How Physicists Solved Graph Neural Net’s Biggest Problem [Oversmoothing]

Added: 2026-05-27

[00:00:00]Imagine you're building an AI to understand Facebook's social network, Google's map of roads, or maybe even Amazon's shopping graph of users and products. In all these cases, we use a type of AI called graph neural networks.

[00:00:15]The idea is that if each thing in the network could listen to its neighbors, then the more rounds of listening you allow, the smarter the system should become. And yet, something strange happens. make graph neural networks deep enough and instead of becoming more insightful, they begin to forget.

[00:00:33]Distinctions blur. Different nodes that started out with their own identities slowly drift toward the same representation.

[00:00:41]In the end, everything looks almost identical. That failure has a name, over smoothing. But the name hides how strange it really is. We tried to make a network think harder by letting information travel farther and we accidentally made it wash out the very differences it needed to reason. To see why, it helps to start with what a graph neural network, often called a GNN, actually is. Despite the intimidating name, the central idea is simple. In ordinary machine learning, you might describe one object at a time. The object could be an image, a sentence, or one row of a spreadsheet. In a graph neural network, the relationships are part of the data. A person is linked to friends. A city is linked to nearby cities by roads. A paper is linked to the papers it sites. A protein is linked to other proteins with which it interacts. The usual way GNN works is through something called message passing. Don't let the term scare you.

[00:01:36]It just means conversation. Each node sends a small summary of itself to its neighbors. Then each node updates its own state based on what it heard. Do this once and a node learns about its immediate neighborhood. Do it again and it learns about neighbors of neighbors.

[00:01:53]Stack many layers and information can travel far across the graph. That sounds obviously useful. A paper may be understood better by knowing not just what it sites but what those papers site too. A molecule may depend on interactions several steps away. Depth in principle should let the model reason over long distances. So where does the forgetting come from? The key insight is that this neighborhood conversation often behaves a lot like diffusion.

[00:02:19]Think of dropping a bit of colored dye into water. At first, the pattern is informative. You can see where the dye entered, where it's concentrated, and where the gradients are. But if you wait long enough, the dye spreads. The sharp structure fades. Eventually, the water becomes nearly uniform. Many GNN's do something very similar in feature space, the internal world where the network stores what it has learned about each node. Early rounds of message passing are helpful. A node picks up local context, but repeated many times, the process starts averaging everything together. Nodes become blends of their surroundings, then blends of blends until much of the original contrast is gone. That is over smoothing. The network talks so much that everyone starts saying the same thing.

[00:03:08]>> Hope you are enjoying my video. To provide you guys the maximum value, I'm going to build a premium service. The problem is I don't know what will be most valuable to you. So, I posted a poll to find that out. Please do me a favor, finish this video, then hit the link in the pinned comment to vote. Now, let's get back to the video. A common misconception in artificial intelligence is that increased network depth guarantees better performance. Although deeper architectures allow image and language models to learn more complex representations, this principle does not apply to graph neural networks. In GNN's, additional layers result in excessive neighborhood averaging. This over smoothing has a severe hidden cost.

[00:03:53]It degrades the distinct features or identities of individual nodes. So why are these models so prone to averaging?

[00:04:00]Because they are built around a quiet assumption. Connected things should become more similar. If your neighbors matter, then your representation should move toward theirs. You can think of this as an attraction. Every message passing step pulls connected nodes closer together in the network's internal space. Sometimes that assumption is exactly right. In a citation network, related papers often cite each other. In a friendship network, friends often share interests.

[00:04:30]In these birds of a feather situations, smoothing across edges can help the AI infer missing information. If the papers around me are about climate science, perhaps I belong in that topic as well.

[00:04:43]But now comes the deeper insight. Not all networks work like that. Sometimes the most meaningful connections are between things that are supposed to be different. A buyer and a seller are connected precisely because they play different roles. A student and a course are linked because one takes the other, not because they are the same kind of entity. In politics, people may interact most intensely with opponents. In biology, predator and prey are linked, but they are not versions of the same thing. In question answer systems, the question is not supposed to become more like the answer. This is the divide between homophyle.

[00:05:22]Homophy means similar connects to similar. Heterophily means opposites, compliments or contrasting roles are linked. Classic GNN's are often much happier in homophilic worlds than in heterophilic ones. And now the flaw becomes obvious. If your model assumes every edge says become more alike than on heterophilic graphs, it does exactly the wrong thing. It blends together things that should remain distinct. It averages enemies into allies. questions into answers, buyers into sellers. The signal is being erased by the model's own design. This is where physics enters the story. The breakthrough idea is to stop viewing graph message passing as pure diffusion like dye spreading peacefully through water and instead view it as a physical system evolving under forces. Imagine each node of the graph, for example, a person in a social network as a particle in a swarm. Edges say who can influence whom. But influence doesn't have to mean only attraction. In physical systems, stable structure often comes from competing forces. Bird flocks stay together, but not so tightly that they crash into each other. Human crowds form organized lanes because people align in some ways and avoid collision in others. Even in magnets and materials, order can emerge from the balance of pulling together and pushing apart. That new mental model changes everything. Some neighbors should pull your representation closer.

[00:06:55]Others should push it away. Attraction can preserve coherence within a group.

[00:07:01]Repulsion can preserve boundaries between groups. And this is an elegant idea because it addresses over smoothing at its root. If attraction alone turns the graph into a mushy clump, then repulsion can stop the collapse. It keeps contrasts alive and gives the system a way to say, "Yes, I hear my neighbor, but I should not become them."

