Neutral stability, rate propagation, and critical branching in feedforward networks.

Abstract:

:Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing patterns. We seek the simplest setting in which these properties emerge, clarifying their origin and relationship in random, feedforward networks of McCullochs-Pitts neurons. Two key parameters are the thresholds at which neurons fire spikes and the overall level of feedforward connectivity. When neurons have low thresholds, we show that there is always a connectivity for which the properties in question all occur, that is, these networks preserve overall firing rates from layer to layer and produce broad distributions of activity in each layer. This fails to occur, however, when neurons have high thresholds. A key tool in explaining this difference is the eigenstructure of the resulting mean-field Markov chain, as this reveals which activity modes will be preserved from layer to layer. We extend our analysis from purely excitatory networks to more complex models that include inhibition and local noise, and find that both of these features extend the parameter ranges over which networks produce the properties of interest.

journal_name

Neural Comput

journal_title

Neural computation

authors

Cayco-Gajic NA,Shea-Brown E

doi

10.1162/NECO_a_00461

subject

Has Abstract

pub_date

2013-07-01 00:00:00

pages

1768-806

issue

7

eissn

0899-7667

issn

1530-888X

journal_volume

25

pub_type

杂志文章
  • Neuronal assembly dynamics in supervised and unsupervised learning scenarios.

    abstract::The dynamic formation of groups of neurons--neuronal assemblies--is believed to mediate cognitive phenomena at many levels, but their detailed operation and mechanisms of interaction are still to be uncovered. One hypothesis suggests that synchronized oscillations underpin their formation and functioning, with a focus...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00502

    authors: Moioli RC,Husbands P

    更新日期:2013-11-01 00:00:00

  • Supervised Determined Source Separation with Multichannel Variational Autoencoder.

    abstract::This letter proposes a multichannel source separation technique, the multichannel variational autoencoder (MVAE) method, which uses a conditional VAE (CVAE) to model and estimate the power spectrograms of the sources in a mixture. By training the CVAE using the spectrograms of training examples with source-class label...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01217

    authors: Kameoka H,Li L,Inoue S,Makino S

    更新日期:2019-09-01 00:00:00

  • Adaptive Learning Algorithm Convergence in Passive and Reactive Environments.

    abstract::Although the number of artificial neural network and machine learning architectures is growing at an exponential pace, more attention needs to be paid to theoretical guarantees of asymptotic convergence for novel, nonlinear, high-dimensional adaptive learning algorithms. When properly understood, such guarantees can g...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01117

    authors: Golden RM

    更新日期:2018-10-01 00:00:00

  • Universal approximation depth and errors of narrow belief networks with discrete units.

    abstract::We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily well. We relax the setting of binary units (Sutskever & Hinton, 2008 ; Le Roux & Bengio, 2008 , 2010 ; Montúfar & Ay, 2...

    journal_title:Neural computation

    pub_type: 信件

    doi:10.1162/NECO_a_00601

    authors: Montúfar GF

    更新日期:2014-07-01 00:00:00

  • On the emergence of rules in neural networks.

    abstract::A simple associationist neural network learns to factor abstract rules (i.e., grammars) from sequences of arbitrary input symbols by inventing abstract representations that accommodate unseen symbol sets as well as unseen but similar grammars. The neural network is shown to have the ability to transfer grammatical kno...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976602320264079

    authors: Hanson SJ,Negishi M

    更新日期:2002-09-01 00:00:00

  • Including long-range dependence in integrate-and-fire models of the high interspike-interval variability of cortical neurons.

    abstract::Many different types of integrate-and-fire models have been designed in order to explain how it is possible for a cortical neuron to integrate over many independent inputs while still producing highly variable spike trains. Within this context, the variability of spike trains has been almost exclusively measured using...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766041732413

    authors: Jackson BS

    更新日期:2004-10-01 00:00:00

  • Deficient GABAergic gliotransmission may cause broader sensory tuning in schizophrenia.

    abstract::We examined how the depression of intracortical inhibition due to a reduction in ambient GABA concentration impairs perceptual information processing in schizophrenia. A neural network model with a gliotransmission-mediated ambient GABA regulatory mechanism was simulated. In the network, interneuron-to-glial-cell and ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00519

    authors: Hoshino O

    更新日期:2013-12-01 00:00:00

  • On the classification capability of sign-constrained perceptrons.

    abstract::The perceptron (also referred to as McCulloch-Pitts neuron, or linear threshold gate) is commonly used as a simplified model for the discrimination and learning capability of a biological neuron. Criteria that tell us when a perceptron can implement (or learn to implement) all possible dichotomies over a given set of ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.20.1.288

    authors: Legenstein R,Maass W

    更新日期:2008-01-01 00:00:00

  • Inhibition and Excitation Shape Activity Selection: Effect of Oscillations in a Decision-Making Circuit.

