Our group has diverse interests in nonequilibrium statistical mechanics, deep learning theory, and experimental + theoretical neuroscience.

Much of our understanding of artificial neural networks stems from the fact that, in the infinite-width limit, they turn out to be equivalent to a class of simple models called *kernel methods.* Given a wide network architecture, it's surprisingly easy to find the equivalent kernel method, allowing us to study popular models in the infinite-width limit. In recent work with Sajant Anand, I showed that, for fully-connected nets (FCNs), this mapping can be run in reverse: given a desired kernel, we can work backwards to find a network that achieves it. Surprisingly, we can always design this network to have only a single hidden layer, and we used that fact to prove that wide shallow FCNs can achieve any kernel a deep FCN can, an analytical conclusion our experiments support. This ability to design nets with desired kernels is a step towards deriving good net architectures *from first principles*, a longtime dream of the field of machine learning. [arXiv][code]

Simultaneous recordings from the cortex have revealed that neural activity is highly variable and that some variability is shared across neurons in a population. Further experimental work has demonstrated that the shared component of a neuronal population's variability is typically comparable to or larger than its private component. Meanwhile, an abundance of theoretical work has assessed the impact that shared variability has on a population code. For example, shared input noise is understood to have a detrimental impact on a neural population's coding fidelity.

However, other contributions to variability, such as common noise, can also play a role in shaping correlated variability. We present a network of linear-nonlinear neurons in which we introduce a common noise input to modelâ€”for instance, variability resulting from upstream action potentials that are irrelevant to the task at hand. We show that by applying a heterogeneous set of synaptic weights to the neural inputs carrying the common noise, the network can improve its coding ability...

Redwood Center and Physics at UC Berkeley