Enhancing Language Model Hypernetworks with Restart: A Study on Optimization (2025)

Abstract: Hypernetworks are a class of meta-networks that generate weights for main neural networks. Their unique parameter spaces necessitate exploring suitable optimization strategies to enhance performance, especially for language models. However, a comprehensive investigation into optimization strategies for hypernetworks remains absent. To address this gap, we analyze the loss landscape of hypernetworks and propose that restart optimization strategies can improve their performance for language models. We find that hypernetworks have inherently more complicated loss landscapes compared to conventional networks due to their distinct parameter spaces. Consequently, a restart strategy that periodically resets the learning rate can facilitate better convergence for hypernetworks. Through experiments on instruction tuning and multi-task training, we demonstrate that the restart strategy consistently enhances the performance of hypernetworks for language models, often more effectively than for conventional deep neural networks. Our findings highlight the importance of tailored optimization techniques to unlock the full potential of hypernetworks in natural language processing tasks.

## introduction in recent research, large language models (llms) have been proven to be useful tools for learning complicated representations. however, llms have limitations regarding their weights and architecture, typically fixed after training. hypernetworks, proposed by @xcite , use one small neural network to generate the weights for the main network, which attracts great attention for their potential to address this gap. hypernetworks create a new parameter space distinct from the one created by the main network. given the significance of model training strategies in the overall training process, it is highly advantageous to investigate optimization techniques within this new parameter space. the existing hypernetworks usually adopt an optimization strategy similar to the standard training of a general llms @xcite . this means that they do not specifically conduct comparative research on different optimizers and schedulers during training, which we believe finally prevents hypernetworks from being used to their full potential. to address the question above, we conduct a study on the optimization of hypernetworks for language models (lms). when considering the optimization of the neural networks, their loss landscapes depict the direction of optimization. this makes loss landscape important when we try to bridge this gap between conventional lms and hypernetworks. the restart strategy @xcite 10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0 10.0 hutter, 2022), by cyclically resetting the learning rate to the initial state during training, can effectively navigate the challenges of ill-conditioned loss functions and saddle points. particularly for hypernetworks with unique parameter spaces, these simple meta networks' loss landscapes tend to be more rugged compared to the main network, with more local minima and saddle points, as shown in figure 1 . this makes traditional optimization methods prone to getting stuck in these areas and unable to proceed further. the restart strategy introduces a certain perturbation to the model and allows it to escape from the blocked regions and more easily reach the global optimum. in this work, we conduct a series of experiments to investigate the influence of the restart strategy in hypernetworks for language models. our investigation also includes an analysis of minima and saddle points, which provides a foundation for the application of the restart strategy in this context. we conduct a series of experiments to assess the robustness and generalizability of the restart strategy when applied to hypernetworks for lms. as a result, we reveal that the restart strategy enhances the performance of hypernetworks when used for lms. notably, this effect is often more obvious in hypernetworks than in conventional lms. in summary, our contributions are as follows: ## preliminaries in the following part, we refer to the hypernetwork and the corresponding main network whose parameters are not generated by the hypernetwork but are learnable, when we analyze the difference in loss landscape between the hypernetwork and the main network. ## experiments our theoretical derivations and methodologies aim to reveal the problem of hypernetwork optimization and investigate the corresponding solution. in the following part, we mainly use two hypernetworks, hyperdecoders and hyperformer. hyperdecoders is a type of hypernetwork that generates the parameters of adapters in decoders and the adapters and ffns are connected in parallel. hyperformer is another type of hypernetwork that generates the parameters of layer normalization and ffns in adapters and the adapters and ffns are connected in series. ## limitations as previously discussed, the hypernetwork introduces a novel parameter space, making it more suitable for incorporating a new restart strategy. we have demonstrated the effectiveness of this approach and hope to explore these directions further in future work. the hypernetwork architecture is not only applicable to natural language processing but also raises the question of whether it can be effectively applied to other modalities, such as images or multimodal data. additionally, due to the efficiency challenges associated with hypernetworks, we have not yet extended our experiments to larger-scale language models. exploring solutions to these challenges remains an important direction for future research. ## conclusions to address the problems due to the introduction of novel parameter spaces, we analyze the loss landscape of hypernetworks and main networks. we propose that the restart strategy for the learning rate can improve the performance and conver-gence speed of hypernetworks. we conduct our experiments on three different tasks and across two different hypernetwork models: hyperformer and hyperdecoders. we anticipate that our work will stimulate further research into hypernetworks optimization, leading to models that are more closely aligned with conventional lms. additionally, we hope our findings will inspire more research into improving hypernetworks optimization strategies.