An approximate line attractor in the hypothalamus encodes an aggressive state.

The hypothalamus regulates innate social behaviors, including mating and aggression. These behaviors can be evoked by optogenetic stimulation of specific neuronal subpopulations within MPOA and VMHvl, respectively. Here, we perform dynamical systems modeling of population neuronal activity in these nuclei during social behaviors. In VMHvl, unsupervised analysis identified a dominant dimension of neural activity with a large time constant (>50 s), generating an approximate line attractor in neural state space. Progression of the neural trajectory along this attractor was correlated with an escalation of agonistic behavior, suggesting that it may encode a scalable state of aggressiveness. Consistent with this, individual differences in the magnitude of the integration dimension time constant were strongly correlated with differences in aggressiveness. In contrast, approximate line attractors were not observed in MPOA during mating; instead, neurons with fast dynamics were tuned to specific actions. Thus, different hypothalamic nuclei employ distinct neural population codes to represent similar social behaviors.

A neural circuit state change underlying skilled movements.

In motor neuroscience, state changes are hypothesized to time-lock neural assemblies coordinating complex movements, but evidence for this remains slender. We tested whether a discrete change from more autonomous to coherent spiking underlies skilled movement by imaging cerebellar Purkinje neuron complex spikes in mice making targeted forelimb-reaches. As mice learned the task, millimeter-scale spatiotemporally coherent spiking emerged ipsilateral to the reaching forelimb, and consistent neural synchronization became predictive of kinematic stereotypy. Before reach onset, spiking switched from more disordered to internally time-locked concerted spiking and silence. Optogenetic manipulations of cerebellar feedback to the inferior olive bi-directionally modulated neural synchronization and reaching direction. A simple model explained the reorganization of spiking during reaching as reflecting a discrete bifurcation in olivary network dynamics. These findings argue that to prepare learned movements, olivo-cerebellar circuits enter a self-regulated, synchronized state promoting motor coordination. State changes facilitating behavioral transitions may generalize across neural systems.

Shared Cortex-Cerebellum Dynamics in the Execution and Learning of a Motor Task.

Throughout mammalian neocortex, layer 5 pyramidal (L5) cells project via the pons to a vast number of cerebellar granule cells (GrCs), forming a fundamental pathway. Yet, it is unknown how neuronal dynamics are transformed through the L5→GrC pathway. Here, by directly comparing premotor L5 and GrC activity during a forelimb movement task using dual-site two-photon Ca2+ imaging, we found that in expert mice, L5 and GrC dynamics were highly similar. L5 cells and GrCs shared a common set of task-encoding activity patterns, possessed similar diversity of responses, and exhibited high correlations comparable to local correlations among L5 cells. Chronic imaging revealed that these dynamics co-emerged in cortex and cerebellum over learning: as behavioral performance improved, initially dissimilar L5 cells and GrCs converged onto a shared, low-dimensional, task-encoding set of neural activity patterns. Thus, a key function of cortico-cerebellar communication is the propagation of shared dynamics that emerge during learning.

Emergent reliability in sensory cortical coding and inter-area communication.

Reliable sensory discrimination must arise from high-fidelity neural representations and communication between brain areas. However, how neocortical sensory processing overcomes the substantial variability of neuronal sensory responses remains undetermined1-6. Here we imaged neuronal activity in eight neocortical areas concurrently and over five days in mice performing a visual discrimination task, yielding longitudinal recordings of more than 21,000 neurons. Analyses revealed a sequence of events across the neocortex starting from a resting state, to early stages of perception, and through the formation of a task response. At rest, the neocortex had one pattern of functional connections, identified through sets of areas that shared activity cofluctuations7,8. Within about 200 ms after the onset of the sensory stimulus, such connections rearranged, with different areas sharing cofluctuations and task-related information. During this short-lived state (approximately 300 ms duration), both inter-area sensory data transmission and the redundancy of sensory encoding peaked, reflecting a transient increase in correlated fluctuations among task-related neurons. By around 0.5 s after stimulus onset, the visual representation reached a more stable form, the structure of which was robust to the prominent, day-to-day variations in the responses of individual cells. About 1 s into stimulus presentation, a global fluctuation mode conveyed the upcoming response of the mouse to every area examined and was orthogonal to modes carrying sensory data. Overall, the neocortex supports sensory performance through brief elevations in sensory coding redundancy near the start of perception, neural population codes that are robust to cellular variability, and widespread inter-area fluctuation modes that transmit sensory data and task responses in non-interfering channels.

Coupling of activity, metabolism and behaviour across the Drosophila brain.

