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

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]

Inferring unobserved neural field intensities from spiking observations

Edit: I am very happy to report that this work has now been published in PLoS Computational Biology.

I'll be presenting our ongoing work on merging neural field models with statistical inference at the Integrated Systems Neuroscience Workshop in Manchester, and at the Bernstein Conference in Göttingen. [get poster PDF]

What's exciting about this work is that it combines modelling principles from statistical physics and statistical inference. We start with a detailed microscopic model, and then construct a second-order neural field model, which is then used directly for statistical inference. Normally, neural field models are only treated as abstract, qualitative mathematical models, and are rarely integrated with data. 

Video: Simulation of 3-state Quiescent-Active-Refractory blue, red, green) neural field model of spontaneous retinal waves that occur during development. Waves are generated by the inner retina, and drive retinal ganglion cell spiking, which we can observe on a high-density multi-electrode array. [get original avi from Github]

Population coding of sensory stimuli through latent variables

Edit: This work is published now, in Entropy [PDF].

Martino Sorbaro has been doing some really interesting work exploring the encoding strategies learned by artificial neural networks. We've found similarities between the statistics of the population codes learned by Restricts Boltzmann Machines (RBMs), and those of the retina. We'll present this work as a poster at the upcoming  Integrated Systems Neuroscience in Manchester.

TL;DR:

RBMs as a model for latent-variable encoding

• Optimal latent-variable encoding of visual stimuli seems to consistently yield models near statistical criticality.  
• Poor fits (too few hidden units,under-fitting) do not exhibit this property.
• Critical RBMs mimic the retina in Zipf laws, sparsity, and decorrelation.
• Above the optimal model size, extra units are weakly constrained as measured by Fisher information.  
• Receptive fields of excess units are less retina-like.

Questions and controversy

• Is statistical criticality a general feature of factorized latent variable models?
• Is criticality in the retina expected based simply on optimal encoding?

[download poster PDF]

Abtract:

Several studies observe power-law statistics consistent with critical scaling exponents in neural data, but it is unclear whether such statistics necessarily imply criticality. In this work, we examine whether the 1/f statistics of retinal populations are inherited from visual stimuli, or whether they might emerge from collective neural dynamics independently of stimulus statistics. We examine, in silico, a latent-variable encoding model of visual scenes, and empirically explore the conditions under which such a model exhibits 1/f statistics thought to reflect criticality. Specifically, we examine the Restricted Boltzmann Machines (RBMs) as a factorized binary latent-variable model for stimulus encoding. We find two surprising results. First, latent variable models need not exhibit 1/f statistics, but that the optimal model size, reflecting the smallest model that can faithfully encode stimuli, does. We illustrate that the optimal model size can be predicted from sloppy dimensions of the Fisher information matrix (FIM), which align with a subspace spanning the superfluous latent variables. Second, the optimal-sized model can exhibit 1/f statistics even when stimuli do not, indicating that this property is not inherited from environmental statistics. Furthermore, such models exhibit properties of statistical criticality, including diverging susceptibilities. This empirical evidence suggests that 1/f statistics are neither inherited from the  environment, nor a necessary feature of accurate encoding. Rather, it suggests that parsimonious latent- variable models are naturally poised close to criticality, generating the observed 1/f statistics. Overall,  these results are consistent with conjectures in other fields that a cost-benefit trade-off between expressivity and parsimony underlies the emergence of criticality and 1/f power-law statistics. Furthermore, this works suggests that in latent-variable encoding models, the emergence of 1/f statistics reflects true criticality and is not inherited from the environmental distribution of stimuli.

The poster can be cited as:

Sorbaro, M, Rule, M., Hilgen, G., Sernagot, E. , D, Hennig, M. H. (2017) Signatures of optimal population coding of sensory stimuli through latent variables. [Poster] The second Integrated Systems Neuroscience Workshop, 7-8th September 2017, at The University of Manchester, Manchester, UK.

Edit: the paper can be cited as

Rule, M.E., Sorbaro, M. and Hennig, M.H., 2020. Optimal encoding in stochastic latent-variable Models. Entropy, 22(7), p.714.

 

Diverse spatiotemporal dynamics in primate motor cortex local field potentials

Edit: this work has now been published as two papers. The first finds that mesoscopic beta-LFP oscillations may arise due to synchronization of rhythmic spiking in single neurons. The second  explores how changes in synchronization relate to the diverse patterns illustrated in the poster below.  

I'll present some of my ongoing thesis research at SfN as a poster this year. (This was originally titled "Identification of (~20 Hz) beta spatiotemporal dynamics in motor cortex LFPs".)

I've been looking into spatiotemporal waves in beta (~20 Hz) LFP oscillations during steady-state movement preparation. The wave dynamics seem to be more complex than previously reported [1, 2]. Patterns vary depending on the properties of the beta-LFP oscillations, perhaps reflecting phase synchronization dynamics between local modules, or a signature of external input? 

[PDF download]

Abstract:

Modulation of beta (10-45Hz) oscillations is a prominent feature of primate motor cortex. Beta power is typically elevated during movement preparation, suppressed around movement onset, and enhanced during isometric force tasks. As shown by previous studies, beta oscillations can also appears as traveling waves in primate motor cortex. Understanding the mechanisms underlying the rapid modulation of beta LFP activity and the associated spatiotemporal patterns may shed light on the functional roles of these oscillations. It may also have important implications for movement disorders where regulation of motor cortex beta activity is abnormal (e.g. Parkinson's disease). Here, we examine motor cortex beta spatiotemporal LFP activity using multielectrode arrays (MEAs) in m. mulatta during a cued reaching and grasping task with instructed delay. Data from two monkeys are analyzed, each with a 96-MEA in ventral premotor cortex (PMv), and two 48-MEAs in the primary motor cortex (M1) and dorsal premotor cortex (PMd), respectively. Our main findings are threefold: (1) The transient nature of beta oscillation events together with variations in the beta band center frequency makes the identification of spatiotemporal structures challenging. In particular, different filtering and preprocessing steps can alter the apparent spatiotemporal dynamics. (2) Furthermore, attempts to summarize wave dynamics in terms of simple global structures, like plane waves, or rotating (radiating) waves around (from) a critical point, may fail to meaningfully describe the full range of beta spatiotemporal activity. (3) Despite these challenges, we find a variety of beta spatiotemporal patterns ranging from asynchronous states, i.e. states with no clear wave dynamics, to more locally synchronized states with complex wave dynamics, to globally coherent states. These globally coherent states may exhibit either traveling wave dynamics or homogeneous synchrony. We conjecture that the transitions among these different patterns may result from fast modulations of the effective lateral connectivity or from changes in spatiotemporal inputs to the cortical area.

This poster can be cited as

Rule, M. E., Vargas-Irwin, C., Donoghue, J., Truccolo, W. (2015) Identification of (~20 Hz) beta spatiotemporal dynamics in motor cortex LFPs. [Poster] Society for Neuroscience 2015, Oct 19th, Chicago, Il, USA. 

Update: This work can now be found in the following papers

Rule, M.E., Vargas-Irwin, C.E., Donoghue, J.P. and Truccolo, W., 2017. Dissociation between sustained single-neuron spiking and transient β-LFP oscillations in primate motor cortex. Journal of neurophysiology, 117(4), pp.1524-1543. 

Rule, M.E., Vargas-Irwin, C., Donoghue, J.P. and Truccolo, W., 2018. Phase reorganization leads to transient β-LFP spatial wave patterns in motor cortex during steady-state movement preparation. Journal of neurophysiology, 119(6), pp.2212-2228.