    abstract::Decision making is a complex task, and its underlying mechanisms that regulate behavior, such as the implementation of the coupling between physiological states and neural networks, are hard to decipher. To gain more insight into neural computations underlying ongoing binary decision-making tasks, we consider a neural...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01185

    authors: Bose T,Reina A,Marshall JAR

    更新日期:2019-05-01 00:00:00

  • Effects of fast presynaptic noise in attractor neural networks.

    abstract::We study both analytically and numerically the effect of presynaptic noise on the transmission of information in attractor neural networks. The noise occurs on a very short timescale compared to that for the neuron dynamics and it produces short-time synaptic depression. This is inspired in recent neurobiological find...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976606775623342

    authors: Cortes JM,Torres JJ,Marro J,Garrido PL,Kappen HJ

    更新日期:2006-03-01 00:00:00

  • Density-weighted Nyström method for computing large kernel eigensystems.

    abstract::The Nyström method is a well-known sampling-based technique for approximating the eigensystem of large kernel matrices. However, the chosen samples in the Nyström method are all assumed to be of equal importance, which deviates from the integral equation that defines the kernel eigenfunctions. Motivated by this observ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.11-07-651

    authors: Zhang K,Kwok JT

    更新日期:2009-01-01 00:00:00

  • McCulloch-Pitts Brains and Pseudorandom Functions.

    abstract::In a pioneering classic, Warren McCulloch and Walter Pitts proposed a model of the central nervous system. Motivated by EEG recordings of normal brain activity, Chvátal and Goldsmith asked whether these dynamical systems can be engineered to produce trajectories that are irregular, disorderly, and apparently unpredict...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00841

    authors: Chvátal V,Goldsmith M,Yang N

    更新日期:2016-06-01 00:00:00

  • Constraint on the number of synaptic inputs to a visual cortical neuron controls receptive field formation.

    abstract::To date, Hebbian learning combined with some form of constraint on synaptic inputs has been demonstrated to describe well the development of neural networks. The previous models revealed mathematically the importance of synaptic constraints to reproduce orientation selectivity in the visual cortical neurons, but biolo...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2009.04-08-752

    authors: Tanaka S,Miyashita M

    更新日期:2009-09-01 00:00:00

  • A Gaussian attractor network for memory and recognition with experience-dependent learning.

    abstract::Attractor networks are widely believed to underlie the memory systems of animals across different species. Existing models have succeeded in qualitatively modeling properties of attractor dynamics, but their computational abilities often suffer from poor representations for realistic complex patterns, spurious attract...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2010.02-09-957

    authors: Hu X,Zhang B

    更新日期:2010-05-01 00:00:00

  • Online adaptive decision trees.

    abstract::Decision trees and neural networks are widely used tools for pattern classification. Decision trees provide highly localized representation, whereas neural networks provide a distributed but compact representation of the decision space. Decision trees cannot be induced in the online mode, and they are not adaptive to ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766041336396

    authors: Basak J

    更新日期:2004-09-01 00:00:00

  • Dependence of neuronal correlations on filter characteristics and marginal spike train statistics.

    abstract::Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.2008.05-07-525

    authors: Tetzlaff T,Rotter S,Stark E,Abeles M,Aertsen A,Diesmann M

    更新日期:2008-09-01 00:00:00

  • The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction.

    abstract::Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attracto...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1996.8.6.1135

    authors: Casey M

    更新日期:1996-08-15 00:00:00

  • An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise.

    abstract::Synaptically generated subthreshold membrane potential (Vm) fluctuations can be characterized within the framework of stochastic calculus. It is possible to obtain analytic expressions for the steady-state Vm distribution, even in the case of conductance-based synaptic currents. However, as we show here, the analytic ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/0899766054796932

    authors: Rudolph M,Destexhe A

    更新日期:2005-11-01 00:00:00

  • Local and global gating of synaptic plasticity.

    abstract::Mechanisms influencing learning in neural networks are usually investigated on either a local or a global scale. The former relates to synaptic processes, the latter to unspecific modulatory systems. Here we study the interaction of a local learning rule that evaluates coincidences of pre- and postsynaptic action pote...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976600300015682

    authors: Sánchez-Montañés MA,Verschure PF,König P

    更新日期:2000-03-01 00:00:00

  • A causal perspective on the analysis of signal and noise correlations and their role in population coding.

    abstract::The role of correlations between neuronal responses is crucial to understanding the neural code. A framework used to study this role comprises a breakdown of the mutual information between stimuli and responses into terms that aim to account for different coding modalities and the distinction between different notions...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00588

    authors: Chicharro D

    更新日期:2014-06-01 00:00:00

  • Neural coding: higher-order temporal patterns in the neurostatistics of cell assemblies.

