Dimension of Activity in Random Neural Networks.

Neural networks are high-dimensional nonlinear dynamical systems that process information through the coordinated activity of many connected units. Understanding how biological and machine-learning networks function and learn requires knowledge of the structure of this coordinated activity, information contained, for example, in cross covariances between units. Self-consistent dynamical mean field theory (DMFT) has elucidated several features of random neural networks-in particular, that they can generate chaotic activity-however, a calculation of cross covariances using this approach has not been provided. Here, we calculate cross covariances self-consistently via a two-site cavity DMFT. We use this theory to probe spatiotemporal features of activity coordination in a classic random-network model with independent and identically distributed (i.i.d.) couplings, showing an extensive but fractionally low effective dimension of activity and a long population-level timescale. Our formulas apply to a wide range of single-unit dynamics and generalize to non-i.i.d. couplings. As an example of the latter, we analyze the case of partially symmetric couplings.

The complete connectome of a learning and memory centre in an insect brain.

Associating stimuli with positive or negative reinforcement is essential for survival, but a complete wiring diagram of a higher-order circuit supporting associative memory has not been previously available. Here we reconstruct one such circuit at synaptic resolution, the Drosophila larval mushroom body. We find that most Kenyon cells integrate random combinations of inputs but that a subset receives stereotyped inputs from single projection neurons. This organization maximizes performance of a model output neuron on a stimulus discrimination task. We also report a novel canonical circuit in each mushroom body compartment with previously unidentified connections: reciprocal Kenyon cell to modulatory neuron connections, modulatory neuron to output neuron connections, and a surprisingly high number of recurrent connections between Kenyon cells. Stereotyped connections found between output neurons could enhance the selection of learned behaviours. The complete circuit map of the mushroom body should guide future functional studies of this learning and memory centre.

Models of heterogeneous dopamine signaling in an insect learning and memory center.

The Drosophila mushroom body exhibits dopamine dependent synaptic plasticity that underlies the acquisition of associative memories. Recordings of dopamine neurons in this system have identified signals related to external reinforcement such as reward and punishment. However, other factors including locomotion, novelty, reward expectation, and internal state have also recently been shown to modulate dopamine neurons. This heterogeneity is at odds with typical modeling approaches in which these neurons are assumed to encode a global, scalar error signal. How is dopamine dependent plasticity coordinated in the presence of such heterogeneity? We develop a modeling approach that infers a pattern of dopamine activity sufficient to solve defined behavioral tasks, given architectural constraints informed by knowledge of mushroom body circuitry. Model dopamine neurons exhibit diverse tuning to task parameters while nonetheless producing coherent learned behaviors. Notably, reward prediction error emerges as a mode of population activity distributed across these neurons. Our results provide a mechanistic framework that accounts for the heterogeneity of dopamine activity during learning and behavior.

Scaling Properties of Dimensionality Reduction for Neural Populations and Network Models.

Recent studies have applied dimensionality reduction methods to understand how the multi-dimensional structure of neural population activity gives rise to brain function. It is unclear, however, how the results obtained from dimensionality reduction generalize to recordings with larger numbers of neurons and trials or how these results relate to the underlying network structure. We address these questions by applying factor analysis to recordings in the visual cortex of non-human primates and to spiking network models that self-generate irregular activity through a balance of excitation and inhibition. We compared the scaling trends of two key outputs of dimensionality reduction-shared dimensionality and percent shared variance-with neuron and trial count. We found that the scaling properties of networks with non-clustered and clustered connectivity differed, and that the in vivo recordings were more consistent with the clustered network. Furthermore, recordings from tens of neurons were sufficient to identify the dominant modes of shared variability that generalize to larger portions of the network. These findings can help guide the interpretation of dimensionality reduction outputs in regimes of limited neuron and trial sampling and help relate these outputs to the underlying network structure.

Inhibitory stabilization and visual coding in cortical circuits with multiple interneuron subtypes.

Recent anatomical and functional characterization of cortical inhibitory interneurons has highlighted the diverse computations supported by different subtypes of interneurons. However, most theoretical models of cortex do not feature multiple classes of interneurons and rather assume a single homogeneous population. We study the dynamics of recurrent excitatory-inhibitory model cortical networks with parvalbumin (PV)-, somatostatin (SOM)-, and vasointestinal peptide-expressing (VIP) interneurons, with connectivity properties motivated by experimental recordings from mouse primary visual cortex. Our theory describes conditions under which the activity of such networks is stable and how perturbations of distinct neuronal subtypes recruit changes in activity through recurrent synaptic projections. We apply these conclusions to study the roles of each interneuron subtype in disinhibition, surround suppression, and subtractive or divisive modulation of orientation tuning curves. Our calculations and simulations determine the architectural and stimulus tuning conditions under which cortical activity consistent with experiment is possible. They also lead to novel predictions concerning connectivity and network dynamics that can be tested via optogenetic manipulations. Our work demonstrates that recurrent inhibitory dynamics must be taken into account to fully understand many properties of cortical dynamics observed in experiments.

