Research
The main goal of Zhang's lab is to address how neural circuit dynamics give rise to neural codes to represent and process uncertain information, and how these produce perception, cognition, and behavior.
Neural circuit implementation of Bayesian (causal) inference
The brain performs Bayesian (causal) inference to interpret the world and to infer the causal relations in the world. Bayesian (causal) inference underlies a wide spectrum of perceptual and cognitive processes, learning, and memory. It is a fundamental question in computational neuroscience how neural circuits implement Bayesian (causal) inference, and how neurons represent uncertainty information. We have conducted a series of theoretical studies along this line. Using multisensory cue integration as an example of Bayesian inference, we proposed that cue integration can be achieved in a decentralized circuit composed of several coupled brain areas (Zhang et al., J. Neurosci., 2016; NeurIPS 2013). We also identified that opposite neurons found in multisensory areas are able to perform casual inference in information integration (Zhang et al., eLife 2019; NeurIPS 2019, 2016). Recently we are studying how the Poisson spiking variability of cortical neurons drives distributed samplingBased Bayesian inference in cortical circuits (Zhang, bioRxiv 2022; 2020).
Neural circuit dynamics
Neuronal responses are dynamic and have large response variability. It is important to study how interactions between neurons give rise to these dynamical and variable responses. We are particularly interested in two canonical circuit dynamics used in computational neuroscience: One is Continuous Attractor Neural Network which has been widely used to explain the processing of continuous stimulus (Zhang et al., 2016; 2012); Another is the ExcitationInhibition balanced spiking network which internally generates large response variability. We are combining the main characteristics of the two canonical networks to study how the network utilizes the structure of recurrent connectivity and its internally generated variability to implement stochastic computation such as samplingbased Bayesian inference.
Invariant and equivariant neural representation
Symmetry (invariance and equivariance) is ubiquitous in the universe and is the foundation of physical laws. Indeed, theoretical physicists have used symmetry to generate and unify physical laws, e.g., unifying four fundamental forces, general relativity, etc. Since the brain stores an internal model of the symmetric world, we hypothesize that symmetry can be used as a designing principle of information processing in neural circuits in the brain. Recently we started an ambitious attempt where we start from the Lie group symmetry to derive concrete, biologically plausible neural circuits in the brain. We have used the 1D translation group to frame the compass neural circuit in fly's brain (Zhang et al., NeurIPS 2022), and study how recurrent circuits implement temporal scaling equivariance (Zuo et al., NeurIPS 2023). We believe the symmetry can be used to interpret neural circuit structures in the brain.
Other research directions

Biological learning and synaptic plasticity.

Neural data analysis.