Self-healing codes: How stable neural populations can track continually reconfiguring neural representations.

As an adaptive system, the brain must retain a faithful representation of the world while continuously integrating new information. Recent experiments have measured population activity in cortical and hippocampal circuits over many days and found that patterns of neural activity associated with fixed behavioral variables and percepts change dramatically over time. Such "representational drift" raises the question of how malleable population codes can interact coherently with stable long-term representations that are found in other circuits and with relatively rigid topographic mappings of peripheral sensory and motor signals. We explore how known plasticity mechanisms can allow single neurons to reliably read out an evolving population code without external error feedback. We find that interactions between Hebbian learning and single-cell homeostasis can exploit redundancy in a distributed population code to compensate for gradual changes in tuning. Recurrent feedback of partially stabilized readouts could allow a pool of readout cells to further correct inconsistencies introduced by representational drift. This shows how relatively simple, known mechanisms can stabilize neural tuning in the short term and provides a plausible explanation for how plastic neural codes remain integrated with consolidated, long-term representations.

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules.

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.

Optimal Encoding in Stochastic Latent-Variable Models.

In this work we explore encoding strategies learned by statistical models of sensory coding in noisy spiking networks. Early stages of sensory communication in neural systems can be viewed as encoding channels in the information-theoretic sense. However, neural populations face constraints not commonly considered in communications theory. Using restricted Boltzmann machines as a model of sensory encoding, we find that networks with sufficient capacity learn to balance precision and noise-robustness in order to adaptively communicate stimuli with varying information content. Mirroring variability suppression observed in sensory systems, informative stimuli are encoded with high precision, at the cost of more variable responses to frequent, hence less informative stimuli. Curiously, we also find that statistical criticality in the neural population code emerges at model sizes where the input statistics are well captured. These phenomena have well-defined thermodynamic interpretations, and we discuss their connection to prevailing theories of coding and statistical criticality in neural populations.

Stable task information from an unstable neural population.

Over days and weeks, neural activity representing an animal's position and movement in sensorimotor cortex has been found to continually reconfigure or 'drift' during repeated trials of learned tasks, with no obvious change in behavior. This challenges classical theories, which assume stable engrams underlie stable behavior. However, it is not known whether this drift occurs systematically, allowing downstream circuits to extract consistent information. Analyzing long-term calcium imaging recordings from posterior parietal cortex in mice (Mus musculus), we show that drift is systematically constrained far above chance, facilitating a linear weighted readout of behavioral variables. However, a significant component of drift continually degrades a fixed readout, implying that drift is not confined to a null coding space. We calculate the amount of plasticity required to compensate drift independently of any learning rule, and find that this is within physiologically achievable bounds. We demonstrate that a simple, biologically plausible local learning rule can achieve these bounds, accurately decoding behavior over many days.

Neural field models for latent state inference: Application to large-scale neuronal recordings.

Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.

Causes and consequences of representational drift.

The nervous system learns new associations while maintaining memories over long periods, exhibiting a balance between flexibility and stability. Recent experiments reveal that neuronal representations of learned sensorimotor tasks continually change over days and weeks, even after animals have achieved expert behavioral performance. How is learned information stored to allow consistent behavior despite ongoing changes in neuronal activity? What functions could ongoing reconfiguration serve? We highlight recent experimental evidence for such representational drift in sensorimotor systems, and discuss how this fits into a framework of distributed population codes. We identify recent theoretical work that suggests computational roles for drift and argue that the recurrent and distributed nature of sensorimotor representations permits drift while limiting disruptive effects. We propose that representational drift may create error signals between interconnected brain regions that can be used to keep neural codes consistent in the presence of continual change. These concepts suggest experimental and theoretical approaches to studying both learning and maintenance of distributed and adaptive population codes.

Phase reorganization leads to transient ß-LFP spatial wave patterns in motor cortex during steady-state movement preparation.

