# Efficient Bilevel Optimization with KFAC-Based Hypergradients

arXiv: https://arxiv.org/abs/2603.29108 · HTML: https://mlsanity.com/paper/2603.29108/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 81 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 30 of 53)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Unlearnable Examples: Making Personal Data Unexploitable](https://mlsanity.com/paper/2101.04898/) (2021)
- [Truncated Back-propagation for Bilevel Optimization](https://mlsanity.com/paper/1810.10667/) (2018)
- [Recasting Gradient-Based Meta-Learning as Hierarchical Bayes](https://mlsanity.com/paper/1801.08930/) (2018)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [A Two-Timescale Framework for Bilevel Optimization: Complexity Analysis and Application to Actor-Critic](https://mlsanity.com/paper/2007.05170/) (2020)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [MetaPoison: Practical General-purpose Clean-label Data Poisoning](https://mlsanity.com/paper/2004.00225/) (2020)
- [BOME! Bilevel Optimization Made Easy: A Simple First-Order Approach](https://mlsanity.com/paper/2209.08709/) (2022)
- [A Fully First-Order Method for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2301.10945/) (2023)
- [A framework for bilevel optimization that enables stochastic and global variance reduction algorithms](https://mlsanity.com/paper/2201.13409/) (2022)
- [EigenDamage: Structured Pruning in the Kronecker-Factored Eigenbasis](https://mlsanity.com/paper/1905.05934/) (2019)
- [WRENCH: A Comprehensive Benchmark for Weak Supervision](https://mlsanity.com/paper/2109.11377/) (2021)
- [BackPACK: Packing more into backprop](https://mlsanity.com/paper/1912.10985/) (2019)
- [Meta-Curvature](https://mlsanity.com/paper/1902.03356/) (2019)

## Built on by (most cited first, 1 of 1)

- [A Light Bilevel Refinement Aligns Self-Supervised Representations for Stronger Task-Specific Learning](https://mlsanity.com/paper/2609.33424/) (2026)

## Abstract (arXiv)

Bilevel optimization (BO) is widely applicable to many machine learning problems. Scaling BO, however, requires repeatedly computing hypergradients, which involves solving inverse Hessian-vector products (IHVPs). In practice, these operations are often approximated using crude surrogates such as one-step gradient unrolling or identity/short Neumann expansions, which discard curvature information. We build on implicit function theorem-based algorithms and propose to incorporate Kronecker-factored approximate curvature (KFAC), yielding curvature-aware hypergradients with a better performance efficiency trade-off than Conjugate Gradient (CG) or Neumann methods and consistently outperforming unrolling. We evaluate this approach across diverse tasks, including meta-learning and AI safety problems. On models up to BERT, we show that curvature information is valuable at scale, and KFAC can provide it with only modest memory and runtime overhead. Our implementation is available at https://github.com/liaodisen/NeuralBo.