Constrained plasticity can compensate for ongoing drift in neural populations

I've started a new postdoc, working on a collaboration between the O'Leary, Ziv, and Harvey labs, on the Human Frontiers Science Program grant, "Building a theory of shifting representations in the mammalian brain". 

To start, I've been working with Adrianna Loback to try to make sense of a puzzling result from Driscoll et al. (2017): the neural code for sensorimotor variables in parietal cortex is unstable, changing dramatically even for habitual tasks in which no learning takes place.

We think the brain might be using a distributed population code. Because there are so many possible ways to read-out a distributed and redundant population code, it could be that there is a stable representation at the population level, despite the apparent instability of single neurons. 

I'll be presenting our work to date as a poster at the UK Neural Computation conference in Nottingham, July 1st-3rd. 

[download poster PDF] 

Abstract:

Recent experiments reveal that neural populations underlying behavior reorganize their tunings over days to weeks, even for routine tasks. How can we reconcile stable behavioral performance with ongoing reconfiguration in the underlying neural populations? We examine drift in the population encoding of learned behaviour in posterior parietal cortex of mice navigating a virtual-reality maze environment. Over five to seven days, we find a subspace of population activity that can partially decode behaviour despite shifts in single-neuron tunings. Additionally, directions of trial-to-trial variability on a single day predict the direction of drift observed on the following day. We conclude that day-to-day drift is concentrated in a subspace that could facilitate stable decoding if trial-to-trial variability lies in an encoding-null space. However, a residual component of drift remains aligned with the task-coding subspace, eventually disrupting a fixed decoder on longer timescales. We illustrate that this slower drift could be compensated in a biologically plausible way, with minimal synaptic weight changes and using a weak error signal. We conjecture that behavioral stability is achieved by active processes that constrain plasticity and drift to directions that preserve decoding, as well as adaptation of brain regions to ongoing changes in the neural code.

This poster can be cited as: 

Rule, M. E., Loback, A. R., Raman, D. V., Harvey, C. D., O'Leary, T. S. (2019) Constrained plasticity can compensate for ongoing drift in neural populations. [Poster] UK Neural Computation 2019, July 1st Nottingham, UK

Exploring a regular-spiking limit of autoregressive point-process models with an absolute refractory period

These notes explore a deterministic limit of Autoregressive Point-Process Generalized Linear Model (AR-PPGLM) of a spiking neuron. We consider a Poisson point process that is either strongly driven or strongly suppressed, and take a limit where spiking output becomes deterministic (and instantaneous rates diverge). This deterministic limit is of interest in clarifying how AR-PPGLM models relate to deterministic models of spiking.

[get as PDF]

Moment-closure approaches to statistical mechanics and inference in models of neural dynamics

At the upcoming SAND meeting in Pittsburgh, I'll be presenting our recent work on using moment closures to combine theoretical models with statistical inference. This work has already been published, but this poster provides a quick summary. 

In my postdoc at Edinburgh, I worked on methods to combine neural field modelling and statistical inference. Neural field models capture how microscopic actions of single neurons combine to create emergent collective dynamics. Statistical modelling of spiking data commonly uses Poisson point-process models. These projects combined the two in an interesting way. 

In "autoregressive point-processes as latent state-space models" [PDF], we convert a popular statistical model for spike-train data into a neural field model. This neural field model is a bit unusual: it extends over time rather than space, and describes correlations as well as mean firing rates. This may lead to new tricks for inference and coarse-graining on these types of models. 

In "neural field models for latent state inference", we use a microscopic model of retinal waves to specify a second-order neural field model that doubles as a latent state-space model for spiking observations. This advances methods for developing data-driven neural field models.

[download poster PDF]

Moment equations for an autoregressive point process with an absolute refractory period

These notes extend the autoregressive point-process moment closures derived in Rule and Sanguinetti (2018) to models that include an absolute refractory period via a gating term that sets the rate to zero after a spike.

[get notes as PDF]

Autoregressive point-processes as latent state-space models

In 2016 I started a postdoc with the labs of Guido Sanguinetti and Matthias H. Hennig—and this is the first paper to result!

[get PDF]

A central challenge in neuroscience is understanding how the activity of single cells combines to create the collective dynamics that underlie perception, cognition, and behavior. One way to study this is to build detailed models, and "coarse grain" them to see which details are important. 

Our paper develops ways to relate detailed point-process models to coarse-grained quantities, like average neuronal firing rates and correlations. Point-process models are used for statistical modelling of spike train data. They can reveal effective neural dynamics by capturing how neurons in a population inhibit or excite each-other and themselves. 

Preview of figures: 

Figure 2: Moment closure of autoregressive PPGLMs combines aspects of three modeling approaches:

(A) Log-linear autoregressive PPGLM framework (e.g., Weber & Pillow, 2017). Dependence on the history of both extrinsic covariates x(t) and the process itself y(t) are mediated by linear filters, which are combined to predict the instantaneous log intensity of the process. (B) Latent state-space models learn a hidden dynamical system, which can be driven by both extrinsic covariates and spiking outputs. Such models are often fit using expectation- maximization, and the learned dynamics are descriptive. (C) Moment closure recasts autoregressive PPGLMs as state-space models. History dependence of the process is subsumed into the state-space dynamics, but the latent states retain a physical interpretation as moments of the process history (dashed arrow). (D) Compare to neural mass and neural field models, which define dynamics on a state space with a physical interpretation as moments of neural population activity

A mechanism for persistent memory in oscillatory networks

I just finished the Methods in Computational Neuroscience "bootcamp". It was intense, but valuable—I can recommend that any student/postdoc who wants to get started in the field take it. 

For a course project, I extended previous work, which showed that oscillatory drive can excite patterned instabilities in visual cortex. These patterns constitute attractor states that are stabilized by an external oscillatory drive. The project explored the idea that similar oscillation-stabilized attractors might serve as a flexible working memory. 

(Unfortunately, these notes are rather brief and incomplete as I never had the time to write this up properly. )

Selective, short-term maintenance of attractor states is important for working memory in neural systems. Neural networks, however, are typically stabilized by feedback inhibition. The delays in this inhibition lead to unavoidable oscillations. 

This project demonstrate a scenario where the attractor dynamics associated with a working memory are not fixed points, but instead fixed limit cycles embedded within a population oscillation. 

External oscillatory drive, perhaps e.g. an attention signal, can switch such a network from a "read-in" mode, in which the system responds to external input, and a "hold" model, in which the system retains a memory of its past states. These concepts may underlie flexible working memory solutions that can coexist with population oscillations.

To better understand the mechanisms underlying this, we explored a switched piece-wise linear model that captured the qualitative dynamics of the original system. We found that firing-rate nonlinearities with positive curvature are important for allowing a synchronous (non-selective) external signal to excite the asymmetric network states associated with a memory trace. 

[get writeup PDF]

[get presentation slides]

Preview: Figure 4

Figure 4: Many-population generalization of the two-population model of Rule et al. (2011), serving as a working memory. Starting from rest, a stimulus is delivered to the first oscillator (green) for $t\in[300,500)$ ms. We test the stability of this stimulus-driven network response during a hold period $t\in[500,1500)$ ms. Without oscillatory drive (top), the memory fades in a few cycles. Periodic stimulation (bottom) preserves the memory. Rightmost plots show the phase-plane dynamics during the readout period $t\in[1000,1500)$. The top system, without drive, has returned to rest. The driven system shows a stable limit cycle, with higher firing rates in the population that initially received the stimulus.