Coordinated activity across networks of neurons is a hallmark of both resting and active behavioural states in many species1-5. These global patterns alter energy metabolism over seconds to hours, which underpins the widespread use of oxygen consumption and glucose uptake as proxies of neural activity6,7. However, whether changes in neural activity are causally related to metabolic flux in intact circuits on the timescales associated with behaviour is unclear. Here we combine two-photon microscopy of the fly brain with sensors that enable the simultaneous measurement of neural activity and metabolic flux, across both resting and active behavioural states. We demonstrate that neural activity drives changes in metabolic flux, creating a tight coupling between these signals that can be measured across brain networks. Using local optogenetic perturbation, we demonstrate that even transient increases in neural activity result in rapid and persistent increases in cytosolic ATP, which suggests that neuronal metabolism predictively allocates resources to anticipate the energy demands of future activity. Finally, our studies reveal that the initiation of even minimal behavioural movements causes large-scale changes in the pattern of neural activity and energy metabolism, which reveals a widespread engagement of the brain. As the relationship between neural activity and energy metabolism is probably evolutionarily ancient and highly conserved, our studies provide a critical foundation for using metabolic proxies to capture changes in neural activity.

Fundamental bounds on the fidelity of sensory cortical coding.

How the brain processes information accurately despite stochastic neural activity is a longstanding question1. For instance, perception is fundamentally limited by the information that the brain can extract from the noisy dynamics of sensory neurons. Seminal experiments2,3 suggest that correlated noise in sensory cortical neural ensembles is what limits their coding accuracy4-6, although how correlated noise affects neural codes remains debated7-11. Recent theoretical work proposes that how a neural ensemble's sensory tuning properties relate statistically to its correlated noise patterns is a greater determinant of coding accuracy than is absolute noise strength12-14. However, without simultaneous recordings from thousands of cortical neurons with shared sensory inputs, it is unknown whether correlated noise limits coding fidelity. Here we present a 16-beam, two-photon microscope to monitor activity across the mouse primary visual cortex, along with analyses to quantify the information conveyed by large neural ensembles. We found that, in the visual cortex, correlated noise constrained signalling for ensembles with 800-1,300 neurons. Several noise components of the ensemble dynamics grew proportionally to the ensemble size and the encoded visual signals, revealing the predicted information-limiting correlations12-14. Notably, visual signals were perpendicular to the largest noise mode, which therefore did not limit coding fidelity. The information-limiting noise modes were approximately ten times smaller and concordant with mouse visual acuity15. Therefore, cortical design principles appear to enhance coding accuracy by restricting around 90% of noise fluctuations to modes that do not limit signalling fidelity, whereas much weaker correlated noise modes inherently bound sensory discrimination.

Neural representational geometry underlies few-shot concept learning.

Understanding the neural basis of the remarkable human cognitive capacity to learn novel concepts from just one or a few sensory experiences constitutes a fundamental problem. We propose a simple, biologically plausible, mathematically tractable, and computationally powerful neural mechanism for few-shot learning of naturalistic concepts. We posit that the concepts that can be learned from few examples are defined by tightly circumscribed manifolds in the neural firing-rate space of higher-order sensory areas. We further posit that a single plastic downstream readout neuron learns to discriminate new concepts based on few examples using a simple plasticity rule. We demonstrate the computational power of our proposal by showing that it can achieve high few-shot learning accuracy on natural visual concepts using both macaque inferotemporal cortex representations and deep neural network (DNN) models of these representations and can even learn novel visual concepts specified only through linguistic descriptors. Moreover, we develop a mathematical theory of few-shot learning that links neurophysiology to predictions about behavioral outcomes by delineating several fundamental and measurable geometric properties of neural representations that can accurately predict the few-shot learning performance of naturalistic concepts across all our numerical simulations. This theory reveals, for instance, that high-dimensional manifolds enhance the ability to learn new concepts from few examples. Intriguingly, we observe striking mismatches between the geometry of manifolds in the primate visual pathway and in trained DNNs. We discuss testable predictions of our theory for psychophysics and neurophysiological experiments.

The Limiting Dynamics of SGD: Modified Loss, Phase-Space Oscillations, and Anomalous Diffusion.

