I, Scientist | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Afterword

After getting back from Berkeley, a place I will forever hold dearly, I started a discussion group with Kalina and Ernie in CLM. We learnt reinforcement learning together. I taught Ernie how to code in python, helped Kalina to prepare her presentation for lab meeting. I also provided some ideas to Ernie regarding an effective uniformity maximization algorithm for his place cell project. And Ernie also taught us about the complex procedures for doing surgery to put an electrode in a rodent brain. For a couple of months, we discussed almost daily. But just when I started to find this long lost enjoyment—to connect and to do science with someone—we had to part once more as I transferred, with Ila, to Brain and Cognitive Sciences at MIT.

You do know how to write this thesis

At MIT, I tried not to let the parting with Kalina and Ernie get to me. I talked to new graduate students I met during the orientation and took a course with them so that I could know them better in preparing a presentation together. But above all these, the stress from my research not going anywhere had finally caught up. Deeply confused, not being able to see a path towards finishing this PhD, I eventually sought help.

I was extremely lucky that I had Laura and Matt agreeing to be my committee. When I first met Matt in his office, I explained my situation and how I did not feel at all that I had anything valuable for writing my thesis. “No, you don’t have any positive results that are ‘publishable’,” he explained. “But from what you just told me, I believe that you have more than enough for writing this thesis,” he continued. “Let’s make a plan! You can try to list everything you did in the past two and half years in neuroscience, and we can then discuss what could be a ‘theme’ for your thesis that will chain these results together in a deep and coherent way.”

Knowing that writing a thesis is about writing every lesson I have learnt, and everything I have predicted wrong and hypothesized differently, instead of gathering a collection of publishable materials, I was free. And slowly, I could see a path forwards in finishing this PhD.

Grid cells, the many ways of how not to be modular

One seemingly self-contained theme for my thesis is an effort to find a functional reason that is responsible for the *modularity* in a grid cell code.

Grid cells in a population only have these discrete lattice periods for their tuning curves. A subpopulation of grid cells therefore form modules each with a distinctive lattice period. [Stensola et al., 2012]

This is challenging for it is notoriously difficult to have modules emerge spontaneously in a system without pre-specifying it. There were only one example in physics for module formation that I knew of—i.e., the theory for ferromagnet in which large magnetic domains occur in low enough temperature through a mechanism called spontaneous symmetry breaking. Within each domain (or module) electron spins tend to align, but due to a nonzero thermal fluctuation, the local alignments cannot extend globally—hence multiple modules instead of one. If one generalizes this mechanism to the domain of continuous attractor, modules can form for a similar reason.

Why grid cells form modules? A consequence of attractor dynamics, or a need for high-capacity coding?

I first heard about this dynamical view to get discrete grid cell modules from John, and subsequently Louis at Berkeley. In John’s simulation, a uniform continuous attractor was set up to produce periodic bumps with a constant spacing under a constant velocity input. But when subject to a velocity gradient (input ranging from weak to strong continuously for different neurons), the symmetry of uniformity was spontaneously broken and modules form.

As illustrated above, a continuous attractor with a uniform connectivity tends to form bumps that move together when they are neighbors. Yet under a gradient velocity input, the bumps to the right want to move faster than the bumps to the left. Between the force of being locally uniform (similar to the local alignment of electron spins) and globally varying (similar to thermal excitation), module formation takes place.

From a pure dynamical viewpoint, the above theory for module formation is self-contained. But if one wishes to answer the question whether there is a functional reason for modules to exist (or perhaps this dynamical constraint is all the reason there is), things become uncertain again.