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

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.

• The paper presents a novel recursive latent reasoning model, Tab-TRM, that refines insurance pricing predictions through iterative token updates.
• It leverages efficient feature embeddings and minimal parameter sharing to achieve competitive Poisson deviance loss on real-world insurance data.
• Experimental results show Tab-TRM matching classical actuarial models with fewer parameters, emphasizing its potential for fair, data-efficient pricing.

Tab-TRM: Recursive Latent Reasoning for Tabular Insurance Pricing

Introduction and Context

Tab-TRM (Tabular-Tiny Recursive Model) presents a novel adaptation of the recursive latent reasoning paradigm pioneered by Tiny Recursive Models (TRMs) [jolicoeur2025trm] to the domain of insurance pricing with tabular data. The architecture draws conceptual and algorithmic connections to the Hierarchical Reasoning Model (HRM) [wang2025hrm], classical actuarial models (GLMs, IRLS), as well as modern tabular machine learning frameworks such as Gradient Boosting Machines (GBMs) [friedman2001gbm]. Tab-TRM maintains compact latent states—specifically an answer token and a reasoning token—refined by a parameter-efficient recursive network. This iterative scheme is analogous to stagewise methods in classical and machine learning approaches and is driven to capture complex, nonlinear feature effects without reliance on deep or wide parameterizations.

The model directly addresses the “small data, high interpretability” regime typical in insurance pricing, side-stepping data and computational constraints associated with LLM-based reasoning mechanisms. Tab-TRM is evaluated on the French Motor Third-Party Liability (MTPL) portfolio, a benchmark for actuarial modeling, and demonstrates competitive predictive metrics with strong parameter efficiency.

Methodology

Tab-TRM formulates insurance claim frequency prediction as a Poisson regression problem, estimating expected claim counts conditioned on categorical and continuous risk factors. Each policy is represented as a fixed-size sequence of tokens—feature-specific embeddings for each covariate, concatenated with answer and reasoning prefix tokens. Initial token embeddings are constructed using robust label encoding for categorical variables and piecewise-linear encodings for continuous variables, designed to capture both nonlinear feature effects and actuarial rating curves.

The core of Tab-TRM consists of a recursive processing layer: for each policy, the answer token $a$ and reasoning token $z$ are jointly updated through $T$ outer iterations (“answer refinements”), each containing $m$ inner loops (“reasoning refinements”). The update operators are small FNNs ($f_a$, $f_z$), leveraging residual connections and parameter sharing to achieve computational depth. The final answer token is linearly decoded with an exponential activation to ensure compatibility with Poisson GLMs. Training is performed via Poisson deviance minimization, using early stopping and hyperparameter optimization (Optuna).

Strong numerical results are achieved with minimal nonlinear depth: hyperparameter search consistently favors zero-hidden-layer update maps, i.e., single affine transformations with GELU activation, significantly reducing overfitting risk and model complexity.

Experimental Results

Tab-TRM’s benchmark evaluation on the French MTPL portfolio yields:

• Out-of-sample Poisson deviance loss: $23.589 \times 10^{-2}$ for a 10-run ensemble.
• Model size: 14,820 parameters, substantially fewer than transformer-based benchmarks (e.g., CAFFT: 27,133).
• Ensemble boosting yields notable gains over single-run scores.

Comparative performance with leading actuarial ML architectures is summarized below.

Model	Parameters	Out-of-sample Poisson loss ($10^{-2}$)
CAFFT	27,133	23.726
Credibility Transformer	1,746	23.711
Tree-like PIN	4,147	23.667
Tab-TRM	14,820	23.589

Tab-TRM matches or slightly exceeds these models, underscoring the effectiveness of recursive parameter sharing and reduced-width architectures.

Latent Dynamics and Interpretability

Analysis of Tab-TRM’s internal latent dynamics reveals rapid convergence of both answer and reasoning tokens within a few recursive steps—a reflection of the model’s learned inductive bias for efficient refinement.

Figure 1: Token magnitude and prediction refinement over recursive steps exhibit early stabilization of latent states and predictions, revealing efficient reasoning dynamics.

Further, the token trajectories in PCA space show answer tokens collapsing toward a common semantic region while reasoning tokens diversify, supporting the architecture's intended separation of scratchpad and output functionalities.

