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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.

We introduce a near-term experimental platform for realizing an associative memory. It can simultaneously store many memories by using spinful bosons coupled to a degenerate multimode optical cavity. The associative memory is realized by a confocal cavity QED neural network, with the cavity modes serving as the synapses, connecting a network of superradiant atomic spin ensembles, which serve as the neurons. Memories are encoded in the connectivity matrix between the spins, and can be accessed through the input and output of patterns of light. Each aspect of the scheme is based on recently demonstrated technology using a confocal cavity and Bose-condensed atoms. Our scheme has two conceptually novel elements. First, it introduces a new form of random spin system that interpolates between a ferromagnetic and a spin-glass regime as a physical parameter is tuned---the positions of ensembles within the cavity. Second, and more importantly, the spins relax via deterministic steepest-descent dynamics, rather than Glauber dynamics. We show that this nonequilibrium quantum-optical scheme has significant advantages for associative memory over Glauber dynamics: These dynamics can enhance the network's ability to store and recall memories beyond that of the standard Hopfield model. Surprisingly, the cavity QED dynamics can retrieve memories even when the system is in the spin glass phase. Thus, the experimental platform provides a novel physical instantiation of associative memories and spin glasses as well as provides an unusual form of relaxational dynamics that is conducive to memory recall even in regimes where it was thought to be impossible., Comment: 35 pages, 16 figures, 6 appendices

SUMMARYCortical function relies on the balanced activation of excitatory and inhibitory neurons. However, little is known about the organization and dynamics of shaft excitatory synapses onto cortical inhibitory interneurons, which cannot be easily identified morphologically. Here, we fluorescently visualize the excitatory postsynaptic marker PSD-95 at endogenous levels as a proxy for excitatory synapses onto layer 2/3 pyramidal neurons and parvalbumin-positive (PV+) inhibitory interneurons in the mouse barrel cortex. Longitudinalin vivoimaging reveals that, while synaptic weights in both neuronal types are log-normally distributed, synapses onto PV+ neurons are less heterogeneous and more stable. Markov-model analyses suggest that the synaptic weight distribution is set intrinsically by ongoing cell type-specific dynamics, and substantial changes are due to accumulated gradual changes. Synaptic weight dynamics are multiplicative, i.e., changes scale with weights, though PV+ synapses also exhibit an additive component. These results reveal that cell type-specific processes govern cortical synaptic strengths and dynamics.

Coherent Ising Machines (CIMs) are an emerging class of computational architectures that embed hard combinatorial optimization problems in the continuous dynamics of a physical system with analog degrees of freedom. While crisp theoretical results on the ultimate performance and scaling of such architectures are lacking, large-scale experimental prototypes have begun to exhibit promising results in practice. Our team at Stanford has begun to study the fundamental properties of CIM dynamics using a combination of techniques from statistical physics, random matrices, and dynamical systems theory. Many connections to recent work in neuroscience and deep learning are noted. Our work focuses specifically on CIMs that utilize the nonlinear threshold behavior of optical parametric oscillators to effect a soft (potentially glassy) transition between linear and binary dynamical regimes.

The ventral visual stream (VVS) is a hierarchically connected series of cortical areas known to underlie core object recognition behaviors, enabling humans and non-human primates to effortlessly recognize objects across a multitude of viewing conditions. While recent feedforward convolutional neural networks (CNNs) provide quantitatively accurate predictions of temporally-averaged neural responses throughout the ventral pathway, they lack two ubiquitous neuroanatomical features: local recurrence within cortical areas and long-range feedback from downstream areas to upstream areas. As a result, such models are unable to account for the temporally-varying dynamical patterns thought to arise from recurrent visual circuits, nor can they provide insight into the behavioral goals that these recurrent circuits might help support. In this work, we augment CNNs with local recurrence and long-range feedback, developing convolutional RNN (ConvRNN) network models that more correctly mimic the gross neuroanatomy of the ventral pathway. Moreover, when the form of the recurrent circuit is chosen properly, ConvRNNs with comparatively small numbers of layers can achieve high performance on a core recognition task, comparable to that of much deeper feedforward networks. We then compared these models to temporally fine-grained neural and behavioral recordings from primates to thousands of images. We found that ConvRNNs better matched these data than alternative models, including the deepest feedforward networks, on two metrics: 1) neural dynamics in V4 and inferotemporal (IT) cortex at late timepoints after stimulus onset, and 2) the varying times at which object identity can be decoded from IT, including more challenging images that take longer to decode. Moreover, these results differentiate within the class of ConvRNNs, suggesting that there are strong functional constraints on the recurrent connectivity needed to match these phenomena. Finally, we find that recurrent circuits that attain high task performance while having a smaller network size as measured by number of units, rather than another metric such as the number of parameters, are overall most consistent with these data. Taken together, our results evince the role of recurrence and feedback in the ventral pathway to reliably perform core object recognition while subject to a strong total network size constraint.

Cortical function relies on the balanced activation of excitatory and inhibitory neurons. However, little is known about the organization and dynamics of shaft excitatory synapses onto cortical inhibitory interneurons, which cannot be easily identified morphologically. Here, we fluorescently visualize the excitatory postsynaptic marker PSD-95 at endogenous levels as a proxy for excitatory synapses onto layer 2/3 pyramidal neurons and parvalbumin-positive (PV+) inhibitory interneurons in the mouse barrel cortex. Longitudinal in vivo imaging reveals that, while synaptic weights in both neuronal types are log-normally distributed, synapses onto PV+ neurons are less heterogeneous and more stable. Markov-model analyses suggest that the synaptic weight distribution is set intrinsically by ongoing cell type-specific dynamics, and substantial changes are due to accumulated gradual changes. Synaptic weight dynamics are multiplicative, i.e., changes scale with weights, though PV+ synapses also exhibit an additive component. These results reveal that cell type-specific processes govern cortical synaptic strengths and dynamics.

SUMMARY During navigation, animals estimate their position using path integration and landmarks, engaging many brain areas. Whether these areas follow specialized or universal cue integration principles remains incompletely understood. We combine electrophysiology with virtual reality to quantify cue integration across thousands of neurons in three navigation-relevant areas: primary visual cortex (V1), retrosplenial cortex (RSC), and medial entorhinal cortex (MEC). Compared with V1 and RSC, path integration influences position estimates more in MEC, and conflicts between path integration and landmarks trigger remapping more readily. Whereas MEC codes position prospectively, V1 codes position retrospectively, and RSC is intermediate between the two. Lowered visual contrast increases the influence of path integration on position estimates only in MEC. These properties are most pronounced in a population of MEC neurons, overlapping with grid cells, tuned to distance run in darkness. These results demonstrate the specialized role that path integration plays in MEC compared with other navigation-relevant cortical areas., Graphical abstract, In brief Campbell et al. use Neuropixels recordings in mice navigating a VR environment to show that MEC neurons are more influenced by path integration than V1 and RSC neurons. These differences are driven by a subset of MEC neurons that exhibit modular distance tuning in darkness, reminiscent of grid cells.

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.

Absence epilepsy is a neurological condition characterized by abnormally synchronous electrical activity within two mutually connected brain regions, the thalamus and cortex, that results in seizures and affects more than 6.5 million people. Epilepsy is commonly studied through the use of the electroencephalogram (EEG), a device that monitors brain waves over time. In this study, we introduced machine learning models to predict epileptic seizures in two ways, one to train logistic regression models to provide an accurate decision boundary to predict based off frequency features, and second to train convolutional neural networks to predict based off spectral power images from EEG. This pipeline employed a two model approach, using logistic regression and convolutional neural networks to predict seizures. The evaluation, performed on data from 9 mice, achieved prediction accuracies of 98%. The proposed methodology introduces a novel aspect of looking at predicting absence seizures, which are known to be short events, in addition to the comparison between a time-dependent and time-agnostic seizure prediction classifier. The overall goal of these experiments were to build a model that can accurately predict whether or not a seizure will occur.

The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might mechanistically emerge in a generic manner from neural circuits, and what their computational significance might be. Here we forge an intimate link between the computational problem of path-integration and the existence of hexagonal grids, by demonstrating that such grids arise generically in biologically plausible neural networks trained to path integrate. Moreover, we develop a unifying theory for why hexagonal grids are so ubiquitous in path-integrator circuits. Such trained networks also yield powerful mechanistic hypotheses, exhibiting realistic levels of biological variability not captured by hand-designed models. We furthermore develop methods to analyze the connectome and activity maps of our trained networks to elucidate fundamental mechanisms underlying path integration. These methods provide an instructive roadmap to go from connectomic and physiological measurements to conceptual understanding in a manner that might be generalizable to other settings.

During navigation, animals estimate their position using path integration and landmarks, engaging many brain areas. Whether these areas follow specialized or universal cue integration principles remains unknown. Here, we combined electrophysiology with virtual reality to quantify cue integration across thousands of neurons in three areas that support navigation: primary visual (V1), retrosplenial (RSC) and medial entorhinal cortex (MEC). Path integration influenced position estimates in MEC more than in V1 and RSC. V1 coded position retrospectively, likely reflecting delays in sensory processing, whereas MEC coded position prospectively, and RSC was intermediate between the two. In combining path integration with landmarks, MEC showed signatures of Kalman filtering, and we report a distance-tuned neural population that could implement such filtering through attractor dynamics. Our results show that during navigation, MEC serves as a specialized cortical hub for reconciling path integration and landmarks to estimate position and suggest an algorithm for calculating these estimates.

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it–to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple tasks, a detailed understanding of how recurrent networks work, or a prescription for how to develop such an understanding, remains elusive. In this work, we use tools from dynamical systems analysis to reverse engineer recurrent networks trained to perform sentiment classification, a foundational natural language processing task. Given a trained network, we find fixed points of the recurrent dynamics and linearize the nonlinear system around these fixed points. Despite their theoretical capacity to implement complex, high-dimensional computations, we find that trained networks converge to highly interpretable, low-dimensional representations. In particular, the topological structure of the fixed points and corresponding linearized dynamics reveal an approximate line attractor within the RNN, which we can use to quantitatively understand how the RNN solves the sentiment analysis task. Finally, we find this mechanism present across RNN architectures (including LSTMs, GRUs, and vanilla RNNs) trained on multiple datasets, suggesting that our findings are not unique to a particular architecture or dataset. Overall, these results demonstrate that surprisingly universal and human interpretable computations can arise across a range of recurrent networks.

Task-based modeling with recurrent neural networks (RNNs) has emerged as a popular way to infer the computational function of different brain regions. These models are quantitatively assessed by comparing the low-dimensional neural representations of the model with the brain, for example using canonical correlation analysis (CCA). However, the nature of the detailed neurobiological inferences one can draw from such efforts remains elusive. For example, to what extent does training neural networks to solve common tasks uniquely determine the network dynamics, independent of modeling architectural choices? Or alternatively, are the learned dynamics highly sensitive to different model choices? Knowing the answer to these questions has strong implications for whether and how we should use task-based RNN modeling to understand brain dynamics. To address these foundational questions, we study populations of thousands of networks, with commonly used RNN architectures, trained to solve neuroscientifically motivated tasks and characterize their nonlinear dynamics. We find the geometry of the RNN representations can be highly sensitive to different network architectures, yielding a cautionary tale for measures of similarity that rely on representational geometry, such as CCA. Moreover, we find that while the geometry of neural dynamics can vary greatly across architectures, the underlying computational scaffold—the topological structure of fixed points, transitions between them, limit cycles, and linearized dynamics—often appears universal across all architectures.