    abstract::Recent advances in the technology of multiunit recordings make it possible to test Hebb's hypothesis that neurons do not function in isolation but are organized in assemblies. This has created the need for statistical approaches to detecting the presence of spatiotemporal patterns of more than two neurons in neuron sp...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976600300014872

    authors: Martignon L,Deco G,Laskey K,Diamond M,Freiwald W,Vaadia E

    更新日期:2000-11-01 00:00:00

  • Permitted and forbidden sets in symmetric threshold-linear networks.

    abstract::The richness and complexity of recurrent cortical circuits is an inexhaustible source of inspiration for thinking about high-level biological computation. In past theoretical studies, constraints on the synaptic connection patterns of threshold-linear networks were found that guaranteed bounded network dynamics, conve...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976603321192103

    authors: Hahnloser RH,Seung HS,Slotine JJ

    更新日期:2003-03-01 00:00:00

  • Resonator Networks, 2: Factorization Performance and Capacity Compared to Optimization-Based Methods.

    abstract::We develop theoretical foundations of resonator networks, a new type of recurrent neural network introduced in Frady, Kent, Olshausen, and Sommer (2020), a companion article in this issue, to solve a high-dimensional vector factorization problem arising in Vector Symbolic Architectures. Given a composite vector formed...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01329

    authors: Kent SJ,Frady EP,Sommer FT,Olshausen BA

    更新日期:2020-12-01 00:00:00

  • Gaussian process approach to spiking neurons for inhomogeneous Poisson inputs.

    abstract::This article presents a new theoretical framework to consider the dynamics of a stochastic spiking neuron model with general membrane response to input spike. We assume that the input spikes obey an inhomogeneous Poisson process. The stochastic process of the membrane potential then becomes a gaussian process. When a ...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976601317098529

    authors: Amemori KI,Ishii S

    更新日期:2001-12-01 00:00:00

  • Locality of global stochastic interaction in directed acyclic networks.

    abstract::The hypothesis of invariant maximization of interaction (IMI) is formulated within the setting of random fields. According to this hypothesis, learning processes maximize the stochastic interaction of the neurons subject to constraints. We consider the extrinsic constraint in terms of a fixed input distribution on the...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976602760805368

    authors: Ay N

    更新日期:2002-12-01 00:00:00

  • How precise is neuronal synchronization?

    abstract::Recent work suggests that synchronization of neuronal activity could serve to define functionally relevant relationships between spatially distributed cortical neurons. At present, it is not known to what extent this hypothesis is compatible with the widely supported notion of coarse coding, which assumes that feature...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco.1995.7.3.469

    authors: König P,Engel AK,Roelfsema PR,Singer W

    更新日期:1995-05-01 00:00:00

  • Topographic mapping of large dissimilarity data sets.

    abstract::Topographic maps such as the self-organizing map (SOM) or neural gas (NG) constitute powerful data mining techniques that allow simultaneously clustering data and inferring their topological structure, such that additional features, for example, browsing, become available. Both methods have been introduced for vectori...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/NECO_a_00012

    authors: Hammer B,Hasenfuss A

    更新日期:2010-09-01 00:00:00

  • Visual Categorization with Random Projection.

    abstract::Humans learn categories of complex objects quickly and from a few examples. Random projection has been suggested as a means to learn and categorize efficiently. We investigate how random projection affects categorization by humans and by very simple neural networks on the same stimuli and categorization tasks, and how...

    journal_title:Neural computation

    pub_type: 信件

    doi:10.1162/NECO_a_00769

    authors: Arriaga RI,Rutter D,Cakmak M,Vempala SS

    更新日期:2015-10-01 00:00:00

  • State-Space Representations of Deep Neural Networks.

    abstract::This letter deals with neural networks as dynamical systems governed by finite difference equations. It shows that the introduction of k -many skip connections into network architectures, such as residual networks and additive dense n...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/neco_a_01165

    authors: Hauser M,Gunn S,Saab S Jr,Ray A

    更新日期:2019-03-01 00:00:00

  • Evaluating auditory performance limits: II. One-parameter discrimination with random-level variation.

    abstract::Previous studies have combined analytical models of stochastic neural responses with signal detection theory (SDT) to predict psychophysical performance limits; however, these studies have typically been limited to simple models and simple psychophysical tasks. A companion article in this issue ("Evaluating Auditory P...

    journal_title:Neural computation

    pub_type: 杂志文章

    doi:10.1162/089976601750541813

    authors: Heinz MG,Colburn HS,Carney LH

    更新日期:2001-10-01 00:00:00