The fall of my sophomore year was a bit like hell. I took the equivalent of three semester-long courses in computer science and physics, in addition to other classwork. Co-leader of a public speaking support group; and coordinated a celebrity visit to campus. I lived at my desk and during office hours and always declined my roommates’ invitations to watch The western wing.
While I was studying, my classmates enjoyed greater ease with the computer science curriculum. You immediately saw how long an algorithm would run while I hesitated and then calculated the running time step by step. I felt back. So I protested when my professor said, “You’re good at it.”
I see now that we have focused on different facets of learning. I explained my lack of intuition. My classmates had gained intuition by studying computer science in high school and then slowly boiling their experiences on a mental backlash. Their long-term contact with the material created familiarity – the ability to recognize a new problem as belonging to a class of which they had seen examples. I cooked course materials in a mental microwave that was set to “high” because one semester’s material at my college was crammed into ten weeks.
My professor didn’t measure my intuition. All he saw was that I knew how to calculate the running time of an algorithm. I had learned the material that was asked of me – more than I realized, distracted from what I hadn’t learned that difficult autumn.
We can learn an amazing amount when we step far from our comfort zones – and it’s not just us humans who can. So can simple accumulations of particles.
Examples are a classic spin glass. A Spin glass is a collection of particles that share some properties with a magnet. Both a magnet and a spin glass are made up of tiny mini magnets known as turns. Although I’ve blogged about quantum spins before, I’ll focus on classic spins here. We can think of a classic spin as a little arrow pointing up or down. A series of twists can form a material. If the twists tend to point in the same direction, the material can be a magnet sticking the faded photo of Fluffy to your fridge.
The spins can interact with each other, much like electrons interact with each other. Not quite similar – electrons push each other away. In contrast, a spin can make its neighbors align with it or align against it. Suppose the interactions are random: each spin can force a neighbor to align, gently ask another neighbor to align, ask a third neighbor to anti-align, and neighbors four and five have nothing to say.
The spin glass can interact with the outside world in two ways. First, we can put the spins in a magnetic field by placing magnets above and below the glass. When a spin is aligned with the field, it has negative energy. and, if not aligned, positive energy. We can shape the field so that it varies across the spinning glass. For example, spin 1 can experience a strong upward field while spin 2 experiences a weak downward field.
Second, let’s say the spins occupy a fixed temperature environment since I occupy a living room at 74 degrees Fahrenheit. The spins can exchange heat with the environment. When heat is released into the environment, a spin changes from positive to negative energy – from antialigning with the field to alignment.
Let’s do an experiment with the rotations. First we design a magnetic field with random numbers. Whether the field is pointing up or down on a given spin is random, as is the strength of the field that occurs on each spin. We form three of these random fields and call the trio a journey.
Let’s randomly select a field from the drive and apply it to the spin glass for a while. Again randomly select a field from the drive and apply it. and go on many times. The energy absorbed by the rotations of the fields decreases and then decreases.
Now let’s create another drive with three random fields. We will randomly select a field from this drive and apply it. Again randomly select a field from this drive and apply it. and so on. Again, the energy absorbed by the spins becomes more acute and then disappears.
Here comes the punch line. Let’s return to applying the initial fields. The energy absorbed by the glass will increase – but not as much as before. The glass reacts differently to a known drive than it does to a new drive. The spin glass recognizes the original drive – it has learned the “fingerprint” of the first fields. This learning happens when the fields throw the glass far off balance.1 As I learned from getting pushed in my slightly hellish fall.
Spin glasses learn drives that throw them far out of balance. So are many other simple, classic systems with many particles: polymers, viscous liquids, crumpled Mylar sheets and more. Researchers have predicted such learning and observed it experimentally.
Scientists have discovered the learning of many particles by measuring thermodynamic observables. Examples are the energy absorbed by the spin glass – what thermodynamics call it job. However, thermodynamics evolved in the 19th century to describe equilibrium systems and not to study learning.
One study on learning – the study of machine learning – has seen a boom over the past two decades. As described in the MIT Technology Review,[m] Machine learning algorithms use statistics to find patterns in huge amounts of data. “Users don’t tell the algorithms how to find these patterns.
It seems natural and appropriate to use machine learning to learn about learning through many-body systems. I did this with colleagues from Jeremy England’s group, a GlaxoSmithKline physicist who studies the complex behavior of many particle systems. Weishun Zhong, Jacob Gold, Sarah Marzen, Jeremy and I published our article last month.
With machine learning, we have recorded and measured the learning of many particles more reliably and more precisely than thermodynamic measures seem to be able to do. Our technology works on multiple facets of learning, analogous to the intuition and arithmetic skills that I learned in my computer science course. We presented our technology on a spin glass, but our approach can also be applied to other systems. I am researching such applications with the University of Maryland staff.
The project threw me off my balance: I had never worked with machine learning or multi-body learning. But it’s amazing what we can learn when we’re far from equilibrium. I first saw this in my sophomore year – and now we can quantify it better than ever.