Hebbian Network Research Articles

Binary pattern retrieval with Kuramoto-type oscillators via a least orthogonal lift of three patterns

Abstract Given a set of standard binary patterns and a defective pattern, the pattern retrieval task is to find the closest pattern to the defective one among these standard patterns. The Hebbian network of Kuramoto oscillators with second-order coupling provides a dynamical model for this task, and the mutual orthogonality in memorised patterns enables us to distinguish these memorised patterns from most others in terms of stability. For the sake of error-free retrieval for general problems lacking orthogonality, a unified approach was proposed which transforms the problem into a series of subproblems with orthogonality using the orthogonal lift for two patterns. In this work, we propose the least orthogonal lift for three patterns, which evidently reduces the time of solving subproblems and even the dimensions of subproblems. Furthermore, we provide an estimate for the critical strength for stability/instability of binary patterns, which is convenient in practical use. Simulation results are presented to illustrate the effectiveness of the proposed approach.

Replica symmetry breaking in supervised and unsupervised Hebbian networks

Abstract Hebbian neural networks with multi-node interactions, often called Dense Associative Memories, have recently attracted considerable interest in the statistical mechanics community, as they have been shown to outperform their pairwise counterparts in a number of features, including resilience against adversarial attacks, pattern retrieval with extremely weak signals and supra-linear storage capacities. However, their analysis has so far been carried out within a replica-symmetric theory. In this manuscript, we relax the assumption of replica symmetry and analyse these systems at one step of replica-symmetry breaking, focusing on two different prescriptions for the interactions that we will refer to as supervised and unsupervised learning. We derive the phase diagram of the model using two different approaches, namely Parisi's hierarchical ansatz for the relationship between different replicas within the replica approach, and the so-called telescope ansatz within Guerra's interpolation method: our results show that replica-symmetry breaking does not alter the threshold for learning and slightly increases the maximal storage capacity. Further, we also derive analytically the instability line of the replica-symmetric theory, using a generalization of the De Almeida and Thouless approach.

Hebbian learning can explain rhythmic neural entrainment to statistical regularities.

In many domains, learners extract recurring units from continuous sequences. For example, in unknown languages, fluent speech is perceived as a continuous signal. Learners need to extract the underlying words from this continuous signal and then memorize them. One prominent candidate mechanism is statistical learning, whereby learners track how predictive syllables (or other items) are of one another. Syllables within the same word predict each other better than syllables straddling word boundaries. But does statistical learning lead to memories of the underlying words-or just to pairwise associations among syllables? Electrophysiological results provide the strongest evidence for the memory view. Electrophysiological responses can be time-locked to statistical word boundaries (e.g., N400s) and show rhythmic activity with a periodicity of word durations. Here, I reproduce such results with a simple Hebbian network. When exposed to statistically structured syllable sequences (and when the underlying words are not excessively long), the network activation is rhythmic with the periodicity of a word duration and activation maxima on word-final syllables. This is because word-final syllables receive more excitation from earlier syllables with which they are associated than less predictable syllables that occur earlier in words. The network is also sensitive to information whose electrophysiological correlates were used to support the encoding of ordinal positions within words. Hebbian learning can thus explain rhythmic neural activity in statistical learning tasks without any memory representations of words. Learners might thus need to rely on cues beyond statistical associations to learn the words of their nativelanguage. RESEARCH HIGHLIGHTS: Statistical learning may be utilized to identify recurring units in continuous sequences (e.g., words in fluent speech) but may not generate explicit memory forwords. Exposure to statistically structured sequences leads to rhythmic activity with a period of the duration of the underlying units (e.g., words). I show that a memory-less Hebbian network model can reproduce this rhythmic neural activity as well as putative encodings of ordinal positions observed in earlier research. Direct tests are needed to establish whether statistical learning leads to declarative memories for words.

Parallel learning by multitasking neural networks

Parallel learning, namely the simultaneous learning of multiple patterns, constitutes a modern challenge for neural networks. While this cannot be accomplished by standard Hebbian associative neural networks, in this paper we show how the multitasking Hebbian network (a variation on the theme of the Hopfield model, working on sparse datasets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) number of patterns, mirroring the low-storage setting of standard associative neural networks. When patterns to be reconstructed are mildly diluted, the network handles them hierarchically, distributing the amplitudes of their signals as power laws w.r.t. the pattern information content (hierarchical regime), while, for strong dilution, the signals pertaining to all the patterns are simultaneously raised with the same strength (parallel regime). Further, we prove that the training protocol (either supervised or unsupervised) neither alters the multitasking performances nor changes the thresholds for learning. We also highlight (analytically and by Monte Carlo simulations) that a standard cost function (i.e. the Hamiltonian) used in statistical mechanics exhibits the same minima as a standard loss function (i.e. the sum of squared errors) used in machine learning.

