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Animals make decisions under the principle of reward value maximization and surprise minimization. It is still unclear how these principles are represented in the brain and are reflected in behavior. We addressed this question using a closed-loop virtual reality system to train adult zebrafish for active avoidance. Analysis of the neural activity of the dorsal pallium during training revealed neural ensembles assigning rules to the colors of the surrounding walls. Additionally, one third of fish generated another ensemble that becomes activated only when the real perceived scenery shows discrepancy from the predicted favorable scenery. The fish with the latter ensemble escape more efficiently than the fish with the former ensembles alone, even though both fish have successfully learned to escape, consistent with the hypothesis that the latter ensemble guides zebrafish to take action to minimize this prediction error. Our results suggest that zebrafish can use both principles of goal-directed behavior, but with different behavioral consequences depending on the repertoire of the adopted principles., Using a closed-loop virtual reality system for fish, the authors show that zebrafish are capable of assigning rules to the scenery they see, and of generating a state prediction error by comparing reality with a prediction derived from an internal model.

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system’s temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system’s correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes., Many mean-field theories are proposed for studying the non-equilibrium dynamics of complex systems, each based on specific assumptions about the system’s temporal evolution. Here, Aguilera et al. propose a unified framework for mean-field theories of asymmetric kinetic Ising systems to study non-equilibrium dynamics.

A data-driven bin-width optimization for the histograms of measured data sets based on inhomogeneous Poisson processes was developed in a neurophysiology study [Shimazaki & Shinomoto (2007). Neural Comput. 19, 1503–1527], and a subsequent study [Muto, Sakamoto, Matsuura, Arima & Okada (2019). J. Phys. Soc. Jpn, 88, 044002] proposed its application to inelastic neutron scattering (INS) data. In the present study, the results of the method on experimental INS time-of-flight data collected under different measurement conditions from a copper single crystal are validated. The extrapolation of the statistics on a given data set to other data sets with different total counts precisely infers the optimal bin widths on the latter. The histograms with the optimized bin widths statistically verify two fine-spectral-feature examples in the energy and momentum transfer cross sections: (i) the existence of phonon band gaps; and (ii) the number of plural phonon branches located close to each other. This indicates that the applied method helps in the efficient and rigorous observation of spectral structures important in physics and materials science like novel forms of magnetic excitation and phonon states correlated to thermal conductivities.

Many physical and biological dynamical systems operate away from thermodynamic equilibrium, driven by their own activity as well as their interaction with the environment. The kinetic Ising model is a prototypical model for studying such non-equilibrium dynamics. Since its behaviour is generally intractable for large sizes due to combinatorial explosion, mean field theories are often employed to approximate network dynamics. However, mean field methods are often unable to capture systems displaying long-range correlations such as those operating near critical phase transitions. To tackle this problem, different variants of mean field approximations have been proposed for kinetic Ising models, each making unique assumptions about the correlation structure of the system. This disparity complicates the challenge of systematically advancing beyond previous contributions. Here, using information geometry, we propose that existing methods can be described and extended in a unified framework. Our method is defined as a family of expansions (called Plefka expansions) of an intractable marginal probability distribution around a specific point of a simplified model, defined in an information geometric space. These points are obtained by an orthogonal projection to a sub-manifold of probability distributions displaying a simplified correlation structure. This approach not only unifies previous methods but allows us to define novel methods that make unusual assumptions for mean field methods, like models preserving specific correlations of the system. By comparing analytic approximations and exact numerical simulations in a kinetic Sherrington Kirkpatrick model, we show that the new approximations found by our method provide more accurate estimates of the dynamics of the systems than classical equations, even near critical phase transitions presenting large fluctuations. In sum, our framework unifies and extends existing mean field methods in the kinetic Ising model from an information theoretic view, constituting a powerful tool for studying the dynamics of complex systems.

Stimulus information and cognitive states of an animal are represented by correlated population activity of neurons. The maximum entropy method provides a principled way to describe the correlated population activity using much less parameters than the number of possible activity patterns. This method successfully explained stationary spiking activity of neural populations such as in vitro retinal ganglion cells. Modeling activity of cortical circuitries in vivo, however, has been challenging because both the spike rates and interactions among neurons can change according to sensory stimulation, behavior, or an internal state of the brain. To capture the non-stationary interactions among neurons, we augmented the maximum entropy model (Ising model) using a state-space modeling framework, which we call the state-space Ising model. We will demonstrate that applications of the state-space Ising model to activity of cortical neurons reveal dynamic neural interactions, and how they contribute to sparseness and fluctuation of the population activity as well as stimulus coding.

