LEAD: Breaking the No-Recovery Bottleneck in Long-Horizon Reasoning
Long-horizon execution in Large Language Models (LLMs) remains unstable even when high-level strategies are provided. Evaluating on controlled algorithmic puzzles, we demonstrate that while decomposition is essential for stability, extreme decomposition creates a “no-recovery bottleneck”. We show that this bottleneck becomes critical due to highly non-uniform error distribution, where consistent errors on a few “hard” steps become irreversible. To address this, we propose Lookahead-Enhanced Atomic Decomposition (LEAD). By incorporating short-horizon future validation and aggregating…
Recent methods have demonstrated that Large Language Models (LLMs) can solve reasoning tasks better when they are encouraged to solve subtasks of the main task first. In this paper we devise a similar strategy that breaks down reasoning tasks into a problem decomposition phase and a problem solving phase and…
In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices -- factored as PSD ×times× unitary -- to any vector field F:Rd→RdF:mathbb{R}^drightarrow mathbb{R}^dF:Rd→Rd. The theorem, known as the polar factorization theorem, states that any field FFF can be recovered as the composition of the gradient of…
This paper was accepted at the Workshop on Navigating and Addressing Data Problems for Foundation Models (NADPFM) at ICLR 2026. Principled domain reweighting can substantially improve sample efficiency and downstream generalization; however, data-mixture optimization for multimodal pretraining remains underexplored. Current multimodal training recipes tune mixtures from only a single perspective…