# Understanding and Improving Transfer Learning of Deep Models via Neural Collapse

arXiv: https://arxiv.org/abs/2212.12206 · HTML: https://mlsanity.com/paper/2212.12206/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 98 references that are in the map.
- First posted on arXiv 23 Dec 2022.

## Builds on (most cited first, 30 of 63)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [CLIP-Adapter: Better Vision-Language Models with Feature Adapters](https://mlsanity.com/paper/2110.04544/) (2021)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Do Better ImageNet Models Transfer Better?](https://mlsanity.com/paper/1805.08974/) (2018)
- [Vision Transformer Adapter for Dense Predictions](https://mlsanity.com/paper/2205.08534/) (2022)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Rethinking Few-Shot Image Classification: a Good Embedding Is All You Need?](https://mlsanity.com/paper/2003.11539/) (2020)

## Built on by (most cited first, 24 of 24)

- [No Fear of Classifier Biases: Neural Collapse Inspired Federated Learning with Synthetic and Fixed Classifier](https://mlsanity.com/paper/2303.10058/) (2023)
- [Deep Neural Collapse Is Provably Optimal for the Deep Unconstrained Features Model](https://mlsanity.com/paper/2305.13165/) (2023)
- [Neural Collapse for Unconstrained Feature Model under Cross-entropy Loss with Imbalanced Data](https://mlsanity.com/paper/2309.09725/) (2023)
- [Linguistic Collapse: Neural Collapse in (Large) Language Models](https://mlsanity.com/paper/2405.17767/) (2024)
- [The Tunnel Effect: Building Data Representations in Deep Neural Networks](https://mlsanity.com/paper/2305.19753/) (2023)
- [The Law of Parsimony in Gradient Descent for Learning Deep Linear Networks](https://mlsanity.com/paper/2306.01154/) (2023)
- [Neural Collapse Terminus: A Unified Solution for Class Incremental Learning and Its Variants](https://mlsanity.com/paper/2308.01746/) (2023)
- [Neural Collapse in Multi-label Learning with Pick-all-label Loss](https://mlsanity.com/paper/2310.15903/) (2023)
- [FedLoGe: Joint Local and Generic Federated Learning under Long-tailed Data](https://mlsanity.com/paper/2401.08977/) (2024)
- [Towards Demystifying the Generalization Behaviors When Neural Collapse Emerges](https://mlsanity.com/paper/2310.08358/) (2023)
- [Neural Collapse in Cumulative Link Models for Ordinal Regression: An Analysis with Unconstrained Feature Model](https://mlsanity.com/paper/2506.05801/) (2025)
- [The Impact of Geometric Complexity on Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2405.15706/) (2024)
- [Efficient Compression of Overparameterized Deep Models through Low-Dimensional Learning Dynamics](https://mlsanity.com/paper/2311.05061/) (2023)
- [Balancing Two Classifiers via A Simplex ETF Structure for Model Calibration](https://mlsanity.com/paper/2504.10007/) (2025)
- [Understanding Prompt Tuning for V-L Models Through the Lens of Neural Collapse](https://mlsanity.com/paper/2306.15955/) (2023)
- [Linearly Separable Features in Shallow Nonlinear Networks: Width Scales Polynomially with Intrinsic Data Dimension](https://mlsanity.com/paper/2501.02364/) (2025)
- [Neural Collapse Dynamics: Depth, Activation, Regularisation, and Feature Norm Threshold](https://mlsanity.com/paper/2604.00230/) (2026)
- [Unleashing the power of Neural Collapse for Transferability Estimation](https://mlsanity.com/paper/2310.05754/) (2023)
- [Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension](https://mlsanity.com/paper/2510.01105/) (2025)
- [Evaluating the Representation Space of Diffusion Models via Self-Supervised Principles](https://mlsanity.com/paper/2606.09718/) (2026)
- [Beyond Coordinate Gauge: An Audited Protocol for Detecting Donor-Specific Functional Fingerprints after Neural Collapse](https://mlsanity.com/paper/2607.11967/) (2026)
- [Optical-Guided Neural Collapse for SAR Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2606.04528/) (2026)
- [Ordinal Neural Collapse as a Representation Prior for Visual Navigation](https://mlsanity.com/paper/2606.26839/) (2026)
- [GeoBalance: Geometry-Aware Monitoring and Reconstruction with Asymmetric Optimization for Balanced Multimodal Learning](https://mlsanity.com/paper/2609.23533/) (2026)

## Abstract (arXiv)

With the ever-increasing complexity of large-scale pre-trained models coupled with a shortage of labeled data for downstream training, transfer learning has become the primary approach in many fields, including natural language processing, computer vision, and multi-modal learning. Despite recent progress, the fine-tuning process for large-scale pre-trained models in vision still mostly relies on trial and error. This work investigates the relationship between neural collapse (NC) and transfer learning for classification problems. NC is an intriguing while prevalent phenomenon that has been recently discovered in terms of the final-layer features and linear classifiers of trained neural networks. Specifically, during the terminal phase of training, NC implies that the variability of the features within each class diminishes to zero, while the means of features between classes are maximally and equally distanced. In this work, we examine the NC attributes of pre-trained models on both downstream and source data for transfer learning, and we find strong correlation between feature collapse and downstream performance. In particular, we discovered a systematic pattern that emerges when linear probing pre-trained models on downstream training data: the more feature collapse of pre-trained models on downstream training data, the higher the transfer accuracy. Additionally, we also studied the relationship between NC and transfer accuracy on the source data. Moreover, these findings allow us to develop a principled, parameter-efficient fine-tuning method that employs skip-connection to induce the last-layer feature collapse on downstream data. Our proposed fine-tuning methods deliver good performances while reducing fine-tuning parameters by at least 90% and mitigating overfitting in situations especially when the downstream data is scarce.