Figure 2: PCA visualization of token trajectories demonstrates convergence behavior consistent with robust, stable prediction and flexible intermediate reasoning.

Feature-to-token alignment highlights which covariates dynamically accrue influence on the answer token during recursion.

Figure 3: Feature-to-token alignment shifts indicate progressive reweighting of covariate evidence through latent refinement steps.

Gradient-based attribution scores elucidate the direct impact of covariates on model output, emphasizing strong, interpretable dependencies on key actuarial features.

Figure 4: Feature-specific gradient attribution confirms strong, interpretable alignment of model predictions with actuarially significant covariates.

Update decomposition and linear surrogate analysis exhibit high $R^2$ values (>0.9), confirming that update dynamics are well-approximated by linear maps in the learned latent space—a critical insight for model transparency and potential downstream regulatory compliance.

Figure 5: Decomposition of per-step token updates reveals direction consistency and magnitude stability across recursion iterations.

Figure 6: Surrogate linear models effectively predict latent updates, with clear partitioning of feature and state contributions.

Linearity diagnostics per recursion step further support stable, controlled dynamics, validated by moderate spectral radii.

Figure 7: Strong linear surrogate fits and spectral radius analysis confirm contractive latent state evolution compatible with finite-step recursive refinement.

Local coefficient analysis for both feature types provides “rating surface” interpretations for continuous and categorical covariates, maintaining parity with actuarial standards for tariff factor interpretability.

Figure 8: Local coefficients elucidate covariate response profiles through data-driven slope estimates and standard deviations.

Figure 9: Encoder bin-based coefficient curves for continuous variables reconstruct interpretable, nonlinear rating factors.

Linearized Tab-TRM variants reaffirm performance and interpretability: even with strictly affine update maps, test set deviance remains highly competitive, attributed to the expressiveness of large-dimensional feature embeddings and the recursive architecture.

Figure 10: Eigenvalue analysis of the linearized transition matrix validates non-contracting, finite-step recursive refinement mechanisms.

Figure 11: Step responses of linearized Tab-TRM quantify direct feature-to-answer influence, guiding practical model interrogation.

Figure 12: Steady-state feature influence decomposition demonstrates signed contributions from all covariates to predicted claim frequency.

Theoretical Connections and Implications

Tab-TRM bridges disciplines. Its recursive dynamics correspond to discrete-time state-space models, with latent refinement akin to additive correction in boosting. The parameter-sharing architecture is shown to provide strong regularization, reduced risk of overfitting in low-data regimes, and technical compatibility with iterative techniques in actuarial modeling (IRLS, minimum bias). Interpretability is enhanced by the separation of answer and scratchpad, allowing for token-level analysis that is typically inaccessible in monolithic feed-forward networks.

Practical implications extend to fair pricing, regulatory explainability, and efficient computation under constrained environments. The “less is more” principle, observed empirically, suggests that future research in tabular ML should emphasize parameter-efficient recursive computation rather than deep stacking or unconditional nonlinearity, particularly in fields like insurance.

Discussion and Future Directions

Tab-TRM proposes a minimal and highly structured alternative to current trends in tabular deep learning. Its strong performance in noisy, mixed-type real-world insurance data—as opposed to synthetic symbolic reasoning environments—shows broad applicability. The model’s amenability to interpretability, regularization, and modularity positions it as a blueprint for advanced actuarial prediction tasks.

Avenues for future work include: extending Tab-TRM to severity and frequency-severity modeling, incorporating portfolio time structure, combination with in-context learning, and formal analysis of generalization bounds and approximation rates. Further investigation into the trade-off between encoder capacity (dimensionality) and recursion depth may drive improved accuracy in domains with greater covariate complexity or data scarcity.

Conclusion

Tab-TRM delivers an efficient, interpretable, and theoretically grounded recursive architecture for insurance pricing with tabular data. Its compact, latent reasoning updates coupled with expressive feature encodings realize competitive predictive accuracy, strong regularization, and actuarially meaningful diagnostics—all with far fewer parameters than conventional transformer-based or feed-forward architectures. The evidence supports recursive computation in latent space as a promising direction for tabular regression and beyond (2601.07675).