In order to cross a street without being run over, we need to be able to extract very fast hidden causes of dynamically changing multi-modal sensory stimuli, and to predict their future evolution. We show here that a generic cortical microcircuit motif, pyramidal cells with lateral excitation and inhibition, provides the basis for this difficult but all-important information processing capability. This capability emerges in the presence of noise automatically through effects of STDP on connections between pyramidal cells in Winner-Take-All circuits with lateral excitation. In fact, one can show that these motifs endow cortical microcircuits with functional properties of a hidden Markov model, a generic model for solving such tasks through probabilistic inference. Whereas in engineering applications this model is adapted to specific tasks through offline learning, we show here that a major portion of the functionality of hidden Markov models arises already from online applications of STDP, without any supervision or rewards. We demonstrate the emergent computing capabilities of the model through several computer simulations. The full power of hidden Markov model learning can be attained through reward-gated STDP. This is due to the fact that these mechanisms enable a rejection sampling approximation to theoretically optimal learning. We investigate the possible performance gain that can be achieved with this more accurate learning method for an artificial grammar task.
Author Summary
It has recently been shown that STDP installs in ensembles of pyramidal cells with lateral inhibition networks for Bayesian inference that are theoretically optimal for the case of stationary spike input patterns. We show here that if the experimentally found lateral excitatory connections between pyramidal cells are taken into account, theoretically optimal probabilistic models for the prediction of time-varying spike input patterns emerge through STDP. Furthermore a rigorous theoretical framework is established that explains the emergence of computational properties of this important motif of cortical microcircuits through learning. We show that the application of an idealized form of STDP approximates in this network motif a generic process for adapting a computational model to data: expectation-maximization. The versatility of computations carried out by these ensembles of pyramidal cells and the speed of the emergence of their computational properties through STDP is demonstrated through a variety of computer simulations. We show the ability of these networks to learn multiple input sequences through STDP and to reproduce the statistics of these inputs after learning.
doi:10.1371/journal.pcbi.1003511
PMCID: PMC3967926
PMID: 24675787
Experimental data from neuroscience suggest that a substantial amount of knowledge is stored in the brain in the form of probability distributions over network states and trajectories of network states. We provide a theoretical foundation for this hypothesis by showing that even very detailed models for cortical microcircuits, with data-based diverse nonlinear neurons and synapses, have a stationary distribution of network states and trajectories of network states to which they converge exponentially fast from any initial state. We demonstrate that this convergence holds in spite of the non-reversibility of the stochastic dynamics of cortical microcircuits. We further show that, in the presence of background network oscillations, separate stationary distributions emerge for different phases of the oscillation, in accordance with experimentally reported phase-specific codes. We complement these theoretical results by computer simulations that investigate resulting computation times for typical probabilistic inference tasks on these internally stored distributions, such as marginalization or marginal maximum-a-posteriori estimation. Furthermore, we show that the inherent stochastic dynamics of generic cortical microcircuits enables them to quickly generate approximate solutions to difficult constraint satisfaction problems, where stored knowledge and current inputs jointly constrain possible solutions. This provides a powerful new computing paradigm for networks of spiking neurons, that also throws new light on how networks of neurons in the brain could carry out complex computational tasks such as prediction, imagination, memory recall and problem solving.
Author Summary
The brain has not only the capability to process sensory input, but it can also produce predictions, imaginations, and solve problems that combine learned knowledge with information about a new scenario. But although these more complex information processing capabilities lie at the heart of human intelligence, we still do not know how they are organized and implemented in the brain. Numerous studies in cognitive science and neuroscience conclude that many of these processes involve probabilistic inference. This suggests that neuronal circuits in the brain process information in the form of probability distributions, but we are missing insight into how complex distributions could be represented and stored in large and diverse networks of neurons in the brain. We prove in this article that realistic cortical microcircuit models can store complex probabilistic knowledge by embodying probability distributions in their inherent stochastic dynamics – yielding a knowledge representation in which typical probabilistic inference problems such as marginalization become straightforward readout tasks. We show that in cortical microcircuit models such computations can be performed satisfactorily within a few . Furthermore, we demonstrate how internally stored distributions can be programmed in a simple manner to endow a neural circuit with powerful problem solving capabilities.
