Drifting neuronal representations: Bug or feature?

Unified theoretical framework for wide neural network learning dynamics

Artificial neural networks have revolutionized machine learning in recent years, but a complete theoretical framework for their learning process is still lacking. Substantial theoretical advances have been achieved for wide networks, within two disparate theoretical frameworks: the neural tangent kernel (NTK), which assumes linearized gradient descent dynamics, and the Bayesian neural network Gaussian process (NNGP) framework. Here we unify these two theories using gradient descent learning dynamics with an additional small noise in an ensemble of wide deep networks. We construct an exact analytical theory for the network input-output function and introduce a new time-dependent neural dynamical kernel (NDK) from which both NTK and NNGP kernels are derived. We identify two learning phases characterized by different time scales: an initial gradient-driven learning phase, dominated by deterministic minimization of the loss, in which the time scale is mainly governed by the variance of the weight initialization. It is followed by a slow diffusive learning stage, during which the network parameters sample the solution space, with a time constant that is determined by the noise level and the variance of the Bayesian prior. The two variance parameters can strongly affect the performance in the two regimes, particularly in sigmoidal neurons. In contrast to the exponential convergence of the mean predictor in the initial phase, the convergence to the final equilibrium is more complex and may exhibit nonmonotonic behavior. By characterizing the diffusive learning phase, our work sheds light on the phenomenon of representational drift in the brain, explaining how neural activity can exhibit continuous changes in internal representations without degrading performance, either by ongoing weak gradient signals that synchronize the drifts of different synapses or by architectural biases that generate invariant code, i.e., task-relevant information that is robust against the drift process. This work closes the gap between the NTK and NNGP theories, providing a comprehensive framework for understanding the learning process of deep wide neural networks and for analyzing learning dynamics in biological neural circuits.

Synaptic plasticity rules driving representational shifting in the hippocampus

Synaptic plasticity is widely thought to support memory storage in the brain, but the rules determining impactful synaptic changes in vivo are not known. We considered the trial-by-trial shifting dynamics of hippocampal place fields (PF) as an indicator of ongoing plasticity during memory formation and familiarization. By implementing different plasticity rules in computational models of spiking place cells and comparing them to experimentally measured PFs from mice navigating familiar and new environments, we found that behavioral timescale synaptic plasticity (BTSP), rather than Hebbian spike-timing-dependent plasticity (STDP), best explains PF shifting dynamics. BTSP-triggering events are rare, but more frequent during new experiences. During exploration, their probability is dynamic-it decays after PF onset, but continually drives a population-level representational drift. Additionally, our results show that BTSP occurs in CA3 but is less frequent and phenomenologically different than in CA1. Overall, our study provides a new framework to understand how synaptic plasticity continuously shapes neuronal representations during learning.

Sampling representational plasticity of simple imagined movements across days enables long-term neuroprosthetic control

The nervous system needs to balance the stability of neural representations with plasticity. It is unclear what the representational stability of simple well-rehearsed actions is, particularly in humans, and their adaptability to new contexts. Using an electrocorticography brain-computer interface (BCI) in tetraplegic participants, we found that the low-dimensional manifold and relative representational distances for a repertoire of simple imagined movements were remarkably stable. The manifold's absolute location, however, demonstrated constrained day-to-day drift. Strikingly, neural statistics, especially variance, could be flexibly regulated to increase representational distances during BCI control without somatotopic changes. Discernability strengthened with practice and was BCI-specific, demonstrating contextual specificity. Sampling representational plasticity and drift across days subsequently uncovered a meta-representational structure with generalizable decision boundaries for the repertoire; this allowed long-term neuroprosthetic control of a robotic arm and hand for reaching and grasping. Our study offers insights into mesoscale representational statistics that also enable long-term complex neuroprosthetic control.

Representational drift in barrel cortex is receptive field dependent

Cortical populations often exhibit changes in activity even when behavior is stable. How behavioral stability is maintained in the face of such "representational drift" remains unclear. One possibility is that some neurons are more stable than others. We examined whisker touch responses in layers 2-4 of the primary vibrissal somatosensory cortex (vS1) over several weeks in mice stably performing an object detection task with two whiskers. Although the number of touch neurons remained constant, individual neurons changed with time. Touch-responsive neurons with broad receptive fields were more stable than narrowly tuned neurons. Transitions between functional types were non-random: before becoming broadly tuned, unresponsive neurons first passed through a period of narrower tuning. Broadly tuned neurons in layers 2 and 3 with higher pairwise correlations to other touch neurons were more stable than neurons with lower correlations. Thus, a small population of broadly tuned and synchronously active touch neurons exhibits elevated stability and may be particularly important for behavior.

