Many multimodal alignment problems require mapping a source modality into a fixed space defined by a target modality, where the target space is not merely an intermediate embedding but is used directly for downstream analysis. In this setting, successful alignment should preserve both the global structure of the target distribution and the instance-level correspondence observed in paired source--target training data. Existing objectives typically address only part of this goal: contrastive losses encourage relative similarity, distribution-matching losses improve marginal agreement, and pointwise regression fits each source sample to its paired target without explicitly modeling target-space path geometry. We propose FlowAlign, a flow-guided target-space alignment method that repurposes conditional flow matching as a training-time alignment signal rather than an inference-time transport model. FlowAlign uses the learned flow field to guide the alignment of source-side representations with the fixed target space, encouraging them to preserve paired correspondence while remaining compatible with the global target-space structure. We further provide theoretical analysis showing how FlowAlign helps improve paired correspondence by controlling endpoint accuracy and capturing local target-space geometry. Experiments on synthetic data, paired single-cell multiome benchmarks, and image--text alignment demonstrate that FlowAlign improves instance level correspondence while preserving target-space structure across different modality settings.
Zeqiu Yu, Xuesheng Zhang, Wenxiao Zhao, Shixiao Wang
原文摘要
Long-to-Short (L2S) model merging seeks to combine the strong reasoning capability of long chain-of-thought models with the concise style of base models, but existing methods that rely on linear interpolation and first-order activation statistics fail to capture how the loss landscape responds to parameter displacement, leading to degraded accuracy on hard tasks. We propose Low-Rank Hierarchical Merging (LHM), a training-free framework that replaces heuristic statistics with lightweight second-order curvature information. LHM consists of three components: (1) a low-rank Hessian approximation that efficiently estimates per-layer Hessian traces via Hutchinson's estimator on random inputs, eliminating the need for task-specific data; (2) a Layer Second-Order Sensitivity (LSOS) index that combines Hessian trace with task-vector norm to quantify per-layer fusion difficulty; and (3) a Dual-Constraint Coefficient Mapping (DCCM) that converts LSOS scores into layer-adaptive merge coefficients while jointly satisfying a fusion-error bound and a global length-reduction target. Experiments across six mathematical benchmarks on 1.5B and 7B models show that LHM outperforms state-of-the-art methods such as ACM-TIES and ORCA, achieving over 4\% accuracy gain and up to 93.1\% reduction in output length relative to the long-CoT model.