doi:10.1371/journal.pcbi.1003311
PMCID: PMC3828141
PMID: 24244126
The principles by which networks of neurons compute, and how spike-timing dependent plasticity (STDP) of synaptic weights generates and maintains their computational function, are unknown. Preceding work has shown that soft winner-take-all (WTA) circuits, where pyramidal neurons inhibit each other via interneurons, are a common motif of cortical microcircuits. We show through theoretical analysis and computer simulations that Bayesian computation is induced in these network motifs through STDP in combination with activity-dependent changes in the excitability of neurons. The fundamental components of this emergent Bayesian computation are priors that result from adaptation of neuronal excitability and implicit generative models for hidden causes that are created in the synaptic weights through STDP. In fact, a surprising result is that STDP is able to approximate a powerful principle for fitting such implicit generative models to high-dimensional spike inputs: Expectation Maximization. Our results suggest that the experimentally observed spontaneous activity and trial-to-trial variability of cortical neurons are essential features of their information processing capability, since their functional role is to represent probability distributions rather than static neural codes. Furthermore it suggests networks of Bayesian computation modules as a new model for distributed information processing in the cortex.
Author Summary
How do neurons learn to extract information from their inputs, and perform meaningful computations? Neurons receive inputs as continuous streams of action potentials or “spikes” that arrive at thousands of synapses. The strength of these synapses - the synaptic weight - undergoes constant modification. It has been demonstrated in numerous experiments that this modification depends on the temporal order of spikes in the pre- and postsynaptic neuron, a rule known as STDP, but it has remained unclear, how this contributes to higher level functions in neural network architectures. In this paper we show that STDP induces in a commonly found connectivity motif in the cortex - a winner-take-all (WTA) network - autonomous, self-organized learning of probabilistic models of the input. The resulting function of the neural circuit is Bayesian computation on the input spike trains. Such unsupervised learning has previously been studied extensively on an abstract, algorithmical level. We show that STDP approximates one of the most powerful learning methods in machine learning, Expectation-Maximization (EM). In a series of computer simulations we demonstrate that this enables STDP in WTA circuits to solve complex learning tasks, reaching a performance level that surpasses previous uses of spiking neural networks.
doi:10.1371/journal.pcbi.1003037
PMCID: PMC3636028
PMID: 23633941
The task of an organism to extract information about the external environment from sensory signals is based entirely on the analysis of ongoing afferent spike activity provided by the sense organs. We investigate the processing of auditory stimuli by an acoustic interneuron of insects. In contrast to most previous work we do this by using stimuli and neurophysiological recordings directly in the nocturnal tropical rainforest, where the insect communicates. Different from typical recordings in sound proof laboratories, strong environmental noise from multiple sound sources interferes with the perception of acoustic signals in these realistic scenarios. We apply a recently developed unsupervised machine learning algorithm based on probabilistic inference to find frequently occurring firing patterns in the response of the acoustic interneuron. We can thus ask how much information the central nervous system of the receiver can extract from bursts without ever being told which type and which variants of bursts are characteristic for particular stimuli. Our results show that the reliability of burst coding in the time domain is so high that identical stimuli lead to extremely similar spike pattern responses, even for different preparations on different dates, and even if one of the preparations is recorded outdoors and the other one in the sound proof lab. Simultaneous recordings in two preparations exposed to the same acoustic environment reveal that characteristics of burst patterns are largely preserved among individuals of the same species. Our study shows that burst coding can provide a reliable mechanism for acoustic insects to classify and discriminate signals under very noisy real-world conditions. This gives new insights into the neural mechanisms potentially used by bushcrickets to discriminate conspecific songs from sounds of predators in similar carrier frequency bands.
doi:10.1371/journal.pone.0037354
PMCID: PMC3368931
PMID: 22701566
Background
The dramatic fall in the cost of genomic sequencing, and the increasing convenience of distributed cloud computing resources, positions the MapReduce coding pattern as a cornerstone of scalable bioinformatics algorithm development. In some cases an algorithm will find a natural distribution via use of map functions to process vectorized components, followed by a reduce of aggregate intermediate results. However, for some data analysis procedures such as sequence analysis, a more fundamental reformulation may be required.
Results
In this report we describe a solution to sequence comparison that can be thoroughly decomposed into multiple rounds of map and reduce operations. The route taken makes use of iterated maps, a fractal analysis technique, that has been found to provide a "alignment-free" solution to sequence analysis and comparison. That is, a solution that does not require dynamic programming, relying on a numeric Chaos Game Representation (CGR) data structure. This claim is demonstrated in this report by calculating the length of the longest similar segment by inspecting only the USM coordinates of two analogous units: with no resort to dynamic programming.
