Bo Zhao is a postdoctoral researcher at Harvard University. She uncovers mathematical structures in neural networks to understand AI models and improve their reliability.
Uncovering Neural Network Architecture and Symmetry
Q | What scientific problem are you trying to solve?
I uncover mathematical structures in neural networks to understand AI models.
Modern neural networks can be remarkably capable, but we still lack a clear map of how they work internally. I study one source of this difficulty: the same network function can often be represented by many different settings of its parameters. This matters because two functionally identical models can look very different internally, which can confuse attempts to compare, interpret, or improve them.
I use symmetry, the study of changes that leave something unchanged, to organize these equivalent versions of neural networks. My goal is to build a mathematical language that characterizes this redundancy, then use this structure to design better methods for optimization, model merging, compression, and interpretability. More broadly, I want to make modern AI systems easier to analyze, more efficient to train, and more reliable to use.
Q | What drew you to understanding AI models?
I was drawn to the way mathematics can reveal simple structure beneath complicated behavior. Neural networks are a striking example: they work extremely well, yet even basic questions about why training succeeds or what their internal representations mean remain unsettled.
Q | What’s one thing you learned from your research that you didn’t expect?
One unexpected lesson was that redundancy is not always something to eliminate. I initially thought of neural-network symmetries mainly as multiple ways of writing the same model. However, two parameter settings can produce the same outputs while behaving differently during training: their gradients and the local shape of the optimization problem can change.
This means symmetry can be used as a tool. We can move a model to an equivalent internal form that is easier to optimize or use symmetry to test whether an interpretation depends on an arbitrary coordinate choice. More broadly, I learned that “the same model” can mean different things depending on whether we care about its outputs, its training process, or its internal explanation. Making those distinctions precise has opened more questions than I expected.
Q | If your research succeeds, what could it change for science or society?
Scientifically, this work could provide a common mathematical language for understanding neural-network architecture, training, and interpretation. Practically, it could help us choose functionally equivalent versions of a model that train faster, merge more cleanly, compress more accurately, or are easier to interpret. For society, the most important benefit may be more trustworthy evaluation of AI systems. If an interpretability or safety method changes its conclusion only because the same computation is represented differently, it can create false confidence. Mathematical tools that identify stable structure could make such analyses more reproducible and harder to fool. Symmetry alone will not solve AI reliability, but it can provide a rigorous foundation for deciding which internal measurements deserve our trust.
Q | What question are you most excited to answer next?
Today’s most capable AI systems are often built by training at scale and observing what emerges. I want to uncover the underlying structures that govern how these systems learn, organize information, and make decisions, then use those structures to design models that are more efficient, interpretable, and reliable. I hope to help move AI from an empirical craft toward a mature science, one in which we can explain not only what a model does, but why it does it and how to make it behave better.
Responses have been edited for length and clarity.