition (iterative GLM-like refinement and stagewise boosting). A linearized variant and extensive interpretability analyses demonstrate that the recursion behaves largely linearly in learned embedding space, validating a state-space interpretation and reinforcing the model’s applicability as a compact, interpretable bridge between classical actuarial workflows and modern latent-reasoning architectures.

Abstract

We introduce Tab-TRM (Tabular-Tiny Recursive Model), a network architecture that adapts the recursive latent reasoning paradigm of Tiny Recursive Models (TRMs) to insurance modeling. Drawing inspiration from both the Hierarchical Reasoning Model (HRM) and its simplified successor TRM, the Tab-TRM model makes predictions by reasoning over the input features. It maintains two learnable latent tokens - an answer token and a reasoning state - that are iteratively refined by a compact, parameter-efficient recursive network. The recursive processing layer repeatedly updates the reasoning state given the full token sequence and then refines the answer token, in close analogy with iterative insurance pricing schemes. Conceptually, Tab-TRM bridges classical actuarial workflows - iterative generalized linear model fitting and minimum-bias calibration - on the one hand, and modern machine learning, in terms of Gradient Boosting Machines, on the other.

Figures (13)

• Figure 1: Token magnitude and prediction refinement. Left: mean $\ell_2$ norms of $\mathbf{a}$ and $\boldsymbol{z}$ across outer steps with $\pm 1$ standard deviation bands over 512 random test policies. Right: per-step predictions computed from the $\mathbf{a}$ token and exposure; line is the median, shaded band is the interquartile range, dashed line is the mean.
• Figure 2: Token trajectories in PCA space. PCA basis is fit to all $\mathbf{a}$ and $\boldsymbol{z}$ token vectors across outer steps for the 512-policy test subset. Faint lines show 80 random trajectories; bold lines highlight five policies selected by final prediction percentiles (5, 25, 50, 75, 95). Markers denote start (after the first outer step, open) and end (after the final outer step, filled) positions.
• Figure 3: Feature-to-token alignment. Left: mean cosine similarity between each feature embedding (encoder feature tokens) and the $\mathbf{a}$ token at each outer step for the 512-policy test subset. Right: alignment shift (final minus initial) for both $\mathbf{a}$ and $\boldsymbol{z}$.
• Figure 4: Gradient-based feature attribution. For each policy, we compute $\nabla_{\mathbf{a}} \hat{\mu}$ from the decoder and project it onto each encoder feature embedding; bars show mean attribution with $\pm$1 standard deviation across the 512-policy test subset.
• Figure 5: Token update decomposition on the 512-policy test subset. Left: distribution of update magnitudes $\lVert \Delta \mathbf{a} \rVert$ and $\lVert \Delta \boldsymbol{z} \rVert$ by transition (differences between successive outer steps). Right: direction consistency defined as $\lVert \mathrm{mean}(\Delta/\lVert\Delta\rVert) \rVert$ across samples.