arXiv subjects

Alexei A. Koulakov

Publications and source records attributed to Alexei A. Koulakov.

17 recordsLinked to original sources

arXiv2019

Neural networks with motivation

How can animals behave effectively in conditions involving different motivational contexts? Here, we propose how reinforcement learning neural networks can learn optimal behavior for dynamically changing motivational salience vectors. First, we show that Q-learning neural networks with motivation can navigate in environment with dynamic rewards. Second, we show that such networks can learn complex behaviors simultaneously directed towards several goals distributed in an environment. Finally, we show that in Pavlovian conditioning task, the responses of the neurons in our model resemble the firing patterns of neurons in the ventral pallidum (VP), a basal ganglia structure involved in motivated behaviors. We show that, similarly to real neurons, recurrent networks with motivation are composed of two oppositely-tuned classes of neurons, responding to positive and negative rewards. Our model generates predictions for the VP connectivity. We conclude that networks with motivation can rapidly adapt their behavior to varying conditions without changes in synaptic strength when expected reward is modulated by motivation. Such networks may also provide a mechanism for how hierarchical reinforcement learning is implemented in the brain.

q-bio.NC↗

arXiv2017

Representations of Sound in Deep Learning of Audio Features from Music

The work of a single musician, group or composer can vary widely in terms of musical style. Indeed, different stylistic elements, from performance medium and rhythm to harmony and texture, are typically exploited and developed across an artist's lifetime. Yet, there is often a discernable character to the work of, for instance, individual composers at the perceptual level - an experienced listener can often pick up on subtle clues in the music to identify the composer or performer. Here we suggest that a convolutional network may learn these subtle clues or features given an appropriate representation of the music. In this paper, we apply a deep convolutional neural network to a large audio dataset and empirically evaluate its performance on audio classification tasks. Our trained network demonstrates accurate performance on such classification tasks when presented with 5 s examples of music obtained by simple transformations of the raw audio waveform. A particularly interesting example is the spectral representation of music obtained by application of a logarithmically spaced filter bank, mirroring the early stages of auditory signal transduction in mammals. The most successful representation of music to facilitate discrimination was obtained via a random matrix transform (RMT). Networks based on logarithmic filter banks and RMT were able to correctly guess the one composer out of 31 possibilities in 68 and 84 percent of cases respectively.

cs.SD↗

arXiv2016

Network cloning using DNA barcodes

The ability to measure or manipulate network connectivity is the main challenge in the field of connectomics. Recently, a set of approaches has been developed that takes advantage of next generation DNA sequencing to scan connections between neurons into a set of DNA barcodes. Individual DNA sequences called markers represent single neurons, while pairs of markers, called barcodes contain information about connections. Here we propose a strategy for 'copying' or 'cloning' connectivity contained in barcodes into a clean slate tabula rasa network. We show that a one marker one cell (OMOC) rule, which forces all markers with the same sequence to condense into the same neuron, leads to fast and reliable formation of desired connectivity in a new network. We show that OMOC rule yields convergence in a number of steps given by a power law function of the network size. We thus propose that copying network connectivity from one network to another is theoretically possible.

q-bio.NC↗

arXiv2014

Statistical model of evolution of brain parcellation

We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We analyze the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model shows that the same evolutionary process may have led to brain parcellation in these three species. Our model suggests that region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-vanishing macaque cortex macroconnectivity (62% for area V1) can be explained by the outer product power-law form suggested by our model. We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose a universal evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals.

q-bio.NC↗

arXiv2014

Odors in olfactory bulb are defined by a short discrete temporal sequence: recognition by brute-force conversion to a spatial pattern (chunking)