Conclusions
The procedure described is an attempt at extreme decomposition and parallelization of sequence alignment in anticipation of a volume of genomic sequence data that cannot be met by current algorithmic frameworks. The solution found is delivered with a browser-based application (webApp), highlighting the browser's emergence as an environment for high performance distributed computing.
Availability
Public distribution of accompanying software library with open source and version control at http://usm.github.com. Also available as a webApp through Google Chrome's WebStore http://chrome.google.com/webstore: search with "usm".
doi:10.1186/1748-7188-7-12
PMCID: PMC3394223
PMID: 22551205
Biological movement generation combines three interesting aspects: its modular organization in movement primitives (MPs), its characteristics of stochastic optimality under perturbations, and its efficiency in terms of learning. A common approach to motor skill learning is to endow the primitives with dynamical systems. Here, the parameters of the primitive indirectly define the shape of a reference trajectory. We propose an alternative MP representation based on probabilistic inference in learned graphical models with new and interesting properties that complies with salient features of biological movement control. Instead of endowing the primitives with dynamical systems, we propose to endow MPs with an intrinsic probabilistic planning system, integrating the power of stochastic optimal control (SOC) methods within a MP. The parameterization of the primitive is a graphical model that represents the dynamics and intrinsic cost function such that inference in this graphical model yields the control policy. We parameterize the intrinsic cost function using task-relevant features, such as the importance of passing through certain via-points. The system dynamics as well as intrinsic cost function parameters are learned in a reinforcement learning (RL) setting. We evaluate our approach on a complex 4-link balancing task. Our experiments show that our movement representation facilitates learning significantly and leads to better generalization to new task settings without re-learning.
doi:10.3389/fncom.2012.00097
PMCID: PMC3534186
PMID: 23293598
movement primitives; motor planning; reinforcement learning; optimal control; graphical models
An important open problem of computational neuroscience is the generic organization of computations in networks of neurons in the brain. We show here through rigorous theoretical analysis that inherent stochastic features of spiking neurons, in combination with simple nonlinear computational operations in specific network motifs and dendritic arbors, enable networks of spiking neurons to carry out probabilistic inference through sampling in general graphical models. In particular, it enables them to carry out probabilistic inference in Bayesian networks with converging arrows (“explaining away”) and with undirected loops, that occur in many real-world tasks. Ubiquitous stochastic features of networks of spiking neurons, such as trial-to-trial variability and spontaneous activity, are necessary ingredients of the underlying computational organization. We demonstrate through computer simulations that this approach can be scaled up to neural emulations of probabilistic inference in fairly large graphical models, yielding some of the most complex computations that have been carried out so far in networks of spiking neurons.
Author Summary
Experimental data from neuroscience have provided substantial knowledge about the intricate structure of cortical microcircuits, but their functional role, i.e. the computational calculus that they employ in order to interpret ambiguous stimuli, produce predictions, and derive movement plans has remained largely unknown. Earlier assumptions that these circuits implement a logic-like calculus have run into problems, because logical inference has turned out to be inadequate to solve inference problems in the real world which often exhibits substantial degrees of uncertainty. In this article we propose an alternative theoretical framework for examining the functional role of precisely structured motifs of cortical microcircuits and dendritic computations in complex neurons, based on probabilistic inference through sampling. We show that these structural details endow cortical columns and areas with the capability to represent complex knowledge about their environment in the form of higher order dependencies among salient variables. We show that it also enables them to use this knowledge for probabilistic inference that is capable to deal with uncertainty in stored knowledge and current observations. We demonstrate in computer simulations that the precisely structured neuronal microcircuits enable networks of spiking neurons to solve through their inherent stochastic dynamics a variety of complex probabilistic inference tasks.
doi:10.1371/journal.pcbi.1002294
PMCID: PMC3240581
PMID: 22219717
The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.
Author Summary
It is well-known that neurons communicate with short electric pulses, called action potentials or spikes. But how can spiking networks implement complex computations? Attempts to relate spiking network activity to results of deterministic computation steps, like the output bits of a processor in a digital computer, are conflicting with findings from cognitive science and neuroscience, the latter indicating the neural spike output in identical experiments changes from trial to trial, i.e., neurons are “unreliable”. Therefore, it has been recently proposed that neural activity should rather be regarded as samples from an underlying probability distribution over many variables which, e.g., represent a model of the external world incorporating prior knowledge, memories as well as sensory input. This hypothesis assumes that networks of stochastically spiking neurons are able to emulate powerful algorithms for reasoning in the face of uncertainty, i.e., to carry out probabilistic inference. In this work we propose a detailed neural network model that indeed fulfills these computational requirements and we relate the spiking dynamics of the network to concrete probabilistic computations. Our model suggests that neural systems are suitable to carry out probabilistic inference by using stochastic, rather than deterministic, computing elements.