This work considers a class of canonical neural networks comprising rate coding models, wherein neural activity and plasticity minimise a common cost function—and plasticity is modulated with a certain delay. We show that such neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Mathematical analyses demonstrate that this biological optimisation can be cast as maximisation of model evidence, or equivalently minimisation of variational free energy, under the well-known form of a partially observed Markov decision process model. This equivalence indicates that the delayed modulation of Hebbian plasticity—accompanied with adaptation of firing thresholds—is a sufficient neuronal substrate to attain Bayes optimal inference and control. We corroborated this proposition using numerical analyses of maze tasks. This theory offers a universal characterisation of canonical neural networks in terms of Bayesian belief updating and provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control., Takuya Isomura, Hideaki Shimazaki and Karl Friston perform mathematical analysis to show that neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Their work provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control.

The noisy threshold regime, where even a small set of presynaptic neurons can significantly affect postsynaptic spike-timing, is suggested as a key requisite for computation in neurons with high variability. It also has been proposed that signals under the noisy conditions are successfully transferred by a few strong synapses and/or by an assembly of nearly synchronous synaptic activities. We analytically investigate the impact of a transient signaling input on a leaky integrate-and-fire postsynaptic neuron that receives background noise near the threshold regime. The signaling input models a single strong synapse or a set of synchronous synapses, while the background noise represents a lot of weak synapses. We find an analytic solution that explains how the first-passage time (ISI) density is changed by transient signaling input. The analysis allows us to connect properties of the signaling input like spike timing and amplitude with postsynaptic first-passage time density in a noisy environment. Based on the analytic solution, we calculate the Fisher information with respect to the signaling input's amplitude. For a wide range of amplitudes, we observe a non-monotonic behavior for the Fisher information as a function of background noise. Moreover, Fisher information non-trivially depends on the signaling input's amplitude; changing the amplitude, we observe one maximum in the high level of the background noise. The single maximum splits into two maximums in the low noise regime. This finding demonstrates the benefit of the analytic solution in investigating signal transfer by neurons.

We advocate cooperative intelligence (CI) that achieves its goals in cooperating with other agents, particularly human beings, with limited resources but in complex and dynamic environments. CI is important because it delivers better performances in achieving a broad range of tasks; furthermore, cooperativeness is key to human intelligence, and the processes of cooperation can contribute to help people gain several life values. This paper discusses elements in CI and our research approach to CI. We identify the four aspects of CI: adaptive intelligence, collective intelligence, coordinative intelligence, and collaborative intelligence. We also take an approach that focuses on the implementation of coordinative intelligence in the form of personal partner agents (PPAs) and consider the design of our robotic research platform to physically realize PPAs.

SummaryHuman predicts future. To ask if fish also has this capacity, we established the virtual reality training system with live imaging of the telencephalic neurons of adult zebrafish in the active avoidance and found that, at the onset of the trial, learned fish conceives two future conditions as the favorable status on its way to the safe goal, i.e. one with the backwardly moving landscape and the other with the color of the safe goal. And the two different neural ensembles monitor the discrepancy between these predictions and the perceived real external status. Once fish reaches the goal, another ensemble is set to work to monitor whether fish keeps staying in the safe goal. The manipulation to artificially enhance these prediction errors elevated the activities of these ensembles and induced fish to behave to correct errors, revealing that fish sets behavioral strategy to actively realize these predictions.

When animals encounter conflict they initiate and escalate aggression to establish and maintain a social hierarchy. The neural mechanisms by which animals resolve fighting behaviors to determine such social hierarchies remain unknown. We identified two subregions of the dorsal habenula (dHb) in zebrafish that antagonistically regulate the outcome of conflict. The losing experience reduced neural transmission in the lateral subregion of dHb (dHbL)-dorsal/intermediate interpeduncular nucleus (d/iIPN) circuit. Silencing of the dHbL or medial subregion of dHb (dHbM) caused a stronger predisposition to lose or win a fight, respectively. These results demonstrate that the dHbL and dHbM comprise a dual control system for conflict resolution of social aggression.

Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific interactions among the binary elements. To extract the dominant correlation structures and their contributions to generating data in a time-dependent manner, we model the dynamics of binary patterns using the state-space model of an Ising-type network that is composed of multiple undirected graphs. We provide a sequential Bayes algorithm to estimate the dynamics of weights on the graphs while gaining the graph structures online. This model can uncover overlapping graphs underlying the data better than a traditional orthogonal decomposition method, and outperforms an original time-dependent Ising model. We assess the performance of the method by simulated data, and demonstrate that spontaneous activity of cultured hippocampal neurons is represented by dynamics of multiple graphs., Comment: 8 pages, 4 figures v2: IJCNN 2019, results unchanged

How do organisms recognize their environment by acquiring knowledge about the world, and what actions do they take based on this knowledge? This article examines hypotheses about organisms' adaptation to the environment from machine learning, information-theoretic, and thermodynamic perspectives. We start with constructing a hierarchical model of the world as an internal model in the brain, and review standard machine learning methods to infer causes by approximately learning the model under the maximum likelihood principle. This in turn provides an overview of the free energy principle for an organism, a hypothesis to explain perception and action from the principle of least surprise. Treating this statistical learning as communication between the world and brain, learning is interpreted as a process to maximize information about the world. We investigate how the classical theories of perception such as the infomax principle relates to learning the hierarchical model. We then present an approach to the recognition and learning based on thermodynamics, showing that adaptation by causal learning results in the second law of thermodynamics whereas inference dynamics that fuses observation with prior knowledge forms a thermodynamic process. These provide a unified view on the adaptation of organisms to the environment., Comment: 22 pages, 6 figures

Identifying network architecture from recorded neural activity is one of the major challenges in neuroscience. A key requirement for this challenge is the knowledge of the statistical input-output relation of single neurons operating under in vivo conditions. However, lack of analytical representation even for a standard neuron model prohibited theoretical investigations. Recently we provided an exact analytical solution of spike timing for a leaky integrate-and-fire (LIF) neuron responding to synaptic inputs under noisy background input balanced near the threshold [Shomali et. al., J Comput Neurosci 44, (2018): 147]. Using that solution, we construct a unified framework that links synaptic inputs, nonlinearity of spiking, network architecture, and statistics of population activity. With this approach, we theoretically predict correlated population activity of in vivo neurons that receive common inputs under different network architectures. It allows us to present a quantitative method to unveil the network architecture behind the sparse population activity ubiquitously observed in visual and hippocampal neurons. We show that two motifs can disclose this activity: Inhibitory common inputs to three (or more) neurons or excitatory common inputs to pairs of neurons. By comparing model prediction with empirical observation of monkey V1 neurons [Ohiorhenuan et. al., Nature 466, (2010): 617], we quantitatively rule out the scenario that common inhibition causes the observed sparse activity characterized by negative triple-wise interactions among the neurons. Instead, we show that an alternative architecture with common excitatory inputs to pairs of neurons well explains it. The proposed analytical approach that connects neural mechanisms with neural interactions could serve as a useful tool to probe network architecture, using recordings of population activity.

This chapter presents a hypothesis that the animal’s brain is acting analogously to a heat engine when it actively modulates incoming sensory information to achieve enhanced perceptual capacity. To articulate this hypothesis, we describe stimulus-evoked activity of a neural population based on the maximum entropy principle with constraints on two types of overlapping activities, one that is controlled by stimulus conditions and the other, termed internal activity, that is regulated internally in an organism. We demonstrate that modulation of the internal activity realizes gain control of stimulus response, and controls stimulus information. The model’s statistical structure common to thermodynamics allows us to construct the first law for neural dynamics, equation of state, and fluctuation-response relation. A cycle of neural dynamics is then introduced to model information processing by the neurons during which the stimulus information is dynamically enhanced by the internal gain-modulation mechanism. Based on the conservation law of entropy, we demonstrate that the cycle generates entropy ascribed to the stimulus-related activity using entropy supplied by the internal mechanism, analogously to a heat engine that produces work from heat. We provide an efficient cycle that achieves the highest entropic efficiency to retain the stimulus information. The theory allows us to quantify efficiency of the internal computation and its theoretical limit, which can be used to test the hypothesis.