The synaptotrophic hypothesis posits that synapse formation stabilizes dendritic branches, but this hypothesis has not been causally tested in vivo in the mammalian brain. The presynaptic ligand cerebellin-1 (Cbln1) and postsynaptic receptor GluD2 mediate synaptogenesis between granule cells and Purkinje cells in the molecular layer of the cerebellar cortex. Here we show that sparse but not global knockout of GluD2 causes under-elaboration of Purkinje cell dendrites in the deep molecular layer and overelaboration in the superficial molecular layer. Developmental, overexpression, structure-function, and genetic epistasis analyses indicate that these dendrite morphogenesis defects result from a deficit in Cbln1/GluD2-dependent competitive interactions. A generative model of dendrite growth based on competitive synaptogenesis largely recapitulates GluD2 sparse and global knockout phenotypes. Our results support the synaptotrophic hypothesis at initial stages of dendrite development, suggest a second mode in which cumulative synapse formation inhibits further dendrite growth, and highlight the importance of competition in dendrite morphogenesis.

Coordinated activity across networks of neurons is a hallmark of both resting and active behavioral states in many species, including worms, flies, fish, mice and humans1–5. These global patterns alter energy metabolism in the brain over seconds to hours, making oxygen consumption and glucose uptake widely used proxies of neural activity6,7. However, whether changes in neural activity are causally related to changes in metabolic flux in intact circuits on the sub-second timescales associated with behavior, is unknown. Moreover, it is unclear whether transitions between rest and action are associated with spatiotemporally structured changes in neuronal energy metabolism. Here, we combine two-photon microscopy of the entire fruit fly brain with sensors that allow simultaneous measurements of neural activity and metabolic flux, across both resting and active behavioral states. We demonstrate that neural activity drives changes in metabolic flux, creating a tight coupling between these signals that can be measured across large-scale brain networks. Further, these studies reveal that the initiation of even minimal behavioral movements causes large-scale changes in the pattern of neural activity and energy metabolism, revealing unexpected structure in the functional architecture of the brain. The relationship between neural activity and energy metabolism is likely evolutionarily ancient. Thus, these studies provide a critical foundation for using metabolic proxies to capture changes in neural activity and reveal that even minimal behavioral movements are associated with changes in large-scale brain network activity.

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. Two-photon microscopy across the fly brain using sensors that permit simultaneous measurement of neural activity and metabolic flux reveals global and local coordination of neural activity and energy metabolism.

Recurrent neural networks empirically generate natural language with high syntactic fidelity. However, their success is not well-understood theoretically. We provide theoretical insight into this success, proving in a finite-precision setting that RNNs can efficiently generate bounded hierarchical languages that reflect the scaffolding of natural language syntax. We introduce Dyck-($k$,$m$), the language of well-nested brackets (of $k$ types) and $m$-bounded nesting depth, reflecting the bounded memory needs and long-distance dependencies of natural language syntax. The best known results use $O(k^{\frac{m}{2}})$ memory (hidden units) to generate these languages. We prove that an RNN with $O(m \log k)$ hidden units suffices, an exponential reduction in memory, by an explicit construction. Finally, we show that no algorithm, even with unbounded computation, can suffice with $o(m \log k)$ hidden units., Comment: EMNLP2020 + appendix typo fixes

In suitably initialized wide networks, small learning rates transform deep neural networks (DNNs) into neural tangent kernel (NTK) machines, whose training dynamics is well-approximated by a linear weight expansion of the network at initialization. Standard training, however, diverges from its linearization in ways that are poorly understood. We study the relationship between the training dynamics of nonlinear deep networks, the geometry of the loss landscape, and the time evolution of a data-dependent NTK. We do so through a large-scale phenomenological analysis of training, synthesizing diverse measures characterizing loss landscape geometry and NTK dynamics. In multiple neural architectures and datasets, we find these diverse measures evolve in a highly correlated manner, revealing a universal picture of the deep learning process. In this picture, deep network training exhibits a highly chaotic rapid initial transient that within 2 to 3 epochs determines the final linearly connected basin of low loss containing the end point of training. During this chaotic transient, the NTK changes rapidly, learning useful features from the training data that enables it to outperform the standard initial NTK by a factor of 3 in less than 3 to 4 epochs. After this rapid chaotic transient, the NTK changes at constant velocity, and its performance matches that of full network training in 15% to 45% of training time. Overall, our analysis reveals a striking correlation between a diverse set of metrics over training time, governed by a rapid chaotic to stable transition in the first few epochs, that together poses challenges and opportunities for the development of more accurate theories of deep learning., Comment: 19 pages, 19 figures, In Advances in Neural Information Processing Systems 34 (NeurIPS 2020)

A coherent Ising machine (CIM) is a network of optical parametric oscillators (OPOs), in which the "strongest" collective mode of oscillation at well above threshold corresponds to an optimum solution of a given Ising problem. When a pump rate or network coupling rate is increased from below to above threshold, however, the eigenvectors with a smallest eigenvalue of Ising coupling matrix [J_ij] appear near threshold and impede the machine to relax to true ground states. Two complementary approaches to attack this problem are described here. One approach is to utilize squeezed/anti-squeezed vacuum noise of OPOs below threshold to produce coherent spreading over numerous local minima via quantum noise correlation, which could enable the machine to access either true ground states or excited states with eigen-energies close enough to that of ground states above threshold. The other approach is to implement real-time error correction feedback loop so that the machine migrates from one local minimum to another during an explorative search for ground states. Finally, a set of qualitative analogies connecting the CIM and traditional computer science techniques are pointed out. In particular, belief propagation and survey propagation used in combinatorial optimization are touched upon., Comment: 32 pages and 7 figures

Biological neural networks face a formidable task: performing reliable computations in the face of intrinsic stochasticity in individual neurons, imprecisely specified synaptic connectivity, and nonnegligible delays in synaptic transmission. A common approach to combatting such biological heterogeneity involves averaging over large redundant networks of $N$ neurons resulting in coding errors that decrease classically as $1/\sqrt{N}$. Recent work demonstrated a novel mechanism whereby recurrent spiking networks could efficiently encode dynamic stimuli, achieving a superclassical scaling in which coding errors decrease as $1/N$. This specific mechanism involved two key ideas: predictive coding, and a tight balance, or cancellation between strong feedforward inputs and strong recurrent feedback. However, the theoretical principles governing the efficacy of balanced predictive coding and its robustness to noise, synaptic weight heterogeneity and communication delays remain poorly understood. To discover such principles, we introduce an analytically tractable model of balanced predictive coding, in which the degree of balance and the degree of weight disorder can be dissociated unlike in previous balanced network models, and we develop a mean field theory of coding accuracy. Overall, our work provides and solves a general theoretical framework for dissecting the differential contributions neural noise, synaptic disorder, chaos, synaptic delays, and balance to the fidelity of predictive neural codes, reveals the fundamental role that balance plays in achieving superclassical scaling, and unifies previously disparate models in theoretical neuroscience.

Recently, deep feedforward neural networks have achieved considerable success in modeling biological sensory processing, in terms of reproducing the input-output map of sensory neurons. However, such models raise profound questions about the very nature of explanation in neuroscience. Are we simply replacing one complex system (a biological circuit) with another (a deep network), without understanding either? Moreover, beyond neural representations, are the deep network's computational mechanisms for generating neural responses the same as those in the brain? Without a systematic approach to extracting and understanding computational mechanisms from deep neural network models, it can be difficult both to assess the degree of utility of deep learning approaches in neuroscience, and to extract experimentally testable hypotheses from deep networks. We develop such a systematic approach by combining dimensionality reduction and modern attribution methods for determining the relative importance of interneurons for specific visual computations. We apply this approach to deep network models of the retina, revealing a conceptual understanding of how the retina acts as a predictive feature extractor that signals deviations from expectations for diverse spatiotemporal stimuli. For each stimulus, our extracted computational mechanisms are consistent with prior scientific literature, and in one case yields a new mechanistic hypothesis. Thus overall, this work not only yields insights into the computational mechanisms underlying the striking predictive capabilities of the retina, but also places the framework of deep networks as neuroscientific models on firmer theoretical foundations, by providing a new roadmap to go beyond comparing neural representations to extracting and understand computational mechanisms.

SUMMARY Cortical function relies on the balanced activation of excitatory and inhibitory neurons. However, little is known about the organization and dynamics of shaft excitatory synapses onto cortical inhibitory interneurons. Here, we use the excitatory postsynaptic marker PSD-95, fluorescently labeled at endogenous levels, as a proxy for excitatory synapses onto layer 2/3 pyramidal neurons and parvalbumin-positive (PV+) interneurons in the barrel cortex of adult mice. Longitudinal in vivo imaging under baseline conditions reveals that, although synaptic weights in both neuronal types are log-normally distributed, synapses onto PV+ neurons are less heterogeneous and more stable. Markov model analyses suggest that the synaptic weight distribution is set intrinsically by ongoing cell-type-specific dynamics, and substantial changes are due to accumulated gradual changes. Synaptic weight dynamics are multiplicative, i.e., changes scale with weights, although PV+ synapses also exhibit an additive component. These results reveal that cell-type-specific processes govern cortical synaptic strengths and dynamics., Graphical Abstract, In brief Melander et al. use a genetic strategy to visualize excitatory neuronal connections that cannot be inferred from morphology, and they monitor how the connections change over weeks in mice. They find distinct characteristics between synapses onto cells that “suppress” brain activity and those onto cells that “excite” brain activity.

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.

Hebbian plasticity, a synaptic mechanism which detects and amplifies co-activity between neurons, is considered a key ingredient underlying learning and memory in the brain. However, Hebbian plasticity alone is unstable, leading to runaway neuronal activity, and therefore requires stabilization by additional compensatory processes. Traditionally, a diversity of homeostatic plasticity phenomena found in neural circuits are thought to play this role. However, recent modelling work suggests that the slow evolution of homeostatic plasticity, as observed in experiments, is insufficient to prevent instabilities originating from Hebbian plasticity. To remedy this situation, we suggest that homeostatic plasticity is complemented by additional rapid compensatory processes, which rapidly stabilize neuronal activity on short timescales.

Systems neuroscience seeks explanations for how the brain implements a wide variety of perceptual, cognitive and motor tasks. Conversely, artificial intelligence attempts to design computational systems based on the tasks they will have to solve. In the case of artificial neural networks, the three components specified by design are the objective functions, the learning rules, and architectures. With the growing success of deep learning, which utilizes brain-inspired architectures, these three designed components have increasingly become central to how we model, engineer and optimize complex artificial learning systems. Here we argue that a greater focus on these components would also benefit systems neuroscience. We give examples of how this optimization-based framework can drive theoretical and experimental progress in neuroscience. We contend that this principled perspective on systems neuroscience will help to generate more rapid progress.

One of the most striking aspects of early visual processing in the retina is the immediate parcellation of visual information into multiple parallel pathways, formed by different retinal ganglion cell types each tiling the entire visual field. Existing theories of efficient coding have been unable to account for the functional advantages of such cell-type diversity in encoding natural scenes. Here we go beyond previous theories to analyze how a simple linear retinal encoding model with different convolutional cell types efficiently encodes naturalistic spatiotemporal movies given a fixed firing rate budget. We find that optimizing the receptive fields and cell densities of two cell types makes them match the properties of the two main cell types in the primate retina, midget and parasol cells, in terms of spatial and temporal sensitivity, cell spacing, and their relative ratio. Moreover, our theory gives a precise account of how the ratio of midget to parasol cells decreases with retinal eccentricity. Also, we train a nonlinear encoding model with a rectifying nonlinearity to efficiently encode naturalistic movies, and again find emergent receptive fields resembling those of midget and parasol cells that are now further subdivided into ON and OFF types. Thus our work provides a theoretical justification, based on the efficient coding of natural movies, for the existence of the four most dominant cell types in the primate retina that together comprise 70% of all ganglion cells.

INTRODUCTION Perceptual experiences in mammals may arise from patterns of neural circuit activity in cerebral cortex. For example, primary visual cortex (V1) is causally capable of initiating visual perception; in human neurosurgery patients, V1 electrical microstimulation has been reported to elicit basic visual percepts including spots of light, patterns, shapes, motions, and colors. Related phenomena have been studied in laboratory animals using similar electrical stimulation procedures, although detailed investigation has been difficult because studies of percept initiation in cortex have not involved groups of neurons individually selected for stimulation. Therefore, it is not clear how different percepts arise in cortex, nor why some stimuli fail to generate perceptual experiences. Answering these questions will require working with basic cellular elements within cortical circuit architecture during perception. RATIONALE To understand how circuits in V1 are specifically involved in visual perception, it is essential to probe, at the most basic cellular level, how behaviorally consequential percepts are initiated and maintained. In this study, we developed and implemented several key technological advances that together enable writing neural activity into dozens of single neurons in mouse V1 at physiological time scales. These methods also enabled us to simultaneously read out the impact of this stimulation on downstream network activity across hundreds of nearby neurons. Successful training of alert mice to discriminate the precisely defined circuit inputs enabled systematic investigation of basic cortical dynamics underlying perception. RESULTS We developed an experimental approach to drive large numbers of individually specified neurons, distributed across V1 volumes and targeted on the basis of natural response-selectivity properties observed during specific visual stimuli (movies of drifting horizontal or vertical gratings). To implement this approach, we built an optical read-write system capable of kilohertz speed, millimeter-scale lateral scope, and three-dimensional (3D) access across superficial to deep layers of cortex to tens or hundreds of individually specified neurons. This system was integrated with an unusual microbial opsin gene identified by crystal structure–based genome mining: ChRmine, named after the deep-red color carmine. This newly identified opsin confers properties crucial for cellular-resolution percept-initiation experiments: red-shifted light sensitivity, extremely large photocurrents alongside millisecond spike-timing fidelity, and compatibility with simultaneous two-photon Ca2+ imaging. Using ChRmine together with custom holographic devices to create arbitrarily specified light patterns, we were able to measure naturally occurring large-scale 3D ensemble activity patterns during visual experience and then replay these natural patterns at the level of many individually specified cells. We found that driving specific ensembles of cells on the basis of natural stimulus-selectivity resulted in recruitment of a broad network with dynamical patterns corresponding to those elicited by real visual stimuli and also gave rise to the correctly selective behaviors even in the absence of visual input. This approach allowed mapping of the cell numbers, layers, network dynamics, and adaptive events underlying generation of behaviorally potent percepts in neocortex, via precise control over naturally occurring, widely distributed, and finely resolved temporal parameters and cellular elements of the corresponding neural representations. CONCLUSION The cortical population dynamics that emerged after optogenetic stimulation both predicted the correctly elicited behavior and mimicked the natural neural representations of visual stimuli.

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.

To guide navigation, the nervous system integrates multisensory self-motion and landmark information. We dissected how these inputs generate spatial representations by recording entorhinal grid, border and speed cells in mice navigating virtual environments. Manipulating the gain between the animal's locomotion and the visual scene revealed that border cells responded to landmark cues while grid and speed cells responded to combinations of locomotion, optic flow and landmark cues in a context-dependent manner, with optic flow becoming more influential when it was faster than expected. A network model explained these results by revealing a phase transition between two regimes in which grid cells remain coherent with or break away from the landmark reference frame. Moreover, during path-integration-based navigation, mice estimated their position following principles predicted by our recordings. Together, these results provide a theoretical framework for understanding how landmark and self-motion cues combine during navigation to generate spatial representations and guide behavior.

Feed-forward convolutional neural networks (CNNs) are currently state-of-the-art for object classification tasks such as ImageNet. Further, they are quantitatively accurate models of temporally-averaged responses of neurons in the primate brain's visual system. However, biological visual systems have two ubiquitous architectural features not shared with typical CNNs: local recurrence within cortical areas, and long-range feedback from downstream areas to upstream areas. Here we explored the role of recurrence in improving classification performance. We found that standard forms of recurrence (vanilla RNNs and LSTMs) do not perform well within deep CNNs on the ImageNet task. In contrast, novel cells that incorporated two structural features, bypassing and gating, were able to boost task accuracy substantially. We extended these design principles in an automated search over thousands of model architectures, which identified novel local recurrent cells and long-range feedback connections useful for object recognition. Moreover, these task-optimized ConvRNNs matched the dynamics of neural activity in the primate visual system better than feedforward networks, suggesting a role for the brain's recurrent connections in performing difficult visual behaviors., NIPS 2018 Camera Ready Version, 16 pages including supplementary information, 6 figures

Understanding how the visual system encodes natural scenes is a fundamental goal of sensory neuroscience. We show here that a three-layer network model predicts the retinal response to natural scenes with an accuracy nearing the fundamental limits of predictability. The model’s internal structure is interpretable, in that model units are highly correlated with interneurons recorded separately and not used to fit the model. We further show the ethological relevance to natural visual processing of a diverse set of phenomena of complex motion encoding, adaptation and predictive coding. Our analysis uncovers a fast timescale of visual processing that is inaccessible directly from experimental data, showing unexpectedly that ganglion cells signal in distinct modes by rapidly (< 0.1 s) switching their selectivity for direction of motion, orientation, location and the sign of intensity. A new approach that decomposes ganglion cell responses into the contribution of interneurons reveals how the latent effects of parallel retinal circuits generate the response to any possible stimulus. These results reveal extremely flexible and rapid dynamics of the retinal code for natural visual stimuli, explaining the need for a large set of interneuron pathways to generate the dynamic neural code for natural scenes.

Perceptions, thoughts and actions unfold over millisecond timescales, while learned behaviors can require many days to mature. While recent experimental advances enable large-scale and long-term neural recordings with high temporal fidelity, it remains a formidable challenge to extract unbiased and interpretable descriptions of how rapid single-trial circuit dynamics change slowly over many trials to mediate learning. We demonstrate a simple tensor components analysis (TCA) can meet this challenge by extracting three interconnected low dimensional descriptions of neural data: neuron factors, reflecting cell assemblies; temporal factors, reflecting rapid circuit dynamics mediating perceptions, thoughts, and actions within each trial; and trial factors, describing both long-term learning and trial-to-trial changes in cognitive state. We demonstrate the broad applicability of TCA by revealing insights into diverse datasets derived from artificial neural networks, large-scale calcium imaging of rodent prefrontal cortex during maze navigation, and multielectrode recordings of macaque motor cortex during brain machine interface learning.

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: (1) systematic path-dependent shifts in the firing field of grid cells towards the most recently encountered landmark, even in a fully learned environment, (2) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers, and (3) 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.

Recent work has shown that tight concentration of the entire spectrum of singular values of a deep network's input-output Jacobian around one at initialization can speed up learning by orders of magnitude. Therefore, to guide important design choices, it is important to build a full theoretical understanding of the spectra of Jacobians at initialization. To this end, we leverage powerful tools from free probability theory to provide a detailed analytic understanding of how a deep network's Jacobian spectrum depends on various hyperparameters including the nonlinearity, the weight and bias distributions, and the depth. For a variety of nonlinearities, our work reveals the emergence of new universal limiting spectral distributions that remain concentrated around one even as the depth goes to infinity., Comment: 17 pages, 4 figures. Appearing at the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018

A central goal of systems neuroscience is to relate an organism’s neural activity to behavior. Neural population analysis often begins by reducing the dimensionality of the data to focus on the patterns most relevant to a given task. A major practical hurdle to data analysis is spike sorting, and this problem is growing rapidly as the number of neurons measured increases. Here, we investigate whether spike sorting is necessary to estimate neural dynamics. The theory of random projections suggests that we can accurately estimate the geometry of low-dimensional manifolds from a small number of linear projections of the data. We re-analyzed data from three previous studies and found that neural dynamics and scientific conclusions are quite similar using multi-unit threshold crossings in place of sorted neurons. This finding unlocks existing data for new analyses and informs the design and use of new electrode arrays for laboratory and clinical use.

In many experiments, neuroscientists tightly control behavior, record many trials, and obtain trial-averaged firing rates from hundreds of neurons in circuits containing billions of behaviorally relevant neurons. Di-mensionality reduction methods reveal a striking simplicity underlying such multi-neuronal data: they can be reduced to a low-dimensional space, and the resulting neural trajectories in this space yield a remarkably insightful dynamical portrait of circuit computation. This simplicity raises profound and timely conceptual questions. What are its origins and its implications for the complexity of neural dynamics? How would the situation change if we recorded more neurons? When, if at all, can we trust dynamical portraits obtained from measuring an infinitesimal fraction of task relevant neurons? We present a theory that answers these questions, and test it using physiological recordings from reaching monkeys. This theory reveals conceptual insights into how task complexity governs both neural dimensionality and accurate recovery of dynamic portraits, thereby providing quantitative guidelines for future large-scale experimental design.