Mitral cells, the principal neurons in the olfactory bulb, respond to odorants by firing bursts of action potentials called sharp events. A given cell produces a sharp event at a fixed phase during the sniff cycle in response to a given odor; different cells have different phases. The olfactory bulb response to an odor is thus a sequence of sharp events. Here, we show that sharp event onset is biased toward certain phases of the ongoing gamma frequency oscillation. Thus, the signature of an odor is a discrete sequence. The fact that this sequence is relatively short suggests a new class of "brute force" solutions to the problem of odor recognition: cortex may contain a small number of modules, each forming a persistent snapshot of what occurs in a certain gamma cycle. Towards the end of the sniff, the collection of these snapshots forms a spatial pattern that could be recognized by standard attractor-based network mechanisms. We demonstrate the feasibility of this solution with simulations of simple network architectures having modules that represent gamma-cycle specific information. Thus "brute force" solutions for converting a discrete temporal sequence into a spatial pattern (chunking) are neurally plausible.

q-bio.NC↗

arXiv2012

Long-term memory stabilized by noise-induced rehearsal

Cortical networks can maintain memories for decades despite the short lifetime of synaptic strength. Can a neural network store long-lasting memories in unstable synapses? Here, we study the effects of random noise on the stability of memory stored in synapses of an attractor neural network. The model includes ongoing spike timing dependent plasticity (STDP). We show that certain classes of STDP rules can lead to the stabilization of memory patterns stored in the network. The stabilization results from rehearsals induced by noise. We show that unstructured neural noise, after passing through the recurrent network weights, carries the imprint of all memory patterns in temporal correlations. Under certain conditions, STDP combined with these correlations, can lead to reinforcement of all existing patterns, even those that are never explicitly visited. Thus, unstructured neural noise can stabilize the existing structure of synaptic connectivity. Our findings may provide the functional reason for highly irregular spiking displayed by cortical neurons and provide justification for models of system memory consolidation. Therefore, we propose that irregular neural activity is the feature that helps cortical networks maintain stable connections.

q-bio.NC↗

arXiv2012

A race model for singular olfactory receptor expression

In vertebrates, olfactory sensory neurons choose only one olfactory receptor to produce out of ~2000 possibilities. The mechanism for how this singular receptor expression occurs is unknown. Here we propose a mechanism that can stochastically select a single gene out of a large number of possibilities. In this model, receptor genes compete for a limited pool of transcription factors (TFs). The gene that recruits a target number of TFs is selected for expression. To support this mechanism, we have attempted to detect repeated motifs within known sequences of mouse olfactory receptor promoters. We find motifs that are significantly overrepresented in olfactory versus other gene promoters. We identify possible TFs that can target these motifs. Our model suggests that a small number of TFs can control the selection of a single gene out of ~2000 possibilities.

q-bio.MN↗

arXiv2012

The Problem of Colliding Networks and its Relation to Cancer

Complex systems, ranging from living cells to human societies, can be represented as attractor networks, whose basic property is to exist in one of allowed states, or attractors. We noted that merging two systems that are in distinct attractors creates uncertainty, as the hybrid system cannot assume two attractors at once. As a prototype of this problem, we explore cell fusion, whose ability to combine distinct cells into hybrids was proposed to cause cancer. By simulating cell types as attractors, we find that hybrids are prone to assume spurious attractors, which are emergent and sporadic states of networks, and propose that cell fusion can make a cell cancerous by placing it into normally inaccessible spurious states. We define basic features of hybrid networks and suggest that the problem of colliding networks has general significance in processes represented by attractor networks, including biological, social, and political phenomena.

q-bio.MN↗

arXiv2010

Sparse incomplete representations: A novel role for olfactory granule cells

Mitral cells of the olfactory bulb form sparse representations of the odorants and transmit this information to the cortex. The olfactory code carried by the mitral cells is sparser than the inputs that they receive. In this study we analyze the mechanisms and functional significance of sparse olfactory codes. We consider a model of olfactory bulb containing populations of excitatory mitral and inhibitory granule cells. We argue that sparse codes may emerge as a result of self organization in the network leading to the precise balance between mitral cells' excitatory inputs and inhibition provided by the granule cells. We propose a novel role for the olfactory granule cells. We show that these cells can build representations of odorant stimuli that are not fully accurate. Due to the incompleteness in the granule cell representation, the exact excitation-inhibition balance is established only for some mitral cells leading to sparse responses of the mitral cell. Our model suggests a functional significance to the dendrodendritic synapses that mediate interactions between mitral and granule cells. The model accounts for the sparse olfactory code in the steady state and predicts that transient dynamics may be less sparse.

