The Plateau
There's a phenomenon in machine learning called grokking, and the first time I learned about it, it genuinely confused me.
Here's what happens. You train a neural network on a simple task, something like modular arithmetic. The network memorizes the training data quickly, gets near-perfect accuracy on everything it's seen. But when you test it on new examples, it performs at chance. Random guessing. The network has memorized the answers, but it hasn't learned the pattern.
This is what overfitting looks like, and everything we know about training neural networks says you should stop here. The model has extracted what it can from the data. Continuing will only reinforce the memorization.
But researchers kept training. And for a long time, nothing changed. Training accuracy stayed perfect. Test accuracy stayed at chance. Thousands of steps, tens of thousands, with no visible sign of progress. A flat line on the graph.
Then, suddenly, test accuracy shot up to near-perfect. Not gradually. In what looks like a single jump. The network went from random guessing to genuine understanding of the underlying pattern.
What This Breaks
This shouldn't happen. Or at least, nobody expected it to.
The standard story in machine learning goes like this: a model learns, it fits the data, and at some point it starts overfitting. Training loss goes down, test loss starts going up, and that's your signal to stop. More training means more overfitting. It's one of the most basic principles in the field.
Grokking says: not always. Sometimes the model needs to memorize first, sit in that memorized state for a very long time, and then something shifts. The generalization comes later, much later, and it comes all at once.
The word itself comes from Robert Heinlein's Stranger in a Strange Land. In the book, to grok something means to understand it so completely that you become one with it. It's not just knowing, it's total comprehension. The researchers who discovered this phenomenon chose that word because what they saw felt like exactly that: a network transitioning from storing answers to actually understanding.
What's Happening Underneath
Here's the part that really gets me.
During that long plateau where nothing seems to be happening, a lot is actually happening. Researchers have looked inside these networks during the grokking process, and what they found is that the network is quietly building a completely different way of solving the problem.
In the memorization phase, the network has essentially created a lookup table. For every input it's seen, it stores an answer. Efficient for training data, useless for anything new. But while this lookup table handles all the outputs, the network is simultaneously developing what researchers call generalizing circuits. These are structures that capture the actual underlying pattern, the algorithm that generates the correct answer for any input, not just the ones it's memorized.
These circuits develop slowly. They're harder to build because they require many parts of the network to coordinate, whereas memorization can happen quickly using relatively independent parameters. So the generalizing solution grows in the background, too weak to influence the network's outputs, invisible in the test accuracy curves.
Until it reaches a tipping point. And then the whole thing flips.
Phase Transitions
There's a concept in physics that maps onto this almost perfectly.
Think about water cooling down. As the temperature drops, the water molecules slow down. Nothing dramatic happens for a while. The water gets colder, but it's still water. The change is continuous, gradual, unremarkable.
Then it hits zero degrees. And within a narrow window, the whole thing becomes ice. The molecules lock into a crystalline structure. Same water, same molecules, same physics the entire time. But the behavior of the system changes suddenly and completely.
This is what a phase transition is. A continuous, gradual change in the underlying conditions that produces a sudden, qualitative change in the observable behavior. Not because anything magical happened at zero degrees, but because the system crossed a threshold where a new organizational state became favorable.
Grokking is a phase transition. The internal representations change continuously throughout training, circuits slowly forming, weights gradually shifting. But the observable behavior, the test accuracy, stays flat until the new organizational state becomes dominant. Then it flips. Just like water becoming ice.
And this isn't just a metaphor. Researchers have actually formalized grokking using tools from statistical physics and found genuine phase transition signatures in the mathematics: critical exponents, scaling laws, sharp transitions between competing solution basins. It's the same kind of phenomenon.
What This Says About Understanding
This is where it gets philosophically interesting to me.
During the plateau, the network simultaneously maintains both solutions. The memorizing one and the generalizing one. They coexist in the same weights, in the same parameters. The network has built the circuits to implement genuine understanding of the pattern. But memorization still dominates its behavior.
So is it understanding or not?
The answer seems to be: that's not really a yes-or-no question. Understanding isn't a switch that flips. It's a reorganization of what's already there. The memorization phase isn't wasted time. It builds the representational raw material that the generalizing circuits eventually reorganize into something deeper. The network can't skip straight to understanding. It has to go through memorization first.
And even during what looks like pure memorization, the weights are already encoding structural information about the task. The understanding is there in seed form from early on. It just needs time to develop, to strengthen, to cross that threshold where it becomes the dominant way the network processes information.
Memorization and understanding aren't opposites. One grows out of the other.
Where I Get Speculative
I think something like this happens in humans too.
Not identically. We have language, prior knowledge, metacognition, all kinds of machinery that neural networks don't have. But the basic shape of it, I think I recognize it.
You study something and it doesn't click. You practice a skill and you plateau. You sit with a question or a problem and nothing seems to move. The effort doesn't feel like it's producing anything.
But maybe it is. Maybe, like the network, you're building structure underneath the surface. Representations that aren't strong enough yet to shift how you think, but that are developing nonetheless. And then one day something tips over and the thing you've been struggling with just makes sense. Not because you learned something new in that moment, but because everything you'd been building quietly crossed a threshold.
Neuroscience research on insight actually supports this to some degree. The "aha moment," that sudden flash of understanding, is preceded by unconscious processing that builds toward a threshold. Brain imaging shows that insight moments involve regions associated with connecting disparate pieces of information, and that this activity is happening before the conscious experience of understanding arrives. The shift feels sudden. But it was building the whole time.
I find something reassuring about that. The plateau isn't nothing. It might be where the real work happens. Invisible and quiet, until it becomes visible all at once.
Still Thinking
I want to be clear that I don't know how far this parallel actually goes. A neural network optimizing a loss function is not the same as a human brain struggling with a concept. And there's a risk of reading too much into the analogy, of seeing connections that aren't really there because the pattern feels satisfying.
But I think grokking points at something real about how understanding works, in any kind of system. That it doesn't always arrive gradually. That it can require a period of what looks like stagnation but isn't. That there might be a phase transition between knowing the pieces and seeing the whole.
And that maybe, when you're on the plateau and nothing seems to be moving, the most important thing is to keep going.
If you've experienced something like this, in learning or practice or anything else, I'd like to hear about it. You can reach me via email or LinkedIn.