Therefore, the Hopfield network model is shown to confuse one stored item with that of another upon retrieval. The Hopfield model accounts for associative memory through the incorporation of memory vectors. Memory vectors can be slightly used, and this would spark the retrieval of the most similar vector in the network. However, we will find out that due to this process, intrusions can occur. In associative memory for the Hopfield network, there are two types of operations: auto-association and hetero-association. The first being when a vector is associated with itself, and the latter being when two different vectors are associated in storage.
Furthermore, both types of operations are possible to store within a single memory matrix, but only if that given representation matrix is not one or the other of the operations, but rather the combination auto-associative and hetero-associative of the two. It is important to note that Hopfield's network model utilizes the same learning rule as Hebb's learning rule , which basically tried to show that learning occurs as a result of the strengthening of the weights by when activity is occurring.
Rizzuto and Kahana were able to show that the neural network model can account for repetition on recall accuracy by incorporating a probabilistic-learning algorithm. During the retrieval process, no learning occurs. As a result, the weights of the network remain fixed, showing that the model is able to switch from a learning stage to a recall stage. By adding contextual drift they were able to show the rapid forgetting that occurs in a Hopfield model during a cued-recall task. The entire network contributes to the change in the activation of any single node.
McCulloch and Pitts' dynamical rule, which describes the behavior of neurons, does so in a way that shows how the activations of multiple neurons map onto the activation of a new neuron's firing rate, and how the weights of the neurons strengthen the synaptic connections between the new activated neuron and those that activated it. Hopfield would use McCulloch-Pitts's dynamical rule in order to show how retrieval is possible in the Hopfield network. However, it is important to note that Hopfield would do so in a repetitious fashion.
Hopfield would use a nonlinear activation function, instead of using a linear function. This would therefore create the Hopfield dynamical rule and with this, Hopfield was able to show that with the nonlinear activation function, the dynamical rule will always modify the values of the state vector in the direction of one of the stored patterns.
From Wikipedia, the free encyclopedia. An Introduction to Neural Networks. Modeling brain function: The world of attractor neural networks. Cerebral cortex: principles of operation. Hopfield Networks". Information Theory, Inference and Learning Algorithms. Cambridge University Press. This convergence proof depends crucially on the fact that the Hopfield network's connections are symmetric. It also depends on the updates being made asynchronously.
The organization of behavior: A neuropsychological theory. Lawrence Erlbaum, Krogh, and Richard G. Introduction to the theory of neural computation. Westview press, Natural Computing. Biological Cybernetics. Hopfield, "Neural networks and physical systems with emergent collective computational abilities" , Proceedings of the National Academy of Sciences of the USA , vol.
Hebb, D. Organization of behavior. New York: Wiley Hertz, J. McCulloch, W. Bulletin of Mathematical Biophysics.
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Polyn, S. Trends in Cognitive Sciences. Rizzuto, D. Neural Computation. Computational Intelligence. Stochastic processes. Bernoulli process Branching process Chinese restaurant process Galton—Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding Biased Maximal entropy.
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Involvement of visual cortices in the healthy brain can be explained by their role in grounding symbolic meaning in visual perception of objects and their features 6 , 68 , However, under sensory deprivation, it is impossible that the correlation between visual and linguistic information leads to the strengthening of neuronal links into visual streams because blind people lack such modality-specific grounding information. Here, we show that a spiking neural network constrained by cortical neuroanatomy and function and obeying well-established neuroscience principles can simulate the known visual cortex recruitment in both sighted and blind individuals during word meaning acquisition.
The neuromechanistic explanatory account that we wish to offer based on these network simulations builds upon two mechanisms. In a network with random connectivity between spontaneously active neurons, a neuron firing above the level of its connected neighbours will strengthen its links to some of these neighbours, therefore giving rise to the spontaneous emergence of a relatively more strongly connected set of neurons Stimulus- and action-induced uncorrelated activity in the extrasylvian streams of the network is critical for preventing the expansion of CA circuits into these streams.
In this sense, it is the variability of visual inputs in processing action-related symbols that guarantees variable activation in the visual stream and therefore neural activity uncorrelated to these symbolic-linguistic activations. Our present simulations suggest that it is the absence of uncorrelated input to the ventral visual stream in the blind network and brain that is necessary for DB-expansion of action-word-related CA circuits.
