Numerical Reasoning in Language Models

Large Language Models (LLMs) have shown strong capabilities in finance-oriented question answering, yet their evaluation on professional quantitative workflows remains fragmented and often stops at factual or document-grounded QA. We introduce QuantEval, a benchmark for evaluating whether LLMs can complete the compute--implement--validate loop required in quantitative finance. QuantEval contains 1,575 expert-validated instances across three complementary dimensions: (i) knowledge-based QA, (ii) quantitative mathematical reasoning, and (iii) quantitative strategy coding. The coding task is evaluated with a deterministic CTA-style backtesting framework that executes model-generated strategies and compares risk--return metrics against expert references, moving beyond syntax or template matching. We evaluate 13 open-source and proprietary LLMs, report prompt and reliability analyses, and observe substantial gaps relative to human experts, especially in multi-step reasoning and framework-constrained coding. We further conduct supervised fine-tuning and reinforcement learning experiments on domain-aligned data, showing that training can improve quantitative reasoning while also exposing trade-offs in factual recall. QuantEval releases the dataset, evaluation scripts, and full backtesting configuration to support reproducible research on LLMs for quantitative finance.

Chain-of-Thought (CoT) prompting is widely adopted for mathematical problem solving, including in low-resource languages, yet its behavior under irrelevant context remains underexplored. To systematically study this challenge, we introduce DISTRACTMATH-BN, a Bangla benchmark that augments MGSM and MSVAMP with semantically coherent but computationally irrelevant information. Evaluating seven models ranging from 3B to 12B parameters, we observe substantial performance degradation under distractors: standard models drop by up to 41 points, while reasoning-specialized models decline by 14 to 20 points despite consuming five times more tokens. We propose †DAGGER, which reformulates mathematical problem solving as executable computational graph generation with explicit modeling of distractor nodes. Fine-tuning Gemma-3 models using supervised fine-tuning followed by Group Relative Policy Optimization achieves comparable weighted accuracy on augmented benchmarks while using 89 percent fewer tokens than reasoning models. Importantly, this robustness emerges without explicit training on distractor-augmented examples. Our results suggest that enforcing structured intermediate representations improves robustness and inference efficiency in mathematical reasoning compared to free-form approaches, particularly in noisy, low-resource settings.

Reliable question answering over long institutional documents requires more than topical retrieval: a system must localize the exact passage that supports a claim and preserve precise numerical and temporal detail when the same indicator recurs across years, countries, and projection horizons in dense, repetitive prose. Existing question-answering benchmarks rarely test this combination of exact grounding and temporal precision at document scale. We introduce AfriEconQA, a benchmark for document-grounded question answering built from 204 World Bank economic reports on African economies, a corpus whose claims are tied to specific fiscal periods, countries, and projection states. AfriEconQA contains 4,138 evidence-linked QA instances across five reasoning categories: Factoid (1,063), List (852), Multiple Choice (889), Synthesis (671), and Comparison (663), targeting quantitative extraction, set recovery, discrimination, causal integration, and cross-period or cross-country reasoning. Each instance carries supporting evidence and source provenance and is constructed through an agentic generation pipeline with evidence-grounding checks and a stratified human-validation subset for gold-label auditing. We evaluate Qwen 3.6 35B, DeepSeek v4-pro, Gemma 4 12B IT, and frontier model GPT-5.5 under zero-shot, oracle, and hybrid retrieval-augmented generation (RAG) conditions on the held-out test split (n = 826). Across all four models, retrieval yields substantial gains, yet the best RAG system reaches only 0.594 F1, with residual errors concentrated in list extraction, synthesis, and temporally scoped comparison. AfriEconQA therefore poses a hard open challenge for exact numerical and temporal grounding over long institutional economic reports.

Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs over novel symbolic representations by introducing an experimental framework that tests their ability to process and manipulate unfamiliar symbols. We introduce semantic deceptions: situations in which symbols carry misleading semantic associations due to their form, such as being embedded in specific contexts, designed to probe whether LLMs can maintain symbolic abstraction or whether they default to exploiting learned semantic associations. We redefine standard digits and mathematical operators using novel symbols, and task LLMs with solving simple calculations expressed in this altered notation. The objective is: (1) to assess LLMs' capacity for abstraction and manipulation of arbitrary symbol systems; (2) to evaluate their ability to resist misleading semantic cues that conflict with the task's symbolic logic. Through experiments with four LLMs we show that semantic cues can significantly deteriorate reasoning models' performance on very simple tasks. They reveal limitations in current LLMs' ability for symbolic manipulations and highlight a tendency to over-rely on surface-level semantics, suggesting that chain-of-thoughts may amplify reliance on statistical correlations. Even in situations where LLMs seem to correctly follow instructions, semantic cues still impact basic capabilities. These limitations raise ethical and societal concerns, undermining the widespread and pernicious tendency to attribute reasoning abilities to LLMs and suggesting how LLMs might fail, in particular in decision-making contexts where robust symbolic reasoning is essential and should not be compromised by residual semantic associations inherited from the model's training.

We develop a transparent, auditable large language model (LLM) pipeline for macro-financial stress testing. Structured prompting, with optional retrieval of country fundamentals and news, emits G7 macroeconomic scenarios (GDP growth, inflation, policy rate), which are converted into deviations from an IMF World Economic Outlook baseline and translated into portfolio losses through a three-channel PCA factor model. The macro-to-factor mapping is stipulated rather than estimated, so every tail-risk multiple is conditional on stated assumptions. Across 2,420 accepted scenarios from two model families and three runs, plus an unanchored-severity run and eight risk-layer ablations, we find three things. First, severity is inherited from scenario design, not generated by the model: prompt variant dominates every variance decomposition, removing the prompted severity bands makes GPT-5.6-luna's recession 1.6 pp milder, apparent country heterogeneity largely reflects the institutional baseline, and retrieval and news matter only where the prompt leaves magnitude free. Second, numerical severity and narrative severity are only weakly coupled. Third, GPT-5.6-luna follows its own arithmetic but anchors on prompted bands, whereas Llama-3.1-8B is four to seven times more dispersed and contradicts its own stated changes in 90% of cases. A repeat run differs at the scenario level yet agrees on aggregate multiples to within 0.007 times. LLM scenario generators are best used for narrative and sector elicitation around a prescribed severity path, not as autonomous calibrators of stress magnitude.

Tasks on complex systems require high-precision numerical computation to support decisions. However, current large language models (LLMs), even with enhanced reasoning capabilities, cannot integrate such computations as an intrinsic and interpretable capability with existing architectures. To this end, we propose Physically-isolated Experts Routing Network (PiERN), an architecture that directs computation and reasoning at token level, thereby enabling iterative alternation within a single chain of thought. We systematically evaluate PiERN on representative computation-reasoning tasks, including PDEBench and battery management tasks. Results show that PiERN achieves not only higher accuracy than directly finetuning LLMs but also significant improvements in response latency, token usage, GPU energy consumption, and experts routing accuracy compared with mainstream multi-agent approaches, while exhibiting no significant degradation in performance on MMLU and GLUE benchmarks. PiERN offers an efficient, interpretable, and scalable paradigm for interfacing language models with scientific systems.