Enterprise AI Analysis: Why Adam Fails with Constant Learning Rates

Executive Summary for Enterprise Leaders

This analysis breaks down a critical finding for any enterprise deploying deep learning models. The research paper by Dereich, Graeber, and Jentzen provides mathematical proof that popular adaptive optimizers, including the industry-standard Adam, fail to converge to a stable solution when using a non-vanishing (e.g., constant) learning rate. While it's known that simpler methods like standard Stochastic Gradient Descent (SGD) have this issue, the common assumption has been that Adam's adaptive nature overcomes it. This paper rigorously demonstrates this assumption is false.

For businesses, this means that models trained with seemingly stable, constant learning rates may not be truly stable. Instead of settling on an optimal set of parameters, the model may be perpetually oscillating within a range of "good enough" solutions. This can lead to inconsistent model performance in production, wasted computational resources during training, and challenges with reproducibilityall significant risks in an enterprise environment.

Key Business Takeaways:

• Adam Is Not a "Set-and-Forget" Solution: Enterprises cannot rely on Adam's adaptivity to compensate for a poorly chosen learning rate schedule. A deliberate learning rate decay strategy is still critical for achieving true model convergence and stability.
• Risk of "Hidden" Instability: Models may appear to train well, with low validation loss, but their parameters are not actually settling. This can cause erratic behavior when faced with real-world data drift, posing a significant MLOps risk.
• Potential for Wasted Compute Spend: Training a model that is only oscillating, not improving, is an inefficient use of expensive GPU resources. Identifying and correcting this can lead to direct cost savings and a higher ROI on AI initiatives.
• Importance of Expert Oversight: These findings underscore the need for deep expertise in model training and optimization. A custom AI solutions partner can help diagnose these subtle issues and implement robust training protocols that ensure models are not just accurate, but also stable and reliable for production.

Client: A major investment bank training real-time fraud detection models.

Problem: The bank used the Adam optimizer with a fixed learning rate for simplicity in their MLOps pipeline. They noticed that while models performed well in testing, their performance in production was inconsistent, with some models flagging legitimate transactions and missing obvious fraud.

Our Analysis & Solution: Drawing on principles like those in the Dereich et al. paper, we immediately suspected non-convergent behavior. Our team implemented advanced monitoring of the model's parameter updates during training and confirmed they were oscillating, not stabilizing. We then designed and implemented a custom learning rate schedule featuring a warm-up phase followed by cosine annealing decay. This forced the model to explore broadly at first and then settle into a stable, optimal solution.

Results: