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Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or ‘frame of reference’. Information can be encoded by the timing of neural activity relative to thephaseof such oscillations. In line with this hypothesis, there have been multiple empirical observations of suchphase codesin the brain. Here we ask: What kind of neural dynamics support phase coding of information with neural oscillations? We tackled this question by analyzing recurrent neural networks (RNNs) that were trained on a working memory task. The networks were given access to an external reference oscillation and tasked to produce an oscillation, such that the phase difference between the reference and output oscillation maintains the identity of transient stimuli. We found that networks converged to stable oscillatory dynamics. Reverse engineering these networks revealed that each phase-coded memory corresponds to a separate limit cycle attractor. We characterized how the stability of the attractor dynamics depends on both reference oscillation amplitude and frequency, properties that can be experimentally observed. To understand the connectivity structures that underlie these dynamics, we showed that trained networks can be described as two phase-coupled oscillators. Using this insight, we condensed our trained networks to a reduced model consisting of two functional modules: One that generates an oscillation and one that implements a coupling function between the internal oscillation and external reference. In summary, by reverse engineering the dynamics and connectivity of trained RNNs, we propose a mechanism by which neural networks can harness reference oscillations for working memory. Specifically, we propose that a phase-coding network generates autonomous oscillations which it couples to an external reference oscillation in a multi-stable fashion.Author summaryMany of our actions are rhythmic—walking, breathing, digesting and more. It is not surprising that neural activity can have a strong oscillatory component. Indeed, such brain waves are common, and can even be measured using EEG from the scalp. Perhaps less obvious is the presence of such oscillations during non-rhythmic behavior—such as memory maintenance and other cognitive functions. Reports of these cognitive oscillations have accumulated over the years, and various theories were raised regarding their origin and utilization. In particular, oscillations have been proposed to serve as a clock signal that can be used for temporal-, or phase-coding of information in working memory. Here, we studied the dynamical systems underlying this kind of coding, by using trained artificial neural networks as hypothesis generators. We trained recurrent neural networks to perform a working memory task, while giving them access to a reference oscillation. We were then able to reverse engineer the learned dynamics of the networks. Our analysis revealed that phase coded memories correspond to stable attractors in the dynamical landscape of the model. These attractors arose from the coupling of the external reference oscillation with oscillations generated internally by the network.

Neonatal apneas and hypopneas present a serious risk for healthy infant development. Treating these adverse events requires frequent manual stimulation by skilled personnel, which can lead to alert fatigue. Automatically predicting these adverse events before they occur would enable the use of methods for automatic intervention. In this work, we propose a neural additive model to predict individual events of neonatal apnea and hypopnea and apply it to a physiological dataset from infants with Robin sequence at risk of upper airway obstruction. The dataset will be made publicly available together with this study. Our model achieved an average area under the receiver operating characteristic curve of 0.80 by additively combining information from different modalities of the respiratory polygraphy recording. This permits the prediction of individual apneas and hypopneas up to 15 seconds before they occur. Its additive nature makes the model inherently interpretable, which allowed insights into how important a given signal modality is for prediction and which patterns in the signal are discriminative. For our problem of predicting apneas and hyponeas in infants with Robin sequence, prior irregularities in breathing-related modalities as well as decreases in SpO2levels were especially discriminative.

We can now measure the connectivity of every neuron in a neural circuit, but we are still blind to other biological details, including the dynamical characteristics of each neuron. The degree to which connectivity measurements alone can inform understanding of neural computation is an open question. Here we show that with only measurements of the connectivity of a biological neural network, we can predict the neural activity underlying neural computation. We constructed a model neural network with the experimentally determined connectivity for 64 cell types in the motion pathways of the fruit fly optic lobe but with unknown parameters for the single neuron and single synapse properties. We then optimized the values of these unknown parameters using techniques from deep learning, to allow the model network to detect visual motion. Our mechanistic model makes detailed experimentally testable predictions for each neuron in the connectome. We found that model predictions agreed with experimental measurements of neural activity across 24 studies. Our work demonstrates a strategy for generating detailed hypotheses about the mechanisms of neural circuit function from connectivity measurements. We show that this strategy is more likely to be successful when neurons are sparsely connected—a universally observed feature of biological neural networks across species and brain regions.

Recent advances in connectomics research enable the acquisition of increasing amounts of data about the connectivity patterns of neurons. How can we use this wealth of data to efficiently derive and test hypotheses about the principles underlying these patterns? A common approach is to simulate neural networks using a hypothesized wiring rule in a generative model and to compare the resulting synthetic data with empirical data. However, most wiring rules have at least some free parameters, and identifying parameters that reproduce empirical data can be challenging as it often requires manual parameter tuning. Here, we propose to use simulation-based Bayesian inference (SBI) to address this challenge. Rather than optimizing a single rule to fit the empirical data, SBI considers many parametrizations of a wiring rule and performs Bayesian inference to identify the parameters that are compatible with the data. It uses simulated data from multiple candidate wiring rules and relies on machine learning methods to estimate a probability distribution (the ‘posterior distribution over rule parameters conditioned on the data’) that characterizes all data-compatible rules. We demonstrate how to apply SBI in connectomics by inferring the parameters of wiring rules in anin silicomodel of the rat barrel cortex, givenin vivoconnectivity measurements. SBI identifies a wide range of wiring rule parameters that reproduce the measurements. We show how access to the posterior distribution over all data-compatible parameters allows us to analyze their relationship, revealing biologically plausible parameter interactions and enabling experimentally testable predictions. We further show how SBI can be applied to wiring rules at different spatial scales to quantitatively rule out invalid wiring hypotheses. Our approach is applicable to a wide range of generative models used in connectomics, providing a quantitative and efficient way to constrain model parameters with empirical connectivity data.Author summaryThe brain is composed of an intricately connected network of cells—what are the factors that contribute to constructing these patterns of connectivity, and how? To answer these questions, amassing connectivity data alone is not enough. We must also be able to efficiently develop and test our ideas about the underlying connectivity principles. For example, we could simulate a hypothetical wiring rule like “neurons near each other are more likely to form connections” in a computational model and generate corresponding synthetic data. If the synthetic, simulated data resembles the real, measured data, then we have some confidence that our hypotheses might be correct. The challenge, however, lies in finding all the potential wiring rules, or equivalently, all the parameters of the computational model that can reproduce the observed data, as this process is often idiosyncratic and labor-intensive. To tackle this challenge, we introduce an approach that combines computational modeling in connectomics, deep learning, and Bayesian statistical inference in order to automatically infer a probability distribution over the model parameters likely to explain the data. We demonstrate our approach by inferring wiring rules in a detailed model of the rat barrel cortex and find that the inferred distribution identifies multiple data-compatible model parameters, reveals biologically plausible parameter interactions, and allows us to make experimentally testable predictions.

Forming a complete picture of the relationship between neural activity and skeletal kinematics requires quantification of skeletal joint biomechanics during free behavior; however, without detailed knowledge of the underlying skeletal motion, inferring limb kinematics using surface-tracking approaches is difficult, especially for animals where the relationship between the surface and underlying skeleton changes during motion. Here we developed a videography-based method enabling detailed three-dimensional kinematic quantification of an anatomically defined skeleton in untethered freely behaving rats and mice. This skeleton-based model was constrained using anatomical principles and joint motion limits and provided skeletal pose estimates for a range of body sizes, even when limbs were occluded. Model-inferred limb positions and joint kinematics during gait and gap-crossing behaviors were verified by direct measurement of either limb placement or limb kinematics using inertial measurement units. Together we show that complex decision-making behaviors can be accurately reconstructed at the level of skeletal kinematics using our anatomically constrained model.

We combine amortized neural posterior estimation with importance sampling for fast and accurate gravitational-wave inference. We first generate a rapid proposal for the Bayesian posterior using neural networks, and then attach importance weights based on the underlying likelihood and prior. This provides (1) a corrected posterior free from network inaccuracies, (2) a performance diagnostic (the sample efficiency) for assessing the proposal and identifying failure cases, and (3) an unbiased estimate of the Bayesian evidence. By establishing this independent verification and correction mechanism we address some of the most frequent criticisms against deep learning for scientific inference. We carry out a large study analyzing 42 binary black hole mergers observed by LIGO and Virgo with the SEOBNRv4PHM and IMRPhenomXPHM waveform models. This shows a median sample efficiency of $\approx 10\%$ (two orders-of-magnitude better than standard samplers) as well as a ten-fold reduction in the statistical uncertainty in the log evidence. Given these advantages, we expect a significant impact on gravitational-wave inference, and for this approach to serve as a paradigm for harnessing deep learning methods in scientific applications., 8+7 pages, 1+5 figures. [v2]: Minor updates to match published version, code available at https://github.com/dingo-gw/dingo

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis . We present a machine learning method that can identify a range of network models that generate activity patterns matching experimental data and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances.

A prominent theory proposes that the temporal order of a sequence of items held in memory is reflected in ordered firing of neurons at different phases of theta oscillations 1. We probe this theory by directly measuring single neuron activity (1420 neurons) and local field potentials (LFP, 921 channels) in the medial temporal lobe of 16 epilepsy patients performing a working memory task for temporal order. We observe theta oscillations and preferential firing of single neurons at theta phase during memory maintenance. We find that - depending on memory performance - phase of firing is related to item position within a sequence. However, in contrast to the theory, phase order did not match item order. To investigate underlying mechanisms, we subsequently trained recurrent neural networks (RNNs) to perform an analogous task. Similar to recorded neural activity, we show that RNNs generate theta oscillations during memory maintenance. Importantly, model neurons exhibit theta phase-dependent firing related to item position, where phase of firing again did not match item order. Instead, we observed a mechanistic link between phase order, stimulus timing and oscillation frequency - a relationship we subsequently confirmed in our neural recordings. Taken together, in both biological and artificial neural networks we provide validating evidence for the role of phase-of-firing in memory processing while at the same time challenging a long-held theory about the functional role of spiking and oscillations in sequence memory.

Inferring parameters of computational models that capture experimental data is a central task in cognitive neuroscience. Bayesian statistical inference methods usually require the ability to evaluate the likelihood of the model—however, for many models of interest in cognitive neuroscience, the associated likelihoods cannot be computed efficiently. Simulation-based inference (SBI) offers a solution to this problem by only requiring access to simulations produced by the model. Previously, Fengler et al. introduced likelihood approximation networks (LANs, Fengler et al., 2021) which make it possible to apply SBI to models of decision-making but require billions of simulations for training. Here, we provide a new SBI method that is substantially more simulation efficient. Our approach, mixed neural likelihood estimation (MNLE), trains neural density estimators on model simulations to emulate the simulator and is designed to capture both the continuous (e.g., reaction times) and discrete (choices) data of decision-making models. The likelihoods of the emulator can then be used to perform Bayesian parameter inference on experimental data using standard approximate inference methods like Markov Chain Monte Carlo sampling. We demonstrate MNLE on two variants of the drift-diffusion model and show that it is substantially more efficient than LANs: MNLE achieves similar likelihood accuracy with six orders of magnitude fewer training simulations and is significantly more accurate than LANs when both are trained with the same budget. Our approach enables researchers to perform SBI on custom-tailored models of decision-making, leading to fast iteration of model design for scientific discovery.

It has become increasingly clear that the neurons in the cerebral cortex are not randomly interconnected. This wiring specificity can result from synapse formation mechanisms that interconnect neurons depending on their activity or genetically defined identity. Here we report that in addition to these synapse formation mechanisms, the structural composition of the neuropil provides a third prominent source by which wiring specificity emerges in cortical networks. This structurally determined wiring specificity reflects the packing density, morphological diversity and similarity of the dendritic and axonal processes. The higher these three factors are, the more recurrent the topology of the networks. Conversely, low density, diversity and similarity yield feedforward networks. These principles predict connectivity patterns from subcellular to network scales that are remarkably consistent with empirical observations from a rich body of literature. Thus, cortical network architectures reflect the specific morphological properties of their constituents to much larger degrees than previously thought.

Stroke is one of the most frequent diseases, and half of the stroke survivors are left with permanent impairment. Prediction of individual outcome is still difficult. Many but not all patients with stroke improve by approximately 1.7 times the initial impairment, that has been termed proportional recovery rule. The present study aims at identifying factors predicting motor outcome after stroke more accurately than before, and observe associations of rehabilitation treatment with outcome.The study is designed as a multi-centre prospective clinical observational trial. An extensive primary data set of clinical, neuroimaging, electrophysiological, and laboratory data will be collected within 96 h of stroke onset from patients with relevant upper extremity deficit, as indexed by a Fugl-Meyer-Upper Extremity (FM-UE) score ≤ 50. At least 200 patients will be recruited. Clinical scores will include the FM-UE score (range 0-66, unimpaired function is indicated by a score of 66), Action Research Arm Test, modified Rankin Scale, Barthel Index and Stroke-Specific Quality of Life Scale. Follow-up clinical scores and applied types and amount of rehabilitation treatment will be documented in the rehabilitation hospitals. Final follow-up clinical scoring will be performed 90 days after the stroke event. The primary endpoint is the change in FM-UE defined as 90 days FM-UE minus initial FM-UE, divided by initial FM-UE impairment. Changes in the other clinical scores serve as secondary endpoints. Machine learning methods will be employed to analyze the data and predict primary and secondary endpoints based on the primary data set and the different rehabilitation treatments.If successful, outcome and relation to rehabilitation treatment in patients with acute motor stroke will be predictable more reliably than currently possible, leading to personalized neurorehabilitation. An important regulatory aspect of this trial is the first-time implementation of systematic patient data transfer between emergency and rehabilitation hospitals, which are divided institutions in Germany.This study was registered at ClinicalTrials.gov ( NCT04688970 ) on 30 December 2020.

Deep learning techniques for gravitational-wave parameter estimation haveemerged as a fast alternative to standard samplers $\unicode{x2013}$ producingresults of comparable accuracy. These approaches (e.g., DINGO) enable amortizedinference by training a normalizing flow to represent the Bayesian posteriorconditional on observed data. By conditioning also on the noise power spectraldensity (PSD) they can even account for changing detector characteristics.However, training such networks requires knowing in advance the distribution ofPSDs expected to be observed, and therefore can only take place once all datato be analyzed have been gathered. Here, we develop a probabilistic model toforecast future PSDs, greatly increasing the temporal scope of DINGO networks.Using PSDs from the second LIGO-Virgo observing run (O2) $\unicode{x2013}$ plusjust a single PSD from the beginning of the third (O3) $\unicode{x2013}$ weshow that we can train a DINGO network to perform accurate inference throughoutO3 (on 37 real events). We therefore expect this approach to be a key componentto enable the use of deep learning techniques for low-latency analyses ofgravitational waves.

Forming a complete picture of the relationship between neural activity and body kinetics requires quantification of skeletal joint biomechanics during behavior. However, without detailed knowledge of the underlying skeletal motion, inferring joint kinetics from surface tracking approaches is difficult, especially for animals where the relationship between surface anatomy and skeleton changes during motion. Here we developed a videography-based method enabling detailed three-dimensional kinetic quantification of an anatomically defined skeleton in untethered freely-behaving animals. This skeleton-based model has been constrained by anatomical principles and joint motion limits and provided skeletal pose estimates for a range of rodent sizes, even when limbs were occluded. Model-inferred joint kinetics for both gait and gap-crossing behaviors were verified by direct measurement of limb placement, showing that complex decision-making behaviors can be accurately reconstructed at the level of skeletal kinetics using our anatomically constrained model.

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here, we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis. We use a novel machine learning method to identify a range of network models that can generate activity patterns matching experimental data, and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures, but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that, despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances.

We demonstrate unprecedented accuracy for rapid gravitational-wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational-wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to a minute per event. Our networks are trained using simulated data, including an estimate of the detector-noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters, and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm -- called "DINGO" -- sets a new standard in fast-and-accurate inference of physical parameters of detected gravitational-wave events, which should enable real-time data analysis without sacrificing accuracy., 7+12 pages, 4+11 figures. [v2]: Minor updates to match published version, code available at https://github.com/dingo-gw/dingo

Single-unit recordings in the brain of behaving human subjects provide a unique opportunity to advance our understanding of neural mechanisms of cognition. These recordings are exclusively performed in medical centers during diagnostic or therapeutic procedures. The presence of medical instruments along with other aspects of the hospital environment limit the control of electrical noise compared to animal laboratory environments. Here, we highlight the problem of an increased occurrence of simultaneous spike events on different recording channels in human single-unit recordings. Most of these simultaneous events were detected in clusters previously labeled as artifacts and showed similar waveforms. These events may result from common external noise sources or from different micro-electrodes recording activity from the same neuron. To address the problem of duplicate recorded events, we introduce an open-source algorithm to identify these artificial spike events based on their synchronicity and waveform similarity. Applying our method to a comprehensive dataset of human single-unit recordings, we demonstrate that our algorithm can substantially increase the data quality of these recordings. Given our findings, we argue that future studies of single-unit activity recorded under noisy conditions should employ algorithms of this kind to improve data quality.

The hippocampal dentate gyrus is an important relay conveying sensory information from the entorhinal cortex to the hippocampus proper. During exploration, the dentate gyrus has been proposed to act as a pattern separator. However, the dentate gyrus also shows structured activity during immobility and sleep. The properties of these activity patterns at cellular resolution, and their role in hippocampal-dependent memory processes have remained unclear. Using dual-color in-vivo two-photon Ca2+ imaging, we show that in immobile mice dentate granule cells generate sparse, synchronized activity patterns associated with entorhinal cortex activation. These population events are structured and modified by changes in the environment; and they incorporate place- and speed cells. Importantly, they are more similar than expected by chance to population patterns evoked during self-motion. Using optogenetic inhibition, we show that granule cell activity is not only required during exploration, but also during immobility in order to form dentate gyrus-dependent spatial memories.

Scientists and engineers employ stochastic numerical simulators to model empirically observed phenomena. In contrast to purely statistical models, simulators express scientific principles that provide powerful inductive biases, improve generalization to new data or scenarios and allow for fewer, more interpretable and domain-relevant parameters. Despite these advantages, tuning a simulator's parameters so that its outputs match data is challenging. Simulation-based inference (SBI) seeks to identify parameter sets that a) are compatible with prior knowledge and b) match empirical observations. Importantly, SBI does not seek to recover a single 'best' data-compatible parameter set, but rather to identify all high probability regions of parameter space that explain observed data, and thereby to quantify parameter uncertainty. In Bayesian terminology, SBI aims to retrieve the posterior distribution over the parameters of interest. In contrast to conventional Bayesian inference, SBI is also applicable when one can run model simulations, but no formula or algorithm exists for evaluating the probability of data given parameters, i.e. the likelihood. We present $\texttt{sbi}$, a PyTorch-based package that implements SBI algorithms based on neural networks. $\texttt{sbi}$ facilitates inference on black-box simulators for practising scientists and engineers by providing a unified interface to state-of-the-art algorithms together with documentation and tutorials., Alvaro Tejero-Cantero, Jan Boelts, Michael Deistler, Jan-Matthis Lueckmann and Conor Durkan contributed equally in shared first authorship. This manuscript has been submitted for consideration to the Journal of Open Source Software (JOSS). 4 pages, no figures; v2: added link to sbi home

The ability to preferentially stimulate different retinal pathways is an important area of research for improving visual prosthetics. Recent work has shown that different classes of retinal ganglion cells (RGCs) have distinct linear electrical input filters for low-amplitude white noise stimulation. The aim of this study is to provide a statistical framework for characterizing how RGCs respond to white-noise electrical stimulation. We used a nested family of Generalized Linear Models (GLMs) to partition neural responses into different components—progressively adding covariates to the GLM which captured non-stationarity in neural activity, a linear dependence on the stimulus, and any remaining non-linear interactions. We found that each of these components resulted in increased model performance, but that even the non-linear model left a substantial fraction of neural variability unexplained. The broad goal of this paper is to provide a much-needed theoretical framework to objectively quantify stimulus paradigms in terms of the types of neural responses that they elicit (linear vs. non-linear vs. stimulus-independent variability). In turn, this aids the prosthetic community in the search for optimal stimulus parameters that avoid indiscriminate retinal activation and adaptation caused by excessively large stimulus pulses, and avoid low fidelity responses (low signal-to-noise ratio) caused by excessively weak stimulus pulses.

The hippocampal dentate gyrus is an important relay conveying sensory information from the entorhinal cortex to the hippocampus proper. During exploration, the dentate gyrus has been proposed to act as a pattern separator. However, the dentate gyrus also shows structured activity during immobility and sleep. The properties of these activity patterns at cellular resolution, and their role in hippocampal-dependent memory processes have remained unclear. Using dual-color in-vivo two-photon Ca2+ imaging, we show that in immobile mice dentate granule cells generate sparse, synchronized activity patterns associated with entorhinal cortex activation. These population events are structured and modified by changes in the environment; and they incorporate place- and speed cells. Importantly, they recapitulate population patterns evoked during self-motion. Using optogenetic inhibition during immobility, we show that granule cell activity during immobility is required to form dentate gyrus-dependent spatial memories. These data suggest that memory formation is supported by dentate gyrus replay of population codes of the current environment.

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics., eLife digest Computational neuroscientists use mathematical models built on observational data to investigate what’s happening in the brain. Models can simulate brain activity from the behavior of a single neuron right through to the patterns of collective activity in whole neural networks. Collecting the experimental data is the first step, then the challenge becomes deciding which computer models best represent the data and can explain the underlying causes of how the brain behaves. Researchers usually find the right model for their data through trial and error. This involves tweaking a model’s parameters until the model can reproduce the data of interest. But this process is laborious and not systematic. Moreover, with the ever-increasing complexity of both data and computer models in neuroscience, the old-school approach of building models is starting to show its limitations. Now, Gonçalves, Lueckmann, Deistler et al. have designed an algorithm that makes it easier for researchers to fit mathematical models to experimental data. First, the algorithm trains an artificial neural network to predict which models are compatible with simulated data. After initial training, the method can rapidly be applied to either raw experimental data or selected data features. The algorithm then returns the models that generate the best match. This newly developed machine learning tool was able to automatically identify models which can replicate the observed data from a diverse set of neuroscience problems. Importantly, further experiments showed that this new approach can be scaled up to complex mechanisms, such as how a neural network in crabs maintains its rhythm of activity. This tool could be applied to a wide range of computational investigations in neuroscience and other fields of biology, which may help bridge the gap between ‘data-driven’ and ‘theory-driven’ approaches.

In the version of this Article initially published, Jacob H. Macke and Jonas Ries were not listed as corresponding authors. Their contact information and designation as corresponding authors are now included. The error has been corrected in the online version of the Article.

Objective. Most neuroprosthetic implants employ pulsatile square-wave electrical stimuli, which are significantly different from physiological inter-neuronal communication. In case of retinal neuroprosthetics, which use a certain type of pulsatile stimuli, reliable object and contrast discrimination by implanted blind patients remained challenging. Here we investigated to what extent simple objects can be discriminated from the output of retinal ganglion cells (RGCs) upon sinusoidal stimulation. Approach. Spatially confined objects were formed by different combinations of 1024 stimulating microelectrodes. The RGC activity in the ex vivo retina of photoreceptor-degenerated mouse, of healthy mouse or of primate was recorded simultaneously using an interleaved recording microelectrode array implemented in a CMOS-based chip. Main results. We report that application of sinusoidal electrical stimuli (40 Hz) in epiretinal configuration instantaneously and reliably modulates the RGC activity in spatially confined areas at low stimulation threshold charge densities (40 nC mm−2). Classification of overlapping but spatially displaced objects (1° separation) was achieved by distinct spiking activity of selected RGCs. A classifier (regularized logistic regression) discriminated spatially displaced objects (size: 5.5° or 3.5°) with high accuracy (90% or 62%). Stimulation with low artificial contrast (10%) encoded by different stimulus amplitudes generated RGC activity, which was classified with an accuracy of 80% for large objects (5.5°). Significance. We conclude that time-continuous smooth-wave stimulation provides robust, localized neuronal activation in photoreceptor-degenerated retina, which may enable future artificial vision at high temporal, spatial and contrast resolution.

To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging to fit such mechanistic spiking networks at the single neuron scale to empirical population data. To close this gap, we propose to fit such data at a meso scale, using a mechanistic but low-dimensional and hence statistically tractable model. The mesoscopic representation is obtained by approximating a population of neurons as multiple homogeneous `pools' of neurons, and modelling the dynamics of the aggregate population activity within each pool. We derive the likelihood of both single-neuron and connectivity parameters given this activity, which can then be used to either optimize parameters by gradient ascent on the log-likelihood, or to perform Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this approach using a model of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived, and show that both single-neuron and connectivity parameters can be recovered from simulated data. In particular, our inference method extracts posterior correlations between model parameters, which define parameter subsets able to reproduce the data. We compute the Bayesian posterior for combinations of parameters using MCMC sampling and investigate how the approximations inherent to a mesoscopic population model impact the accuracy of the inferred single-neuron parameters., 1st revision: 48 pages, 13 figures Improved statistical validation of results. Rewrite of Section 4.2 to clarify the link between the mesoscopic model and a transport equation. Multiple small improvements to the presentation Original: 46 pages, 12 figures

One challenge in neuroscience, as in other areas of science, is to make inferences about the underlying causal structure from correlational data. Here, we discuss this challenge in the context of choice correlations in sensory neurons, that is, trial-by-trial correlations, unexplained by the stimulus, between the activity of sensory neurons and an animal’s perceptual choice. Do these choice-correlations reflect feedforward, feedback signalling, both, or neither? We highlight recent results of correlational and causal examinations of choice and choice-history signals in sensory, and in part sensorimotor, cortex and address formal statistical frameworks to infer causal interactions from data.

The psychometric function describes how an experimental variable, such as stimulus strength, influences the behaviour of an observer. Estimation of psychometric functions from experimental data plays a central role in fields such as psychophysics, experimental psychology and in the behavioural neurosciences. Experimental data may exhibit substantial overdispersion, which may result from non-stationarity in the behaviour of observers. Here we extend the standard binomial model which is typically used for psychometric function estimation to a beta-binomial model. We show that the use of the beta-binomial model makes it possible to determine accurate credible intervals even in data which exhibit substantial overdispersion. This goes beyond classical measures for overdispersion goodness-of-fit which can detect overdispersion but provide no method to do correct inference for overdispersed data. We use Bayesian inference methods for estimating the posterior distribution of the parameters of the psychometric function. Unlike previous Bayesian psychometric inference methods our software implementation-psignifit 4 performs numerical integration of the posterior within automatically determined bounds. This avoids the use of Markov chain Monte Carlo (MCMC) methods typically requiring expert knowledge. Extensive numerical tests show the validity of the approach and we discuss implications of overdispersion for experimental design. A comprehensive MATLAB toolbox implementing the method is freely available; a python implementation providing the basic capabilities is also available. (C) 2016 The Authors. Published by Elsevier Ltd.

Deep neural networks (DNNs) transform stimuli across multiple processing stages to produce representations that can be used to solve complex tasks, such as object recognition in images. However, a full understanding of how they achieve this remains elusive. The complexity of biological neural networks substantially exceeds the complexity of DNNs, making it even more challenging to understand the representations that they learn. Thus, both machine learning and computational neuroscience are faced with a shared challenge: how can we analyze their representations in order to understand how they solve complex tasks? We review how data-analysis concepts and techniques developed by computational neuroscientists can be useful for analyzing representations in DNNs, and in turn, how recently developed techniques for analysis of DNNs can be useful for understanding representations in biological neural networks. We explore opportunities for synergy between the two fields, such as the use of DNNs as in-silico model systems for neuroscience, and how this synergy can lead to new hypotheses about the operating principles of biological neural networks.

In recent years, two-photon calcium imaging has become a standard tool to probe the function of neural circuits and to study computations in neuronal populations. However, the acquired signal is only an indirect measurement of neural activity due to the comparatively slow dynamics of fluorescent calcium indicators. Different algorithms for estimating spike trains from noisy calcium measurements have been proposed in the past, but it is an open question how far performance can be improved. Here, we report the results of the spikefinder challenge, launched to catalyze the development of new spike inference algorithms through crowd-sourcing. We present ten of the submitted algorithms which show improved performance compared to previously evaluated methods. Interestingly, the top-performing algorithms are based on a wide range of principles from deep neural networks to generative models, yet provide highly correlated estimates of the neural activity. The competition shows that benchmark challenges can drive algorithmic developments in neuroscience.

During perceptual decisions the activity of sensory neurons covaries with choice, a covariation often quantified as “choice-probability”. Moreover, choices are influenced by a subject's previous choice (serial dependence) and neuronal activity often shows temporal correlations on long (seconds) timescales. Here, we test whether these findings are linked. Using generalized linear models, we analyze simultaneous measurements of behavior and V2 neural activity in macaques performing a visual discrimination task. Both, decisions and spiking activity show substantial temporal correlations and cross-correlations but seem to reflect two mostly separate processes. Indeed, removing history effects using semipartial correlation analysis leaves choice probabilities largely unchanged. The serial dependencies in choices and neural activity therefore cannot explain the observed choice probability. Rather, serial dependencies in choices and spiking activity reflect two predominantly separate but parallel processes, which are coupled on each trial by covariations between choices and activity. These findings provide important constraints for computational models of perceptual decision-making that include feedback signals.SIGNIFICANCE STATEMENTCorrelations, unexplained by the sensory input, between the activity of sensory neurons and an animal's perceptual choice (“choice probabilities”) have received attention from both a systems and computational neuroscience perspective. Conversely, whereas temporal correlations for both spiking activity (“non-stationarities”) and for a subject's choices in perceptual tasks (“serial dependencies”) have long been established, they have typically been ignored when measuring choice probabilities. Some accounts of choice probabilities incorporating feedback predict that these observations are linked. Here, we explore the extent to which this is the case. We find that, contrasting with these predictions, choice probabilities are largely independent of serial dependencies, which adds new constraints to accounts of choice probabilities that include feedback.

Summary Despite their growing popularity as models of visual functions, it remains unclear whether rodents are capable of deploying advanced shape-processing strategies when engaged in visual object recognition. In rats, for instance, pattern vision has been reported to range from mere detection of overall object luminance to view-invariant processing of discriminative shape features. Here we sought to clarify how refined object vision is in rodents, and how variable the complexity of their visual processing strategy is across individuals. To this aim, we measured how well rats could discriminate a reference object from 11 distractors, which spanned a spectrum of image-level similarity to the reference. We also presented the animals with random variations of the reference, and processed their responses to these stimuli to derive subject-specific models of rat perceptual choices. Our models successfully captured the highly variable discrimination performance observed across subjects and object conditions. In particular, they revealed that the animals that succeeded with the most challenging distractors were those that integrated the wider variety of discriminative features into their perceptual strategies. Critically, these strategies were largely preserved when the rats were required to discriminate outlined and scaled versions of the stimuli, thus showing that rat object vision can be characterized as a transformation-tolerant, feature-based filtering process. Overall, these findings indicate that rats are capable of advanced processing of shape information, and point to the rodents as powerful models for investigating the neuronal underpinnings of visual object recognition and other high-level visual functions., Graphical Abstract, Highlights • The ability of rats to discriminate visual objects varies greatly across subjects • Such variability is accounted for by the diversity of rat perceptual strategies • Animals building richer perceptual templates achieve higher accuracy • Perceptual strategies remain largely invariant across object transformations, Djurdjevic et al. show that the ability of rats to successfully discriminate visual objects depends on the complexity of their perceptual strategy, which remains largely unchanged under variations in object appearance. This implies that rats process visual objects using mechanisms not dissimilar from those of more evolved species, such as primates.

The rise of large-scale recordings of neuronal activity has fueled the hope to gain new insights into the collective activity of neural ensembles. How can one link the statistics of neural population activity to underlying principles and theories? One attempt to interpret such data builds upon analogies to the behaviour of collective systems in statistical physics. Divergence of the specific heat—a measure of population statistics derived from thermodynamics—has been used to suggest that neural populations are optimized to operate at a “critical point”. However, these findings have been challenged by theoretical studies which have shown that common inputs can lead to diverging specific heat. Here, we connect “signatures of criticality”, and in particular the divergence of specific heat, back to statistics of neural population activity commonly studied in neural coding: firing rates and pairwise correlations. We show that the specific heat diverges whenever the average correlation strength does not depend on population size. This is necessarily true when data with correlations is randomly subsampled during the analysis process, irrespective of the detailed structure or origin of correlations. We also show how the characteristic shape of specific heat capacity curves depends on firing rates and correlations, using both analytically tractable models and numerical simulations of a canonical feed-forward population model. To analyze these simulations, we develop efficient methods for characterizing large-scale neural population activity with maximum entropy models. We find that, consistent with experimental findings, increases in firing rates and correlation directly lead to more pronounced signatures. Thus, previous reports of thermodynamical criticality in neural populations based on the analysis of specific heat can be explained by average firing rates and correlations, and are not indicative of an optimized coding strategy. We conclude that a reliable interpretation of statistical tests for theories of neural coding is possible only in reference to relevant ground-truth models., Author summary Understanding how populations of neurons collectively encode sensory information is one of the central goals of computational neuroscience. In physics, systems are often characterized by identifying and describing critical points (e.g. the transition between two states of matter). The success of this approach has inspired a series of studies to search for analogous phenomena in nervous systems, and has lead to the hypothesis that these might be optimized to be poised at ‘thermodynamic critical points’. However, translating concepts from thermodynamics to neural data analysis has been a challenging endeavour. We here study the data analysis approaches that have been used to provide evidence for criticality in the brain. We find that observing signatures of criticality is closely linked to observing activity correlations between neurons– a ubiquitous phenomenon in neural data. Our study questions the experimental evidence that neural systems are optimised to exhibit thermodynamic critical behaviour. Finally, we provide practical, open-source tools for analyzing large-scale measurements of neural population activity using maximum entropy models.

Maximum entropy models have become popular statistical models in neuroscience and other areas in biology and can be useful tools for obtaining estimates of mutual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias, i.e., the true entropy of the data can be severely underestimated. Here, we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We focus on pairwise binary models, which are used extensively to model neural population activity. We show that if the data is well described by a pairwise model, the bias is equal to the number of parameters divided by twice the number of observations. If, however, the higher order correlations in the data deviate from those predicted by the model, the bias can be larger. Using a phenomenological model of neural population recordings, we find that this additional bias is highest for small firing probabilities, strong correlations and large population sizes—for the parameters we tested, a factor of about four higher. We derive guidelines for how long a neurophysiological experiment needs to be in order to ensure that the bias is less than a specified criterion. Finally, we show how a modified plug-in estimate of the entropy can be used for bias correction.

The activity of cortical neurons in sensory areas covaries with perceptual decisions, a relationship that is often quantified by choice probabilities. Although choice probabilities have been measured extensively, their interpretation has remained fraught with difficulty. We derive the mathematical relationship between choice probabilities, read-out weights and correlated variability in the standard neural decision-making model. Our solution allowed us to prove and generalize earlier observations on the basis of numerical simulations and to derive new predictions. Notably, our results indicate how the read-out weight profile, or decoding strategy, can be inferred from experimentally measurable quantities. Furthermore, we developed a test to decide whether the decoding weights of individual neurons are optimal for the task, even without knowing the underlying correlations. We confirmed the practicality of our approach using simulated data from a realistic population model. Thus, our findings provide a theoretical foundation for a growing body of experimental results on choice probabilities and correlations.

We explored the manner in which spatial information is encoded by retinal ganglion cell populations. We flashed a set of 36 shape stimuli onto the tiger salamander retina and used different decoding algorithms to read out information from a population of 162 ganglion cells. We compared the discrimination performance of linear decoders, which ignore correlation induced by common stimulation, with nonlinear decoders, which can accurately model these correlations. Similar to previous studies, decoders that ignored correlation suffered only a modest drop in discrimination performance for groups of up to ∼30 cells. However, for more realistic groups of 100+ cells, we found order-of-magnitude differences in the error rate. We also compared decoders that used only the presence of a single spike from each cell with more complex decoders that included information from multiple spike counts and multiple time bins. More complex decoders substantially outperformed simpler decoders, showing the importance of spike timing information. Particularly effective was the first spike latency representation, which allowed zero discrimination errors for the majority of shape stimuli. Furthermore, the performance of nonlinear decoders showed even greater enhancement compared with linear decoders for these complex representations. Finally, decoders that approximated the correlation structure in the population by matching all pairwise correlations with a maximum entropy model fit to all 162 neurons were quite successful, especially for the spike latency representation. Together, these results suggest a picture in which linear decoders allow a coarse categorization of shape stimuli, whereas nonlinear decoders, which take advantage of both correlation and spike timing, are needed to achieve high-fidelity discrimination.

Ongoing advances in experimental technique are making commonplace simultaneous recordings of the activity of tens to hundreds of cortical neurons at high temporal resolution. Latent population models, including Gaussian-process factor analysis and hidden linear dynamical system (LDS) models, have proven effective at capturing the statistical structure of such data sets. They can be estimated efficiently, yield useful visualisations of population activity, and are also integral building-blocks of decoding algorithms for brain-machine interfaces (BMI). One practical challenge, particularly to LDS models, is that when parameters are learned using realistic volumes of data the resulting models often fail to reflect the true temporal continuity of the dynamics; and indeed may describe a biologically-implausible unstable population dynamic that is, it may predict neural activity that grows without bound. We propose a method for learning LDS models based on expectation maximisation that constrains parameters to yield stable systems and at the same time promotes capture of temporal structure by appropriate regularisation. We show that when only little training data is available our method yields LDS parameter estimates which provide a substantially better statistical description of the data than alternatives, whilst guaranteeing stable dynamics. We demonstrate our methods using both synthetic data and extracellular multi-electrode recordings from motor cortex.

A striking feature of cortical organization is that the encoding of many stimulus features, for example orientation or direction selectivity, is arranged into topographic maps. Functional imaging methods such as optical imaging of intrinsic signals, voltage sensitive dye imaging or functional magnetic resonance imaging are important tools for studying the structure of cortical maps. As functional imaging measurements are usually noisy, statistical processing of the data is necessary to extract maps from the imaging data. We here present a probabilistic model of functional imaging data based on Gaussian processes. In comparison to conventional approaches, our model yields superior estimates of cortical maps from smaller amounts of data. In addition, we obtain quantitative uncertainty estimates, i.e. error bars on properties of the estimated map. We use our probabilistic model to study the coding properties of the map and the role of noise-correlations by decoding the stimulus from single trials of an imaging experiment.

Introduction State space models for neural population spike trains Neural computations at all scales of evolutionary and behavioural complexity are carried out by recurrently connected networks of neurons that communicate with each other, with neurons elsewhere in the brain, and with muscles through the firing of action potentials or “spikes.” To understand how nervous tissue computes, it is therefore necessary to understand how the spiking of neurons is shaped both by inputs to the network and by the recurrent action of existing network activity. Whereas most historical spike data were collected one neuron at a time, new techniques including silicon multielectrode array recording and scanning 2-photon, light-sheet or light-field fluorescence calcium imaging increasingly make it possible to record spikes from dozens, hundreds and potentially thousands of individual neurons simultaneously. These new data offer unprecedented empirical access to network computation, promising breakthroughs both in our understanding of neural coding and computation (Stevenson & Kording 2011), and our ability to build prosthetic neural interfaces (Santhanam et al . 2006). Fulfillment of this promise will require powerful methods for data modeling and analysis, able to capture the structure of statistical dependence of network activity across neurons and time. Probabilistic latent state space models (SSMs) are particularly well-suited to this task. Neural activity often appears stochastic, in that repeated trials under the same controlled experimental conditions can evoke quite different patterns of firing. Some part of this variation may reflect differences in the way the computation unfolds on each trial. Another part might reflect noisy creation and transmission of neural signals. Yet more may come from chaotic amplification of small perturbations. As computational signals are thought to be distributed across the population (in a “population code”), variation in the computation may be distinguished by its common impact on different neurons and the systematic evolution of these common effects in time. An SSM is able to capture such structured variation through the evolution of its latent state trajectory. This latent state provides a summary description of all factors modulating neural activity that are not observed directly. These factors could include processes such as arousal, attention, cortical state (Harris & Thiele 2011) or behavioural states of the animal (Niell & Stryker 2010; Maimon 2011).

Bayesian analysis of electrophysiological data refers to the statistical processing of data obtained in electrophysiological experiments (i.e., recordings of action potentials or voltage measurements with electrodes or imaging devices) which utilize methods from Bayesian statistics. Bayesian statistics is a framework for describing and modelling empirical data using the mathematical language of probability to model uncertainty. Bayesian statistics provides a principled and flexible framework for combining empirical observations with prior knowledge and for quantifying uncertainty. These features are especially useful for analysis questions in which the dataset sizes are small in comparison to the complexity of the model, which is often the case in neurophysiological data analysis.

Highlights • Neural population codes are organized at multiple spatial scales. • Microscopic organization of neural codes reveals a key role of neural heterogeneity. • Microscopic and population dynamics interact to make processing state-dependent. • Additional computational analyses of neural activity across resolutions are needed., Behavior relies on the distributed and coordinated activity of neural populations. Population activity can be measured using multi-neuron recordings and neuroimaging. Neural recordings reveal how the heterogeneity, sparseness, timing, and correlation of population activity shape information processing in local networks, whereas neuroimaging shows how long-range coupling and brain states impact on local activity and perception. To obtain an integrated perspective on neural information processing we need to combine knowledge from both levels of investigation. We review recent progress of how neural recordings, neuroimaging, and computational approaches begin to elucidate how interactions between local neural population activity and large-scale dynamics shape the structure and coding capacity of local information representations, make them state-dependent, and control distributed populations that collectively shape behavior.

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease with substantial heterogeneity in its clinical presentation. This makes diagnosis and effective treatment difficult, so better tools for estimating disease progression are needed. Here, we report results from the DREAM-Phil Bowen ALS Prediction Prize4Life challenge. In this crowdsourcing competition, competitors developed algorithms for the prediction of disease progression of 1,822 ALS patients from standardized, anonymized phase 2/3 clinical trials. The two best algorithms outperformed a method designed by the challenge organizers as well as predictions by ALS clinicians. We estimate that using both winning algorithms in future trial designs could reduce the required number of patients by at least 20%. The DREAM-Phil Bowen ALS Prediction Prize4Life challenge also identified several potential nonstandard predictors of disease progression including uric acid, creatinine and surprisingly, blood pressure, shedding light on ALS pathobiology. This analysis reveals the potential of a crowdsourcing competition that uses clinical trial data for accelerating ALS research and development.

In the perceptual sciences, experimenters study the causal mechanisms of perceptual systems by probing observers with carefully constructed stimuli. It has long been known, however, that perceptual decisions are not only determined by the stimulus, but also by internal factors. Internal factors could lead to a statistical influence of previous stimuli and responses on the current trial, resulting in serial dependencies, which complicate the causal inference between stimulus and response. However, the majority of studies do not take serial dependencies into account, and it has been unclear how strongly they influence perceptual decisions. We hypothesize that one reason for this neglect is that there has been no reliable tool to quantify them and to correct for their effects. Here we develop a statistical method to detect, estimate, and correct for serial dependencies in behavioral data. We show that even trained psychophysical observers suffer from strong history dependence. A substantial fraction of the decision variance on difficult stimuli was independent of the stimulus but dependent on experimental history. We discuss the strong dependence of perceptual decisions on internal factors and its implications for correct data interpretation.

Imaging Science and Biomedical Engineering, University ofManchester, Manchester M13 9PL, UKSummaryfMRI, one of the most important noninvasive brain imagingmethods, relies on the blood oxygen level-dependent(BOLD) signal, whose precise underpinnings are still notfully understood [1]. It is a widespread assumption that thecomponents of the hemodynamic response function (HRF)are fixed relative to each other in time, leading most studiesas well as analysis tools to focus on trial-averaged re-sponses, thus using or estimating a condition- or location-specific ‘‘canonical HRF’’ [2–4]. In the current study, weexamined the nature of the variability of the BOLD responseand asked in particular whether the positive BOLD peak issubject to trial-to-trial temporal jitter. Our results showthat the positive peak of the stimulus-evoked BOLD signalexhibits a trial-to-trial temporal jitter on the order ofseconds. Moreover, the trial-to-trial variability can be ex-ploited to uncover the initial dip in the majority of voxelsby pooling trial responses with large peak latencies. Initialdips exposed by this procedure possess higher spatial res-olution compared to the positive BOLD signal in the humanvisual cortex. These findings allow for the reliable observa-tion of fMRI signals that are physiologically closer to neuralactivity, leading to improvements in both temporal andspatial resolution.ResultsTrial-to-Trial Temporal Jitter of the BOLD Positive PeakInthefirst experiment, weinvestigated thetrial-to-trial tempo-ral variability of the positive blood oxygen level-dependent(BOLD)peakinthehumanvisualcortexusinganevent-relatedvisual stimulation paradigm with long poststimulus periods. Apolar-transformed checkerboard (width: 18 degrees visualangle, duration: 4 s; Figure 1A) was presented centrally withrandomizedinterstimulusintervalsof40–46stoobtainvisuallyevoked fMRI BOLD responses compared to baseline (seeExperimental Procedures). In order to quantify the latency ofthe peak of the positive BOLD response for a given trial, wedefined it as thetime of the highest BOLD signal of the tempo-rally smoothed and detrended BOLD time course relative tostimulus onset. Figure 1B plots the standard deviation of thedetectedpeaklatenciesinrelationtothewidthoftheGaussiankernel used for temporal smoothing. Hereafter, we use theGaussian kernel width value of 3.8 s that resulted in the small-est trial-to-trial variability of positive peak latencies, whichnevertheless amounted to a considerable 4.1 s SD. Figure 1Cshows trial-by-trial response time courses of a single voxel,sorted by positive BOLD signal peak latencies. Also, here thepeak latency of the BOLD response varied in the range ofseveral seconds. This was typical for most visually responsivevoxels and can be quantified by the SD of the peak times thatranged between 2 and 5 s. (For further analysis showing evi-dence that the BOLD temporal jitter has a biological origin,see Figure S1 available online.)The Jitter-Uncovered Initial DipWhen single-trial responses of BOLD signal were sortedaccording to their positive peak latency, we saw two negativeresponse components that are independent of the temporalshiftofthepositiveBOLDsignal.Figure2Ashowsaveragedre-sponses,pooledfromtrialswithdifferentpeaklatencyranges.Eachcurvecontainsdatafromthesamesetofvoxels,butfromdifferent trials, revealing two response properties. First theso-called initial dip, i.e., the early negative component of theBOLD response, is clearly visible in trials with long peaklatencies (hereafter termed the ‘‘jitter-uncovered initial dip’’).Second,asharppostresponseundershootbecomesapparentin trials with short peak latencies. Interestingly, both proper-ties are cancelled out in the average response across all trials(black line in Figure 2A). The same procedure, applied to dataof asingle voxel, isillustrated in Figure 2B.Although thisvoxeldoesnotshowtheinitialdipwhenalltrialsareaveraged,itcanbe detected when only the 50% of trials with late BOLD peakare considered.In the following, we examine the fundamental properties ofthe jitter-uncovered initial dip in voxelwise analyses in whichwe relate its magnitude to that of the conventional initial dip,to the positive peak amplitude, and to the positive peaklatency, using data obtained from the first human experiment.Scatterplots of the magnitudes of dips detected convention-ally (all-trial average) or using jitter analysis are shown for arepresentative subject in Figure 2C. Results show that themagnitude of the jitter-uncovered initial dip was on averagelargerthanthatoftheconventionalinitialdip,whichwassignif-icant for every subject (pairwise t test; p < 1.0 3 10

