To perceive is to build a generative model of the world that allows one to resolve ambiguity, correct errors, and infer missing information when sensory input is incomplete or inconsistent.

Our research covers machine learning, representation learning, generative models, mechanistic interpretability, inverse problems, and NeuroAI. We study what makes a representation interpretable and how to build models that find one. We focus on generative models whose internal structure reflects the geometry and statistics of the data, and that learn representations which are disentangled and compositional.

Our research is inspired by the brain: A core challenge in neuroscience and AI is understanding how intelligent systems perceive and interpret the world from incomplete or noisy data. Humans, for instance, can robustly recognize visual scenes or sounds even under significant noise or occlusion. The Bayesian brain hypothesis posits that the brain achieves this by treating perception as an active inference, integrating sensory information with internal models to deduce the most likely explanation. However, how the brain forms internal representations that are meaningful, interpretable, robust, and generalizable from noisy inputs remains unknown. What internal model does the brain construct, and how is it learned? The same question shapes what we should ask of AI systems. Two questions guide our work:

• What learning architectures allow AI systems to perform mechanistically interpretable and robust inference?
• What representations should AI systems learn? Which structural properties make them interpretable, understandable by humans, or aligned with meaningful physical variables?

What are inverse problems? Scientists and engineers study systems in neuroscience, physics, biology, and engineering by taking measurements and inferring the underlying causes or system properties that generated them. Such problems are ill-posed: without prior knowledge, the solution may be indeterminate or unstable. Solving one means combining evidence from data with prior knowledge to infer the most likely explanation. Understanding how biological systems, like the brain, perform this integration can guide the design of more interpretable and effective AI systems.

We are currently working on problems that combine the statistical and geometric properties of data to learn better representations. If you are interested in mathematics, topology, topography, symmetries, and the intersection of statistics and geometry, feel free to reach out.