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Calibrated Dataset Condensation for Faster Hyperparameter Search

Mucong Ding, Yuancheng Xu, Tahseen Rabbani, Xiaoyu Liu, Brian Gravelle, Teresa Ranadive, Tai-Ching Tuan, Furong Huang

TL;DR

The paper tackles the high cost of hyperparameter search by proposing Hyperparameter Calibrated Dataset Condensation (HCDC), which preserves hyperparameter optimization outcomes rather than single-model generalization. By aligning hypergradients computed on condensed data with those from the full dataset, and using implicit differentiation with a Neumann-series inverse-Hessian, HCDC learns a synthetic validation set that mirrors hyperparameter rankings across architectures and hyperparameters. The method enables scalable, memory-efficient hypergradient computation and extends the hyperparameter space to handle discrete and continuous settings, achieving strong empirical preservation of NAS rankings on both image and graph tasks, while accelerating search. This approach provides a practical pathway to faster, data-efficient hyperparameter and architecture search with broad applicability to vision and graph learning problems.

Abstract

Dataset condensation can be used to reduce the computational cost of training multiple models on a large dataset by condensing the training dataset into a small synthetic set. State-of-the-art approaches rely on matching the model gradients between the real and synthetic data. However, there is no theoretical guarantee of the generalizability of the condensed data: data condensation often generalizes poorly across hyperparameters/architectures in practice. This paper considers a different condensation objective specifically geared toward hyperparameter search. We aim to generate a synthetic validation dataset so that the validation-performance rankings of the models, with different hyperparameters, on the condensed and original datasets are comparable. We propose a novel hyperparameter-calibrated dataset condensation (HCDC) algorithm, which obtains the synthetic validation dataset by matching the hyperparameter gradients computed via implicit differentiation and efficient inverse Hessian approximation. Experiments demonstrate that the proposed framework effectively maintains the validation-performance rankings of models and speeds up hyperparameter/architecture search for tasks on both images and graphs.

Calibrated Dataset Condensation for Faster Hyperparameter Search

TL;DR

The paper tackles the high cost of hyperparameter search by proposing Hyperparameter Calibrated Dataset Condensation (HCDC), which preserves hyperparameter optimization outcomes rather than single-model generalization. By aligning hypergradients computed on condensed data with those from the full dataset, and using implicit differentiation with a Neumann-series inverse-Hessian, HCDC learns a synthetic validation set that mirrors hyperparameter rankings across architectures and hyperparameters. The method enables scalable, memory-efficient hypergradient computation and extends the hyperparameter space to handle discrete and continuous settings, achieving strong empirical preservation of NAS rankings on both image and graph tasks, while accelerating search. This approach provides a practical pathway to faster, data-efficient hyperparameter and architecture search with broad applicability to vision and graph learning problems.

Abstract

Dataset condensation can be used to reduce the computational cost of training multiple models on a large dataset by condensing the training dataset into a small synthetic set. State-of-the-art approaches rely on matching the model gradients between the real and synthetic data. However, there is no theoretical guarantee of the generalizability of the condensed data: data condensation often generalizes poorly across hyperparameters/architectures in practice. This paper considers a different condensation objective specifically geared toward hyperparameter search. We aim to generate a synthetic validation dataset so that the validation-performance rankings of the models, with different hyperparameters, on the condensed and original datasets are comparable. We propose a novel hyperparameter-calibrated dataset condensation (HCDC) algorithm, which obtains the synthetic validation dataset by matching the hyperparameter gradients computed via implicit differentiation and efficient inverse Hessian approximation. Experiments demonstrate that the proposed framework effectively maintains the validation-performance rankings of models and speeds up hyperparameter/architecture search for tasks on both images and graphs.
Paper Structure (36 sections, 5 theorems, 38 equations, 18 figures, 6 tables, 1 algorithm)

This paper contains 36 sections, 5 theorems, 38 equations, 18 figures, 6 tables, 1 algorithm.

Key Result

Theorem 1

Hypergradient alignment (def:hg-align) is equivalent to hyperparameter calibration (def:hc) on a connected and compact set, e.g., the extended search space $\tilde{\Lambda}$.

Figures (18)

  • Figure 1: Hyperparameter Calibrated Dataset Condensation (HCDC) aims to find a small validationdataset such that the validation-performance rankings of the models with different hyperparameters are comparable to the large original dataset's. Our method realizes this goal (\ref{['eq:hc']}) by learning the synthetic validation set to match the hypergradients w.r.t the hyperparameters (\ref{['eq:hcdc']} in the "Loss" box). Our contribution is depicted within the big black dashed box: the algorithm flow is indicated through the red dashed arrows. The synthetic training set is predetermined by any standard dataset condensation (SDC) methods (e.g., \ref{['eq:sdc-bl']}). The synthetic training and validation datasets obtained can later be used for hyperparameter search using only a fraction of the original computational load. A more detailed diagram is depicted in \ref{['fig:schematic-appendix']} in \ref{['apd:diagram']}.
  • Figure 2: Visualization of the performance rankings of architectures (subsampled from the search space) evaluated on different condensed datasets. Colors indicate the performance ranking on the original dataset, while lighter shades refer to better performance. Spearman's rank correlations are shown on the right.
  • Figure 3: Visualization of some example condensed validation set images using our HCDC algorithm on CIFAR-10.
  • Figure 4: Speed-up of graph NAS's search process, when evaluated on the small proxy dataset condensed by HCDC.
  • Figure 5: Hyperparameter Calibrated Dataset Condensation (HCDC) aims to find a small validationdataset such that the validation-performance rankings of the models with different hyperparameters are comparable to the large original dataset's (\ref{['eq:hc']} in the "Goal" box). Our method realizes this goal by learning the synthetic validation set to match the hypergradients w.r.t the hyperparameters (\ref{['eq:hcdc']} in the "Loss" box). Our contribution is depicted within the big black dashed box. The algorithm flow is indicated through the red dashed arrows. Solid arrows (blue, yellow and green) indicate forward passes. To calculate the hypergradients with respect to hyperparameters $\lambda$, we backpropagate to compute both implicit/direct gradients (thin/thick green dashed arrows). The synthetic training set is predetermined by any standard dataset condensation (SDC) methods (e.g., \ref{['eq:sdc-bl']}). The synthetic training and validation datasets obtained can later be used for hyperparameter search using only a fraction of the original computational load.
  • ...and 13 more figures

Theorems & Definitions (8)

  • Definition 1: Hyperparameter Calibration
  • Definition 2: Hypergradient Alignment
  • Theorem 1: Equivalence between Hypergradient Alignment and Hyperparameter Calibration
  • Proposition 2: Successful Generalization of SDC across 1D-CNNs
  • Proposition 3: Condensed Adjacency Overfits SDC Objective
  • Proposition 4: Failed Generalization of SDC across GNNs
  • Lemma 5
  • proof