doi:10.1371/journal.pcbi.1002211
PMCID: PMC3207943
PMID: 22096452
Background
The value and usefulness of data increases when it is explicitly interlinked with related data. This is the core principle of Linked Data. For life sciences researchers, harnessing the power of Linked Data to improve biological discovery is still challenged by a need to keep pace with rapidly evolving domains and requirements for collaboration and control as well as with the reference semantic web ontologies and standards. Knowledge organization systems (KOSs) can provide an abstraction for publishing biological discoveries as Linked Data without complicating transactions with contextual minutia such as provenance and access control.
We have previously described the Simple Sloppy Semantic Database (S3DB) as an efficient model for creating knowledge organization systems using Linked Data best practices with explicit distinction between domain and instantiation and support for a permission control mechanism that automatically migrates between the two. In this report we present a domain specific language, the S3DB query language (S3QL), to operate on its underlying core model and facilitate management of Linked Data.
Results
Reflecting the data driven nature of our approach, S3QL has been implemented as an application programming interface for S3DB systems hosting biomedical data, and its syntax was subsequently generalized beyond the S3DB core model. This achievement is illustrated with the assembly of an S3QL query to manage entities from the Simple Knowledge Organization System. The illustrative use cases include gastrointestinal clinical trials, genomic characterization of cancer by The Cancer Genome Atlas (TCGA) and molecular epidemiology of infectious diseases.
Conclusions
S3QL was found to provide a convenient mechanism to represent context for interoperation between public and private datasets hosted at biomedical research institutions and linked data formalisms.
doi:10.1186/1471-2105-12-285
PMCID: PMC3155508
PMID: 21756325
S3DB; Linked Data; KOS; RDF; SPARQL; knowledge organization system, policy
It has recently been shown in a brain-computer interface experiment that motor cortical neurons change their tuning properties selectively to compensate for errors induced by displaced decoding parameters. In particular, it was shown that the 3D tuning curves of neurons whose decoding parameters were re-assigned changed more than those of neurons whose decoding parameters had not been re-assigned. In this article, we propose a simple learning rule that can reproduce this effect. Our learning rule uses Hebbian weight updates driven by a global reward signal and neuronal noise. In contrast to most previously proposed learning rules, this approach does not require extrinsic information to separate noise from signal. The learning rule is able to optimize the performance of a model system within biologically realistic periods of time under high noise levels. Furthermore, when the model parameters are matched to data recorded during the brain-computer interface learning experiments described above, the model produces learning effects strikingly similar to those found in the experiments.
doi:10.1523/JNEUROSCI.4284-09.2010
PMCID: PMC2917246
PMID: 20573887
brain computer interface; motor learning; reinforcement learning; synaptic plasticity; self tuning; Reward
Background
Biomedical research is set to greatly benefit from the use of semantic web technologies in the design of computational infrastructure. However, beyond well defined research initiatives, substantial issues of data heterogeneity, source distribution, and privacy currently stand in the way towards the personalization of Medicine.
Results
A computational framework for bioinformatic infrastructure was designed to deal with the heterogeneous data sources and the sensitive mixture of public and private data that characterizes the biomedical domain. This framework consists of a logical model build with semantic web tools, coupled with a Markov process that propagates user operator states. An accompanying open source prototype was developed to meet a series of applications that range from collaborative multi-institution data acquisition efforts to data analysis applications that need to quickly traverse complex data structures. This report describes the two abstractions underlying the S3DB-based infrastructure, logical and numerical, and discusses its generality beyond the immediate confines of existing implementations.
Conclusions
The emergence of the "web as a computer" requires a formal model for the different functionalities involved in reading and writing to it. The S3DB core model proposed was found to address the design criteria of biomedical computational infrastructure, such as those supporting large scale multi-investigator research, clinical trials, and molecular epidemiology.
