Prof Julian Hiscox, chair in infection and global health at the University of Liverpool, says that, through the efforts of scientists to sequence the virus, "we've got a really good handle on variants that emerge". In the short-term, only the harshest of lockdowns will reduce case numbers, he says.
But in the long term, Prof Hiscox suspects, we may face a scenario like flu, where new vaccines are developed and administered every year. Follow Helen on Twitter. New coronavirus variant: What do we know? Image source, Getty Images. Are mutations making coronavirus more infectious?
Hundreds of thousands of viral genomes have been analysed across the world. South Africa coronavirus variant: What's the risk? UK has two cases of variant found in South Africa. The spike protein foreground enables the virus to enter and infect human cells. Figure 1. Comparison of neuron models. A The neuron model used in most artificial neural networks has few synapses and no dendrites. B A neocortical pyramidal neuron has thousands of excitatory synapses located on dendrites inset.
The co-activation of a set of synapses on a dendritic segment will cause an NMDA spike and depolarization at the soma. There are three sources of input to the cell.
The feedforward inputs shown in green which form synapses proximal to the soma, directly lead to action potentials.
NMDA spikes generated in the more distal basal and apical dendrites depolarize the soma but typically not sufficiently to generate a somatic action potential. Active dendrites suggest a different view of the neuron, where neurons recognize many independent unique patterns Poirazi et al.
Experimental results show that the coincident activation of 8—20 synapses in close spatial proximity on a dendrite will combine in a non-linear fashion and cause an NMDA dendritic spike Larkum et al. Thus, a small set of neighboring synapses acts as a pattern detector. It follows that the thousands of synapses on a cell's dendrites act as a set of independent pattern detectors.
The detection of any of these patterns causes an NMDA spike and subsequent depolarization at the soma. It might seem that 8—20 synapses could not reliably recognize a pattern of activity in a large population of cells.
However, robust recognition is possible if the patterns to be recognized are sparse; i. We want a neuron to detect when a particular pattern occurs in the K cells. If a section of the neuron's dendrite forms new synapses to just 10 of the active cells, and the threshold for generating an NMDA spike is 10, then the dendrite will detect the target pattern when all 10 synapses receive activation at the same time.
Note that the dendrite could falsely detect many other patterns that share the same 10 active cells. However, if the patterns are sparse, the chance that the 10 synapses would become active for a different random pattern is small. In this example it is only 9. The probability of a false match can be calculated precisely as follows. Assuming a random distribution of patterns, the exact probability of a false match is given by:. The denominator is simply the total number of possible patterns containing a active cells in a population of n total cells.
A more detailed description of this equation can be found in Ahmad and Hawkins The equation shows that a non-linear dendritic segment can robustly classify a pattern by sub-sampling forming synapses to only a small number of the cells in the pattern to be classified. Table A in S1 Text lists representative error probabilities calculated from Equation 1. By forming more synapses than necessary to generate an NMDA spike, recognition becomes robust to noise and variation. The extra synapses also increase the likelihood of a false positive error.
Although the chance of error has increased, Equation 1 shows that it is still tiny when the patterns are sparse. Table B in S1 Text lists representative error rates when the number of synapses exceeds the threshold. The synapses recognizing a given pattern have to be co-located on a dendritic segment. If the synapses are spread out along the dendritic segment, then up to 20 synapses are needed Major et al.
A dendritic segment can contain several hundred synapses; therefore each segment can detect multiple patterns. If synapses that recognize different patterns are mixed together on the dendritic segment, it introduces an additional possibility of error by co-activating synapses from different patterns. The probability of this type of error depends on how many sets of synapses share the dendritic segment and the sparsity of the patterns to be recognized.
For a wide range of values the chance for this type of error is still low Table C in S1 Text. If we assume an average of 20 synapses are allocated to recognize each pattern, and that a neuron has synapses, then a cell would have the ability to recognize approximately different patterns.
