Closed-Form Linear-Probe Dataset Distillation for Pre-trained Vision Models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917471456329728 |
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| author | Peng, Bincheng Li, Guang Liu, Ping Ogawa, Takahiro Haseyama, Miki |
| author_facet | Peng, Bincheng Li, Guang Liu, Ping Ogawa, Takahiro Haseyama, Miki |
| contents | Dataset distillation compresses a large training set into a small synthetic set that preserves downstream training utility. While most existing methods target training networks from scratch, modern visual transfer learning often uses frozen pre-trained encoders followed by lightweight linear probing. Existing distillation methods for this setting either unroll iterative linear-probe updates with trajectory-based gradient matching, or rely on closed-form formulations originally designed for from-scratch training with neural-tangent-kernel (NTK) approximations. Neither route exploits the fact that frozen-feature linear probing admits a closed-form solution determined directly by the pre-trained features themselves, with no infinite-width approximation and no inner-loop trajectory. We propose Closed-Form Linear-Probe Dataset Distillation (CLP-DD), a bilevel formulation that computes the linear probe induced by the synthetic set with a sample-space kernel ridge solver. The synthetic images are then updated by evaluating this induced classifier on real features through a temperature-scaled softmax cross-entropy, where the classifier columns act as learned class anchors in feature space. We further show that the choice of outer objective is decisive: pairing the closed-form inner solver with a standard MSE outer loss substantially underperforms trajectory-based methods, while the discriminative outer loss closes most of the gap. On ImageNet-100 with four pre-trained backbones, CLP-DD substantially improves over LGM without DSA and approaches LGM with DSA at a fraction of the computational cost. On ImageNet-1K, CLP-DD matches or surpasses LGM with DSA on three of four backbones while running roughly $14\times$ faster and using less than one-eighth of the GPU memory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_07194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Closed-Form Linear-Probe Dataset Distillation for Pre-trained Vision Models Peng, Bincheng Li, Guang Liu, Ping Ogawa, Takahiro Haseyama, Miki Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning Dataset distillation compresses a large training set into a small synthetic set that preserves downstream training utility. While most existing methods target training networks from scratch, modern visual transfer learning often uses frozen pre-trained encoders followed by lightweight linear probing. Existing distillation methods for this setting either unroll iterative linear-probe updates with trajectory-based gradient matching, or rely on closed-form formulations originally designed for from-scratch training with neural-tangent-kernel (NTK) approximations. Neither route exploits the fact that frozen-feature linear probing admits a closed-form solution determined directly by the pre-trained features themselves, with no infinite-width approximation and no inner-loop trajectory. We propose Closed-Form Linear-Probe Dataset Distillation (CLP-DD), a bilevel formulation that computes the linear probe induced by the synthetic set with a sample-space kernel ridge solver. The synthetic images are then updated by evaluating this induced classifier on real features through a temperature-scaled softmax cross-entropy, where the classifier columns act as learned class anchors in feature space. We further show that the choice of outer objective is decisive: pairing the closed-form inner solver with a standard MSE outer loss substantially underperforms trajectory-based methods, while the discriminative outer loss closes most of the gap. On ImageNet-100 with four pre-trained backbones, CLP-DD substantially improves over LGM without DSA and approaches LGM with DSA at a fraction of the computational cost. On ImageNet-1K, CLP-DD matches or surpasses LGM with DSA on three of four backbones while running roughly $14\times$ faster and using less than one-eighth of the GPU memory. |
| title | Closed-Form Linear-Probe Dataset Distillation for Pre-trained Vision Models |
| topic | Computer Vision and Pattern Recognition Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2605.07194 |