Version classiqueVersion mobile
OpenEdition Books

Les arts de la mémoire et les images mentales

 | 
Alain Berthoz
, 
John Scheid

A scientific theory of ars memoriae: spatial view cells in a continuous attractor network with linked items

Edmund T. Rolls

Texte intégral

1. Introduction

  • 1 Cicero, 55 BC.
  • 2 Yates, 1992.

1Simonides of Ceos lived to tell the story of how, when a banquet hall collapsed in an earthquake, he could identify all the victims by recalling from each place at the table who had been sitting there1. This way of remembering items was developed into what has become known as ars memoriae, used by Roman senators to present the steps of a complex legal argument in a speech that might last an entire day. They would do so by associating each step in the argument with a location in a spatial scene, through which their memory could progress from one end to the other during the speech to recall each item in the correct order2.

  • 3 Rolls, 2017a.

2Why is ars memoriae so successful in helping us to remember complex series of points, arguments, people, or objects? The aim of this chapter is to provide a scientific theory of why ars memoriae is very effective. I first develop the theory by describing the empirical and theoretical foundations (sections 2 and 3), and then present the theory itself (section 4). A more detailed account of the theory is available elsewhere3.

2. Empirical foundations: spatial view cells in the primate hippocampus

  • 4 O’Keefe, 1990; O’Keefe and Dostrovsky, 1971.
  • 5 Hafting et al., 2005; Moser et al., 2014.

3We can start with the well-known place cells discovered in the rat hippocampus by O’Keefe and colleagues4, and which were recognized in the award of the Nobel prize in 2015 to John O’Keefe, and to Edvard and May-Britt Moser for the discovery of entorhinal cortex grid cells, which fire to repeated places in the environment as the rat traverses the places5. Unfortunately, these rat place and grid cells will not help to explain the memory of items in a spatial scene when a human is in one place moving the eyes across the whole spatial scene, for no place or grid cells would alter their firing if the subject was stationary.

  • 6 Feigenbaum and Rolls, 1991; Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 19 (...)
  • 7 Rolls et al., 1998.
  • 8 Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1997; Rolls et al., 1998.
  • 9 Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1997; Rolls et al., 1998.
  • 10 Robertson et al., 1998.
  • 11 Rolls and Xiang, 2006.

4More promising are the hippocampal spatial view cells which respond when a macaque looks at one point in a spatial scene with relative independence of the place where the monkey is located6 (see example of a typical spatial view neuron in Fig. 1). Each hippocampal neuron responds to a different spatial view, that is, when a different part of the spatial scene is looked at7. Each spatial view cell has an approximately Gaussian shape of its spatial view field, with the peak of activity at one point in a scene, and gradually decreasing the further away from its peak is fixated8. Provided that the monkey is looking at a given part of the scene, the exact place where the monkey is has little effect9. In other words, the neurons encode spatial view, not place. Many of these spatial view neurons respond when a scene is being remembered, for example when the scene is obscured with curtains and the lights are turned off10, or when a position in a spatial scene is recalled from an object originally shown at that position in the scene, or vice versa11.

Figure 1

Figure 1

Examples of the firing of a hippocampal spatial view cell when the monkey was walking around the laboratory. (a) The firing of the cell is indicated by the spots in the outer set of 4 rectangles, each of which represents one of the walls of the room. There is one spot in the outer rectangle for each action potential. The base of the wall is towards the centre of each rectangle. The positions on the walls fixated during the recording sessions are indicated by points in the inner set of 4 rectangles, each of which also represents a wall of the room. The central square is a plan view of the room, with a triangle printed every 250 ms to indicate the position of the monkey, thus showing that many different places were visited during the recording sessions. A spot is printed every 250 ms in the inner rectangles to show that a wide range of spatial locations was viewed. (b) A similar representation of the same 3 recording sessions as in (a), but modified to indicate more fully the range of places when the cell fired at more than 12 spikes/s, to indicate that this is not a place cell, but a spatial view cell. The triangle indicates the current position of the monkey. The same data are shown in the inner and outer rectangles, and each dot represents one action potential. c1–c4 are cups in which food may be found. T1 and T2 are trolleys at fixed positions within the space within which the monkey can walk freely. The four walls of the room are situated 1-3 mm from the 3 × 3 m space in which the monkey can walk, and are part of a rich laboratory environment with windows, door, apparatus etc.

After Georges-François, Rolls and Robertson, 1999

  • 12 Rolls et al., 2005.
  • 13 Rolls and Xiang, 2006.
  • 14 Rolls and Xiang, 2005.

5Now these spatial view cells do appear to be involved in memory, for in a task in which the location in the scene where an object was seen must be remembered, some macaque hippocampal neurons respond to the place in the scene where the object is shown, some to the object, and some to a combination of the two12. Moreover, some of these neurons respond in an object-place memory task when a place in a scene is recalled from an object13. Primate hippocampal neurons also associate spatial view with the reward available at a viewed location14.