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses.

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.

Correlated neural variability in persistent state networks.

Neural activity that persists long after stimulus presentation is a biological correlate of short-term memory. Variability in spiking activity causes persistent states to drift over time, ultimately degrading memory. Models of short-term memory often assume that the input fluctuations to neural populations are independent across cells, a feature that attenuates population-level variability and stabilizes persistent activity. However, this assumption is at odds with experimental recordings from pairs of cortical neurons showing that both the input currents and output spike trains are correlated. It remains unclear how correlated variability affects the stability of persistent activity and the performance of cognitive tasks that it supports. We consider the stochastic long-timescale attractor dynamics of pairs of mutually inhibitory populations of spiking neurons. In these networks, persistent activity was less variable when correlated variability was globally distributed across both populations compared with the case when correlations were locally distributed only within each population. Using a reduced firing rate model with a continuum of persistent states, we show that, when input fluctuations are correlated across both populations, they drive firing rate fluctuations orthogonal to the persistent state attractor, thereby causing minimal stochastic drift. Using these insights, we establish that distributing correlated fluctuations globally as opposed to locally improves network's performance on a two-interval, delayed response discrimination task. Our work shows that the correlation structure of input fluctuations to a network is an important factor when determining long-timescale, persistent population spiking activity.

Prediction of neural activity in connectome-constrained recurrent networks.

We develop a theory of connectome-constrained neural networks in which a "student" network is trained to reproduce the activity of a ground-truth "teacher," representing a neural system for which a connectome is available. Unlike standard paradigms with unconstrained connectivity, here the two networks have the same connectivity but different biophysical parameters, reflecting uncertainty in neuronal and synaptic properties. We find that a connectome is often insufficient to constrain the dynamics of networks that perform a specific task, illustrating the difficulty of inferring function from connectivity alone. However, recordings from a small subset of neurons can remove this degeneracy, producing dynamics in the student that agree with the teacher. Our theory can also prioritize which neurons to record from to most efficiently predict unmeasured network activity. Our analysis shows that the solution spaces of connectome-constrained and unconstrained models are qualitatively different and provides a framework to determine when such models yield consistent dynamics.

Dynamics of striatal action selection and reinforcement learning.

Spiny projection neurons (SPNs) in dorsal striatum are often proposed as a locus of reinforcement learning in the basal ganglia. Here, we identify and resolve a fundamental inconsistency between striatal reinforcement learning models and known SPN synaptic plasticity rules. Direct-pathway (dSPN) and indirect-pathway (iSPN) neurons, which promote and suppress actions, respectively, exhibit synaptic plasticity that reinforces activity associated with elevated or suppressed dopamine release. We show that iSPN plasticity prevents successful learning, as it reinforces activity patterns associated with negative outcomes. However, this pathological behavior is reversed if functionally opponent dSPNs and iSPNs, which promote and suppress the current behavior, are simultaneously activated by efferent input following action selection. This prediction is supported by striatal recordings and contrasts with prior models of SPN representations. In our model, learning and action selection signals can be multiplexed without interference, enabling learning algorithms beyond those of standard temporal difference models.

Diversity of visual inputs to Kenyon cells of the Drosophila mushroom body.

The arthropod mushroom body is well-studied as an expansion layer representing olfactory stimuli and linking them to contingent events. However, 8% of mushroom body Kenyon cells in Drosophila melanogaster receive predominantly visual input, and their function remains unclear. Here, we identify inputs to visual Kenyon cells using the FlyWire adult whole-brain connectome. Input repertoires are similar across hemispheres and connectomes with certain inputs highly overrepresented. Many visual neurons presynaptic to Kenyon cells have large receptive fields, while interneuron inputs receive spatially restricted signals that may be tuned to specific visual features. Individual visual Kenyon cells randomly sample sparse inputs from combinations of visual channels, including multiple optic lobe neuropils. These connectivity patterns suggest that visual coding in the mushroom body, like olfactory coding, is sparse, distributed, and combinatorial. However, the specific input repertoire to the smaller population of visual Kenyon cells suggests a constrained encoding of visual stimuli.

Evolution of connectivity architecture in the Drosophila mushroom body.