This is a rough approximation, but makes evident that a neuron with active dendrites can learn to reliably recognize hundreds of patterns within a large population of cells. The recognition of any one of these patterns will depolarize the cell.
Since all excitatory neurons in the neocortex have thousands of synapses, and, as far as we know, they all have active dendrites, then each and every excitatory neocortical neuron recognizes hundreds of patterns of neural activity.
In the next section we propose that most of the patterns recognized by a neuron do not directly lead to an action potential, but instead play a role in how networks of neurons make predictions and learn sequences. Neurons receive excitatory input from different sources that are segregated on different parts of the dendritic tree. Figure 1B shows a typical pyramidal cell, the most common excitatory neuron in the neocortex.
We show the input to the cell divided into three zones. The proximal zone receives feedforward input. The basal zone receives contextual input, mostly from nearby cells in the same cortical region Yoshimura et al. The apical zone receives feedback input Spruston, The second most common excitatory neuron in the neocortex is the spiny stellate cell; we suggest they be considered similar to pyramidal cells minus the apical dendrites.
We propose the three zones of synaptic integration on a neuron proximal, basal, and apical serve the following purposes. The synapses on the proximal dendrites typically several hundred have a relatively large effect at the soma and therefore are best situated to define the basic receptive field response of the neuron Spruston, If the coincident activation of a subset of the proximal synapses is sufficient to generate a somatic action potential and if the inputs to the proximal synapses are sparsely active, then the proximal synapses will recognize multiple unique feedforward patterns in the same manner as discussed earlier.
Therefore, the feedforward receptive field of a cell can be thought of as a union of feedforward patterns. We propose that basal dendrites of a neuron recognize patterns of cell activity that precede the neuron firing, in this way the basal dendrites learn and store transitions between activity patterns. When a pattern is recognized on a basal dendrite it generates an NMDA spike.
The depolarization due to an NMDA spike attenuates in amplitude by the time it reaches the soma, therefore when a basal dendrite recognizes a pattern it will depolarize the soma but not enough to generate a somatic action potential Antic et al. We propose this sub-threshold depolarization is an important state of the cell. It represents a prediction that the cell will become active shortly and plays an important role in network behavior.
A slightly depolarized cell fires earlier than it would otherwise if it subsequently receives sufficient feedforward input. By firing earlier it inhibits neighboring cells, creating highly sparse patterns of activity for correctly predicted inputs.
We will explain this mechanism more fully in a later section. An apical NMDA spike does not directly affect the soma. We propose that the depolarization caused by the apical dendrites is used to establish a top-down expectation, which can be thought of as another form of prediction.
Figure 1C shows an abstract model of a pyramidal neuron we use in our software simulations. We model a cell's dendrites as a set of threshold coincidence detectors; each with its own synapses. The coincidence detectors are in three groups corresponding to the proximal, basal, and apical dendrites of a pyramidal cell. For clarity, Figure 1C shows only a few dendrites and synapses. Because all tissue in the neocortex consists of neurons with active dendrites and thousands of synapses, it suggests there are common network principles underlying everything the neocortex does.
This leads to the question, what network property is so fundamental that it is a necessary component of sensory inference, prediction, language, and motor planning?
More specifically, we propose that each cellular layer in the neocortex implements a variation of a common sequence memory algorithm. We propose cellular layers use sequence memory for different purposes, which is why cellular layers vary in details such as size and connectivity. In this paper we illustrate what we believe is the basic sequence memory algorithm without elaborating on its variations.
We started our exploration of sequence memory by listing several properties required of our network in order to model the neocortex. Learning must be continuous.
If the statistics of the world change, the network should gradually and continually adapt with each new input. Making correct predictions with complex sequences requires the ability to incorporate contextual information from the past. The network needs to dynamically determine how much temporal context is needed to make the best predictions.