We show that dynamical gain modulation of neurons' stimulus response is described as an information-theoretic cycle that generates entropy associated with the stimulus-related activity from entropy produced by the modulation. To articulate this theory, we describe stimulus-evoked activity of a neural population based on the maximum entropy principle with constraints on two types of overlapping activities, one that is controlled by stimulus conditions and the other, termed internal activity, that is regulated internally in an organism. We demonstrate that modulation of the internal activity realises gain control of stimulus response, and controls stimulus information. A cycle of neural dynamics is then introduced to model information processing by the neurons during which the stimulus information is dynamically enhanced by the internal gain-modulation mechanism. Based on the conservation law for entropy production, we demonstrate that the cycle generates entropy ascribed to the stimulus-related activity using entropy supplied by the internal mechanism, analogously to a heat engine that produces work from heat. We provide an efficient cycle that achieves the highest entropic efficiency to retain the stimulus information. The theory allows us to quantify efficiency of the internal computation and its theoretical limit.

In this study, we analyzed the activity of monkey V1 neurons responding to grating stimuli of different orientations using inference methods for a time-dependent Ising model. The method provides optimal estimation of time-dependent neural interactions with credible intervals according to the sequential Bayes estimation algorithm. Furthermore, it allows us to trace dynamics of macroscopic network properties such as entropy, sparseness, and fluctuation. Here we report that, in all examined stimulus conditions, pairwise interactions contribute to increasing sparseness and fluctuation. We then demonstrate that the orientation of the grating stimulus is in part encoded in the pairwise interactions of the neural populations. These results demonstrate the utility of the state-space Ising model in assessing contributions of neural interactions during stimulus processing.

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm., National Science Foundation (U.S.) (Grant DMS-1127914), National Institute of Mental Health (U.S.) (Grant MH064537)

Natural scenes contain higher-order statistical structures that can be encoded in their spatial phase information. Nevertheless, little progress has been made in modeling phase information of images, and understanding efficient representation of the image phases in the brain. In order to capture spatial phase structure under the efficient coding hypothesis, here we introduce a generative model of natural scenes by assuming independent source signals in a complex domain and non-uniform phase priors for the complex signals. Parameters of the proposed model are then estimated under the maximum-likelihood principle. This approach extends existing methods of independent component analysis for complex-valued signals to the one that utilizes phase information. Using simulated data, we demonstrate that the proposed model outperforms conventional models with a uniform phase prior in blind source separation of complex-valued signals. We then apply the proposed model to natural scenes in the Fourier domain. Real and imaginary parts of the learned complex features exhibit a pair of Gabor-like filters in quadratic phase structure with a similar shape. The proposed model significantly improved the goodness-of-the-fit from the model with a uniform phase prior, indicating that the structured spatial phases are important for removing redundancy in natural scenes. These results predict the presence of phase sensitive complex cells in the visual cortex.

Kernel smoother and a time-histogram are classical tools for estimating an instantaneous rate of spike occurrences. We recently established a method for selecting the bin width of the time-histogram, based on the principle of minimizing the mean integrated square error (MISE) between the estimated rate and unknown underlying rate. Here we apply the same optimization principle to the kernel density estimation in selecting the width or “bandwidth” of the kernel, and further extend the algorithm to allow a variable bandwidth, in conformity with data. The variable kernel has the potential to accurately grasp non-stationary phenomena, such as abrupt changes in the firing rate, which we often encounter in neuroscience. In order to avoid possible overfitting that may take place due to excessive freedom, we introduced a stiffness constant for bandwidth variability. Our method automatically adjusts the stiffness constant, thereby adapting to the entire set of spike data. It is revealed that the classical kernel smoother may exhibit goodness-of-fit comparable to, or even better than, that of modern sophisticated rate estimation methods, provided that the bandwidth is selected properly for a given set of spike data, according to the optimization methods presented here.