In this work, we explore the limiting dynamics of deep neural networks trained with stochastic gradient descent (SGD). As observed previously, long after performance has converged, networks continue to move through parameter space by a process of anomalous diffusion in which distance traveled grows as a power law in the number of gradient updates with a nontrivial exponent. We reveal an intricate interaction among the hyperparameters of optimization, the structure in the gradient noise, and the Hessian matrix at the end of training that explains this anomalous diffusion. To build this understanding, we first derive a continuous-time model for SGD with finite learning rates and batch sizes as an underdamped Langevin equation. We study this equation in the setting of linear regression, where we can derive exact, analytic expressions for the phase-space dynamics of the parameters and their instantaneous velocities from initialization to stationarity. Using the Fokker-Planck equation, we show that the key ingredient driving these dynamics is not the original training loss but rather the combination of a modified loss, which implicitly regularizes the velocity, and probability currents that cause oscillations in phase space. We identify qualitative and quantitative predictions of this theory in the dynamics of a ResNet-18 model trained on ImageNet. Through the lens of statistical physics, we uncover a mechanistic origin for the anomalous limiting dynamics of deep neural networks trained with SGD. Understanding the limiting dynamics of SGD, and its dependence on various important hyperparameters like batch size, learning rate, and momentum, can serve as a basis for future work that can turn these insights into algorithmic gains.

Optimal noise level for coding with tightly balanced networks of spiking neurons in the presence of transmission delays.

Neural circuits consist of many noisy, slow components, with individual neurons subject to ion channel noise, axonal propagation delays, and unreliable and slow synaptic transmission. This raises a fundamental question: how can reliable computation emerge from such unreliable components? A classic strategy is to simply average over a population of N weakly-coupled neurons to achieve errors that scale as [Formula: see text]. But more interestingly, recent work has introduced networks of leaky integrate-and-fire (LIF) neurons that achieve coding errors that scale superclassically as 1/N by combining the principles of predictive coding and fast and tight inhibitory-excitatory balance. However, spike transmission delays preclude such fast inhibition, and computational studies have observed that such delays can cause pathological synchronization that in turn destroys superclassical coding performance. Intriguingly, it has also been observed in simulations that noise can actually improve coding performance, and that there exists some optimal level of noise that minimizes coding error. However, we lack a quantitative theory that describes this fascinating interplay between delays, noise and neural coding performance in spiking networks. In this work, we elucidate the mechanisms underpinning this beneficial role of noise by deriving analytical expressions for coding error as a function of spike propagation delay and noise levels in predictive coding tight-balance networks of LIF neurons. Furthermore, we compute the minimal coding error and the associated optimal noise level, finding that they grow as power-laws with the delay. Our analysis reveals quantitatively how optimal levels of noise can rescue neural coding performance in spiking neural networks with delays by preventing the build up of pathological synchrony without overwhelming the overall spiking dynamics. This analysis can serve as a foundation for the further study of precise computation in the presence of noise and delays in efficient spiking neural circuits.

Synaptic balancing: A biologically plausible local learning rule that provably increases neural network noise robustness without sacrificing task performance.

We introduce a novel, biologically plausible local learning rule that provably increases the robustness of neural dynamics to noise in nonlinear recurrent neural networks with homogeneous nonlinearities. Our learning rule achieves higher noise robustness without sacrificing performance on the task and without requiring any knowledge of the particular task. The plasticity dynamics-an integrable dynamical system operating on the weights of the network-maintains a multiplicity of conserved quantities, most notably the network's entire temporal map of input to output trajectories. The outcome of our learning rule is a synaptic balancing between the incoming and outgoing synapses of every neuron. This synaptic balancing rule is consistent with many known aspects of experimentally observed heterosynaptic plasticity, and moreover makes new experimentally testable predictions relating plasticity at the incoming and outgoing synapses of individual neurons. Overall, this work provides a novel, practical local learning rule that exactly preserves overall network function and, in doing so, provides new conceptual bridges between the disparate worlds of the neurobiology of heterosynaptic plasticity, the engineering of regularized noise-robust networks, and the mathematics of integrable Lax dynamical systems.

Recurrent Connections in the Primate Ventral Visual Stream Mediate a Trade-Off Between Task Performance and Network Size During Core Object Recognition.