Natural data streams often have overlapping and branching sequences. The sequence memory therefore needs to make multiple predictions at the same time. The sequence memory must only use learning rules that are local to each neuron. The rules must be local in both space and time, without the need for a global objective function. The memory should exhibit robustness to high levels of noise, loss of neurons, and natural variation in the input.
Degradation in performance under these conditions should be gradual. All these properties must occur simultaneously in the context of continuously streaming data. High-order sequence memory requires two simultaneous representations. One represents the feedforward input to the network and the other represents the feedforward input in a particular temporal context. Figure 2 illustrates how we propose these two representations are manifest in a cellular layer of cortical neurons.
The panels in Figure 2 represent a slice through a single cellular layer in the neocortex Figure 2A. The panels are greatly simplified for clarity. Figure 2B shows how the network represents two input sequences before the sequences are learned. Figure 2C shows how the network represents the same input after the sequences are learned. Each feedforward input to the network is converted into a sparse set of active mini-columns.
Mini-columns in the neocortex span multiple cellular layers. Here we are only referring to the cells in a mini-column in one cellular layer. All the neurons in a mini-column share the same feedforward receptive fields.
If an unanticipated input arrives, then all the cells in the selected mini-columns will recognize the input pattern and become active.
However, in the context of a previously learned sequence, one or more of the cells in the mini-columns will be depolarized. The depolarized cells will be the first to generate an action potential, inhibiting the other cells nearby. Thus, a predicted input will lead to a very sparse pattern of cell activation that is unique to a particular element, at a particular location, in a particular sequence.
Figure 2. Representing sequences in cortical cellular layers. A The neocortex is divided into cellular layers. The panels in this figure show part of one generic cellular layer. For clarity, the panels only show 21 mini-columns with 6 cells per column.
Each sequence element invokes a sparse set of mini-columns, only three in this illustration. All the cells in a mini-column become active if the input is unexpected, which is the case prior to learning the sequences.
In this theory, cells use their basal synapses to learn the transitions between input patterns. With each new feedforward input some cells become active via their proximal synapses. Other cells, using their basal synapses, learn to recognize this active pattern and upon seeing the pattern again, become depolarized, thereby predicting their own feedforward activation in the next input.
Feedforward input activates cells, while basal input generates predictions. As long as the next input matches the current prediction, the sequence continues, Figure 3.
Figure 3A shows both active cells and predicted cells while the network follows a previously learned sequence. Figure 3. Basal connections to nearby neurons predict the next input. If the subsequent input matches the prediction then only the depolarized cells will become active third panel , which leads to a new prediction fourth panel.
The lateral synaptic connections used by one of the predicted cells are shown in the rightmost panel. In a realistic network every predicted cell would have 15 or more connections to a subset of a large population of active cells.
The third panel shows the system after input C. Both sets of predicted cells become active, which leads to predicting both D and Y fourth panel. In complex data streams there are typically many simultaneous predictions. Often the network will make multiple simultaneous predictions. The number of simultaneous predictions that can be made with low chance of error can again be calculated via Equation 1.
Because the predictions tend to be highly sparse, it is possible for a network to predict dozens of patterns simultaneously without confusion. If an input matches any of the predictions it will result in the correct highly-sparse representation. If an input does not match any of the predictions all the cells in a column will become active, indicating an unanticipated input.
Although every cell in a mini-column shares the same feedforward response, their basal synapses recognize different patterns. Therefore, cells within a mini-column will respond uniquely in different learned temporal contexts, and overall levels of activity will be sparser when inputs are anticipated. Both of these attributes have been observed Vinje and Gallant, ; Yen et al. For one of the cells in the last panel of Figure 3A , we show three connections the cell used to make a prediction.
In real neurons, and in our simulations, a cell would form 15 to 40 connections to a subset of a larger population of active cells. Feedback axons between neocortical regions often form synapses in layer 1 with apical dendrites of pyramidal neurons whose cell bodies are in layers 2, 3, and 5. It has long been speculated that these feedback connections implement some form of expectation or bias Lamme et al.