q-bio.NC↗

arXiv2010

On the scaling law for cortical magnification factor

Primate visual system samples different parts of the world unevenly. The part of the visual scene corresponding to the eye center is represented densely, while away from the center the sampling becomes progressively sparser. Such distribution allows a more effective use of the limited transfer rate of the optic nerve, since animals can aim area centralis (AC) at the relevant position in the scene by performing saccadic eye movements. To locate a new saccade target the animal has to sample the corresponding region of the visual scene, away from AC. In this work we derive the sampling density away from AC, which optimizes the trajectory of saccadic eye movements. We obtain the scaling law for the sampling density as a function of eccentricity, which results from the evolutionary pressure to locate the target in the shortest time under the constraint of limited transfer rate of the optic nerve. In case of very small AC the visual scene is optimally represented by logarithmic conformal mapping, in which geometrically similar circular bands around AC are equally represented by the visual system. We also obtain corrections to the logarithmic scaling for the case of a larger AC and compare them to experimental findings.

q-bio.NC↗

arXiv2009

The structure of human olfactory space

We analyze the psychophysical responses of human observers to an ensemble of monomolecular odorants. Each odorant is characterized by a set of 146 perceptual descriptors obtained from a database of odor character profiles. Each odorant is therefore represented by a point in highly multidimensional sensory space. In this work we study the arrangement of odorants in this perceptual space. We argue that odorants densely sample a two-dimensional curved surface embedded in the multidimensional sensory space. This surface can account for more than half of the variance of the psychophysical data. We also show that only 12 percent of experimental variance cannot be explained by curved surfaces of substantially small dimensionality (<10). We suggest that these curved manifolds represent the relevant spaces sampled by the human olfactory system, thereby providing surrogates for olfactory sensory space. For the case of 2D approximation, we relate the two parameters on the curved surface to the physico-chemical parameters of odorant molecules. We show that one of the dimensions is related to eigenvalues of the molecule connectivity matrix, while the other is correlated with measures of the molecule polarity. We discuss the behavioral significance of these findings.

q-bio.NC↗

arXiv2004

Can repulsion be induced by attraction: a role of ephrin-B1 in retinotectal mapping?

We study a role of EphB receptors and their ligand ephrin-B1 in dorsal-ventral retinotopic mapping. Earlier studies suggested that ephrin-B1 acts as an attractant for EphB expressing axons. We address the results of the recent experiment in chick tectum (McLaughlin et al., 2003b) in which axons of retinal ganglion cells were shown to be repelled by high ephrin-B1 density. Thus it was proposed that ephrin-B1 might act as both attractant and repellent. We show that the same axonal behavior may follow from attraction to ephrin-B1 density and axonal competition for space. Therefore, we show how apparent repulsive interaction can be induced by a combination of attraction to the target and competitive interactions between axons. We suggest an experimental test that may distinguish repulsive interaction with the target from repulsion induced by attraction and competition.

q-bio.NC↗

arXiv2004

How to find decision makers in neural circuits?