Memory engram stability and flexibility

Many studies have shown that memories are encoded in sparse neural ensembles distributed across the brain. During the post-encoding period, often during sleep, many of the cells that were active during encoding are reactivated, supporting consolidation of this memory. During memory recall, many of the same cells that were active during encoding and reactivated during consolidation are reactivated during recall. These ensembles of cells have been referred to as the memory engram cells, stably representing a specific memory. However, recent studies question the rigidity of the "stable memory engram." Here we review the past literature of how episodic-like memories are encoded, consolidated, and recalled. We also highlight more recent studies (as well as some older literature) that suggest that these stable memories and their representations are much more dynamic and flexible than previously thought. We highlight some of these processes, including memory updating, reconsolidation, forgetting, schema learning, memory-linking, and representational drift.

Co-existence of synaptic plasticity and metastable dynamics in a spiking model of cortical circuits

Evidence for metastable dynamics and its role in brain function is emerging at a fast pace and is changing our understanding of neural coding by putting an emphasis on hidden states of transient activity. Clustered networks of spiking neurons have enhanced synaptic connections among groups of neurons forming structures called cell assemblies; such networks are capable of producing metastable dynamics that is in agreement with many experimental results. However, it is unclear how a clustered network structure producing metastable dynamics may emerge from a fully local plasticity rule, i.e., a plasticity rule where each synapse has only access to the activity of the neurons it connects (as opposed to the activity of other neurons or other synapses). Here, we propose a local plasticity rule producing ongoing metastable dynamics in a deterministic, recurrent network of spiking neurons. The metastable dynamics co-exists with ongoing plasticity and is the consequence of a self-tuning mechanism that keeps the synaptic weights close to the instability line where memories are spontaneously reactivated. In turn, the synaptic structure is stable to ongoing dynamics and random perturbations, yet it remains sufficiently plastic to remap sensory representations to encode new sets of stimuli. Both the plasticity rule and the metastable dynamics scale well with network size, with synaptic stability increasing with the number of neurons. Overall, our results show that it is possible to generate metastable dynamics over meaningful hidden states using a simple but biologically plausible plasticity rule which co-exists with ongoing neural dynamics.

Co-existence of synaptic plasticity and metastable dynamics in a spiking model of cortical circuits

Evidence for metastable dynamics and its role in brain function is emerging at a fast pace and is changing our understanding of neural coding by putting an emphasis on hidden states of transient activity. Clustered networks of spiking neurons have enhanced synaptic connections among groups of neurons forming structures called cell assemblies; such networks are capable of producing metastable dynamics that is in agreement with many experimental results. However, it is unclear how a clustered network structure producing metastable dynamics may emerge from a fully local plasticity rule, i.e., a plasticity rule where each synapse has only access to the activity of the neurons it connects (as opposed to the activity of other neurons or other synapses). Here, we propose a local plasticity rule producing ongoing metastable dynamics in a deterministic, recurrent network of spiking neurons. The metastable dynamics co-exists with ongoing plasticity and is the consequence of a self-tuning mechanism that keeps the synaptic weights close to the instability line where memories are spontaneously reactivated. In turn, the synaptic structure is stable to ongoing dynamics and random perturbations, yet it remains sufficiently plastic to remap sensory representations to encode new sets of stimuli. Both the plasticity rule and the metastable dynamics scale well with network size, with synaptic stability increasing with the number of neurons. Overall, our results show that it is possible to generate metastable dynamics over meaningful hidden states using a simple but biologically plausible plasticity rule which co-exists with ongoing neural dynamics.

Unsupervised restoration of a complex learned behavior after large-scale neuronal perturbation

Reliable execution of precise behaviors requires that brain circuits are resilient to variations in neuronal dynamics. Genetic perturbation of the majority of excitatory neurons in HVC, a brain region involved in song production, in adult songbirds with stereotypical songs triggered severe degradation of the song. The song fully recovered within 2 weeks, and substantial improvement occurred even when animals were prevented from singing during the recovery period, indicating that offline mechanisms enable recovery in an unsupervised manner. Song restoration was accompanied by increased excitatory synaptic input to neighboring, unmanipulated neurons in the same brain region. A model inspired by the behavioral and electrophysiological findings suggests that unsupervised single-cell and population-level homeostatic plasticity rules can support the functional restoration after large-scale disruption of networks that implement sequential dynamics. These observations suggest the existence of cellular and systems-level restorative mechanisms that ensure behavioral resilience.

