Towards a Deterministic Math Solver for Clinical Language Models
Authors: Felipe Ocampo Osorio, Sebastián Andrés Cajas Ordoñez, Maximin Lange, Rafi Al Attrach, Sahil Kapadia, Zakaria Laouabdia Sellami, Angelo Antonio Talio, Leo Anthony Celi
Large language models are unreliable at arithmetic, which is a problem for clinical calculators where a single numerical error changes the recommendation. The standard response is to hardcode each calculator as a validated function, one at a time. We test an alternative: the model does not calculate. Instead, it writes case-specific Python that a restricted local executor runs as a deterministic solver, and the model's task reduces to deciding how to use it. We evaluate this Program-Solve interface on MedCalc-Bench Verified (1,100 cases, 55 calculators) against direct model arithmetic and a hand-written 22-calculator library, using Qwen2.5-7B and Qwen2.5-32B-AWQ, after auditing the benchmark's formulas against current clinical guidelines and flagging 16 of 55 with version, use or coefficient concerns. With formulas and gold variables supplied and both routes reading the whole note, handing off to the solver is not a reliable advantage at 7B (75.31% against 72.02%, a paired +3.29 points with a 95% calculator-cluster interval of [-3.49, 10.38]) but is one at 32B (90.53% against 83.47%, +7.05 [0.47, 14.60], clear of zero). The hand-written library is exact on its 440 supported cases but abstains elsewhere (40.0% overall). Adding an executor thus helps some open-weight models more than others even under matched formula, variable and note access, and is not a substitute for verified formulas or reliable variable extraction either way.
Current benchmarks for evaluating large language models (LLMs) in medical calculation are largely based on simplified settings, where each patient case corresponds to a single calculator and the required tool is explicitly specified in the query. However, real clinical scenarios often require multiple calculators for joint evaluation, nested-scale calculation, and fuzzy queries that do not directly specify the target calculator. To this end, we propose a new medical calculation benchmark, MedCalc-Pro, which covers three progressively challenging task settings: single-calculator, multi-calculator, and nested-calculator calculation settings. MedCalc-Pro contains 2,268 real-world clinical cases, covering 77 medical calculators across 14 clinical departments. Meanwhile, to address the limited performance of existing frameworks and methods in complex clinical scenarios, we further propose a more generalizable agent framework that supports multi-tool selection and nested-tool calling, while suppressing parameter error propagation through structured validation and evidence review. We conduct systematic comparisons across open-source, closed-source, and medical-specialized LLMs, and the results show that our framework achieves the best performance across all three task settings. This work provides a new benchmark and method for evaluating and applying LLMs in challenging medical calculation scenarios.
Large language models (LLMs) often achieve strong performance on reasoning benchmarks, but final-answer accuracy alone does not show whether they faithfully execute the procedure specified in a prompt. We introduce a controlled diagnostic benchmark for procedural execution, where models are given a step-wise arithmetic procedure and two numeric inputs, and must return the final computed value. Complexity is varied through procedure length and look-back dependencies over intermediate variables. Average first-answer accuracy drops from 63% on 5-step procedures to 20% on 95-step procedures. Generation-level analysis shows that failures often involve missing answers, premature answers, self-correction after an initial error and under-executed traces. These findings suggest that apparent reasoning ability can mask substantial weaknesses in faithful long-horizon procedural execution.
As frontier language models attain near-ceiling performance on static mathematical benchmarks, existing evaluations are increasingly unable to differentiate model capabilities, largely because they cast models solely as solvers of fixed problem sets. We introduce MathDuels, a self-play benchmark in which models occupy dual roles: each authors math problems under adversarial prompting and solves problems authored by every other participant. Problems are produced through a three-stage generation pipeline (meta-prompting, problem generation, and difficulty amplification), and validated by an independent verifier that excludes ill-posed questions. A Rasch model (Rasch, 1993) jointly estimates solver abilities and problem difficulties; author quality is derived from the difficulties of each model's authored problems. Experiments across 19 frontier models reveal that authoring and solving capabilities are partially decoupled, and that dual-role evaluation reveals capability separations invisible in single-role benchmarks. As newer models enter the arena, they produce problems that defeat previously dominant solvers, so the benchmark's difficulty co-evolves with participant strength rather than saturating at a fixed ceiling. We host a public leaderboard that updates as new models are released.