doi:10.1186/1471-2105-11-387
PMCID: PMC2918582
PMID: 20646315
Recent developments in neuromorphic hardware engineering make mixed-signal VLSI neural network models promising candidates for neuroscientific research tools and massively parallel computing devices, especially for tasks which exhaust the computing power of software simulations. Still, like all analog hardware systems, neuromorphic models suffer from a constricted configurability and production-related fluctuations of device characteristics. Since also future systems, involving ever-smaller structures, will inevitably exhibit such inhomogeneities on the unit level, self-regulation properties become a crucial requirement for their successful operation. By applying a cortically inspired self-adjusting network architecture, we show that the activity of generic spiking neural networks emulated on a neuromorphic hardware system can be kept within a biologically realistic firing regime and gain a remarkable robustness against transistor-level variations. As a first approach of this kind in engineering practice, the short-term synaptic depression and facilitation mechanisms implemented within an analog VLSI model of I&F neurons are functionally utilized for the purpose of network level stabilization. We present experimental data acquired both from the hardware model and from comparative software simulations which prove the applicability of the employed paradigm to neuromorphic VLSI devices.
doi:10.3389/fncom.2010.00129
PMCID: PMC2965017
PMID: 21031027
neuromorphic hardware; spiking neural networks; self-regulation; short-term synaptic plasticity; robustness; leaky integrate-and-fire neuron; parallel computing; PCSIM
The brain has a one-back memory for visual stimuli. Neural responses to an image contain as much information about the current image as it does about another image presented immediately before.
It is currently not known how distributed neuronal responses in early visual areas carry stimulus-related information. We made multielectrode recordings from cat primary visual cortex and applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons. We used sequences of up to three different visual stimuli (letters of the alphabet) presented for 100 ms and with intervals of 100 ms or larger. Most of the information about visual stimuli extractable by sophisticated methods of machine learning, i.e., support vector machines with nonlinear kernel functions, was also extractable by simple linear classification such as can be achieved by individual neurons. New stimuli did not erase information about previous stimuli. The responses to the most recent stimulus contained about equal amounts of information about both this and the preceding stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and, when using short time constants for integration (e.g., 20 ms), in the precise timing of individual spikes (≤∼20 ms), and persisted for several 100 ms beyond the offset of stimuli. The results indicate that the network from which we recorded is endowed with fading memory and is capable of performing online computations utilizing information about temporally sequential stimuli. This result challenges models assuming frame-by-frame analyses of sequential inputs.
Author Summary
Researchers usually assume that neuronal responses carry primarily information about the stimulus that evoked these responses. We show here that, when multiple images are shown in a fast sequence, the response to an image contains as much information about the preceding image as about the current one. Importantly, this memory capacity extends only to the most recent stimulus in the sequence. The effect can be explained only partly by adaptation of neuronal responses. These discoveries were made with the help of novel methods for analyzing high-dimensional data obtained by recording the responses of many neurons (e.g., 100) in parallel. The methods enabled us to study the information contents of neural activity as accessible to neurons in the cortex, i.e., by collecting information only over short time intervals. This one-back memory has properties similar to the iconic storage of visual information—which is a detailed image of the visual scene that stays for a short while (<1 s) when we close our eyes. Thus, one-back memory may be the neural foundation of iconic memory. Our results are consistent with recent detailed computer simulations of local cortical networks of neurons (“generic cortical microcircuits”), which suggested that integration of information over time is a fundamental computational operation of these networks.
doi:10.1371/journal.pbio.1000260
PMCID: PMC2785877
PMID: 20027205
Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged as
a candidate for a learning rule that could explain how behaviorally relevant
adaptive changes in complex networks of spiking neurons could be achieved in a
self-organizing manner through local synaptic plasticity. However, the
capabilities and limitations of this learning rule could so far only be tested
through computer simulations. This article provides tools for an analytic
treatment of reward-modulated STDP, which allows us to predict under which
conditions reward-modulated STDP will achieve a desired learning effect. These
analytical results imply that neurons can learn through reward-modulated STDP to
classify not only spatial but also temporal firing patterns of presynaptic
neurons. They also can learn to respond to specific presynaptic firing patterns
with particular spike patterns. Finally, the resulting learning theory predicts
that even difficult credit-assignment problems, where it is very hard to tell
which synaptic weights should be modified in order to increase the global reward
for the system, can be solved in a self-organizing manner through
reward-modulated STDP. This yields an explanation for a fundamental experimental
result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys
were rewarded for increasing the firing rate of a particular neuron in the
cortex and were able to solve this extremely difficult credit assignment
problem. Our model for this experiment relies on a combination of
reward-modulated STDP with variable spontaneous firing activity. Hence it also
provides a possible functional explanation for trial-to-trial variability, which
is characteristic for cortical networks of neurons but has no analogue in
currently existing artificial computing systems. In addition our model
demonstrates that reward-modulated STDP can be applied to all synapses in a
large recurrent neural network without endangering the stability of the network
dynamics.