The computational role of the abundant feedback connections in the ventral visual stream is unclear, enabling humans and nonhuman primates to effortlessly recognize objects across a multitude of viewing conditions. Prior studies have augmented feedforward convolutional neural networks (CNNs) with recurrent connections to study their role in visual processing; however, often these recurrent networks are optimized directly on neural data or the comparative metrics used are undefined for standard feedforward networks that lack these connections. In this work, we develop task-optimized convolutional recurrent (ConvRNN) network models that more correctly mimic the timing and gross neuroanatomy of the ventral pathway. Properly chosen intermediate-depth ConvRNN circuit architectures, which incorporate mechanisms of feedforward bypassing and recurrent gating, can achieve high performance on a core recognition task, comparable to that of much deeper feedforward networks. We then develop methods that allow us to compare both CNNs and ConvRNNs to finely grained measurements of primate categorization behavior and neural response trajectories across thousands of stimuli. We find that high-performing ConvRNNs provide a better match to these data than feedforward networks of any depth, predicting the precise timings at which each stimulus is behaviorally decoded from neural activation patterns. Moreover, these ConvRNN circuits consistently produce quantitatively accurate predictions of neural dynamics from V4 and IT across the entire stimulus presentation. In fact, we find that the highest-performing ConvRNNs, which best match neural and behavioral data, also achieve a strong Pareto trade-off between task performance and overall network size. Taken together, our results suggest the functional purpose of recurrence in the ventral pathway is to fit a high-performing network in cortex, attaining computational power through temporal rather than spatial complexity.

A mathematical theory of semantic development in deep neural networks.

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: What are the theoretical principles governing the ability of neural networks to acquire, organize, and deploy abstract knowledge by integrating across many individual experiences? We address this question by mathematically analyzing the nonlinear dynamics of learning in deep linear networks. We find exact solutions to this learning dynamics that yield a conceptual explanation for the prevalence of many disparate phenomena in semantic cognition, including the hierarchical differentiation of concepts through rapid developmental transitions, the ubiquity of semantic illusions between such transitions, the emergence of item typicality and category coherence as factors controlling the speed of semantic processing, changing patterns of inductive projection over development, and the conservation of semantic similarity in neural representations across species. Thus, surprisingly, our simple neural model qualitatively recapitulates many diverse regularities underlying semantic development, while providing analytic insight into how the statistical structure of an environment can interact with nonlinear deep-learning dynamics to give rise to these regularities.

Emergent elasticity in the neural code for space.

Upon encountering a novel environment, an animal must construct a consistent environmental map, as well as an internal estimate of its position within that map, by combining information from two distinct sources: self-motion cues and sensory landmark cues. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to accomplish this feat? Here we show analytically how a neural attractor model that combines path integration of self-motion cues with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network. Moreover, our model makes several experimentally testable predictions, including (i) systematic path-dependent shifts in the firing fields of grid cells toward the most recently encountered landmark, even in a fully learned environment; (ii) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers; and (iii) the creation of topological defects in grid cell firing patterns through specific environmental manipulations. Taken together, our results conceptually link known aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

Compressed sensing, sparsity, and dimensionality in neuronal information processing and data analysis.

The curse of dimensionality poses severe challenges to both technical and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a complex world. We review recent mathematical advances that provide ways to combat dimensionality in specific situations. These advances shed light on two dual questions in neuroscience. First, how can we as neuroscientists rapidly acquire high-dimensional data from the brain and subsequently extract meaningful models from limited amounts of these data? And second, how do brains themselves process information in their intrinsically high-dimensional patterns of neural activity as well as learn meaningful, generalizable models of the external world from limited experience?

Inferring hidden structure in multilayered neural circuits.

A central challenge in sensory neuroscience involves understanding how neural circuits shape computations across cascaded cell layers. Here we attempt to reconstruct the response properties of experimentally unobserved neurons in the interior of a multilayered neural circuit, using cascaded linear-nonlinear (LN-LN) models. We combine non-smooth regularization with proximal consensus algorithms to overcome difficulties in fitting such models that arise from the high dimensionality of their parameter space. We apply this framework to retinal ganglion cell processing, learning LN-LN models of retinal circuitry consisting of thousands of parameters, using 40 minutes of responses to white noise. Our models demonstrate a 53% improvement in predicting ganglion cell spikes over classical linear-nonlinear (LN) models. Internal nonlinear subunits of the model match properties of retinal bipolar cells in both receptive field structure and number. Subunits have consistently high thresholds, supressing all but a small fraction of inputs, leading to sparse activity patterns in which only one subunit drives ganglion cell spiking at any time. From the model's parameters, we predict that the removal of visual redundancies through stimulus decorrelation across space, a central tenet of efficient coding theory, originates primarily from bipolar cell synapses. Furthermore, the composite nonlinear computation performed by retinal circuitry corresponds to a boolean OR function applied to bipolar cell feature detectors. Our methods are statistically and computationally efficient, enabling us to rapidly learn hierarchical non-linear models as well as efficiently compute widely used descriptive statistics such as the spike triggered average (STA) and covariance (STC) for high dimensional stimuli. This general computational framework may aid in extracting principles of nonlinear hierarchical sensory processing across diverse modalities from limited data.

SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks.