The architectonic subdivisions of the brain are believed to be functional modules, each processing parts of global functions. Previously, we showed that neurons in different regions operate in different firing regimes in monkeys. It is possible that firing regimes reflect differences in underlying information processing, and consequently the firing regimes in homologous regions across animal species might be similar. We analyzed neuronal spike trains recorded from behaving mice, rats, cats, and monkeys. The firing regularity differed systematically, with differences across regions in one species being greater than the differences in similar areas across species. Neuronal firing was consistently most regular in motor areas, nearly random in visual and prefrontal/medial prefrontal cortical areas, and bursting in the hippocampus in all animals examined. This suggests that firing regularity (or irregularity) plays a key role in neural computation in each functional subdivision, depending on the types of information being carried.SIGNIFICANCE STATEMENTBy analyzing neuronal spike trains recorded from mice, rats, cats, and monkeys, we found that different brain regions have intrinsically different firing regimes that are more similar in homologous areas across species than across areas in one species. Because different regions in the brain are specialized for different functions, the present finding suggests that the different activity regimes of neurons are important for supporting different functions, so that appropriate neuronal codes can be used for different modalities.

Activity patterns of neural population are constrained by underlying biological mechanisms. These patterns are characterized not only by individual activity rates and pairwise correlations but also by statistical dependencies among groups of neurons larger than two, known as higher-order interactions (HOIs). While HOIs are ubiquitous in neural activity, primary characteristics of HOIs remain unknown. Here, we report that simultaneous silence (SS) of neurons concisely summarizes neural HOIs. Spontaneously active neurons in cultured hippocampal slices express SS that is more frequent than predicted by their individual activity rates and pairwise correlations. The SS explains structured HOIs seen in the data, namely, alternating signs at successive interaction orders. Inhibitory neurons are necessary to maintain significant SS. The structured HOIs predicted by SS were observed in a simple neural population model characterized by spiking nonlinearity and correlated input. These results suggest that SS is a ubiquitous feature of HOIs that constrain neural activity patterns and can influence information processing.

Activity patterns of neural population are constrained by underlying biological mechanisms. These patterns are characterized not only by individual activity rates and pairwise correlations but also by statistical dependencies among groups of neurons larger than two, known as higher-order interactions (HOIs). While HOIs are ubiquitous in neural activity, primary characteristics of HOIs remain unknown. Here, we report that simultaneous silence (SS) of neurons concisely summarizes neural HOIs. Spontaneously active neurons in cultured hippocampal slices express SS that is more frequent than predicted by their individual activity rates and pairwise correlations. The SS explains structured HOIs seen in the data, namely, alternating signs at successive interaction orders. Inhibitory neurons are necessary to maintain significant SS. The structured HOIs predicted by SS were observed in a simple neural population model characterized by spiking nonlinearity and correlated input. These results suggest that SS is a ubiquitous feature of HOIs that constrain neural activity patterns and can influence information processing.

We develop an oscillator model of selective attention based on spread spectrum communication. Stimulus intensity and attention are differentially encoded in the time average of phase velocities of sender oscillators and their temporal structure respectively. Receiver oscillators are driven by a mixture of phase velocities of the sender oscillators. With the aid of top-down modulatory signals that do not change the mean rotational velocity of sender oscillators, our proposed communication scheme allows the receiver oscillators to selectively correlate their velocity with the attended stimulus.

Natural scenes contain richer perceptual information in their spatial phase structure than their amplitudes. Modeling phase structure of natural scenes may explain higher-order structure inherent to the natural scenes, which is neglected in most classical models of redundancy reduction. Only recently, a few models have represented images using a complex form of receptive fields (RFs) and analyze their complex responses in terms of amplitude and phase. However, these complex representation models often tacitly assume a uniform phase distribution without empirical support. The structure of spatial phase distributions of natural scenes in the form of relative contributions of paired responses of RFs in quadrature has not been explored statistically until now. Here, we investigate the spatial phase structure of natural scenes using complex forms of various Gabor-like RFs. To analyze distributions of the spatial phase responses, we constructed a mixture model that accounts for multi-modal circular distributions, and the EM algorithm for estimation of the model parameters. Based on the likelihood, we report presence of both uniform and structured bimodal phase distributions in natural scenes. The latter bimodal distributions were symmetric with two peaks separated by about 180°. Thus, the redundancy in the natural scenes can be further removed by using the bimodal phase distributions obtained from these RFs in the complex representation models. These results predict that both phase invariant and phase sensitive complex cells are required to represent the regularities of natural scenes in visual systems.