# AdaCap: Adaptive Capacity control for Feed-Forward Neural Networks

arXiv: https://arxiv.org/abs/2205.07860 · HTML: https://mlsanity.com/paper/2205.07860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 79 references that are in the map.
- First posted on arXiv 9 May 2022.

## Builds on (most cited first, 30 of 36)

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- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
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- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
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- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
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- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Characterizing Implicit Bias in Terms of Optimization Geometry](https://mlsanity.com/paper/1802.08246/) (2018)
- [Understanding and Utilizing Deep Neural Networks Trained with Noisy Labels](https://mlsanity.com/paper/1905.05040/) (2019)
- [Neural Oblivious Decision Ensembles for Deep Learning on Tabular Data](https://mlsanity.com/paper/1909.06312/) (2019)
- [Super-Convergence: Very Fast Training of Neural Networks Using Large Learning Rates](https://mlsanity.com/paper/1708.07120/) (2017)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://mlsanity.com/paper/2007.04074/) (2020)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [Challenges in Deploying Machine Learning: a Survey of Case Studies](https://mlsanity.com/paper/2011.09926/) (2020)

## Abstract (arXiv)

The capacity of a ML model refers to the range of functions this model can approximate. It impacts both the complexity of the patterns a model can learn but also memorization, the ability of a model to fit arbitrary labels. We propose Adaptive Capacity (AdaCap), a training scheme for Feed-Forward Neural Networks (FFNN). AdaCap optimizes the capacity of FFNN so it can capture the high-level abstract representations underlying the problem at hand without memorizing the training dataset. AdaCap is the combination of two novel ingredients, the Muddling labels for Regularization (MLR) loss and the Tikhonov operator training scheme. The MLR loss leverages randomly generated labels to quantify the propensity of a model to memorize. We prove that the MLR loss is an accurate in-sample estimator for out-of-sample generalization performance and that it can be used to perform Hyper-Parameter Optimization provided a Signal-to-Noise Ratio condition is met. The Tikhonov operator training scheme modulates the capacity of a FFNN in an adaptive, differentiable and data-dependent manner. We assess the effectiveness of AdaCap in a setting where DNN are typically prone to memorization, small tabular datasets, and benchmark its performance against popular machine learning methods.