NumericJev: Jev-like LLM Numerical Decoding with Multiway Decision Trees

Typed decision models such as Jev offer an efficient alternative to generative LLMs in decision-making workflows by selecting directly from predefined options. When candidate sets contain no valid answer, TypeSafe recommends including an "other" or "none-of-the-above" option to enable rejection. In this report, however, we identify an arithmetic-dependent rejection bottleneck: Jev reliably selects correct numerical answers when available but frequently accepts incorrect alternatives when they are absent despite an explicit rejection option. On paired arithmetic problems, answer-present accuracy reaches 99%, while correct rejection falls to 7%. Moreover, this gap persists across numerical magnitudes, operation depths, contextual formulations, and rejection labels, and extends to scenarios such as time calculation and capacity rounding. Yet native Boolean verification achieves 99% exact-match accuracy on the same answer-absent arithmetic cases, showing that categorical rejection can fail even when the model successfully verifies candidate correctness. Finally, we show that a simple decision threshold selected on separate development problems raises arithmetic rejection accuracy from 7% to 79% while retaining 97% answer-present accuracy, substantially mitigating the failure without retraining or additional inference.

Jev-style decision models return categorical probability distributions over predefined options without generating free-form text, enabling software systems to act on their outputs directly. In this work, we investigate the extent to which general-purpose LLMs already possess this capability out of the box, and when fine-tuning is actually necessary. We present LLM2Jev, an architecture-preserving framework that extracts calibrated decisions directly from next-token probabilities over bracketed numeric identifiers. LLM2Jev provides both a training-free inference recipe and a fine-tuning objective that optimizes candidate selection via a tree-factorized listwise loss while anchoring auxiliary predictions to the base model using KL divergence penalties. Evaluating on Qwen3.5-4B and Qwen3-0.6B, we find that modern LLMs are inherently effective decision models: without training, the 4B model matches community Jev-style models built on the same backbone, outperforms letter-logit readouts, supports arbitrary option counts, and natively handles multimodal decisions over images. Fine-tuning provides targeted rather than universal benefits -- substantially improving weaker models and specific tasks (such as many-option intent routing), but offering diminishing returns for strong backbones. Crucially, our KL anchors prevent behavioral degradation in conversational text generation, with LoRA delivering the strongest performance on capable models.

Number prediction stands as a fundamental capability of large language models (LLMs) in mathematical problem-solving and code generation. The widely adopted maximum likelihood estimation (MLE) for LLM training is not tailored to number prediction. Recently, penalty-driven approaches, e.g., Number Token Loss and Discretized Distance Loss, introduce an inductive bias of numerical distance but induce over-sharpened and over-flattened digit distributions, respectively. In this paper, we make an in-depth analysis on LLM numerical learning, and show that existing numerical learning methods conceptually follow a criterion-distance formulation, where the criterion term represents optimization pattern and the distance term instills geometric prior. Consequently, we present Digit Entropy Loss (DEL) for auto-regressive numerical learning, which reformulates the conventional unsupervised entropy optimization in three key designs: leveraging digit conditional probability and binary cross-entropy to guide the entropy optimization into a supervised manner; deprecating the distance term to bypass the issue of numerical distance; and generalizing the integer-based numerical learning to floating-point number optimization, enabling more accurate number prediction. Our DEL formulation can incorporate integers, decimals, and decimal points, expanding the learning objective from a single digit to the floating-point number domain. Experiments conducted on seven mathematical reasoning benchmarks with four representative LLMs, including CodeLlama, Mistral, DeepSeek, and Qwen-2.5, demonstrate that DEL consistently outperforms its counterparts in both overall prediction accuracy and numerical distance. Source codes are at https://github.com/PolyU-VCLab/DEL