In essence, as observed in previous simulations 16 , 17 , 18 , the uncorrelated visual input is crucial for preventing DB-expansion of action-word-related circuits into visual areas of the undeprived brain. The relatively weaker visual activation in language processing in healthy people is explained by noise-related CA growth suppression. As mentioned in the Introduction, neuroimaging studies documented relatively stronger activation of the primary visual area fMRI activity in V1 in blind than in undeprived individuals when generating semantically related verbs to given nouns 22 , 23 , Consistently, a study employing transcranial magnetic stimulation TMS in the primary visual area reported impairments in the verb generation task in blind but not in sighted individuals The verb generation task implies the activation of multiple CA circuits for verbs, most of which are action-related 71 , and this engages the ventral visual system more in blind people than in undeprived control subjects.
Stronger V1 activation in blind than in sighted people has also been reported during sentence processing see Fig. These results represent a significant advance in the debate about the mechanisms underlying the neural changes in the visual cortex: evidence indicates that such cortical areas can take over a particular function depending on input information received during the developmental period 45 ; On the basis of our results, it is precisely the lack of informative input to visual cortex that drives the Hebbian synaptic modifications and consequent extension of linguistic representations into visual cortex seen in congenitally blind individuals.
The underlying mechanisms are consistent with general neurobiological plasticity principles documented in other deprived sensory systems 72 , 73 and, even though a higher cognitive function, language, is involved, the explanation rests on the same neuroscience principles.
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Sustained neural activity is a neural correlate of working memory 74 , 75 , which, in the present study, persisted longer in the blind compared to the sighted model. This phenomenon in the network is consistent with the observation of enhanced verbal working memory performance in congenitally blind individuals compared to control sighted ones 22 , 31 , 32 , In the present simulation of undeprived referential-semantic learning, CA circuits emerged spontaneously across the fronto-temporo-occipital areas of the spiking neural network linking word-form in the perisylvian cortex with semantic information about referent objects and actions in the extrasylvian system.
This was meant to specifically simulate a learning situation in which the meaning of such action words is acquired in the absence of any visual input i. The current observations and their possible explanation in terms of DB-expansion of CA circuits and noise-related suppression of such growth suggest that these mechanisms are more broadly applicable to cases of sensory deprivation. Similar to blind individuals, deaf individuals activate their deprived auditory cortex in processing visual stimuli 78 and in the processing of visually presented units of their native language, typically a manual signing system Some of these results had previously been used to strongly argue for an inborn mechanism linking abstract but not acoustic or other sensory or motor features of language to specific brain parts.
Our present work offers an alternative explanation based on established neurobiological mechanisms see Results, points i — v — vi. For object-related words, simulation results indicate a generally reduced relevance of extrasylvian areas in blind people — both compared with action words in the same population and compared with the same word type in the healthy undeprived see Fig.
This suggests reduced grounded semantic knowledge in blind people, at least for some specific word types requiring visual knowledge for complete acquisition of their related concepts. For the semantics of colour terms, such partially deficient semantic knowledge in the blind has been supported by experimental studies 80 , 81 , although other work reported comparable semantic similarity ratings However, for other object-related words, it is less plausible that substantial differences in semantic knowledge are present between congenitally blind and sighted infants.
It is known that, when blind people learn words for objects, they naturally draw more on manual exploration and touch than undeprived individuals. This and similar observations suggest that, for a range of words typically grounded in visual experience, congenitally blind individuals use tactile and motor knowledge in the semantic grounding process. This difference in stimulation modality implies a degree of similarity between semantic grounding processes of object and action words in the blind.
On the other hand, this difference in modality also implies that congenitally blind people can use similar grounding information for object words as healthy subjects, although this same or very similar information is provided through a different channel. This is particularly the case if information about the form or shape of referent objects is acquired through vision or tactile exploration.
Future experimental works and simulation studies are still needed to explore more closely the learning of different subtypes of visually-related words in blind brains and networks taking into account, in particular, information in the tactile modality. Instead of aiming at capturing such fine-grained differences in semantic grounding, our present study specifically addressed the effect of sensory deprivation and the consequent conquering of visual cortex by linguistic and semantic processes.
We wish to conclude by pointing to further obvious limitations of the present work. Useful next steps in the modelling effort shall focus on the acquisition of novel word meaning in the context of already grounded meaningful words 84 , 85 and on the learning of word sequences and whole constructions along with their semantics. With regard to blind individuals, we have restricted our scope to congenitally blind subjects, because they provide the clearest case of deprivation. The more complex situation of later deprivation, where normal learning takes place first and deprivation kicks in at a later stage, may also provide a basis for fruitful future simulations.
We note that there are some important differences in reorganisation processes between congenitally, early and late blind persons 23 , 86 , 87 , which may be attributed to altered learning histories and possibly also to altered neural substrates and plasticity at different developmental stages. In spite of its focus on only one type of semantic learning and only the most typical type of visual sensory deprivation, our model offers a novel neurobiological explanation of the linguistic recruitment of visual cortex.
