What the Primary Lund Plane Omits: A Model-Stitching Diagnosis of a Jet-Tagger Representation Gap

In the high-energy collisions of particle physics, protons smash together at nearly the speed of light, shattering into sprays of new particles called jets. To understand the fundamental forces of nature, physicists must sort these sprays into categories: some jets come from heavy particles like the top quark, while others are merely background noise from lighter particles. The challenge is that these sprays look remarkably similar to the naked eye of a detector. For decades, scientists have relied on two main strategies to tell them apart. One approach uses deep knowledge of physics to manually select the most telling features of a jet, essentially creating a simplified map of its internal structure. The other approach feeds the raw data directly into powerful artificial intelligence, letting the computer learn to find patterns on its own. While these methods often produce similar results on paper, they can fail in very different ways when the going gets tough. The question remains: if a physics-based map performs worse than a learned AI, is the map itself missing crucial information, or is the computer simply bad at reading the map it was given?

A team of researchers at the Indian Institute of Technology Kanpur set out to solve this puzzle by building a bridge between the two approaches. They took a sophisticated AI model trained on raw data and a network trained on the simplified physics map, and they surgically connected them. Imagine taking the early layers of one trained brain and wiring them directly to the late layers of another, forcing them to work together through a single, trainable connector. This technique, known as model stitching, allowed them to isolate the problem. They tested whether the simplified physics map was inherently weak, or if the AI reading it was just underperforming. They used a specific, known limitation of the physics map as a control: a version that only follows the hardest path through a jet's history, deliberately ignoring most of the softer, surrounding radiation.

The results were clear and decisive. When the researchers forced the powerful AI to read this incomplete, simplified map, its performance dropped significantly, but not because the AI was struggling to understand. In fact, the AI could extract just as much information from the simplified map as the map's own native reader could. The shortfall was not in the reader; it was in the map itself. The simplified physics representation was genuinely missing information. The researchers then pinpointed exactly what was missing. The failure occurred almost entirely for a tiny, specific group of background jets that happened to have a high mass and a large number of particles, mimicking the signature of a heavy top quark. These jets had their radiation scattered off the main path that the simplified map follows, leaving the map with an incomplete picture.

To confirm this diagnosis, the team rebuilt the physics map to include every single branch of the jet's history, not just the main path. When they fed this complete, full-tree map into the network, the performance gap closed by more than 70 percent. The network suddenly became much better at rejecting the tricky background jets. However, a deeper investigation revealed a surprising twist about how the network actually uses this information. Once the network was trained on the full, complete map, it relied almost entirely on that original, main path to make its final decisions. If the researchers removed the extra branches during the final test, the network's performance barely changed. But if they removed the main path, the network collapsed. This suggests that the extra branches were not supplying new facts that the network read at the end; rather, they were essential during the learning process, helping the network understand how to build a useful representation in the first place.

The study also looked at where the most important information sits along that main path. They found that for identifying heavy top quarks, the very first, widest-angle split in the jet's history carried nearly all the weight. This single step, which corresponds to the opening angle of the heavy particle's decay, was worth far more than any other step in the chain. This pattern held true for other types of particle identification as well, though the effect was much weaker. The researchers also tested whether a more complex type of AI, one capable of seeing relationships between three points at once instead of just pairs, could fix the missing information in the simplified map. It could not. Even with this advanced reading ability, the network could not recover the lost information that the full map provided.

Ultimately, the work demonstrates that the gap between physics-based models and raw-data AI is not a failure of the AI's ability to learn, but a genuine lack of information in the simplified physics representation. The missing piece is the "off-path" radiation that gets discarded by traditional methods. While the final decision-making relies heavily on the main structural path, that path only becomes powerful because the network was trained on the full, messy reality of the jet. The study provides a precise map of where these models succeed and where they fail, showing that the difference lies in the data itself, not in the intelligence of the machine reading it.