Author Summary
A major open problem in computational neuroscience is to explain how learning,
i.e., behaviorally relevant modifications in the central nervous system, can be
explained on the basis of experimental data on synaptic plasticity.
Spike-timing-dependent plasticity (STDP) is a rule for changes in the strength
of an individual synapse that is supported by experimental data from a variety
of species. However, it is not clear how this synaptic plasticity rule can
produce meaningful modifications in networks of neurons. Only if one takes into
account that consolidation of synaptic plasticity requires a third signal, such
as changes in the concentration of a neuromodulator (that might, for example, be
related to rewards or expected rewards), then meaningful changes in the
structure of networks of neurons may occur. We provide in this article an
analytical foundation for such reward-modulated versions of STDP that predicts
when this type of synaptic plasticity can produce functionally relevant changes
in networks of neurons. In particular we show that seemingly inexplicable
experimental data on biofeedback, where a monkey learnt to increase the firing
rate of an arbitrarily chosen neuron in the motor cortex, can be explained on
the basis of this new learning theory.
doi:10.1371/journal.pcbi.1000180
PMCID: PMC2543108
PMID: 18846203
It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.
Author Summary
Circuits of neurons in the brain have an abundance of feedback connections, both on the level of local microcircuits and on the level of synaptic connections between brain areas. But the functional role of these feedback connections is largely unknown. We present a computational theory that characterizes the gain in computational power that feedback can provide in such circuits. It shows that feedback endows standard models for neural circuits with the capability to emulate arbitrary Turing machines. In fact, with suitable feedback they can simulate any dynamical system, in particular any conceivable analog computer. Under realistic noise conditions, the computational power of these circuits is necessarily reduced. But we demonstrate through computer simulations that feedback also provides a significant gain in computational power for quite detailed models of cortical microcircuits with in vivo–like high levels of noise. In particular it enables generic cortical microcircuits to carry out computations that combine information from working memory and persistent internal states in real time with new information from online input streams.
doi:10.1371/journal.pcbi.0020165
PMCID: PMC1779299
PMID: 17238280
It has previously been shown that generic cortical microcircuit models can perform complex real-time computations on continuous input streams, provided that these computations can be carried out with a rapidly fading memory. We investigate the computational capability of such circuits in the more realistic case where not only readout neurons, but in addition a few neurons within the circuit, have been trained for specific tasks. This is essentially equivalent to the case where the output of trained readout neurons is fed back into the circuit. We show that this new model overcomes the limitation of a rapidly fading memory. In fact, we prove that in the idealized case without noise it can carry out any conceivable digital or analog computation on time-varying inputs. But even with noise, the resulting computational model can perform a large class of biologically relevant real-time computations that require a nonfading memory. We demonstrate these computational implications of feedback both theoretically, and through computer simulations of detailed cortical microcircuit models that are subject to noise and have complex inherent dynamics. We show that the application of simple learning procedures (such as linear regression or perceptron learning) to a few neurons enables such circuits to represent time over behaviorally relevant long time spans, to integrate evidence from incoming spike trains over longer periods of time, and to process new information contained in such spike trains in diverse ways according to the current internal state of the circuit. In particular we show that such generic cortical microcircuits with feedback provide a new model for working memory that is consistent with a large set of biological constraints. Although this article examines primarily the computational role of feedback in circuits of neurons, the mathematical principles on which its analysis is based apply to a variety of dynamical systems. Hence they may also throw new light on the computational role of feedback in other complex biological dynamical systems, such as, for example, genetic regulatory networks.
Author Summary
Circuits of neurons in the brain have an abundance of feedback connections, both on the level of local microcircuits and on the level of synaptic connections between brain areas. But the functional role of these feedback connections is largely unknown. We present a computational theory that characterizes the gain in computational power that feedback can provide in such circuits. It shows that feedback endows standard models for neural circuits with the capability to emulate arbitrary Turing machines. In fact, with suitable feedback they can simulate any dynamical system, in particular any conceivable analog computer. Under realistic noise conditions, the computational power of these circuits is necessarily reduced. But we demonstrate through computer simulations that feedback also provides a significant gain in computational power for quite detailed models of cortical microcircuits with in vivo–like high levels of noise. In particular it enables generic cortical microcircuits to carry out computations that combine information from working memory and persistent internal states in real time with new information from online input streams.
doi:10.1371/journal.pcbi.0020165
PMCID: PMC1779299
PMID: 17238280