The activity of cortical neurons in sensory areas covaries with perceptual decisions, a relationship often quantified by choice probabilities. While choice probabilities have been measured extensively, their interpretation has remained fraught with difficulty. Here, we derive the mathematical relationship between choice probabilities, read-out weights and noise correlations within the standard neural decision making model. Our solution allows us to prove and generalize earlier observations based on numerical simulations, and to derive novel predictions. Importantly, we show how the read-out weight profile, or decoding strategy, can be inferred from experimentally measurable quantities. Furthermore, we present a test to decide whether the decoding weights of individual neurons are optimal, even without knowing the underlying noise correlations. We confirm the practical feasibility of our approach using simulated data from a realistic population model. Our work thus provides the theoretical foundation for a growing body of experimental results on choice probabilities and correlations.

Modern recording techniques such as multi-electrode arrays and two-photon imaging methods are capable of simultaneously monitoring the activity of large neuronal ensembles at single cell resolution. These methods finally give us the means to address some of the most crucial questions in systems neuroscience: what are the dynamics of neural population activity? How do populations of neurons perform computations? What is the functional organization of neural ensembles? While the wealth of new experimental data generated by these techniques provides exciting opportunities to test ideas about how neural ensembles operate, it also provides major challenges: multi-cell recordings necessarily yield data which is high-dimensional in nature. Understanding this kind of data requires powerful statistical techniques for capturing the structure of the neural population responses, as well as their relationship with external stimuli or behavioral observations. Furthermore, linking recorded neural population activity to the predictions of theoretical models of population coding has turned out not to be straightforward. These challenges motivated us to organize a workshop at the 2009 Computational Neuroscience Meeting in Berlin to discuss these issues. In order to collect some of the recent progress in this field, and to foster discussion on the most important directions and most pressing questions, we issued a call for papers for this Research Topic. We asked authors to address the following four questions: What classes of statistical methods are most useful for modeling population activity? What are the main limitations of current approaches, and what can be done to overcome them? How can statistical methods be used to empirically test existing models of (probabilistic) population coding? What role can statistical methods play in formulating novel hypotheses about the principles of information processing in neural populations? A total of 15 papers addressing questions related to these themes are now collected in this Research Topic. Three of these articles have resulted in “Focused reviews” in Frontiers in Neuroscience (Crumiller et al., 2011; Rosenbaum et al., 2011; Tchumatchenko et al., 2011), illustrating the great interest in the topic. Many of the articles are devoted to a better understanding of how correlations arise in neural circuits, and how they can be detected, modeled, and interpreted. For example, by modeling how pairwise correlations are transformed by spiking non-linearities in simple neural circuits, Tchumatchenko et al. (2010) show that pairwise correlation coefficients have to be interpreted with care, since their magnitude can depend strongly on the temporal statistics of their input-correlations. In a similar spirit, Rosenbaum et al. (2010) study how correlations can arise and accumulate in feed-forward circuits as a result of pooling of correlated inputs. Lyamzin et al. (2010) and Krumin et al. (2010) present methods for simulating correlated population activity and extend previous work to more general settings. The method of Lyamzin et al. (2010) allows one to generate synthetic spike trains which match commonly reported statistical properties, such as time varying firing rates as well signal and noise correlations. The Hawkes framework presented by Krumin et al. (2010) allows one to fit models of recurrent population activity to the correlation-structure of experimental data. Louis et al. (2010) present a novel method for generating surrogate spike trains which can be useful when trying to assess the significance and time-scale of correlations in neural spike trains. Finally, Pipa and Munk (2011) study spike synchronization in prefrontal cortex during working memory. A number of studies are also devoted to advancing our methodological toolkit for analyzing various aspects of population activity (Gerwinn et al., 2010; Machens, 2010; Staude et al., 2010; Yu et al., 2010). For example, Gerwinn et al. (2010) explain how full probabilistic inference can be performed in the popular model class of generalized linear models (GLMs), and study the effect of using prior distributions on the parameters of the stimulus and coupling filters. Staude et al. (2010) extend a method for detecting higher-order correlations between neurons via population spike counts to non-stationary settings. Yu et al. (2010) describe a new technique for estimating the information rate of a population of neurons using frequency-domain methods. Machens (2010) introduces a novel extension of principal component analysis for separating the variability of a neural response into different sources. Focusing less on the spike responses of neural populations but on aggregate signals of population activity, Boatman-Reich et al. (2010) and Hoerzer et al. (2010) describe methods for a quantitative analysis of field potential recordings. While Boatman-Reich et al. (2010) discuss a number of existing techniques in a unified framework and highlight the potential pitfalls associated with such approaches, Hoerzer et al. (2010) demonstrate how multivariate autoregressive models and the concept of Granger causality can be used to infer local functional connectivity in area V4 of behaving macaques. A final group of studies is devoted to understanding experimental data in light of computational models (Galan et al., 2010; Pandarinath et al., 2010; Shteingart et al., 2010). Pandarinath et al. (2010) present a novel mechanism that may explain how neural networks in the retina switch from one state to another by a change in gap junction coupling, and conjecture that this mechanism might also be found in other neural circuits. Galan et al. (2010) present a model of how hypoxia may change the network structure in the respiratory networks in the brainstem, and analyze neural correlations in multi-electrode recordings in light of this model. Finally, Shteingart et al. (2010) show that the spontaneous activation sequences they find in cultured networks cannot be explained by Zipf's law, but rather require a wrestling model. The papers of this Research Topic thus span a wide range of topics in the statistical modeling of multi-cell recordings. Together with other recent advances, they provide us with a useful toolkit to tackle the challenges presented by the vast amount of data collected with modern recording techniques. The impact of novel statistical methods on the field and their potential to generate scientific progress, however, depends critically on how readily they can be adopted and applied by laboratories and researchers working with experimental data. An important step toward this goal is to also publish computer code along with the articles (Barnes, 2010) as a successful implementation of advanced methods also relies on many details which are hard to communicate in the article itself. In this way it becomes much more likely that other researchers can actually use the methods, and unnecessary re-implementations can be avoided. Some of the papers in this Research Topic already follow this goal (Gerwinn et al., 2010; Louis et al., 2010; Lyamzin et al., 2010). We hope that this practice becomes more and more common in the future and encourage authors and editors of Research Topics to make as much code available as possible, ideally in a format that can be easily integrated with existing software sharing initiatives (Herz et al., 2008; Goldberg et al., 2009).