Demystifying and Improving Large Model Training under Uncertainty via Optimization Theory

Large machine learning models, including large language models and large vision models, have achieved great success but suffer from poor robustness due to their tendency to overfit to meaningless noise in real-life data. This may lead to hallucination and unexpected behaviors, such as inadvertently inciting users to engage in dangerous activities, costing billions of dollars. To address this issue, practitioners often resort to labor-intensive data cleaning, which is accessible primarily to large organizations.  Recognizing that such short-term fixes are insufficient, the academic community is moving towards more sustainable practices. This involves mitigating noise during training and even leveraging randomness to improve efficiency. Achieving this requires a deeper understanding of the training process. Instead of relying on traditional statistical theories that depend on strong assumptions, optimization theory emerges as a compelling, versatile alternative. Viewing the optimization landscape as a complex terrain, we aim to chart out paths to optimal solutions, a task complicated by noiseinduced obstacles that grow larger and more frequent as model size increases. Our initial even when detours are unavoidable due to these obstacles. Inspired by this discovery, our project will be conducted in three phases: 1) we will establish precise theories for a specific class of non-convex problems to explain the relationship between model size and robustness. Our early findings suggest that this could be done by focusing on singular values of critical points, a universal optimization feature, enabling this approach to be further generalized. 2) Next, we will adapt existing learning algorithms for large models with these new insights to help find routes with less noise-induced obstacles. For example, we plan to modify the popular ADAM optimizer to iteratively weigh gradients based on the landscape properties we have previously discovered. 3) Finally, we will advance our research on harnessing the power of randomness by studying how large model sizes and noise can together increase training performance. Our preliminary results show that structured noise can eliminate bad solutions in matrix completion tasks, only at the cost of a little accuracy. This project could lead to real-life benefits like improved detection of pedestrians and obstacles by self-driving cars in poor weather conditions or at night. It may also reduce the need for data pre-processing and pave way for a new paradigm that could assure users of guaranteed robustness.