[00:07:21]But repulsion introduces a new danger.

[00:07:24]If everything is allowed to push away without limit, the system can become unstable. Instead of a mushy collapse, you get an explosion. Representations fly apart, growing more extreme and less meaningful. If attractiononly GNN's give you feature soup, then repulsion only GNN's give you chaos. So the problem is no longer just add repulsion. It becomes a more subtle engineering challenge. How do you create stable diversity? How do you preserve meaningful differences without letting the system blow up? To overcome this challenge, the reference article in the description borrows a beautiful idea from physics called Alen Con dynamics, which comes from the study of phase separation. You've seen phase separation even if you've never heard the term. Oil and water separate into distinct regions. Some materials cool into patches or domains instead of becoming a featureless blend. The system settles into stable patterns. The intuition behind Alen Con is easiest to picture as a landscape with two valleys.

[00:08:26]A marble rolling around on that landscape won't drift forever. It tends to settle into one valley or the other.

[00:08:33]In physics language, this is sometimes called a double well potential. In plain English, it means the system has preferred stable states. That idea acts like a container. Attraction pulls related things into coherence. Repulsion prevents everything from merging. And the stabilizing landscape keeps the whole process bounded so the representations don't shoot off to infinity.

[00:08:58]Instead of forcing one giant consensus, the system self-organizes into stable regions with clear boundaries. That is the real conceptual leap. A graph neural net now learns like an ecosystem.

[00:09:13]Coherence, difference, and stability all matter. There's another elegant way to understand this using the idea of energy. Think of energy as a score that measures how much contrast still exists across connected nodes of GNN. If neighboring nodes are still meaningfully different, the score is higher. If everything has become nearly identical, the score falls towards zero. In many standard GNN's, repeated smoothing steadily drains the contrast away. The graph's internal representation becomes flatter and flatter like ironing a wrinkled sheet until every ridge disappears. That flattening is over smoothing in disguise. The technical term often used is dirishlay energy, but the intuitive meaning is simple. It tracks whether the graph still has meaningful variation left. The physics inspired model changes the energy story because repulsion and stabilization maintain boundaries. The system does not automatically flatten itself into uniformity. It can keep some ridges and valleys. That means it can remain expressive even when it becomes very deep. And depth matters. This is not just a stylistic preference. More rounds of communication let a node learn about faraway structures such as distant dependencies in social networks.

[00:10:31]Traditional GNN's often hit a wall after only a few layers because deeper propagation causes homogenization.

[00:10:38]So they face a painful trade-off. Stay shallow and preserve identity or go deep and lose it. Physics helps break that trade-off. Depth can become what it was supposed to be in the first place. More reasoning, not more forgetting. The article pushes this idea even further by treating the network as a continuous time system. Instead of thinking in terms of 50 repeated update steps, you can think of the node representations evolving smoothly like a simulation governed by forces. This is where ideas related to neural ordinary differential equations come in. You don't need the math to get the intuition. A traditional deep GNN can feel like making a photocopy of a photocopy of a photocopy until the image blurs. A continuous time physicsguided model is more like running a controlled simulation where attraction, repulsion, and stabilization shape the evolution at every moment. The process is deep but not careless. One especially useful part of this framework is that repulsion becomes a tunable knob. If your graph is mostly homophilic, for example, friends look like friends, you may want relatively little repulsion. If your graph is strongly heterophilic, for example, neighbors are informative because they are different, you turn repulsion up.

[00:11:57]That is a surprisingly profound idea.

[00:12:00]Intelligence on graphs is not only about learning what to combine. It is also about learning what not to combine. This helps explain why physics inspired methods can shine on benchmark data sets where classic GNN struggle, especially those networks in which nearby nodes often belong to different categories.

[00:12:19]Older models tend to smooth away the distinction. The newer approach matches the social logic of the graph better.

[00:12:25]Your neighbor can be useful precisely because they are not like you. Along the way, it also clears up some common misunderstandings. Over smoothing is not the same thing as overfitting.

[00:12:37]Overfitting means memorizing quirks in the training data. Over smoothing is a structural collapse caused by too much averaging and it can happen even if data is plentiful. And repulsion is not anti-learning.

[00:12:51]Instead, it is structurepreserving.

[00:12:54]It helps keep categories separable when the graph itself connects contrasting roles. And physics here contributes real tools for stability, boundary formation, and controlled dynamics. For a long time, graph learning was dominated by a diffusion mindset. Let the network move toward consensus. The physics perspective offers a richer view.

[00:13:15]Intelligence on graphs may be more about self-organization under competing forces. Real systems like social networks often stay structured not by eliminating differences, but by balancing them. They share information without erasing identity. That may be the most interesting lesson here. The failure of deep GNN's was not just a bug. It exposed a deeper assumption about what learning is supposed to do.

[00:13:40]If we treat understanding as endless averaging, then yes, depth becomes forgetting. But if we treat understanding as the formation of stable, meaningful structure, then physics becomes an unexpected guide. And physics supplied a new picture of what a graph AI should be doing. And once you see it that way, the paradox at the beginning dissolves. Graph neural networks were failing because they were missing half the story. They knew how to pull things together, but not how to keep important things apart. Physics added the missing forces.

[00:14:12]>> And that wraps it up for today. Please don't forget to cast your vote on what PhysicsML premium service I can build that you will find most valuable. The direct link is in the pinned comment and the description. Thanks a lot and I'll see you in the next