Pattern recognition is an altisonant name to a rather common, if complex, activity we perform countless times in our daily lives. Our brain is capable of interpreting successions of sounds, written symbols, or images almost infallibly - so much so that people like me, who have sometimes trouble to recognize a face that should be familiar, get their own disfunctionality term - in this case, prosopagnosia.
Pattern recognition is also an all-important task in machine learning. Indeed, if it is true that the whole process of learning goes through the categorization of objects in their equivalence class, so that analogies can be drawn and inference made about the working of different objects or systems, e.g., then a fortiori pattern recognition should be recognized for its even more elemental importance in the process of learning, as analogies and categorization won't work without the identification of similar patterns.
Today, algorithms for self-driving, large language models, and image processing and recognition all use basic or less basic forms of machine pattern recognition. And of course, in fundamental physics we do the same: for example, when we try to reconstruct the trajectories of charged particles in a tracking detector, what we are called for is to search for hits (positions where particles have left some ionization) that "line up" along a possible particle path. More and more sophisticated tracking algorithms that find particle trajectories have been developed over the years, and today one important challenge is to develop fast machine learning algorithms that can do it better than what we could previously accomplish. A recent "Kaggle challenge" was indeed cast with the very problem of reconstructing particles in the harsh, background-ridden conditions of high-luminosity running of the Large Hadron Collider - and ML algorithms did not fare that well yet.
When we try to reconstruct the helical trajectories of particles that traverse a detector immersed in a solenoidal magnetic field, we are going for known patterns: these are helices of fixed radius, propagating from the ballpark of the primary collision point. There are a number of subtleties, of course, but the problem is, in machine learning terms, firmly in the "supervised" domain - we can, in other words, construct a training sample where trajectories are labeled based on the particle momenta (momentum is proportional to the radius of curvature).
How can we then even conceive the reconstruction of particle trajectories in a unsupervised fashion? Suppose, that is, that you give a bunch of hits to a machine, most of which are due to random noise, and ask it to find a pattern in them. In most cases, the machine would frown and reply "what pattern? You'll have to tell me more, buddy."
But not all machines. In fact, if you show a bunch of event display to a human, each one showing a dot where a hit was produced in the detector, sooner or later the human will realize that there often exist sets of hits that sort of "align" along some curved path. We have it in our genome, in some way! Can a real machine learning algorithm pull that off, too?
[Above, Russell Crowe in a famous scene from the movie "A beautiful mind', where he finds patterns in large tables of digits.]
Yes, it can. In a paper we recently uploaded on the arXiv, and submitted to MDPI Particles, with a few students and colleagues I showed how it is possible to encode the problem in a way that a neuromorphic computing system can sort out whether a bunch of detector hits includes real particle trajectories or not. And it also learns to distinguish trajectories of particles of different momenta, by firing with different output neurons when different momenta and particle charges are present.
The neuromorphic network is a collection of neurons that exchange information encoded in the time of arrival of electric impulses - "spikes" that add to the neuron soma an electric potential, eventually causing it to fire other signals to downstream neurons. We simulated the hits left by particles and noise in a tracker designed like the CMS Phase 2 silicon tracking detector, and encoded their position in the time of those impulses. By showering the neurons with many such "events" in succession, we showed how the neurons "self-organized" their synapses such that they would fire only when particles were present in the event.
[Above: spike-based encoding (a) and processing of information using a spiking neuron unit (b)]
In the picture below you can see (top panel) the potential of three neurons subjected to a stream of spikes from one encoded event. In the top image, neuron 10 reaches the threshold voltage at t=233ns, whereby it produces a spike downstream, and simultaneously inhibits the potential of the nearby neurons. In the bottom panel the three neurons are receiving one encoded event which does not have a track in it. Spikes do not coherently activate the neurons, and no spiking occurs.
[Above: voltage of neurons subjected to input data. See the text for detail]
But how does the learning mechanism really works? In our model, the neurons learn by a mechanism called "Spike-timing dependent plasticity", which modifies the synaptic weights (the strenght of coupling of a neuron with its afferents) and also the delay of the signal caused by the afferents. It is something like a positive reinforcement that is operated when a recurrent pattern is observed.
In the figure below you see a cut-away view of the CMS Phase 2 tracker with simulated hits from noise and a particle track. As you can see, the identification of the track is not difficult if you colour the signal pixels in red, but it might be challenging otherwise, especially if you did not specify what you are looking for!
[Above, the 10 layers of the silicon tracker in the transverse plane, with hits from signal and background from one event at high luminosity]
The view encoded in spike timing is a bit less clear still, but as can be seen in the graph, the neurons fire only when the track hits are arriving.
[Above: the 10 streams of hits and the resulting neuron firings]
The considered scenario - encoding particle hits in 10 time series, one per detector layer - is not realistically what one would think of implementing in a particle collider detector; still, the exercise we carried out shows how it is possible to use neuromorphic computing for physics applications and how they can sometimes present distinct advantages. Neuromorphic computing, for one thing, is a highly energy-efficient alternative to digital computing; in addition, the completely unsupervised manner in which the considered system can identify particles is potentially useful both for triggering applications and for "signal-agnostic" searches of detector signals that might be different from those we imagine, lending themselves to new physics searches.
Finally, let me congratulate with my students for their hard work in this analysis: Muhammad Awais, Emanuele Coradin, Fabio Cufino, Enrico Lupi, Eleonora Porcu, Jinu Raj. And many thanks to the other supervisors Fredrik Sandin (Lulea University of Technology) and Mia Tosi (University of Padova)!