Brain evolution has primarily been studied at the macroscopic level by comparing the relative size of homologous brain centers between species. How neuronal circuits change at the cellular level over evolutionary time remains largely unanswered. Here, using a phylogenetically informed framework, we compare the olfactory circuits of three closely related Drosophila species that differ in their chemical ecology: the generalists Drosophila melanogaster and Drosophila simulans and Drosophila sechellia that specializes on ripe noni fruit. We examine a central part of the olfactory circuit that, to our knowledge, has not been investigated in these species-the connections between projection neurons and the Kenyon cells of the mushroom body-and identify species-specific connectivity patterns. We found that neurons encoding food odors connect more frequently with Kenyon cells, giving rise to species-specific biases in connectivity. These species-specific connectivity differences reflect two distinct neuronal phenotypes: in the number of projection neurons or in the number of presynaptic boutons formed by individual projection neurons. Finally, behavioral analyses suggest that such increased connectivity enhances learning performance in an associative task. Our study shows how fine-grained aspects of connectivity architecture in an associative brain center can change during evolution to reflect the chemical ecology of a species.

Specific connectivity optimizes learning in thalamocortical loops.

Thalamocortical loops have a central role in cognition and motor control, but precisely how they contribute to these processes is unclear. Recent studies showing evidence of plasticity in thalamocortical synapses indicate a role for the thalamus in shaping cortical dynamics through learning. Since signals undergo a compression from the cortex to the thalamus, we hypothesized that the computational role of the thalamus depends critically on the structure of corticothalamic connectivity. To test this, we identified the optimal corticothalamic structure that promotes biologically plausible learning in thalamocortical synapses. We found that corticothalamic projections specialized to communicate an efference copy of the cortical output benefit motor control, while communicating the modes of highest variance is optimal for working memory tasks. We analyzed neural recordings from mice performing grasping and delayed discrimination tasks and found corticothalamic communication consistent with these predictions. These results suggest that the thalamus orchestrates cortical dynamics in a functionally precise manner through structured connectivity.

A cerebellar granule cell-climbing fiber computation to learn to track long time intervals.

In classical cerebellar learning, Purkinje cells (PkCs) associate climbing fiber (CF) error signals with predictive granule cells (GrCs) that were active just prior (∼150 ms). The cerebellum also contributes to behaviors characterized by longer timescales. To investigate how GrC-CF-PkC circuits might learn seconds-long predictions, we imaged simultaneous GrC-CF activity over days of forelimb operant conditioning for delayed water reward. As mice learned reward timing, numerous GrCs developed anticipatory activity ramping at different rates until reward delivery, followed by widespread time-locked CF spiking. Relearning longer delays further lengthened GrC activations. We computed CF-dependent GrC→PkC plasticity rules, demonstrating that reward-evoked CF spikes sufficed to grade many GrC synapses by anticipatory timing. We predicted and confirmed that PkCs could thereby continuously ramp across seconds-long intervals from movement to reward. Learning thus leads to new GrC temporal bases linking predictors to remote CF reward signals-a strategy well suited for learning to track the long intervals common in cognitive domains.

The spatial structure of stimuli shapes the timescale of correlations in population spiking activity.

Throughout the central nervous system, the timescale over which pairs of neural spike trains are correlated is shaped by stimulus structure and behavioral context. Such shaping is thought to underlie important changes in the neural code, but the neural circuitry responsible is largely unknown. In this study, we investigate a stimulus-induced shaping of pairwise spike train correlations in the electrosensory system of weakly electric fish. Simultaneous single unit recordings of principal electrosensory cells show that an increase in the spatial extent of stimuli increases correlations at short (≈ 10 ms) timescales while simultaneously reducing correlations at long (≈ 100 ms) timescales. A spiking network model of the first two stages of electrosensory processing replicates this correlation shaping, under the assumptions that spatially broad stimuli both saturate feedforward afferent input and recruit an open-loop inhibitory feedback pathway. Our model predictions are experimentally verified using both the natural heterogeneity of the electrosensory system and pharmacological blockade of descending feedback projections. For weak stimuli, linear response analysis of the spiking network shows that the reduction of long timescale correlation for spatially broad stimuli is similar to correlation cancellation mechanisms previously suggested to be operative in mammalian cortex. The mechanism for correlation shaping supports population-level filtering of irrelevant distractor stimuli, thereby enhancing the population response to relevant prey and conspecific communication inputs.

Optimal routing to cerebellum-like structures.

The vast expansion from mossy fibers to cerebellar granule cells (GrC) produces a neural representation that supports functions including associative and internal model learning. This motif is shared by other cerebellum-like structures and has inspired numerous theoretical models. Less attention has been paid to structures immediately presynaptic to GrC layers, whose architecture can be described as a 'bottleneck' and whose function is not understood. We therefore develop a theory of cerebellum-like structures in conjunction with their afferent pathways that predicts the role of the pontine relay to cerebellum and the glomerular organization of the insect antennal lobe. We highlight a new computational distinction between clustered and distributed neuronal representations that is reflected in the anatomy of these two brain structures. Our theory also reconciles recent observations of correlated GrC activity with theories of nonlinear mixing. More generally, it shows that structured compression followed by random expansion is an efficient architecture for flexible computation.