Technological advances have dramatically expanded our ability to probe multi-neuronal dynamics and connectivity in the brain. However, our ability to extract a simple conceptual understanding from complex data is increasingly hampered by the lack of theoretically principled data analytic procedures, as well as theoretical frameworks for how circuit connectivity and dynamics can conspire to generate emergent behavioral and cognitive functions. We review and outline potential avenues for progress, including new theories of high dimensional data analysis, the need to analyze complex artificial networks, and methods for analyzing entire spaces of circuit models, rather than one model at a time. Such interplay between experiments, data analysis and theory will be indispensable in catalyzing conceptual advances in the age of large-scale neuroscience., 11 pages, 3 figures

Technological advances in profiling cells along genetic, anatomical and physiological axes have fomented interest in identifying all neuronal cell types. This goal nears completion in specialized circuits such as the retina, while remaining more elusive in higher order cortical regions. We propose that this differential success of cell type identification may not simply reflect technological gaps in co-registering genetic, anatomical and physiological features in the cortex. Rather, we hypothesize it reflects evolutionarily driven differences in the computational principles governing specialized circuits versus more general-purpose learning machines. In this framework, we consider the question of cell types in medial entorhinal cortex (MEC), a region likely to be involved in memory and navigation. While MEC contains subsets of identifiable functionally defined cell types, recent work employing unbiased statistical methods and more diverse tasks reveals unsuspected heterogeneity and adaptivity in MEC firing patterns. This suggests MEC may operate more as a generalist circuit, obeying computational design principles resembling those governing other higher cortical regions.

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.

A central challenge in sensory neuroscience is to understand neural computations and circuit mechanisms that underlie the encoding of ethologically relevant, natural stimuli. In multilayered neural circuits, nonlinear processes such as synaptic transmission and spiking dynamics present a significant obstacle to the creation of accurate computational models of responses to natural stimuli. Here we demonstrate that deep convolutional neural networks (CNNs) capture retinal responses to natural scenes nearly to within the variability of a cell’s response, and are markedly more accurate than linear-nonlinear (LN) models and Generalized Linear Models (GLMs). Moreover, we find two additional surprising properties of CNNs: they are less susceptible to overfitting than their LN counterparts when trained on small amounts of data, and generalize better when tested on stimuli drawn from a different distribution (e.g. between natural scenes and white noise). An examination of the learned CNNs reveals several properties. First, a richer set of feature maps is necessary for predicting the responses to natural scenes compared to white noise. Second, temporally precise responses to slowly varying inputs originate from feedforward inhibition, similar to known retinal mechanisms. Third, the injection of latent noise sources in intermediate layers enables our model to capture the sub-Poisson spiking variability observed in retinal ganglion cells. Fourth, augmenting our CNNs with recurrent lateral connections enables them to capture contrast adaptation as an emergent property of accurately describing retinal responses to natural scenes. These methods can be readily generalized to other sensory modalities and stimulus ensembles. Overall, this work demonstrates that CNNs not only accurately capture sensory circuit responses to natural scenes, but also can yield information about the circuit’s internal structure and function.

Tracking the coordinated activity of cellular events through volumes of intact tissue is a major challenge in biology that has inspired significant technological innovation. Yet scanless measurement of the high-speed activity of individual neurons across three dimensions in scattering mammalian tissue remains an open problem. Here we develop and validate a computational imaging approach (SWIFT) that integrates high-dimensional, structured statistics with light field microscopy to allow the synchronous acquisition of single-neuron resolution activity throughout intact tissue volumes as fast as a camera can capture images (currently up to 100 Hz at full camera resolution), attaining rates needed to keep pace with emerging fast calcium and voltage sensors. We demonstrate that this large field-of-view, single-snapshot volume acquisition method—which requires only a simple and inexpensive modification to a standard fluorescence microscope—enables scanless capture of coordinated activity patterns throughout mammalian neural volumes. Further, the volumetric nature of SWIFT also allows fast in vivo imaging, motion correction, and cell identification throughout curved subcortical structures like the dorsal hippocampus, where cellular-resolution dynamics spanning hippocampal subfields can be simultaneously observed during a virtual context learning task in a behaving animal. SWIFT’s ability to rapidly and easily record from volumes of many cells across layers opens the door to widespread identification of dynamical motifs and timing dependencies among coordinated cell assemblies during adaptive, modulated, or maladaptive physiological processes in neural systems.

A central challenge in sensory neuroscience involves understanding how neural circuits shape computations across cascaded cell layers. Here we develop a computational framework to reconstruct the response properties of experimentally unobserved neurons in the interior of a multilayered neural circuit. 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. 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. For example, with our regularization framework, we can learn the STA and STC using 5 and 10 minutes of data, respectively, at a level of accuracy that otherwise requires 40 minutes of data without regularization. We apply our framework to retinal ganglion cell processing, learning cascaded linear-nonlinear (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 had consistently high thresholds, 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 general computational framework may aid in extracting principles of nonlinear hierarchical sensory processing across diverse modalities from limited data.Author SummaryComputation in neural circuits arises from the cascaded processing of inputs through multiple cell layers. Each of these cell layers performs operations such as filtering and thresholding in order to shape a circuit’s output. It remains a challenge to describe both the computations and the mechanisms that mediate them given limited data recorded from a neural circuit. A standard approach to describing circuit computation involves building quantitative encoding models that predict the circuit response given its input, but these often fail to map in an interpretable way onto mechanisms within the circuit. In this work, we build two layer linear-nonlinear cascade models (LN-LN) in order to describe how the retinal output is shaped by nonlinear mechanisms in the inner retina. We find that these LN-LN models, fit to ganglion cell recordings alone, identify filters and nonlinearities that are readily mapped onto individual circuit components inside the retina, namely bipolar cells and the bipolar-to-ganglion cell synaptic threshold. This work demonstrates how combining simple prior knowledge of circuit properties with partial experimental recordings of a neural circuit’s output can yield interpretable models of the entire circuit computation, including parts of the circuit that are hidden or not directly observed in neural recordings.