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.

Direction Selectivity in Drosophila Emerges from Preferred-Direction Enhancement and Null-Direction Suppression.

UNLABELLED: Across animal phyla, motion vision relies on neurons that respond preferentially to stimuli moving in one, preferred direction over the opposite, null direction. In the elementary motion detector of Drosophila, direction selectivity emerges in two neuron types, T4 and T5, but the computational algorithm underlying this selectivity remains unknown. We find that the receptive fields of both T4 and T5 exhibit spatiotemporally offset light-preferring and dark-preferring subfields, each obliquely oriented in spacetime. In a linear-nonlinear modeling framework, the spatiotemporal organization of the T5 receptive field predicts the activity of T5 in response to motion stimuli. These findings demonstrate that direction selectivity emerges from the enhancement of responses to motion in the preferred direction, as well as the suppression of responses to motion in the null direction. Thus, remarkably, T5 incorporates the essential algorithmic strategies used by the Hassenstein-Reichardt correlator and the Barlow-Levick detector. Our model for T5 also provides an algorithmic explanation for the selectivity of T5 for moving dark edges: our model captures all two- and three-point spacetime correlations relevant to motion in this stimulus class. More broadly, our findings reveal the contribution of input pathway visual processing, specifically center-surround, temporally biphasic receptive fields, to the generation of direction selectivity in T5. As the spatiotemporal receptive field of T5 in Drosophila is common to the simple cell in vertebrate visual cortex, our stimulus-response model of T5 will inform efforts in an experimentally tractable context to identify more detailed, mechanistic models of a prevalent computation. SIGNIFICANCE STATEMENT: Feature selective neurons respond preferentially to astonishingly specific stimuli, providing the neurobiological basis for perception. Direction selectivity serves as a paradigmatic model of feature selectivity that has been examined in many species. While insect elementary motion detectors have served as premiere experimental models of direction selectivity for 60 years, the central question of their underlying algorithm remains unanswered. Using in vivo two-photon imaging of intracellular calcium signals, we measure the receptive fields of the first direction-selective cells in the Drosophila visual system, and define the algorithm used to compute the direction of motion. Computational modeling of these receptive fields predicts responses to motion and reveals how this circuit efficiently captures many useful correlations intrinsic to moving dark edges.

Evidence for a causal inverse model in an avian cortico-basal ganglia circuit.

Learning by imitation is fundamental to both communication and social behavior and requires the conversion of complex, nonlinear sensory codes for perception into similarly complex motor codes for generating action. To understand the neural substrates underlying this conversion, we study sensorimotor transformations in songbird cortical output neurons of a basal-ganglia pathway involved in song learning. Despite the complexity of sensory and motor codes, we find a simple, temporally specific, causal correspondence between them. Sensory neural responses to song playback mirror motor-related activity recorded during singing, with a temporal offset of roughly 40 ms, in agreement with short feedback loop delays estimated using electrical and auditory stimulation. Such matching of mirroring offsets and loop delays is consistent with a recent Hebbian theory of motor learning and suggests that cortico-basal ganglia pathways could support motor control via causal inverse models that can invert the rich correspondence between motor exploration and sensory feedback.

Spatial information outflow from the hippocampal circuit: distributed spatial coding and phase precession in the subiculum.

Hippocampal place cells convey spatial information through a combination of spatially selective firing and theta phase precession. The way in which this information influences regions like the subiculum that receive input from the hippocampus remains unclear. The subiculum receives direct inputs from area CA1 of the hippocampus and sends divergent output projections to many other parts of the brain, so we examined the firing patterns of rat subicular neurons. We found a substantial transformation in the subicular code for space from sparse to dense firing rate representations along a proximal-distal anatomical gradient: neurons in the proximal subiculum are more similar to canonical, sparsely firing hippocampal place cells, whereas neurons in the distal subiculum have higher firing rates and more distributed spatial firing patterns. Using information theory, we found that the more distributed spatial representation in the subiculum carries, on average, more information about spatial location and context than the sparse spatial representation in CA1. Remarkably, despite the disparate firing rate properties of subicular neurons, we found that neurons at all proximal-distal locations exhibit robust theta phase precession, with similar spiking oscillation frequencies as neurons in area CA1. Our findings suggest that the subiculum is specialized to compress sparse hippocampal spatial codes into highly informative distributed codes suitable for efficient communication to other brain regions. Moreover, despite this substantial compression, the subiculum maintains finer scale temporal properties that may allow it to participate in oscillatory phase coding and spike timing-dependent plasticity in coordination with other regions of the hippocampal circuit.