A Unified Framework for Knowledge Transfer in Bidirectional Model Scaling

Transferring knowledge by fine-tuning large-scale pre-trained networks has become a standard paradigm for downstream tasks, yet the knowledge of a pre-trained model is tightly coupled with monolithic architecture, which restricts flexible reuse across models of varying scales. In response to this challenge, recent approaches typically resort to either parameter selection, which fails to capture the interdependent structure of this knowledge, or parameter prediction using generative models that depend on impractical access to large network collections. In this paper, we identify the low-frequency components of model weights as the concrete carrier of foundational, task-agnostic knowledge, its learngene", and validate this by demonstrating its efficient inheritance by downstream models and tasks. Based on this insight, we propose FRONT (FRequency dOmain kNowledge Transfer), a novel framework that uses the Discrete Cosine Transform (DCT) to isolate the low-frequency learngene". This learngene can be seamlessly adapted to initialize models of arbitrary size via simple truncation or padding, a process that is entirely training-free. For enhanced performance, we propose an optional low-cost refinement process that introduces a spectral regularizer to further improve the learngene's transferability. Extensive experiments demonstrate that FRONT achieves the state-of-the-art performance, accelerates convergence by up to $15\times$ in vision tasks, and reduces training FLOPs by an average of 40.5% in language tasks. Code is available at https://github.com/LUcy0505/FRONT.

Model families are trained size by size. Can a pretrained large model instead be converted into a smaller sibling? We study the 1.4B->410M conversion in Pythia end to end. Representations align strongly across sizes (ridge R^2=0.84); parameters align weakly. Dense weight projection is destructive; a bit-exact control places the fault in basis mixing, which breaks rotary, per-head, GELU, and LayerNorm structure. Residuals after the best-fit linear operator carry no learnable or transferable signal under shuffle controls, so conversion value lives in initialization. Matched-budget continued pre-training separates two independent levers: least-squares compensation (function lever, best zero-shot) and variance-preserving rescale (dynamics lever, best endpoints). Placement follows the architecture: compensation is well-posed exactly where no normalization sits between cut and read; norm-fronted paths take rescale. Compensation is a low-budget, token-efficiency win, not a universal one. At 30M tokens it beats the best subcloning variant on a width-reduced pair (84.0+-1.8 vs. 89.7+-3.7, 3/3 seeds) and a held-out depth-reduced pair (109.3 vs. 117.9, 3/3 seeds). Selection given the same activation statistics recovers under half of that gap (3/3 seeds): the gain is the re-fit, not the information. At 33x the budget the two reach parity (40.3+-0.3 vs. 40.3+-0.5, 3 seeds), both far ahead of from-scratch, which transfer always beats (up to 18x at low budget, narrowing at convergence and at the largest scale). At ~5x the donor scale (6.9B->1.4B) stacking both levers over-corrects, consistent with an ill-conditioned compensation solve at large width, pointing to dimension-aware regularization as a fix. The init also beats structured pruning plus distillation, the standard pipeline, at matched budget, and improves further combined with it. Code, checkpoints, and the frozen eval corpus are released.

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.