Improving LoRA with Variational Learning

Bayesian methods have recently been used to improve LoRA finetuning and, although they improve calibration, their effect on other metrics (such as accuracy) is marginal and can sometimes even be detrimental. Moreover, Bayesian methods also increase computational overheads and require additional tricks for them to work well. Here, we fix these issues by using a recently proposed variational algorithm called IVON. We show that IVON is easy to implement and has similar costs to AdamW, and yet it can also drastically improve many metrics by using a simple posterior pruning technique. We present extensive results on billion-scale LLMs (Llama and Qwen series) going way beyond the scale of existing applications of IVON. For example, we finetune a Llama-3.2-3B model on a set of commonsense reasoning tasks and improve accuracy over AdamW by 1.3% and reduce ECE by 5.4%, outperforming AdamW and other recent Bayesian methods like Laplace-LoRA and BLoB. Overall, our results show that variational learning with IVON can effectively improve LoRA finetuning.

Variational Learning Finds Flatter Solutions at the Edge of Stability

Variational Learning (VL) has recently gained popularity for training deep neural networks and is competitive to standard learning methods. Part of its empirical success can be explained by theories such as PAC-Bayes bounds, minimum description length and marginal likelihood, but there are few tools to unravel the implicit regularization in play. Here, we analyze the implicit regularization of VL through the Edge of Stability (EoS) framework. EoS has previously been used to show that gradient descent can find flat solutions and we extend this result to VL to show that it can find even flatter solutions. This is obtained by controlling the posterior covariance and the number of Monte Carlo samples from the posterior. These results are derived in a similar fashion as the standard EoS literature for deep learning, by first deriving a result for a quadratic problem and then extending it to deep neural networks. We empirically validate these findings on a wide variety of large networks, such as ResNet and ViT, to find that the theoretical results closely match the empirical ones. Ours is the first work to analyze the EoS dynamics in VL.

Variational Low-Rank Adaptation Using IVON

We show that variational learning can significantly improve the accuracy and calibration of Low-Rank Adaptation (LoRA) without a substantial increase in the cost. We replace AdamW by the Improved Variational Online Newton (IVON) algorithm to finetune large language models. For Llama-2 with 7 billion parameters, IVON improves the accuracy over AdamW by 2.8% and expected calibration error by 4.6%. The accuracy is also better than the other Bayesian alternatives, yet the cost is lower and the implementation is easier. Our work provides additional evidence for the effectiveness of IVON for large language models. The code is available at https://github.com/team-approx-bayes/ivon-lora.

Variational Learning is Effective for Large Deep Networks

We give extensive empirical evidence against the common belief that variational learning is ineffective for large neural networks. We show that an optimizer called Improved Variational Online Newton (IVON) consistently matches or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of IVON where we improve fine-tuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence in support of effectiveness of variational learning.