Our neuron model suggests a mechanism for top-down expectation in the neocortex. Figure 4 shows how a stable feedback pattern to apical dendrites can predict multiple elements in a sequence all at the same time. When a new feedforward input arrives it will be interpreted as part of the predicted sequence. The feedback biases the input toward a particular interpretation. Again, because the patterns are sparse, many patterns can be simultaneously predicted.
Figure 4. Feedback to apical dendrites predicts entire sequences. This figure uses the same network and representations as Figure 2. In the figure, the following assumptions have been made. After the feedback connections have been learned, presentation of the feedback pattern to the apical dendrites is simultaneously recognized by all the cells that would be active sequentially in the sequence. These cells, shown in red, become depolarized left pane.
When a new feedforward input arrives it will lead to the sparse representation relevant to the predicted sequence middle panel. If a feedforward pattern cannot be interpreted as part of the expected sequence right panel then all cells in the selected columns become active indicative of an anomaly.
In this manner apical feedback biases the network to interpret any input as part of an expected sequence and detects if an input does not match any one of the elements in the expected sequence. Thus, there are two types of prediction occurring at the same time. Lateral connections to basal dendrites predict the next input, and top-down connections to apical dendrites predict multiple sequence elements simultaneously.
The physiological interaction between apical and basal dendrites is an area of active research Larkum, and will likely lead to a more nuanced interpretation of their roles in inference and prediction. However, we propose that the mechanisms shown in Figures 2 — 4 are likely to continue to play a role in that final interpretation.
Our neuron model requires two changes to the learning rules by which most neural models learn. For a neuron to recognize a pattern of activity it requires a set of co-located synapses typically 15—20 that connect to a subset of the cells that are active in the pattern to be recognized. Learning to recognize a new pattern is accomplished by the formation of a set of new synapses collocated on a dendritic segment. Figure 5 shows how we model the formation of new synapses in a simulated HTM neuron.
The number of potential synapses is larger than the number of actual synapses. A permanence value close to zero represents an axon and dendrite with the potential to form a synapse but that have not commenced growing one. Figure 5. Learning by growing new synapses. Learning in an HTM neuron is modeled by the growth of new synapses from a set of potential synapses.
Learning occurs by incrementing or decrementing permanence values. The synapse weight is a binary value set to 1 if the permanence is above a threshold. The permanence value is incremented and decremented using a Hebbian-like rule. If the permanence value exceeds a threshold, such as 0.
The threshold represents the establishment of a synapse, albeit one that could easily disappear. A synapse with a permanence value of 1. Using a scalar permanence value enables on-line learning in the presence of noise. A previously unseen input pattern could be noise or it could be the start of a new trend that will repeat in the future.
By growing new synapses, the network can start to learn a new pattern when it is first encountered, but only act differently after several presentations of the new pattern. Increasing permanence beyond the threshold means that patterns experienced more than others will take longer to forget. HTM neurons and HTM networks rely on distributed patterns of cell activity, thus the activation strength of any one neuron or synapse is not very important.
Therefore, in HTM simulations we model neuron activations and synapse weights with binary states. Additionally, it is well known that biological synapses are stochastic Faisal et al.
Although scalar states and weights might improve performance, they are not required from a theoretical point of view and all of our simulations have performed well without them. The formal learning rules used in our HTM network simulations are presented in the Materials and Methods section.
Figure 6 illustrates the performance of a network of HTM neurons implementing a high-order sequence memory. The network used in Figure 6 consists of mini-columns with 32 neurons per mini-column.
Each neuron has basal dendritic segments, and each dendritic segment has up to 40 actual synapses. Because this simulation is designed to only illustrate properties of sequence memory it does not include apical synapses. The network exhibits all five of the desired properties for sequence memory listed earlier. Collaborations: The rise of research networks Oct Trendwatch: the decline of the single author. Reprints and Permissions. Castelvecchi, D. Physics paper sets record with more than 5, authors.
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