Modeling the development of cortical responses in primate dorsal ("where") pathway to optic flow using hierarchical neural field models.

Although there is a plethora of modeling literature dedicated to the object recognition processes of the ventral ("what") pathway of primate visual systems, modeling studies on the motion-sensitive regions like the Medial superior temporal area (MST) of the dorsal ("where") pathway are relatively scarce. Neurons in the MST area of the macaque monkey respond selectively to different types of optic flow sequences such as radial and rotational flows. We present three models that are designed to simulate the computation of optic flow performed by the MST neurons. Model-1 and model-2 each composed of three stages: Direction Selective Mosaic Network (DSMN), Cell Plane Network (CPNW) or the Hebbian Network (HBNW), and the Optic flow network (OF). The three stages roughly correspond to V1-MT-MST areas, respectively, in the primate motion pathway. Both these models are trained stage by stage using a biologically plausible variation of Hebbian rule. The simulation results show that, neurons in model-1 and model-2 (that are trained on translational, radial, and rotational sequences) develop responses that could account for MSTd cell properties found neurobiologically. On the other hand, model-3 consists of the Velocity Selective Mosaic Network (VSMN) followed by a convolutional neural network (CNN) which is trained on radial and rotational sequences using a supervised backpropagation algorithm. The quantitative comparison of response similarity matrices (RSMs), made out of convolution layer and last hidden layer responses, show that model-3 neuron responses are consistent with the idea of functional hierarchy in the macaque motion pathway. These results also suggest that the deep learning models could offer a computationally elegant and biologically plausible solution to simulate the development of cortical responses of the primate motion pathway.

Deep Reinforcement Learning With Modulated Hebbian Plus Q-Network Architecture.

In this article, we consider a subclass of partially observable Markov decision process (POMDP) problems which we termed confounding POMDPs. In these types of POMDPs, temporal difference (TD)-based reinforcement learning (RL) algorithms struggle, as TD error cannot be easily derived from observations. We solve these types of problems using a new bio-inspired neural architecture that combines a modulated Hebbian network (MOHN) with deep Q-network (DQN), which we call modulated Hebbian plus Q-network architecture (MOHQA). The key idea is to use a Hebbian network with rarely correlated bio-inspired neural traces to bridge temporal delays between actions and rewards when confounding observations and sparse rewards result in inaccurate TD errors. In MOHQA, DQN learns low-level features and control, while the MOHN contributes to high-level decisions by associating rewards with past states and actions. Thus, the proposed architecture combines two modules with significantly different learning algorithms, a Hebbian associative network and a classical DQN pipeline, exploiting the advantages of both. Simulations on a set of POMDPs and on the Malmo environment show that the proposed algorithm improved DQN's results and even outperformed control tests with advantage-actor critic (A2C), quantile regression DQN with long short-term memory (QRDQN + LSTM), Monte Carlo policy gradient (REINFORCE), and aggregated memory for reinforcement learning (AMRL) algorithms on most difficult POMDPs with confounding stimuli and sparse rewards.

Hebbian Network of Kuramoto Oscillators with Second-Order Couplings for Binary Pattern Retrieve: II. Nonorthogonal Standard Patterns and Structural Stability

Hebbian Network of Kuramoto Oscillators with Second-Order Couplings for Binary Pattern Retrieve: II. Nonorthogonal Standard Patterns and Structural Stability

Unsupervised repetition enables rapid perceptual learning

This study examined how listeners disambiguate an auditory scene comprising multiple competing unknown sources and determine a salient source. Experiment 1 replicated findings from McDermott, Wrobleski, and Oxenham. [(2011). Proc. Natl. Acad. Sci. U. S. A. 108(3), 1188-1193] using a multivariate Gaussian model to generate mixtures of two novel sounds. The results showed that listeners were unable to identify either sound in the mixture despite repeated exposure unless one sound was repeated several times while being mixed with a different distractor each time. The results support the idea that repetition provides a basis for segregating a single source from competing novel sounds. In subsequent experiments, the previous identification task was extended to a recognition task and the results were modeled. To confirm the repetition benefit, experiment 2 asked listeners to recognize a temporal ramp in either a repeating sound or non-repeating sounds. The results showed that perceptual salience of the repeating sound allowed robust recognition of its temporal ramp, whereas similar features were ignored in the non-repeating sounds. The response from two neural models of learning, generalized Hebbian learning and anti-Hebbian learning, were compared with the human listener results from experiment 2. The Hebbian network showed a similar response pattern as for the listener results, whereas the opposite pattern was observed for the anti-Hebbian output.

