# The Tunnel Effect: Building Data Representations in Deep Neural Networks

arXiv: https://arxiv.org/abs/2305.19753 · HTML: https://mlsanity.com/paper/2305.19753/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 72 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 54)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Rethinking the Value of Network Pruning](https://mlsanity.com/paper/1810.05270/) (2018)
- [Opening the Black Box of Deep Neural Networks via Information](https://mlsanity.com/paper/1703.00810/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [The large learning rate phase of deep learning: the catapult mechanism](https://mlsanity.com/paper/2003.02218/) (2020)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Complexity of Linear Regions in Deep Networks](https://mlsanity.com/paper/1901.09021/) (2019)
- [Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics](https://mlsanity.com/paper/2007.07400/) (2020)
- [The Low-Rank Simplicity Bias in Deep Networks](https://mlsanity.com/paper/2103.10427/) (2021)
- [Adversarial Continual Learning](https://mlsanity.com/paper/2003.09553/) (2020)
- [Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel](https://mlsanity.com/paper/1810.05369/) (2018)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [What makes instance discrimination good for transfer learning?](https://mlsanity.com/paper/2006.06606/) (2020)
- [One ticket to win them all: generalizing lottery ticket initializations across datasets and optimizers](https://mlsanity.com/paper/1906.02773/) (2019)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)

## Built on by (most cited first, 30 of 34)

- [Linguistic Collapse: Neural Collapse in (Large) Language Models](https://mlsanity.com/paper/2405.17767/) (2024)
- [Parseval Regularization for Continual Reinforcement Learning](https://mlsanity.com/paper/2412.07224/) (2024)
- [Neural Collapse versus Low-rank Bias: Is Deep Neural Collapse Really Optimal?](https://mlsanity.com/paper/2405.14468/) (2024)
- [Intermediate Layer Classifiers for OOD generalization](https://mlsanity.com/paper/2504.05461/) (2025)
- [What Variables Affect Out-of-Distribution Generalization in Pretrained Models?](https://mlsanity.com/paper/2405.15018/) (2024)
- [A Global Geometric Analysis of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2406.01909/) (2024)
- [Parameter Symmetry Potentially Unifies Deep Learning Theory](https://mlsanity.com/paper/2502.05300/) (2025)
- [Controlling Neural Collapse Enhances Out-of-Distribution Detection and Transfer Learning](https://mlsanity.com/paper/2502.10691/) (2025)
- [Formation of Representations in Neural Networks](https://mlsanity.com/paper/2410.03006/) (2024)
- [Neural Collapse is Globally Optimal in Deep Regularized ResNets and Transformers](https://mlsanity.com/paper/2505.15239/) (2025)
- [Register and [CLS] tokens yield a decoupling of local and global features in large ViTs](https://mlsanity.com/paper/2505.05892/) (2025)
- [End-to-End Training Induces Information Bottleneck through Layer-Role Differentiation: A Comparative Analysis with Layer-wise Training](https://mlsanity.com/paper/2402.09050/) (2024)
- [Neural Collapse Meets Differential Privacy: Curious Behaviors of NoisyGD with Near-perfect Representation Learning](https://mlsanity.com/paper/2405.08920/) (2024)
- [Proof of a perfect platonic representation hypothesis](https://mlsanity.com/paper/2507.01098/) (2025)
- [Effective Layer Pruning Through Similarity Metric Perspective](https://mlsanity.com/paper/2405.17081/) (2024)
- [Neural Collapse in Cumulative Link Models for Ordinal Regression: An Analysis with Unconstrained Feature Model](https://mlsanity.com/paper/2506.05801/) (2025)
- [Why and How Auxiliary Tasks Improve JEPA Representations](https://mlsanity.com/paper/2509.12249/) (2025)
- [Efficient LLM Moderation with Multi-Layer Latent Prototypes](https://mlsanity.com/paper/2502.16174/) (2025)
- [Synthetic Speech Source Tracing using Metric Learning](https://mlsanity.com/paper/2506.02590/) (2025)
- [Towards Optimal Adapter Placement for Efficient Transfer Learning](https://mlsanity.com/paper/2410.15858/) (2024)
- [Unpacking Softmax: How Temperature Drives Representation Collapse, Compression, and Generalization](https://mlsanity.com/paper/2506.01562/) (2025)
- [Improving Continual Learning Performance and Efficiency with Auxiliary Classifiers](https://mlsanity.com/paper/2403.07404/) (2024)
- [Quantifying uncertainty in lung cancer segmentation with foundation models applied to mixed-domain datasets](https://mlsanity.com/paper/2403.13113/) (2024)
- [DualFed: Enjoying both Generalization and Personalization in Federated Learning via Hierachical Representations](https://mlsanity.com/paper/2407.17754/) (2024)
- [Linearly Separable Features in Shallow Nonlinear Networks: Width Scales Polynomially with Intrinsic Data Dimension](https://mlsanity.com/paper/2501.02364/) (2025)
- [Diagnosing Generalization Failures from Representational Geometry Markers](https://mlsanity.com/paper/2603.01879/) (2026)
- [Optimizer choice matters for the emergence of Neural Collapse](https://mlsanity.com/paper/2602.16642/) (2026)
- [Layer Pruning with Consensus: A Triple-Win Solution](https://mlsanity.com/paper/2411.14345/) (2024)
- [Random forest-based out-of-distribution detection for robust lung cancer segmentation](https://mlsanity.com/paper/2508.19112/) (2025)
- [Logit-Based Losses Limit the Effectiveness of Feature Knowledge Distillation](https://mlsanity.com/paper/2511.14981/) (2025)

## Abstract (arXiv)

Deep neural networks are widely known for their remarkable effectiveness across various tasks, with the consensus that deeper networks implicitly learn more complex data representations. This paper shows that sufficiently deep networks trained for supervised image classification split into two distinct parts that contribute to the resulting data representations differently. The initial layers create linearly-separable representations, while the subsequent layers, which we refer to as textitthe tunnel, compress these representations and have a minimal impact on the overall performance. We explore the tunnel's behavior through comprehensive empirical studies, highlighting that it emerges early in the training process. Its depth depends on the relation between the network's capacity and task complexity. Furthermore, we show that the tunnel degrades out-of-distribution generalization and discuss its implications for continual learning.