GIFT: Games as Informal Training for Generalizable LLMs

While Large Language Models (LLMs) have achieved remarkable success in formal learning tasks such as mathematics and code generation, they still struggle with the "practical wisdom" and generalizable intelligence, such as strategic creativity and social reasoning, that characterize human cognition. This gap arises from a lack of informal learning, which thrives on interactive feedback rather than goal-oriented instruction. In this paper, we propose treating Games as a primary environment for LLM informal learning, leveraging their intrinsic reward signals and abstracted complexity to cultivate diverse competencies. To address the performance degradation observed in multi-task learning, we introduce a Nested Training Framework. Unlike naive task mixing optimizing an implicit "OR" objective, our framework employs sequential task composition to enforce an explicit "AND" objective, compelling the model to master multiple abilities simultaneously to achieve maximal rewards. Using GRPO-based reinforcement learning across Matrix Games, TicTacToe, and Who's the Spy games, we demonstrate that integrating game-based informal learning not only prevents task interference but also significantly bolsters the model's generalization across broad ability-oriented benchmarks. The framework and implementation are publicly available.

Learning from Mistakes: Negative Reasoning Samples Enhance Out-of-Domain Generalization

Supervised fine-tuning (SFT) on chain-of-thought (CoT) trajectories demonstrations is a common approach for enabling reasoning in large language models. Standard practices typically only retain trajectories with correct final answers (positives) while ignoring the rest (negatives). We argue that this paradigm discards substantial supervision and exacerbates overfitting, limiting out-of-domain (OOD) generalization. Specifically, we surprisingly find that incorporating negative trajectories into SFT yields substantial OOD generalization gains over positive-only training, as these trajectories often retain valid intermediate reasoning despite incorrect final answers. To understand this effect in depth, we systematically analyze data, training dynamics, and inference behavior, identifying 22 recurring patterns in negative chains that serve a dual role: they moderate loss descent to mitigate overfitting during training and boost policy entropy by 35.67% during inference to facilitate exploration. Motivated by these observations, we further propose Gain-based LOss Weighting (GLOW), an adaptive, sample-aware scheme that exploits such distinctive training dynamics by rescaling per-sample loss based on inter-epoch progress. Empirically, GLOW efficiently leverages unfiltered trajectories, yielding a 5.51% OOD gain over positive-only SFT on Qwen2.5-7B and boosting MMLU from 72.82% to 76.47% as an RL initialization.