Stability in a Hebbian Network of Kuramoto Oscillators with Second-Order Couplings for Binary Pattern Retrieve

We study the stability of an oscillatory associative memory network consisting of $N$ coupled Kuramoto oscillators with applications in binary pattern retrieve. In this model, the coupling function...

A computational implementation of a Hebbian learning network and its application to configural forms of acquired equivalence.

We describe and report the results of computer simulations of the three-layer Hebbian network informally described by Honey, Close, and Lin (2010): A general account of discrimination that has been shaped by data from configural acquired equivalence experiments that are beyond the scope of alternative models. Simulations implemented a conditional principle-components analysis Hebbian learning algorithm and were of four published experimental demonstrations of configural acquired equivalence. Experiments involved training rats on appetitive biconditional discriminations in which discrete cues (w and x) signaled food delivery (+) or its absence (-) in 4 different contexts (A, B, C, and D): Aw+ Bw- Cw+ Dw- Ax- Bx+ Cx- Dx+. Contexts A and C acquired equivalence. In 3 of the experiments acquired equivalence was evident from subsequent revaluation, from compound testing or from whole-/part-reversal training. The fourth experiment added concurrent biconditional discriminations with the same contexts but a pair of additional discrete cues (y and z). The congruent form of the discrimination, in which A and C provided the same information about y and z, was solved relatively readily. Parametric variation allowed the network to successfully simulate the results of each of the 4 experiments. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

A Gestalt inference model for auditory scene segregation.

Our current understanding of how the brain segregates auditory scenes into meaningful objects is in line with a Gestaltism framework. These Gestalt principles suggest a theory of how different attributes of the soundscape are extracted then bound together into separate groups that reflect different objects or streams present in the scene. These cues are thought to reflect the underlying statistical structure of natural sounds in a similar way that statistics of natural images are closely linked to the principles that guide figure-ground segregation and object segmentation in vision. In the present study, we leverage inference in stochastic neural networks to learn emergent grouping cues directly from natural soundscapes including speech, music and sounds in nature. The model learns a hierarchy of local and global spectro-temporal attributes reminiscent of simultaneous and sequential Gestalt cues that underlie the organization of auditory scenes. These mappings operate at multiple time scales to analyze an incoming complex scene and are then fused using a Hebbian network that binds together coherent features into perceptually-segregated auditory objects. The proposed architecture successfully emulates a wide range of well established auditory scene segregation phenomena and quantifies the complimentary role of segregation and binding cues in driving auditory scene segregation.

HebbPlot: an intelligent tool for learning and visualizing chromatin mark signatures

BackgroundHistone modifications play important roles in gene regulation, heredity, imprinting, and many human diseases. The histone code is complex and consists of more than 100 marks. Therefore, biologists need computational tools to characterize general signatures representing the distributions of tens of chromatin marks around thousands of regions.ResultsTo this end, we developed a software tool, HebbPlot, which utilizes a Hebbian neural network in learning a general chromatin signature from regions with a common function. Hebbian networks can learn the associations between tens of marks and thousands of regions. HebbPlot presents a signature as a digital image, which can be easily interpreted. Moreover, signatures produced by HebbPlot can be compared quantitatively. We validated HebbPlot in six case studies. The results of these case studies are novel or validating results already reported in the literature, indicating the accuracy of HebbPlot. Our results indicate that promoters have a directional chromatin signature; several marks tend to stretch downstream or upstream. H3K4me3 and H3K79me2 have clear directional distributions around active promoters. In addition, the signatures of high- and low-CpG promoters are different; H3K4me3, H3K9ac, and H3K27ac are the most different marks. When we studied the signatures of enhancers active in eight tissues, we observed that these signatures are similar, but not identical. Further, we identified some histone modifications — H3K36me3, H3K79me1, H3K79me2, and H4K8ac — that are associated with coding regions of active genes. Other marks — H4K12ac, H3K14ac, H3K27me3, and H2AK5ac — were found to be weakly associated with coding regions of inactive genes.ConclusionsThis study resulted in a novel software tool, HebbPlot, for learning and visualizing the chromatin signature of a genetic element. Using HebbPlot, we produced a visual catalog of the signatures of multiple genetic elements in 57 cell types available through the Roadmap Epigenomics Project. Furthermore, we made a progress toward a functional catalog consisting of 22 histone marks. In sum, HebbPlot is applicable to a wide array of studies, facilitating the deciphering of the histone code.

