Neural Dynamics and Control Group

How does the brain control behaviour? Every movement, decision and percept unfolds in time, driven by the coordinated activity of millions of neurons; a major challenge of modern neuroscience is to infer the computational and mechanistic principles that underlie such adaptive control from increasingly rich neural and behavioural datasets. The lab tackles this question along two complementary fronts:

• Building network-level theories of brain computation, with an emphasis on motor control and cortical dynamics. Using tools from dynamical systems and control theory, we ask how recurrent circuits of excitatory and inhibitory neurons give rise to the rich, low-dimensional activity patterns seen in behaving animals: how balanced, non-normal networks (PRE 2012) transiently amplify specific activity states to generate complex movements (Neuron 2014), how these initial states are reached during motor preparation (Neuron 2021), when and why networks should prepare at all (eLife 2024), how motor primitives (Nature Neuroscience 2018) might be assembled through simple gain modulation. On the sensory side, we study how circuit structure shapes neural variability (Neuron 2018) and sequential dynamics (Neuron 2022), and how stochastic recurrent circuits can implement sampling-based probabilistic inference (NeurIPS 2014; Nature Neuroscience 2020).

• Developing machine learning methodology — both statistical tools for extracting interpretable structure from large-scale neural recordings, and optimisation algorithms for training recurrent neural network models on behavioural tasks. On the statistics side, we develop probabilistic latent-variable models of population activity that infer latent neural trajectories on Euclidean (NeurIPS 2021) and curved (NeurIPS 2020) manifolds, and describe their dynamical structure via identification of nonlinear latent dynamics (ICLR 2022) or non-reversible structure (NeurIPS 2020). Nonlinear system identification for neuroscience is a major area of ongoing work in the lab. Finally, a substantial part of our methods work is devoted to the effective optimisation of recurrent neural networks on complex tasks, which we use to generate hypotheses about how brain circuits compute. We have developed scalable second-order optimisers such as FishLeg (ICLR 2023), SOFO (NeurIPS 2024) and Symo (ICML 2026). Much of this optimisation work is done in collaboration with Alberto Bernacchia’s team at MediaTek Research UK — building on our exact natural-gradient theory (NeurIPS 2018) — and its focus on scalability gives it broad applicability well beyond neuroscience.

The two strands feed each other continuously. Theoretical questions about brain function motivate new mathematical tools, and those tools in turn let us test theory against real data, often through close collaborations with experimental groups — see e.g. our work with Mitra Javadzadeh on multi-area dynamics in the mouse visual cortex (Nature Neuroscience 2026).

We are always keen to hear from prospective PhD students and postdocs interested in systems and computational neuroscience, or in probabilistic machine learning and optimisation. Joining the group means acquiring deep expertise in dynamical systems, control theory, probabilistic modelling and large-scale optimisation — and putting that expertise to work on some of the hardest questions about how brains compute. The group is part of the Computational and Biological Learning lab (CBL) at the University of Cambridge, offering a rich environment of interactions across theory, methods and experiment.