# Train Faster, Perform Better: Modular Adaptive Training in Over-Parameterized Models

arXiv: https://arxiv.org/abs/2405.07527 · HTML: https://mlsanity.com/paper/2405.07527/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 46 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [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)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [Neural Architecture Search on ImageNet in Four GPU Hours: A Theoretically Inspired Perspective](https://mlsanity.com/paper/2102.11535/) (2021)
- [Gradient Descent with Early Stopping is Provably Robust to Label Noise for Overparameterized Neural Networks](https://mlsanity.com/paper/1903.11680/) (2019)
- [Group Fisher Pruning for Practical Network Compression](https://mlsanity.com/paper/2108.00708/) (2021)
- [Are All Layers Created Equal?](https://mlsanity.com/paper/1902.01996/) (2019)
- [Dynamic Sparse Training: Find Efficient Sparse Network From Scratch With Trainable Masked Layers](https://mlsanity.com/paper/2005.06870/) (2020)
- [Generalization Guarantees for Neural Networks via Harnessing the Low-rank Structure of the Jacobian](https://mlsanity.com/paper/1906.05392/) (2019)
- [Fast Finite Width Neural Tangent Kernel](https://mlsanity.com/paper/2206.08720/) (2022)
- [Tensor Programs IIb: Architectural Universality of Neural Tangent Kernel Training Dynamics](https://mlsanity.com/paper/2105.03703/) (2021)

## Built on by (most cited first, 3 of 3)

- [Inductive Gradient Adjustment For Spectral Bias In Implicit Neural Representations](https://mlsanity.com/paper/2410.13271/) (2024)
- [F3OCUS -- Federated Finetuning of Vision-Language Foundation Models with Optimal Client Layer Updating Strategy via Multi-objective Meta-Heuristics](https://mlsanity.com/paper/2411.11912/) (2024)
- [SD-MoE: Spectral Decomposition for Effective Expert Specialization](https://mlsanity.com/paper/2602.12556/) (2026)

## Abstract (arXiv)

Despite their prevalence in deep-learning communities, over-parameterized models convey high demands of computational costs for proper training. This work studies the fine-grained, modular-level learning dynamics of over-parameterized models to attain a more efficient and fruitful training strategy. Empirical evidence reveals that when scaling down into network modules, such as heads in self-attention models, we can observe varying learning patterns implicitly associated with each module's trainability. To describe such modular-level learning capabilities, we introduce a novel concept dubbed modular neural tangent kernel (mNTK), and we demonstrate that the quality of a module's learning is tightly associated with its mNTK's principal eigenvalue λmax. A large λmax indicates that the module learns features with better convergence, while those miniature ones may impact generalization negatively. Inspired by the discovery, we propose a novel training strategy termed Modular Adaptive Training (MAT) to update those modules with their λmax exceeding a dynamic threshold selectively, concentrating the model on learning common features and ignoring those inconsistent ones. Unlike most existing training schemes with a complete BP cycle across all network modules, MAT can significantly save computations by its partially-updating strategy and can further improve performance. Experiments show that MAT nearly halves the computational cost of model training and outperforms the accuracy of baselines.