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Hyperparameter optimization of neural networks can be elegantly formulated asa bilevel optimization problem. While research on bilevel optimization ofneural networks has been dominated by implicit differentiation and unrolling,hypernetworks such as Self-Tuning Networks (STNs) have recently gained tractiondue to their ability to amortize the optimization of the inner objective. Inthis paper, we diagnose several subtle pathologies in the training of STNs.Based on these observations, we propose the $\Delta$-STN, an improvedhypernetwork architecture which stabilizes training and optimizeshyperparameters much more efficiently than STNs. The key idea is to focus onaccurately approximating the best-response Jacobian rather than the fullbest-response function; we achieve this by reparameterizing the hypernetworkand linearizing the network around the current parameters. We demonstrateempirically that our $\Delta$-STN can tune regularization hyperparameters (e.g.weight decay, dropout, number of cutout holes) with higher accuracy, fasterconvergence, and improved stability compared to existing approaches.

Delta-STN: Efficient Bilevel Optimization for Neural Networks using Structured Response Jacobians