Across many studies, animals with enhanced synaptic plasticity exhibit either enhanced or impaired learning, raising a conceptual puzzle: how enhanced plasticity can yield opposite learning outcomes? Here, we show that the recent history of experience can determine whether mice with enhanced plasticity exhibit enhanced or impaired learning in response to the same training. Mice with enhanced cerebellar LTD, due to double knockout (DKO) of MHCI H2-Kb/H2-Db (KbDb−/−), exhibited oculomotor learning deficits. However, the same mice exhibited enhanced learning after appropriate pre-training. Theoretical analysis revealed that synapses with history-dependent learning rules could recapitulate the data, and suggested that saturation may be a key factor limiting the ability of enhanced plasticity to enhance learning. Optogenetic stimulation designed to saturate LTD produced the same impairment in WT as observed in DKO mice. Overall, our results suggest that the recent history of activity and the threshold for synaptic plasticity conspire to effect divergent learning outcomes. DOI: http://dx.doi.org/10.7554/eLife.20147.001, eLife digest All animals can learn from their experiences. One of the main ideas for how learning occurs is that it involves changes in the strength of the connections between neurons, known as synapses. The ability of synapses to become stronger or weaker is referred to as synaptic plasticity. High levels of synaptic plasticity are generally thought to be good for learning, while low levels of synaptic plasticity make learning more difficult. Nevertheless, studies have also reported that high levels of synaptic plasticity can sometimes impair learning. To explain these mixed results, Nguyen-Vu, Zhao, Lahiri et al. studied mice that had been genetically modified to show greater synaptic plasticity than normal mice. The same individual mutant animals were sometimes less able to learn an eye-movement task than unmodified mice, and at other times better able to learn exactly the same task. The main factor that determined how well the mice could learn was what the mice had experienced shortly before they began the training. Nguyen-Vu et al. propose that some experiences change the strength of synapses so much that they temporarily prevent those synapses from undergoing any further changes. Animals with these “saturated” synapses will struggle to learn a new task, even if their brains are normally capable of high levels of synaptic plasticity. Notably, even normal activity appears to be able to put the synapses of the mutant mice into a saturated state, whereas this saturation would only occur in normal mice under a restricted set of circumstances. Consistent with this idea, Nguyen-Vu et al. showed that a specific type of pre-training that desaturates synapses improved the ability of the modified mice to learn the eye-movement task. Conversely, a different procedure that is known to saturate synapses impaired the learning ability of the unmodified mice. A future challenge is to test these predictions experimentally by measuring changes in synaptic plasticity directly, both in brain slices and in living animals. The results could ultimately help to develop treatments that improve the ability to learn and so could provide benefits to a wide range of individuals, including people who have suffered a brain injury or stroke. DOI: http://dx.doi.org/10.7554/eLife.20147.002

It is well known that the initialization of weights in deep neural networks can have a dramatic impact on learning speed. For example, ensuring the mean squared singular value of a network's input-output Jacobian is $O(1)$ is essential for avoiding the exponential vanishing or explosion of gradients. The stronger condition that all singular values of the Jacobian concentrate near $1$ is a property known as dynamical isometry. For deep linear networks, dynamical isometry can be achieved through orthogonal weight initialization and has been shown to dramatically speed up learning; however, it has remained unclear how to extend these results to the nonlinear setting. We address this question by employing powerful tools from free probability theory to compute analytically the entire singular value distribution of a deep network's input-output Jacobian. We explore the dependence of the singular value distribution on the depth of the network, the weight initialization, and the choice of nonlinearity. Intriguingly, we find that ReLU networks are incapable of dynamical isometry. On the other hand, sigmoidal networks can achieve isometry, but only with orthogonal weight initialization. Moreover, we demonstrate empirically that deep nonlinear networks achieving dynamical isometry learn orders of magnitude faster than networks that do not. Indeed, we show that properly-initialized deep sigmoidal networks consistently outperform deep ReLU networks. Overall, our analysis reveals that controlling the entire distribution of Jacobian singular values is an important design consideration in deep learning., Comment: 13 pages, 6 figures. Appearing at the 31st Conference on Neural Information Processing Systems (NIPS 2017)

Summary Medial entorhinal grid cells display strikingly symmetric spatial firing patterns. The clarity of these patterns motivated the use of specific activity pattern shapes to classify entorhinal cell types. While this approach successfully revealed cells that encode boundaries, head direction, and running speed, it left a majority of cells unclassified, and its pre-defined nature may have missed unconventional, yet important coding properties. Here, we apply an unbiased statistical approach to search for cells that encode navigationally relevant variables. This approach successfully classifies the majority of entorhinal cells and reveals unsuspected entorhinal coding principles. First, we find a high degree of mixed selectivity and heterogeneity in superficial entorhinal neurons. Second, we discover a dynamic and remarkably adaptive code for space that enables entorhinal cells to rapidly encode navigational information accurately at high running speeds. Combined, these observations advance our current understanding of the mechanistic origins and functional implications of the entorhinal code for navigation. Video Abstract

Summary A central goal of systems neuroscience is to relate an organism’s neural activity to behavior. Neural population analyses often reduce the data dimensionality to focus on relevant activity patterns. A major hurdle to data analysis is spike sorting, and this problem is growing as the number of recorded neurons increases. Here, we investigate whether spike sorting is necessary to estimate neural population dynamics. The theory of random projections suggests that we can accurately estimate the geometry of low-dimensional manifolds from a small number of linear projections of the data. We recorded data using Neuropixels probes in motor cortex of nonhuman primates and reanalyzed data from three previous studies and found that neural dynamics and scientific conclusions are quite similar using multiunit threshold crossings rather than sorted neurons. This finding unlocks existing data for new analyses and informs the design and use of new electrode arrays for laboratory and clinical use.