Task-dependent optimal representations for cerebellar learning.

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

Diversity of visual inputs to Kenyon cells of the Drosophila mushroom body.

The arthropod mushroom body is well-studied as an expansion layer that represents olfactory stimuli and links them to contingent events. However, 8% of mushroom body Kenyon cells in Drosophila melanogaster receive predominantly visual input, and their tuning and function are poorly understood. Here, we use the FlyWire adult whole-brain connectome to identify inputs to visual Kenyon cells. The types of visual neurons we identify are similar across hemispheres and connectomes with certain inputs highly overrepresented. Many visual projection neurons presynaptic to Kenyon cells receive input from large swathes of visual space, while local visual interneurons, providing smaller fractions of input, receive more spatially restricted signals that may be tuned to specific features of the visual scene. Like olfactory Kenyon cells, visual Kenyon cells receive sparse inputs from different combinations of visual channels, including inputs from multiple optic lobe neuropils. The sets of inputs to individual visual Kenyon cells are consistent with random sampling of available inputs. These connectivity patterns suggest that visual coding in the mushroom body, like olfactory coding, is sparse, distributed, and combinatorial. However, the expansion coding properties appear different, with a specific repertoire of visual inputs projecting onto a relatively small number of visual Kenyon cells.

Evolution of connectivity architecture in the Drosophila mushroom body.

Brain evolution has primarily been studied at the macroscopic level by comparing the relative size of homologous brain centers between species. How neuronal circuits change at the cellular level over evolutionary time remains largely unanswered. Here, using a phylogenetically informed framework, we compare the olfactory circuits of three closely related Drosophila species that differ radically in their chemical ecology: the generalists Drosophila melanogaster and Drosophila simulans that feed on fermenting fruit, and Drosophila sechellia that specializes on ripe noni fruit. We examine a central part of the olfactory circuit that has not yet been investigated in these species - the connections between the projection neurons of the antennal lobe and the Kenyon cells of the mushroom body, an associative brain center - to identify species-specific connectivity patterns. We found that neurons encoding food odors - the DC3 neurons in D. melanogaster and D. simulans and the DL2d neurons in D. sechellia - connect more frequently with Kenyon cells, giving rise to species-specific biases in connectivity. These species-specific differences in connectivity reflect two distinct neuronal phenotypes: in the number of projection neurons or in the number of presynaptic boutons formed by individual projection neurons. Finally, behavioral analyses suggest that such increased connectivity enhances learning performance in an associative task. Our study shows how fine-grained aspects of connectivity architecture in an associative brain center can change during evolution to reflect the chemical ecology of a species.

Hierarchical architecture of dopaminergic circuits enables second-order conditioning in Drosophila.

Dopaminergic neurons with distinct projection patterns and physiological properties compose memory subsystems in a brain. However, it is poorly understood whether or how they interact during complex learning. Here, we identify a feedforward circuit formed between dopamine subsystems and show that it is essential for second-order conditioning, an ethologically important form of higher-order associative learning. The Drosophila mushroom body comprises a series of dopaminergic compartments, each of which exhibits distinct memory dynamics. We find that a slow and stable memory compartment can serve as an effective 'teacher' by instructing other faster and transient memory compartments via a single key interneuron, which we identify by connectome analysis and neurotransmitter prediction. This excitatory interneuron acquires enhanced response to reward-predicting odor after first-order conditioning and, upon activation, evokes dopamine release in the 'student' compartments. These hierarchical connections between dopamine subsystems explain distinct properties of first- and second-order memory long known by behavioral psychologists.

Balanced synaptic input shapes the correlation between neural spike trains.

Stimulus properties, attention, and behavioral context influence correlations between the spike times produced by a pair of neurons. However, the biophysical mechanisms that modulate these correlations are poorly understood. With a combined theoretical and experimental approach, we show that the rate of balanced excitatory and inhibitory synaptic input modulates the magnitude and timescale of pairwise spike train correlation. High rate synaptic inputs promote spike time synchrony rather than long timescale spike rate correlations, while low rate synaptic inputs produce opposite results. This correlation shaping is due to a combination of enhanced high frequency input transfer and reduced firing rate gain in the high input rate state compared to the low state. Our study extends neural modulation from single neuron responses to population activity, a necessary step in understanding how the dynamics and processing of neural activity change across distinct brain states.