Neural Circuits for Fast Poisson Compressed Sensing in the Olfactory Bulb

Within a single sniff, the mammalian olfactory system can decode the identity and concentration of odorants wafted on turbulent plumes of air. Yet, it must do so given access only to the noisy, dimensionally-reduced representation of the odor world provided by olfactory receptor neurons. As a result, the olfactory system must solve a compressed sensing problem, relying on the fact that only a handful of the millions of possible odorants are present in a given scene. Inspired by this principle, past works have proposed normative compressed sensing models for olfactory decoding. However, these models have not captured the unique anatomy and physiology of the olfactory bulb, nor have they shown that sensing can be achieved within the 100-millisecond timescale of a single sniff. Here, we propose a rate-based Poisson compressed sensing circuit model for the olfactory bulb. This model maps onto the neuron classes of the olfactory bulb, and recapitulates salient features of their connectivity and physiology. For circuit sizes comparable to the human olfactory bulb, we show that this model can accurately detect tens of odors within the timescale of a single sniff. We also show that this model can perform Bayesian posterior sampling for accurate uncertainty estimation. Fast inference is possible only if the geometry of the neural code is chosen to match receptor properties, yielding a distributed neural code that is not axis-aligned to individual odor identities. Our results illustrate how normative modeling can help us map function onto specific neural circuits to generate new hypotheses.

Representational drift in barrel cortex is receptive field dependent

Cortical populations often exhibit changes in activity even when behavior is stable. How behavioral stability is maintained in the face of such 'representational drift' remains unclear. One possibility is that some neurons are stable despite broader instability. We examine whisker touch responses in superficial layers of primary vibrissal somatosensory cortex (vS1) over several weeks in mice stably performing an object detection task with two whiskers. While the number of touch neurons remained constant, individual neurons changed with time. Touch-responsive neurons with broad receptive fields were more stable than narrowly tuned neurons. Transitions between functional types were non-random: before becoming broadly tuned neurons, unresponsive neurons first pass through a period of narrower tuning. Broadly tuned neurons with higher pairwise correlations to other touch neurons were more stable than neurons with lower correlations. Thus, a small population of broadly tuned and synchronously active touch neurons exhibit elevated stability and may be particularly important for downstream readout.

BTSP, not STDP, Drives Shifts in Hippocampal Representations During Familiarization

Synaptic plasticity is widely thought to support memory storage in the brain, but the rules determining impactful synaptic changes in-vivo are not known. We considered the trial-by-trial shifting dynamics of hippocampal place fields (PFs) as an indicator of ongoing plasticity during memory formation. By implementing different plasticity rules in computational models of spiking place cells and comparing to experimentally measured PFs from mice navigating familiar and novel environments, we found that Behavioral-Timescale-Synaptic-Plasticity (BTSP), rather than Hebbian Spike-Timing-Dependent-Plasticity, is the principal mechanism governing PF shifting dynamics. BTSP-triggering events are rare, but more frequent during novel experiences. During exploration, their probability is dynamic: it decays after PF onset, but continually drives a population-level representational drift. Finally, our results show that BTSP occurs in CA3 but is less frequent and phenomenologically different than in CA1. Overall, our study provides a new framework to understand how synaptic plasticity shapes neuronal representations during learning.

Effects of stochastic coding on olfactory discrimination in flies and mice

Sparse coding can improve discrimination of sensory stimuli by reducing overlap between their representations. Two factors, however, can offset sparse coding's benefits: similar sensory stimuli have significant overlap and responses vary across trials. To elucidate the effects of these 2 factors, we analyzed odor responses in the fly and mouse olfactory regions implicated in learning and discrimination-the mushroom body (MB) and the piriform cortex (PCx). We found that neuronal responses fall along a continuum from extremely reliable across trials to extremely variable or stochastic. Computationally, we show that the observed variability arises from noise within central circuits rather than sensory noise. We propose this coding scheme to be advantageous for coarse- and fine-odor discrimination. More reliable cells enable quick discrimination between dissimilar odors. For similar odors, however, these cells overlap and do not provide distinguishing information. By contrast, more unreliable cells are decorrelated for similar odors, providing distinguishing information, though these benefits only accrue with extended training with more trials. Overall, we have uncovered a conserved, stochastic coding scheme in vertebrates and invertebrates, and we identify a candidate mechanism, based on variability in a winner-take-all (WTA) inhibitory circuit, that improves discrimination with training.

