Generalizing Numerical Reasoning in Table Data through Operation Sketches and Self-Supervised Learning

Numerical reasoning over expert-domain tables often exhibits high in-domain accuracy but limited robustness to domain shift. Models trained with supervised fine-tuning (SFT) on specific datasets tend to rely on header-operation shortcuts rather than structural reasoning. We introduce TaNOS, a continual pre-training framework comprising three components: (i) header anonymization to reduce lexical memorization, (ii) operation sketches that provide minimal structural cues, and (iii) self-supervised pretraining that constructs correctness-guaranteed program-question pairs from given tables in a program-first manner. By decoupling domain semantics and numerical operation structure, TaNOS improves the transferability of numerical reasoning. Applied to an 8B instruction-tuned model, TaNOS achieves 80.13% execution accuracy on FinQA with only 10% train data, outperforming SFT baseline (73.97%) with full train data and proprietary models such as GPT-5, Gemini-2.5-Pro. Furthermore, in the domain-shift experiments, TaNOS displays nearly-negligible cross-domain gap (<2pp) when standard SFT shows over 10pp gap. These results suggest that structural guidance with operation sketches, header-agnostic representations, and correctness-guaranteed self-supervision can improve the robustness of numerical reasoning across diverse expert-domain tables.

QE-EBM: Using Quality Estimators as Energy Loss for Machine Translation

Reinforcement learning has shown great promise in aligning language models with human preferences in a variety of text generation tasks, including machine translation. For translation tasks, rewards can easily be obtained from quality estimation (QE) models which can generate rewards for unlabeled data. Despite its usefulness, reinforcement learning cannot exploit the gradients with respect to the QE score. We propose QE-EBM, a method of employing quality estimators as trainable loss networks that can directly backpropagate to the NMT model. We examine our method on several low and high resource target languages with English as the source language. QE-EBM outperforms strong baselines such as REINFORCE and proximal policy optimization (PPO) as well as supervised fine-tuning for all target languages, especially low-resource target languages. Most notably, for English-to-Mongolian translation, our method achieves improvements of 2.5 BLEU, 7.1 COMET-KIWI, 5.3 COMET, and 6.4 XCOMET relative to the supervised baseline.