Let’s talk about Adam — not the ancient figure, but the optimizer that’s quietly revolutionizing machine learning. At its core, Adam thrives in the world of large language models (LLMs) where its speed and efficiency outshine conventional methods like SGD. Stochastic Gradient Descent (SGD) is an optimization algorithm that updates model parameters incrementally using a small random subset of data, efficiently minimizing the loss function in machine learning models. The secret sauce? A deep exploitation of ℓ∞ geometry, a specific type of mathematical landscape that allows Adam to glide through the loss function with precision. In a space where every move counts, this change in geometry tweaks how Adam senses the gradients. It’s like trading clunky hiking boots for sleek running shoes — each step becomes faster and more efficient.
Beyond Rotations: Why Adam Thrives
Here’s the catch: while SGD remains unaffected by rotations of the loss landscape, Adam isn’t so lucky. When the loss landscape rotates, Adam’s performance can plummet, as if its internal compass gets scrambled. This is a clue — an indicator that Adam is leveraging a property unique to itself. The difference, ignored by most until now, lies in how Adam adjusts its learning trajectory. This suggests that Adam is not just fast but also dependent on an intricate, non-rotation-invariant geometry. Imagine if your car drove perfectly straight on one road, but swerved uncontrollably on another — Adam is like that, a high-performance machine that excels in very particular conditions.
The graph above illustrates the convergence of training loss for Adam, SGD, and Rotated Adam optimizers over 100,000 iterations. Adam shows the fastest convergence, while Rotated Adam lags behind due to its sensitivity to changes in loss landscape geometry.
When Adaptive Algorithms Go Blockwise
In a fascinating twist, Adam can be generalized into something called “blockwise Adam,” which breaks down the learning process into chunks. Think of this as Adam becoming more modular, adapting not just at the coordinate level but in larger, block-based strategies. This shift gives Adam a broader toolkit, a flexibility that allows it to tackle tasks like training GPT-2 and ResNet models with even greater agility. The technology doesn’t just stop at recognizing shapes — it begins to understand them more intuitively, shifting from pixel-level scrutiny to pattern recognition across entire datasets.
Little-Known Forces Shaping Adam’s Efficiency
Coordinate-wise Adaptivity
Adam adapts its learning rate for each parameter individually, making it excel in complex models like GPT-2.
Loss Landscape Sensitivity
Its success is tied to specific geometries, making it faster under the right conditions but vulnerable to rotations.
Blockwise Optimization
The flexibility of Adam extends beyond individual coordinates, allowing for smarter, larger-scale adaptation.
Empirical Smoothness
Adam outperforms SGD due to its exploitation of a less-known smoothness property in the loss function, particularly under ℓ∞ geometry.
Hessian Sensitivity
Adam’s efficiency is linked to the Hessian matrix — a structure that helps describe the curvature of the loss landscape, especially when measured with ℓ∞ norms.
The Road Ahead for Adam’s Disruption
If there’s one thing we can learn from Adam’s unique performance, it’s that the future of machine learning won’t be driven by brute-force calculations alone. Instead, algorithms like Adam will leverage more sophisticated geometry, allowing AI to become faster, more efficient, and more tailored to the specific problems they face. As these optimizers continue to evolve, they’ll not only shape how we train models but also redefine what’s possible in AI research. The next frontier lies in making these tools more adaptable to different terrains, ensuring their supremacy in diverse applications, from natural language processing to image recognition.
About Disruptive Concepts
Welcome to @Disruptive Concepts — your crystal ball into the future of technology. 🚀 Subscribe for new insight videos every Saturday!
See us on https://twitter.com/DisruptConcept
Read us on https://medium.com/@disruptiveconcepts
Enjoy us at https://disruptive-concepts.com
Whitepapers for you at: https://disruptiveconcepts.gumroad.com/l/emjml