In sum, the present study aimed to simulate the effect of visual deprivation on the neuronal mechanisms of semantic and language processing in sighted and congenitally blind people by means of a neurobiological constrained neural network of the frontal, temporal and occipital lobes.
Specifically, we focus on the mechanisms responsible for the activation of the deprived areas during semantic processing consistently reported by a number of experimental studies described above, and show that the interaction of three main factors may lead to the takeover of visual cortex for linguistic and semantic processing: i the changes in the balance of activity related to the absence of uncorrelated sensory input, ii constrained neuroanatomical connectivity and iii Hebbian correlation learning.
The present architecture explains action-related word processing in both dorsal motor and deprived ventral visual streams. Here we bridge the gap between neural mechanisms and conceptual brain functions, offering a biological account of visual cortex reorganization following sensory loss from birth and its functional recruitment for language and semantic processing.
The state of each cell x is uniquely defined by its membrane potential V x , t , specified by the following equation:. Note that noise is an inherent property of each model cell, intended to mimic the spontaneous activity baseline firing of real neurons. Local lateral inhibitory connections see Fig. More precisely, in Eq. Excitatory links within and between possibly non-adjacent model areas are established at random and limited to a local topographic neighbourhood; weights are initialised at random, in the range [0, 0.
This produces a sparse, patchy and topographic connectivity, as typically found in the mammalian cortex 59 , 61 , 93 , This rule provides a realistic approximation of known experience-dependent neuronal plasticity and learning 96 , 97 , 98 , and includes both homo- and hetero-synaptic, or associative LTP, as well as homo- and hetero-synaptic LTD.
Following Artola et al. The between-area connectivity binds adjacent cortical areas together 99 , , In the perisylvian system, next-neighbour connections between cortically adjacent areas are implemented within the auditory A1, AB, PB , , , as well as within the articulatory PF i , PM i , M1 i sub-systems 99 , The long distance cortico-cortical connections implemented reciprocally link all pairs of multimodal hub areas PB, PF i , AT and PF L of the four sub-systems, modelling documented anatomical connections between inferior pre-frontal PF i and auditory parabelt PB , , , , , , and between anterior-temporal AT and lateral prefrontal PF L areas, realised by the arcuate and the uncinated fascicles , , , , , , These links exist within auditory superior temporal and articulatory inferior frontal cortex of the perisylvian cortex, that is amongst: primary auditory A1 - parabelt PB areas 99 , , parabelt PB - inferior premotor PM i areas , auditory belt AB - inferior prefrontal PF i , , and as well inferior prefrontal PF i - primary motor M1 i areas , , The ventral visual and the dorsolateral motor sub-systems of the extrasylvian cortex were also endowed with jumping links, similarly to the perisylvian cortices listed above.
In particular, primary visual V1 area is reciprocally linked to anterior-temporo AT area , , as well as anterior-temporo AT and dorsolateral premotor PM L area, as documented by both anatomical , and monkey studies , , Additional jumping links were implemented between temporo-occipital TO and dorsolateral prefrontal areas PF L , as supported by evidence from anatomical studies in humans and monkeys , , , , and between dorsolateral prefrontal PF L and dorsolateral premotor M1 L areas , , Further neuroanatomical DTI studies also showed connections within the extrasylvian system as described above Notice that the connectivity structure of both sighted and blind models was kept the same, as a number of DTI studies have shown similar anatomical connectivity structure between sighted and blind populations 38 , 39 , 40 , Similar to previous simulation studies 16 , 17 , 18 , 55 , word-meaning acquisition was then simulated under the impact of repeated sensorimotor pattern presentations to the primary areas of the network.
Each network instance used 12 different sets of sensorimotor word patterns representing six object- and six action-related words. This partly accounted for a degree of variability during word meaning acquisition of the two word-types.
A trial started with a word pattern presentation for 16 simulation time steps, followed by a period during which no input interstimulus interval — ISI was given. The next word pattern learning step was presented to the network only when the global inhibition of the PF i and PB areas decreased below a specific fixed threshold; this allowed the activity to return to a baseline value, so as to minimise the possibility of one trial affecting the next one.
Cell assemblies, which are strongly interconnected networks of neurons, spontaneously emerged during word learning simulation.
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More formally,. This was computed for each of the 13 trained network instances, averaging the number of CA cells per area over the 6 object- and 6 action-related words. To investigate the presence of significant statistical differences between sighted and blind neural network models, we performed an initial statistical analysis including both neural network models. Blind , WordType two levels: Object vs. Additionally, to further investigate differences of the modelled cortical regions between the two models a 5-way ANOVA was run with factors Model two levels: Sighted vs. Broca, P. Wernicke, C.
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