# Towards Flexible Inductive Bias via Progressive Reparameterization Scheduling

arXiv: https://arxiv.org/abs/2210.01370 · HTML: https://mlsanity.com/paper/2210.01370/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 36 references that are in the map.
- First posted on arXiv 4 Oct 2022.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
- [Going deeper with Image Transformers](https://mlsanity.com/paper/2103.17239/) (2021)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Transformer in Transformer](https://mlsanity.com/paper/2103.00112/) (2021)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases](https://mlsanity.com/paper/2103.10697/) (2021)
- [Conditional Positional Encodings for Vision Transformers](https://mlsanity.com/paper/2102.10882/) (2021)
- [Early Convolutions Help Transformers See Better](https://mlsanity.com/paper/2106.14881/) (2021)
- [Conditional Convolutions for Instance Segmentation](https://mlsanity.com/paper/2003.05664/) (2020)
- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [On the Relationship between Self-Attention and Convolutional Layers](https://mlsanity.com/paper/1911.03584/) (2019)
- [DeepViT: Towards Deeper Vision Transformer](https://mlsanity.com/paper/2103.11886/) (2021)
- [Escaping the Big Data Paradigm with Compact Transformers](https://mlsanity.com/paper/2104.05704/) (2021)
- [Incorporating Convolution Designs into Visual Transformers](https://mlsanity.com/paper/2103.11816/) (2021)
- [LocalViT: Analyzing Locality in Vision Transformers](https://mlsanity.com/paper/2104.05707/) (2021)
- [FCOS: A simple and strong anchor-free object detector](https://mlsanity.com/paper/2006.09214/) (2020)
- [A Survey of Visual Transformers](https://mlsanity.com/paper/2111.06091/) (2021)
- [ResT: An Efficient Transformer for Visual Recognition](https://mlsanity.com/paper/2105.13677/) (2021)
- [Can Vision Transformers Perform Convolution?](https://mlsanity.com/paper/2111.01353/) (2021)

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

- [Towards Practical Plug-and-Play Diffusion Models](https://mlsanity.com/paper/2212.05973/) (2022)
- [Navigating Scaling Laws: Compute Optimality in Adaptive Model Training](https://mlsanity.com/paper/2311.03233/) (2023)
- [Toward Onboard AI-Enabled Solutions to Space Object Detection for Space Sustainability](https://mlsanity.com/paper/2505.01650/) (2025)
- [Adaptive Voxel-Weighted Loss Using L1 Norms in Deep Neural Networks for Detection and Segmentation of Prostate Cancer Lesions in PET/CT Images](https://mlsanity.com/paper/2502.02756/) (2025)

## Abstract (arXiv)

There are two de facto standard architectures in recent computer vision: Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs). Strong inductive biases of convolutions help the model learn sample effectively, but such strong biases also limit the upper bound of CNNs when sufficient data are available. On the contrary, ViT is inferior to CNNs for small data but superior for sufficient data. Recent approaches attempt to combine the strengths of these two architectures. However, we show these approaches overlook that the optimal inductive bias also changes according to the target data scale changes by comparing various models' accuracy on subsets of sampled ImageNet at different ratios. In addition, through Fourier analysis of feature maps, the model's response patterns according to signal frequency changes, we observe which inductive bias is advantageous for each data scale. The more convolution-like inductive bias is included in the model, the smaller the data scale is required where the ViT-like model outperforms the ResNet performance. To obtain a model with flexible inductive bias on the data scale, we show reparameterization can interpolate inductive bias between convolution and self-attention. By adjusting the number of epochs the model stays in the convolution, we show that reparameterization from convolution to self-attention interpolates the Fourier analysis pattern between CNNs and ViTs. Adapting these findings, we propose Progressive Reparameterization Scheduling (PRS), in which reparameterization adjusts the required amount of convolution-like or self-attention-like inductive bias per layer. For small-scale datasets, our PRS performs reparameterization from convolution to self-attention linearly faster at the late stage layer. PRS outperformed previous studies on the small-scale dataset, e.g., CIFAR-100.