Previous studies on the origin and properties of spatial patterns in motor cortex ß-local field potential (ß-LFP) oscillations have focused on planar traveling waves. However, it is unclear 1) whether ß-LFP waves are limited to plane waves, or even 2) whether they are propagating waves of excito-excitatory activity, i.e., primarily traveling waves in excitable media; they could reflect, instead, reorganization in the relative phases of transient oscillations at different spatial sites. We addressed these two problems in ß-LFPs recorded via microelectrode arrays implanted in three adjacent motor cortex areas of nonhuman primates during steady-state movement preparation. Our findings are fourfold: 1) ß-LFP wave patterns emerged as transient events, despite stable firing rates of single neurons concurrently recorded during the same periods. 2) ß-LFP waves showed a richer variety of spatial dynamics, including rotating and complex waves. 3) ß-LFP wave patterns showed no characteristic wavelength, presenting instead a range of scales with global zero-lag phase synchrony as a limiting case, features surprising for purely excito-excitatory waves but consistent with waves in coupled oscillator systems. 4) Furthermore, excito-excitatory traveling waves induced by optogenetic stimulation in motor cortex showed, in contrast, a characteristic wavelength and reduced phase synchrony. Overall, ß-LFP wave statistics differed from those of induced traveling waves in excitable media recorded under the same microelectrode array setup. Our findings suggest phase reorganization in neural coupled oscillators contribute significantly to the origin of transient ß-LFP spatial dynamics during preparatory steady states and outline important constraints for spatially extended models of ß-LFP dynamics in motor cortex. NEW & NOTEWORTHY We show that a rich variety of transient ß-local field potential (ß-LFP) wave patterns emerge in motor cortex during preparatory steady states, despite stable neuronal firing rates. Furthermore, unlike optogenetically induced traveling waves, ß-LFP waves showed no characteristic wavelength, presenting instead a range of scales with global phase synchrony as a limiting case. Overall, our statistical analyses suggest that transient phase reorganization in neural coupled oscillators, beyond purely excito-excitatory traveling waves, contribute significantly to the origin of motor cortex ß-LFP wave patterns.

Dissociation between sustained single-neuron spiking and transient ß-LFP oscillations in primate motor cortex.

Determining the relationship between single-neuron spiking and transient (20 Hz) ß-local field potential (ß-LFP) oscillations is an important step for understanding the role of these oscillations in motor cortex. We show that whereas motor cortex firing rates and beta spiking rhythmicity remain sustained during steady-state movement preparation periods, ß-LFP oscillations emerge, in contrast, as short transient events. Single-neuron mean firing rates within and outside transient ß-LFP events showed no differences, and no consistent correlation was found between the beta oscillation amplitude and firing rates, as was the case for movement- and visual cue-related ß-LFP suppression. Importantly, well-isolated single units featuring beta-rhythmic spiking (43%, 125/292) showed no apparent or only weak phase coupling with the transient ß-LFP oscillations. Similar results were obtained for the population spiking. These findings were common in triple microelectrode array recordings from primary motor (M1), ventral (PMv), and dorsal premotor (PMd) cortices in nonhuman primates during movement preparation. Although beta spiking rhythmicity indicates strong membrane potential fluctuations in the beta band, it does not imply strong phase coupling with ß-LFP oscillations. The observed dissociation points to two different sources of variation in motor cortex ß-LFPs: one that impacts single-neuron spiking dynamics and another related to the generation of mesoscopic ß-LFP signals. Furthermore, our findings indicate that rhythmic spiking and diverse neuronal firing rates, which encode planned actions during movement preparation, may naturally limit the ability of different neuronal populations to strongly phase-couple to a single dominant oscillation frequency, leading to the observed spiking and ß-LFP dissociation.NEW & NOTEWORTHY We show that whereas motor cortex spiking rates and beta (~20 Hz) spiking rhythmicity remain sustained during steady-state movement preparation periods, ß-local field potential (ß-LFP) oscillations emerge, in contrast, as transient events. Furthermore, the ß-LFP phase at which neurons spike drifts: phase coupling is typically weak or absent. This dissociation points to two sources of variation in the level of motor cortex beta: one that impacts single-neuron spiking and another related to the generation of measured mesoscopic ß-LFPs.

Contribution of LFP dynamics to single-neuron spiking variability in motor cortex during movement execution.

Understanding the sources of variability in single-neuron spiking responses is an important open problem for the theory of neural coding. This variability is thought to result primarily from spontaneous collective dynamics in neuronal networks. Here, we investigate how well collective dynamics reflected in motor cortex local field potentials (LFPs) can account for spiking variability during motor behavior. Neural activity was recorded via microelectrode arrays implanted in ventral and dorsal premotor and primary motor cortices of non-human primates performing naturalistic 3-D reaching and grasping actions. Point process models were used to quantify how well LFP features accounted for spiking variability not explained by the measured 3-D reach and grasp kinematics. LFP features included the instantaneous magnitude, phase and analytic-signal components of narrow band-pass filtered (δ,θ,α,ß) LFPs, and analytic signal and amplitude envelope features in higher-frequency bands. Multiband LFP features predicted single-neuron spiking (1ms resolution) with substantial accuracy as assessed via ROC analysis. Notably, however, models including both LFP and kinematics features displayed marginal improvement over kinematics-only models. Furthermore, the small predictive information added by LFP features to kinematic models was redundant to information available in fast-timescale (<100 ms) spiking history. Overall, information in multiband LFP features, although predictive of single-neuron spiking during movement execution, was redundant to information available in movement parameters and spiking history. Our findings suggest that, during movement execution, collective dynamics reflected in motor cortex LFPs primarily relate to sensorimotor processes directly controlling movement output, adding little explanatory power to variability not accounted by movement parameters.