# Helen: Optimizing CTR Prediction Models with Frequency-wise Hessian Eigenvalue Regularization

arXiv: https://arxiv.org/abs/2403.00798 · HTML: https://mlsanity.com/paper/2403.00798/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 77 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 30 of 38)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [DeepFM: A Factorization-Machine based Neural Network for CTR Prediction](https://mlsanity.com/paper/1703.04247/) (2017)
- [Deep Interest Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1706.06978/) (2017)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [Deep Interest Evolution Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1809.03672/) (2018)
- [DCN V2: Improved Deep & Cross Network and Practical Lessons for Web-scale Learning to Rank Systems](https://mlsanity.com/paper/2008.13535/) (2020)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [Empirical Analysis of the Hessian of Over-Parametrized Neural Networks](https://mlsanity.com/paper/1706.04454/) (2017)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [When Vision Transformers Outperform ResNets without Pre-training or Strong Data Augmentations](https://mlsanity.com/paper/2106.01548/) (2021)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Product-based Neural Networks for User Response Prediction](https://mlsanity.com/paper/1611.00144/) (2016)
- [Efficient Sharpness-aware Minimization for Improved Training of Neural Networks](https://mlsanity.com/paper/2110.03141/) (2021)
- [Causal Intervention for Leveraging Popularity Bias in Recommendation](https://mlsanity.com/paper/2105.06067/) (2021)
- [Asymmetric Valleys: Beyond Sharp and Flat Local Minima](https://mlsanity.com/paper/1902.00744/) (2019)
- [Causal Embeddings for Recommendation](https://mlsanity.com/paper/1706.07639/) (2017)
- [The Unfairness of Popularity Bias in Recommendation](https://mlsanity.com/paper/1907.13286/) (2019)
- [PEPNet: Parameter and Embedding Personalized Network for Infusing with Personalized Prior Information](https://mlsanity.com/paper/2302.01115/) (2023)
- [Normalized Flat Minima: Exploring Scale Invariant Definition of Flat Minima for Neural Networks using PAC-Bayesian Analysis](https://mlsanity.com/paper/1901.04653/) (2019)

## Abstract (arXiv)

Click-Through Rate (CTR) prediction holds paramount significance in online advertising and recommendation scenarios. Despite the proliferation of recent CTR prediction models, the improvements in performance have remained limited, as evidenced by open-source benchmark assessments. Current researchers tend to focus on developing new models for various datasets and settings, often neglecting a crucial question: What is the key challenge that truly makes CTR prediction so demanding? In this paper, we approach the problem of CTR prediction from an optimization perspective. We explore the typical data characteristics and optimization statistics of CTR prediction, revealing a strong positive correlation between the top hessian eigenvalue and feature frequency. This correlation implies that frequently occurring features tend to converge towards sharp local minima, ultimately leading to suboptimal performance. Motivated by the recent advancements in sharpness-aware minimization (SAM), which considers the geometric aspects of the loss landscape during optimization, we present a dedicated optimizer crafted for CTR prediction, named Helen. Helen incorporates frequency-wise Hessian eigenvalue regularization, achieved through adaptive perturbations based on normalized feature frequencies. Empirical results under the open-source benchmark framework underscore Helen's effectiveness. It successfully constrains the top eigenvalue of the Hessian matrix and demonstrates a clear advantage over widely used optimization algorithms when applied to seven popular models across three public benchmark datasets on BARS. Our code locates at github.com/NUS-HPC-AI-Lab/Helen.