Neural circuits often face the problem of classifying stimuli into discrete groups and making decisions based on such classifications. Neurons of these circuits can be distinguished according to their correlations with different features of stimulus or response, which allows defining sensory or motor neuronal types. In this study we define the third class of neurons, which is responsible for making decision. We suggest two descriptions for contribution of units to decision making: first, as a spatial derivative of correlations between neural activity and the decision; second, as an impact of variability in a given neuron on the response. These two definitions are shown to be equivalent, when they can be compared. We also suggest an experimental strategy for determining contributions to decision making, which uses electric stimulation with time- varying random current.

q-bio.NC↗

arXiv2003

Ocular dominance patterns and the wire length minimization: a numerical study

We study a mathematical model for ocular dominance patterns (ODPs) in primary visual cortex. This model is based on the premise that ODP is an adaptation to minimize the length of intra-cortical wiring. Thus we attempt to understand the existing ODPs by solving a wire length minimization problem. We divide all the neurons into two classes: left- and right-eye dominated. We find that segregation of neurons into monocular regions reduces wire length if the number of connections to the neurons of the same class (intraocular) differs from the number of interocular connections. The shape of the regions depends on the relative fraction of neurons in the two classes. We find that if both classes are almost equally represented, the optimal ODP consists of interdigitating stripes. If one class is less numerous than the other, the optimal ODP consists of patches of the less abundant class surrounded by the neurons of the other class. We predict that the transition from stripes to patches occurs when the fraction of neurons dominated by the underrepresented eye is about 40%. This prediction agrees with the data in macaque and Cebus monkeys. We also study the dependence of the periodicity of ODP on the parameters of our model.

q-bio.NC↗

arXiv2003

A stochastic model for retinocollicular map development

We present a theoretical model for retinocollicular map development, which can account for intriguing behaviors observed in gain-of-function experiments in knock-in mice by Brown et al., including bifurcation in heterozygous Isl2/EphA3 knock-ins. The model is based on known chemical labels, axonal repulsion/competition, stochasticity and uses Markov chain description. Our model suggests that the map in heterozygotes is single-valued in the temporal region of retina due to reduced gradient of ephrin in the corresponding region of SC. The remaining map is double-valued since the gradient of ephrin is high there. We predict therefore that if gradient of ephrin is reduced by a genetic manipulation, the single-valued region of the map should occupy a larger portion of temporal retina, i.e. the point of transition between single- and doulble-valued maps should move to a more nasal position in Isl2-EphA3 heterozygotes. We also discuss the importance of inhomogeneous EphA gradient and mapping in Isl2/EphB knock-ins.

physics.bio-ph↗

arXiv1999

Instantons in the working memory: implications for schizophrenia

The influence of the synaptic channel properties on the stability of delayed activity maintained by recurrent neural network is studied. The duration of excitatory post-synaptic current (EPSC) is shown to be essential for the global stability of the delayed response. NMDA receptor channel is a much more reliable mediator of the reverberating activity than AMPA receptor, due to a longer EPSC. This allows to interpret the deterioration of working memory observed in the NMDA channel blockade experiments. The key mechanism leading to the decay of the delayed activity originates in the unreliability of the synaptic transmission. The optimum fluctuation of the synaptic conductances leading to the decay is identified. The decay time is calculated analytically and the result is confirmed computationally.

cond-mat.dis-nn↗

arXiv1999

Ocular dominance patterns in mammalian visual cortex: A wire length minimization approach

We propose a theory for ocular dominance (OD) patterns in mammalian primary visual cortex. This theory is based on the premise that OD pattern is an adaptation to minimize the length of intra-cortical wiring. Thus we can understand the existing OD patterns by solving a wire length minimization problem. We divide all the neurons into two classes: left-eye dominated and right-eye dominated. We find that segregation of neurons into monocular regions reduces wire length if the number of connections with the neurons of the same class differs from that with the other class. The shape of the regions depends on the relative fraction of neurons in the two classes. If the numbers are close we find that the optimal OD pattern consists of interdigitating stripes. If one class is less numerous than the other, the optimal OD pattern consists of patches of the first class neurons in the sea of the other class neurons. We predict the transition from stripes to patches when the fraction of neurons dominated by the ipsilateral eye is about 40%. This prediction agrees with the data in macaque and Cebus monkeys. This theory can be applied to other binary cortical systems.

cond-mat.soft↗