Fixed points

A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well. Low-rank recurrent neural networks (RNNs) exhibit such interpretability by having tractable dynamics. However, it is unclear how to best fit low-rank RNNs to data consisting of noisy observations of an underlying stochastic system. Here, we propose to fit stochastic low-rank RNNs with variational sequential Monte Carlo methods. We validate our method on severa

…Previous studies leveraged fixed points to compare RNNs across limited tasks and found that while the geometry of neural representations varies, fixed point topology is consistent across RNNs despite differences in model architecture [1]. However, linearizing dyna

A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well. Low-rank recurrent neural networks (RNNs) exhibit such interpretability by having tractable dynamics. However, it is unclear how to best fit low-rank RNNs to data consisting of noisy observations of an underlying stochastic system. Here, we propose to fit stochastic low-rank RNNs with variational sequential Monte Carlo methods. We validate our method on severa

Neural activity in many sensory systems is organized on low-dimensional manifolds by means of convex receptive fields. Neural codes in these areas are constrained by this organization, as not every neural code is compatible with convex receptive fields. The same codes are also constrained by the structure of the underlying neural network. In my talk I will attempt to provide answers to the following natural questions: (i) How do recurrent circuits generate codes that are compatible with the convexity of receptive fields? (ii) How can we utilize the constraints imposed by the convex receptive

Humans can robustly store and retrieve information with complex and hierarchical structure. Some ex- amples are temporal sequences, where each event is associated to a particular time, episodic memories where each event is associated with a particular context, cognitive maps representing spatial environ- ments through landmarks associated with relative locations, and semantic structures in language in which meaning is conveyed through both the identity of individual words and their role in the sentence. While working memory tasks typically process one structure at a time, a long-term associati

…One central feature is the fixed (or slow) point: the fixed points of the system and the linearized dynamics around them can explain important aspects of the computation that is being performed. While successful in many cases, fixed-points analysis has limitations. Finding fixed points is ge

…theory relating stable and unstable fixed points of TLNs to graph-theoretic properties of the underlying network. In particular, we have discovered that a special type of unstable fixed points, corresponding to "core motifs," are predictive of dynamic attractors. Recently, we have used these ideas to classify dynamic attractors in a two-parameter family of inhibition-dominate

…symmetry, there exists a unique stable fixed point. Using a cavity-like approach, we develop a quantitative theory that describes the statistics of the activity in this unique fixed point, and the conditions for its stability. Increasing the synaptic gain, the unique fixed point destabilizes, and the network exhibits