# Trap of Feature Diversity in the Learning of MLPs

arXiv: https://arxiv.org/abs/2112.00980 · HTML: https://mlsanity.com/paper/2112.00980/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 55 references that are in the map.
- First posted on arXiv 2 Dec 2021.

## Builds on (most cited first, 30 of 42)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Three Factors Influencing Minima in SGD](https://mlsanity.com/paper/1711.04623/) (2017)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks](https://mlsanity.com/paper/1901.06053/) (2019)
- [Sensitivity and Generalization in Neural Networks: an Empirical Study](https://mlsanity.com/paper/1802.08760/) (2018)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Toward Deeper Understanding of Neural Networks: The Power of Initialization and a Dual View on Expressivity](https://mlsanity.com/paper/1602.05897/) (2016)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice](https://mlsanity.com/paper/1711.04735/) (2017)
- [Convergence of Gradient Descent on Separable Data](https://mlsanity.com/paper/1803.01905/) (2018)
- [Identity Matters in Deep Learning](https://mlsanity.com/paper/1611.04231/) (2016)
- [Rethinking Bias-Variance Trade-off for Generalization of Neural Networks](https://mlsanity.com/paper/2002.11328/) (2020)
- [Traditional and Heavy-Tailed Self Regularization in Neural Network Models](https://mlsanity.com/paper/1901.08276/) (2019)

## Built on by (most cited first, 4 of 4)

- [Tracking the Feature Dynamics in LLM Training: A Mechanistic Study](https://mlsanity.com/paper/2412.17626/) (2024)
- [Batch Normalization Is Blind to the First and Second Derivatives of the Loss](https://mlsanity.com/paper/2205.15146/) (2022)
- [Towards Theoretical Analysis of Transformation Complexity of ReLU DNNs](https://mlsanity.com/paper/2205.01940/) (2022)
- [Unified Batch Normalization: Identifying and Alleviating the Feature Condensation in Batch Normalization and a Unified Framework](https://mlsanity.com/paper/2311.15993/) (2023)

## Abstract (arXiv)

In this paper, we focus on a typical two-phase phenomenon in the learning of multi-layer perceptrons (MLPs), and we aim to explain the reason for the decrease of feature diversity in the first phase. Specifically, people find that, in the training of MLPs, the training loss does not decrease significantly until the second phase. To this end, we further explore the reason why the diversity of features over different samples keeps decreasing in the first phase, which hurts the optimization of MLPs. We explain such a phenomenon in terms of the learning dynamics of MLPs. Furthermore, we theoretically explain why four typical operations can alleviate the decrease of the feature diversity.