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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.10785 |
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| _version_ | 1866912961707114496 |
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| author | Xiong, Zhinan Yuan, Shunqi |
| author_facet | Xiong, Zhinan Yuan, Shunqi |
| contents | In this work, we analyze the optimization dynamics of generative fine-tuning. We observe that under the Flow Matching framework, the standard MSE objective can be formulated as a Quadratic Form governed by a dynamically evolving Neural Tangent Kernel (NTK). This geometric perspective reveals a latent Data Interaction Matrix, where diagonal terms represent independent sample learning and off-diagonal terms encode residual correlation between heterogeneous features. Although standard training implicitly optimizes these cross-term interferences, it does so without explicit control; moreover, the prevailing data-homogeneity assumption may constrain the model's effective capacity. Motivated by this insight, we propose Semantic Granularity Alignment (SGA), using Text-to-Image synthesis as a testbed. SGA engineers targeted interventions in the vector residual field to mitigate gradient conflicts. Evaluations across DiT and U-Net architectures confirm that SGA advances the efficiency-quality trade-off by accelerating convergence and improving structural integrity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10785 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Quadratic Geometry of Flow Matching: Semantic Granularity Alignment for Text-to-Image Synthesis Xiong, Zhinan Yuan, Shunqi Computer Vision and Pattern Recognition In this work, we analyze the optimization dynamics of generative fine-tuning. We observe that under the Flow Matching framework, the standard MSE objective can be formulated as a Quadratic Form governed by a dynamically evolving Neural Tangent Kernel (NTK). This geometric perspective reveals a latent Data Interaction Matrix, where diagonal terms represent independent sample learning and off-diagonal terms encode residual correlation between heterogeneous features. Although standard training implicitly optimizes these cross-term interferences, it does so without explicit control; moreover, the prevailing data-homogeneity assumption may constrain the model's effective capacity. Motivated by this insight, we propose Semantic Granularity Alignment (SGA), using Text-to-Image synthesis as a testbed. SGA engineers targeted interventions in the vector residual field to mitigate gradient conflicts. Evaluations across DiT and U-Net architectures confirm that SGA advances the efficiency-quality trade-off by accelerating convergence and improving structural integrity. |
| title | The Quadratic Geometry of Flow Matching: Semantic Granularity Alignment for Text-to-Image Synthesis |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2603.10785 |