An Oscillatory Neural Autoencoder Based on Frequency Modulation and Multiplexing.

Oscillatory phenomena are ubiquitous in the brain. Although there are oscillator-based models of brain dynamics, their universal computational properties have not been explored much unlike in the case of rate-coded and spiking neuron network models. Use of oscillator-based models is often limited to special phenomena like locomotor rhythms and oscillatory attractor-based memories. If neuronal ensembles are taken to be the basic functional units of brain dynamics, it is desirable to develop oscillator-based models that can explain a wide variety of neural phenomena. Autoencoders are a special type of feed forward networks that have been used for construction of large-scale deep networks. Although autoencoders based on rate-coded and spiking neuron networks have been proposed, there are no autoencoders based on oscillators. We propose here an oscillatory neural network model that performs the function of an autoencoder. The model is a hybrid of rate-coded neurons and neural oscillators. Input signals modulate the frequency of the neural encoder oscillators. These signals are then multiplexed using a network of rate-code neurons that has afferent Hebbian and lateral anti-Hebbian connectivity, termed as Lateral Anti Hebbian Network (LAHN). Finally the LAHN output is de-multiplexed using an output neural layer which is a combination of adaptive Hopf and Kuramoto oscillators for the signal reconstruction. The Kuramoto-Hopf combination performing demodulation is a novel way of describing a neural phase-locked loop. The proposed model is tested using both synthetic signals and real world EEG signals. The proposed model arises out of the general motivation to construct biologically inspired, oscillatory versions of some of the standard neural network models, and presents itself as an autoencoder network based on oscillatory neurons applicable to time series signals. As a demonstration, the model is applied to compression of EEG signals.

Neural Networks Retrieving Boolean Patterns in a Sea of Gaussian Ones

Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for associative memory. In this equivalence, weights in the former play as patterns in the latter. As Boltzmann machines usually require real weights to be trained with gradient descent like methods, while Hopfield networks typically store binary patterns to be able to retrieve, the investigation of a mixed Hebbian network, equipped with both real (e.g., Gaussian) and discrete (e.g., Boolean) patterns naturally arises. We prove that, in the challenging regime of a high storage of real patterns, where retrieval is forbidden, an extra load of Boolean patterns can still be retrieved, as long as the ratio among the overall load and the network size does not exceed a critical threshold, that turns out to be the same of the standard Amit-Gutfreund-Sompolinsky theory. Assuming replica symmetry, we study the case of a low load of Boolean patterns combining the stochastic stability and Hamilton-Jacobi interpolating techniques. The result can be extended to the high load by a non rigorous but standard replica computation argument.

Hebbian Network of Self-Organizing Receptive Field Neurons as Associative Incremental Learner

Associative learning plays a major role in the formation of the internal dynamic engine of an adaptive system or a cognitive robot. Interaction with the environment can provide a sparse and discrete set of sample correlations of input–output incidences. These incidences of associative data points can provide useful hints for capturing underlying mechanisms that govern the system’s behavioral dynamics. In many approaches to solving this problem, of learning system’s input–output relation, a set of previously prepared data points need to be presented to the learning mechanism, as a training data, before a useful estimations can be obtained. Besides data-coding is usually based on symbolic or nonimplicit representation schemes. In this paper, we propose an incremental learning mechanism that can bootstrap from a state of complete ignorance of any representative sample associations. Besides, the proposed system provides a novel mechanism for data representation in nonlinear manner through the fusion of self-organizing maps and Gaussian receptive fields. Our architecture is based solely on cortically-inspired techniques of coding and learning as: Hebbian plasticity and adaptive populations of neural circuitry for stimuli representation. We define a neural network that captures the problem’s data space components using emergent arrangement of receptive field neurons that self-organize incrementally in response to sparse experiences of system–environment interactions. These learned components are correlated using a process of Hebbian plasticity that relates major components of input space to those of the output space. The viability of the proposed mechanism is demonstrated through multiple experimental setups from real-world regression and robotic arm sensory-motor learning problems.