Flexible regulation of representations on a drifting manifold enables long-term stable complex neuroprosthetic control

The nervous system needs to balance the stability of neural representations with plasticity. It is unclear what is the representational stability of simple actions, particularly those that are well-rehearsed in humans, and how it changes in new contexts. Using an electrocorticography brain-computer interface (BCI), we found that the mesoscale manifold and relative representational distances for a repertoire of simple imagined movements were remarkably stable. Interestingly, however, the manifold's absolute location demonstrated day-to-day drift. Strikingly, representational statistics, especially variance, could be flexibly regulated to increase discernability during BCI control without somatotopic changes. Discernability strengthened with practice and was specific to the BCI, demonstrating remarkable contextual specificity. Accounting for drift, and leveraging the flexibility of representations, allowed neuroprosthetic control of a robotic arm and hand for over 7 months without recalibration. Our study offers insight into how electrocorticography can both track representational statistics across long periods and allow long-term complex neuroprosthetic control.

Distinct ventral stream and prefrontal cortex representational dynamics during sustained conscious visual perception

Instances of sustained stationary sensory input are ubiquitous. However, previous work focused almost exclusively on transient onset responses. This presents a critical challenge for neural theories of consciousness, which should account for the full temporal extent of experience. To address this question, we use intracranial recordings from ten human patients with epilepsy to view diverse images of multiple durations. We reveal that, in sensory regions, despite dramatic changes in activation magnitude, the distributed representation of categories and exemplars remains sustained and stable. In contrast, in frontoparietal regions, we find transient content representation at stimulus onset. Our results highlight the connection between the anatomical and temporal correlates of experience. To the extent perception is sustained, it may rely on sensory representations and to the extent perception is discrete, centered on perceptual updating, it may rely on frontoparietal representations.

Time and experience differentially affect distinct aspects of hippocampal representational drift

Hippocampal activity is critical for spatial memory. Within a fixed, familiar environment, hippocampal codes gradually change over timescales of days to weeks-a phenomenon known as representational drift. The passage of time and the amount of experience are two factors that profoundly affect memory. However, thus far, it has remained unclear to what extent these factors drive hippocampal representational drift. Here, we longitudinally recorded large populations of hippocampal neurons in mice while they repeatedly explored two different familiar environments that they visited at different time intervals over weeks. We found that time and experience differentially affected distinct aspects of representational drift: the passage of time drove changes in neuronal activity rates, whereas experience drove changes in the cells' spatial tuning. Changes in spatial tuning were context specific and largely independent of changes in activity rates. Thus, our results suggest that representational drift is a multi-faceted process governed by distinct neuronal mechanisms.

Coordinated drift of receptive fields in Hebbian/anti-Hebbian network models during noisy representation learning

Recent experiments have revealed that neural population codes in many brain areas continuously change even when animals have fully learned and stably perform their tasks. This representational 'drift' naturally leads to questions about its causes, dynamics and functions. Here we explore the hypothesis that neural representations optimize a representational objective with a degenerate solution space, and noisy synaptic updates drive the network to explore this (near-)optimal space causing representational drift. We illustrate this idea and explore its consequences in simple, biologically plausible Hebbian/anti-Hebbian network models of representation learning. We find that the drifting receptive fields of individual neurons can be characterized by a coordinated random walk, with effective diffusion constants depending on various parameters such as learning rate, noise amplitude and input statistics. Despite such drift, the representational similarity of population codes is stable over time. Our model recapitulates experimental observations in the hippocampus and posterior parietal cortex and makes testable predictions that can be probed in future experiments.

Representational drift: Emerging theories for continual learning and experimental future directions

Recent work has revealed that the neural activity patterns correlated with sensation, cognition, and action often are not stable and instead undergo large scale changes over days and weeks-a phenomenon called representational drift. Here, we highlight recent observations of drift, how drift is unlikely to be explained by experimental confounds, and how the brain can likely compensate for drift to allow stable computation. We propose that drift might have important roles in neural computation to allow continual learning, both for separating and relating memories that occur at distinct times. Finally, we present an outlook on future experimental directions that are needed to further characterize drift and to test emerging theories for drift's role in computation.