# Constraint-based Pre-training: From Structured Constraints to Scalable Model Initialization

arXiv: https://arxiv.org/abs/2604.14769 · HTML: https://mlsanity.com/paper/2604.14769/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 64 references that are in the map.
- First posted on arXiv 16 Apr 2026.

## Builds on (most cited first, 30 of 43)

- [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)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Once-for-All: Train One Network and Specialize it for Efficient Deployment](https://mlsanity.com/paper/1908.09791/) (2019)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [Measuring and Improving Consistency in Pretrained Language Models](https://mlsanity.com/paper/2102.01017/) (2021)
- [Rethinking Pre-training and Self-training](https://mlsanity.com/paper/2006.06882/) (2020)
- [Knowledge Distillation and Student-Teacher Learning for Visual Intelligence: A Review and New Outlooks](https://mlsanity.com/paper/2004.05937/) (2020)
- [A Survey on Deep Neural Network Pruning-Taxonomy, Comparison, Analysis, and Recommendations](https://mlsanity.com/paper/2308.06767/) (2023)
- [Embodied Intelligence via Learning and Evolution](https://mlsanity.com/paper/2102.02202/) (2021)
- [MetaMorph: Learning Universal Controllers with Transformers](https://mlsanity.com/paper/2203.11931/) (2022)
- [MiniViT: Compressing Vision Transformers with Weight Multiplexing](https://mlsanity.com/paper/2204.07154/) (2022)
- [IntroVAE: Introspective Variational Autoencoders for Photographic Image Synthesis](https://mlsanity.com/paper/1807.06358/) (2018)
- [Learning to Grow Pretrained Models for Efficient Transformer Training](https://mlsanity.com/paper/2303.00980/) (2023)
- [Fine-Grained Car Detection for Visual Census Estimation](https://mlsanity.com/paper/1709.02480/) (2017)
- [Learning a Universal Template for Few-shot Dataset Generalization](https://mlsanity.com/paper/2105.07029/) (2021)
- [The Herbarium Challenge 2019 Dataset](https://mlsanity.com/paper/1906.05372/) (2019)
- [Mimetic Initialization of Self-Attention Layers](https://mlsanity.com/paper/2305.09828/) (2023)
- [LAPTOP-Diff: Layer Pruning and Normalized Distillation for Compressing Diffusion Models](https://mlsanity.com/paper/2404.11098/) (2024)

## Abstract (arXiv)

The pre-training and fine-tuning paradigm has become the dominant approach for model adaptation. However, conventional pre-training typically yields models at a fixed scale, whereas practical deployment often requires models of varying sizes, exposing its limitations when target model scales differ from those used during pre-training. To address this, we propose an innovative constraint-based pre-training paradigm that imposes structured constraints during pre-training to disentangle size-agnostic knowledge into reusable weight templates, while assigning size-specific adaptation to lightweight weight scalers, thereby reformulating variable-sized model initialization as a multi-task adaptation problem. Within this paradigm, we further introduce WeiT, which employs Kronecker-based constraints to regularize the pre-training process. Specifically, model parameters are represented as compositions of weight templates via concatenation and weighted aggregation, with adaptive connections governed by lightweight weight scalers whose parameters are learned from limited data. This design enables flexible and efficient construction of model weights across diverse downstream scales. Extensive experiments demonstrate the efficiency and effectiveness of WeiT, achieving state-of-the-art performance in initializing models with varying depths and widths across a broad range of perception and embodied learning tasks, including Image Classification, Image Generation, and Embodied Control. Moreover, its effectiveness generalizes to both Transformer-based and Convolution-based architectures, consistently enabling faster convergence and improved performance even under full training.