Novel FPGA Implementation of Hand Sign Recognition System With SOM–Hebb Classifier

This paper proposes a hardware posture recognition system with a hybrid network. The hybrid network consists of self-organizing map (SOM) and Hebbian network. Feature vectors are extracted from input posture images, which are mapped to a lower dimensional map of neurons in the SOM. The Hebbian network is a single-layer feedforward neural network trained with a Hebbian learning algorithm to identify categories. The recognition algorithm is robust to the change in location of hand signs, but it is not immune to rotation or scaling. Its robustness to rotation and scaling was improved by adding perturbation to the training data for the SOM–Hebb classifier. In addition, neuron culling is proposed to improve performance. The whole system is implemented on a field-programmable gate array employing novel video processing architecture. The system was designed to recognize 24 American sign language hand signs, and its feasibility was verified through both simulations and experiments. The experimental results revealed that the system could accomplish recognition at a speed of 60 frames/s, while achieving an accuracy of 97.1%. Due to a novel hardware implementation, the circuit size of the proposed system is very small, which is highly suitable for embedded applications.

Stability and Long Term Behavior of a Hebbian Network of Kuramoto Oscillators

We investigate the limit sets of a network of coupled Kuramoto oscillators with a coupling matrix determined by a Hebb rule. These limit sets are the output of the network if used for the recognition of a defective binary pattern out of several given patterns, with the output pattern encoded in the oscillators' phases. We show that if all pairs of given patterns have maximum Hamming distance, there exists a degenerate attractive limit set that contains the steady states corresponding to each of the given patterns. As a result, switching between output patterns occurs for arbitrarily small modifications of the dynamics (for example, due to frequency inaccuracies). Even if the maximum Hamming distance constraint is dropped, numerical results suggest that the structural instability of the vector field persists. We conclude that the unique interchangeability of output patterns in Hebbian networks of Kuramoto oscillators, while sacrificing robustness, makes these networks more flexible than similar neural networks with separated, attractive output states.

Pattern recognition minimizes entropy production in a neural network of electrical oscillators

Abstract We investigate the physical principle driving pattern recognition in a previously introduced Hopfield-like neural network circuit (Holzel and Krischer, 2011 [13] ). Effectively, this system is a network of Kuramoto oscillators with a coupling matrix defined by the Hebbian rule. We calculate the average entropy production 〈 d S / d t 〉 of all neurons in the network for an arbitrary network state and show that the obtained expression for 〈 d S / d t 〉 is a potential function for the dynamics of the network. Therefore, pattern recognition in a Hebbian network of Kuramoto oscillators is equivalent to the minimization of entropy production for the implementation at hand. Moreover, it is likely that all Hopfield-like networks implemented as open systems follow this mechanism.

Integrated Intelligent Control and Fault System for Wind Generators

The goal of this paper is to show the possibility of combining fault detection analysis, detection, modeling, and control of the doubly-fed induction generator (DFIG) wind turbine using intelligent control and diagnostic techniques. To enable online detection of problems inside the power electronics converter we apply the wave direct analysis method which enables a complete model for fault detection that includes the power electronic stage itself. A neural network system based on Hebbian networks is applied for fault classification with good detection results in simulation. For controlling the wind turbine a number different artificial intelligence techniques are presented including fuzzy logic and an adaptive fuzzy inference systems (ANFIS) which combines the characteristics of fuzzy logic and neural networks. A Grey predictor is also integrated in the control scheme for predicting the wind profile. The combined fault detection and control scheme are validated using simulation results. The software devel...

Pyramidal Neuron Conductance State Gates Spike-Timing-Dependent Plasticity

Neocortical neurons in vivo process each of their individual inputs in the context of ongoing synaptic background activity, produced by the thousands of presynaptic partners a typical neuron has. Previous work has shown that background activity affects multiple aspects of neuronal and network function. However, its effect on the induction of spike-timing dependent plasticity (STDP) is not clear. Here we report that injections of simulated background conductances (produced by a dynamic-clamp system) into pyramidal cells in rat brain slices selectively reduced the magnitude of timing-dependent synaptic potentiation while leaving the magnitude of timing-dependent synaptic depression unchanged. The conductance-dependent suppression also sharpened the STDP curve, with reliable synaptic potentiation induced only when EPSPs and action potentials (APs) were paired within 8 ms of each other. Dual somatic and dendritic patch recordings suggested that the deficit in synaptic potentiation arose from shunting of dendritic EPSPs and APs. Using a biophysically detailed computational model, we were not only able to replicate the conductance-dependent shunting of dendritic potentials, but show that synaptic background can truncate calcium dynamics within dendritic spines in a way that affects potentiation more strongly than depression. This conductance-dependent regulation of synaptic plasticity may constitute a novel homeostatic mechanism that can prevent the runaway synaptic potentiation to which Hebbian networks are vulnerable.