3. Theoretical foundations: a theory of the hippocampal CA3 system as an object-spatial view memory system

  • 15 Kesner and Rolls, 2015; Rolls, 1989a, 1990, 2016; Rolls and Kesner, 2006; Rolls and Treves, 1994; T (...)

6Figure 2 shows how object representations, for example from the temporal lobes, are brought together with spatial representations, for example from the parietal lobe, especially in the CA3 hippocampal recurrent collateral network. This network potentially allows objects to be associated with places15.

Figure 2

Figure 2

Forward connections (solid lines) from areas of cerebral association neocortex via the parahippocampal gyrus and perirhinal cortex, and entorhinal cortex, to the hippocampus; and backprojections (dashed lines) via the hippocampal CA1 pyramidal cells, subiculum, and parahippocampal gyrus to the neocortex.There is wide convergence in the forward connections down to the single network implemented in the CA3 pyramidal cells; and wide divergence again in the back projections. Left: block diagram. Right: more detailed representation of some of the principal excitatory neurons in the pathways. Abbreviations: D stands for Deep pyramidal cells. DG: Dentate Granule cells. F: Forward inputs to areas of the association cortex from preceding cortical areas in the hierarchy. mf: mossy fibres. PHG: parahippocampal gyrus and perirhinal cortex. pp: perforant path. rc: recurrent collateral of the CA3 hippocampal pyramidal cells. S: Superficial pyramidal cells. 2: pyramidal cells in layer 2 of the entorhinal cortex. 3: pyramidal cells in layer 3 of the entorhinal cortex. The thick lines above the cell bodies represent the dendrites.

All rights reserved

3.1. The functional architecture of the CA3 recurrent collateral network

  • 16 Kesner and Rolls, 2015; Rolls, 1987, 1989a, 1989b, 1990, 1996, 2008, 2016; Rolls and Kesner, 2006; (...)
  • 17 Kondo et al., 2009.

7A quantitative theory has been developed on how the hippocampus helps to encode episodic memory, for example the memory of a particular scene with people or objects in it16. Within this theory, the CA3 pyramidal cell to CA3 pyramidal cell recurrent collateral system, which is highly developed in primates17 provides the basis for an autoassociation or attractor network. In such a network, a particular object activating a small subset of neurons becomes associated with a particular place by associative synaptic modification. Later, presentation of the object can recall the place using the strengthened synapses; or a place can be recalled from the object.

  • 18 See Andersen et al., 2007; Jackson, 2013; Lynch, 2004; Morris, 2003; Morris et al., 2003; Nakazawa (...)
  • 19 Rolls, 2016; Rolls and Treves, 1998.
  • 20 Hertz et al., 1991; Hopfield, 1982; Rolls, 2008, 2016; Rolls and Treves, 1998; Treves and Rolls, 19 (...)
  • 21 Rolls, 2016.

8More formally, many of the synapses in the hippocampus show associative modification as shown by long-term potentiation, and this synaptic modification appears to be involved in learning18. The architecture of an autoassociation network is shown in Fig. 3, and the learning rule is as shown in Eqn. (1) below19. The operation and properties of autoassociation or attractor networks have been described in detail elsewhere20. Neuronal network software to illustrate the properties of attractor networks is available21 (see http://www.oxcns.org).

Figure 3

Figure 3

The architecture of a continuous attractor neural network (CANN). The architecture is the same as that of a discrete attractor neural network. During learning, external inputs ei with Gaussian spatial fields force the output neurons to fire with rates ri, the recurrent collaterals produce the same rates rj as the presynaptic inputs to the neurons, and the synapses wij become associatively modified. Many different inputs, each corresponding to a different spatial representation, are applied during learning, and the synapses between every pair of neurons come to represent the distance between the positions represented by each pair of neurons. The neurons shown are excitatory, and inhibitory neurons maintain the average firing so that some of the neurons that correspond to one part of the space are firing, and keep one another firing by the excitatory synaptic connections between them, to provide a packet or bubble of neuronal activity, as illustrated in Fig. 4. Because of the Gaussian spatial response profile of each neuron, the space defined is continuous. Thus, as the space is traversed from one end to the other, the bubble of activity moves continuously through the space.

All rights reserved

  • 22 Ishizuka et al., 1990; Witter, 2007.
  • 23 Kondo et al., 2009.

9The hypothesis is that because the CA3 operates effectively as a single autoassociation network, it can allow arbitrary associations between inputs originating from very different parts of the cerebral cortex to be formed. These might involve associations between information originating in the temporal visual cortex about the presence of an object, and information originating in the parietal cortex about where it is. I note that although there is some spatial gradient in the CA3 recurrent connections, so that the connectivity is not fully uniform22, the network will nevertheless still have the properties of a single interconnected autoassociation network allowing associations between arbitrary neurons to be formed, given the presence of many long-range connections which overlap from different CA3 cells. It is very interesting indeed that in primates (macaques), the associational projections from CA3 to CA3 travel extensively along the longitudinal axis, and overall the radial, transverse, and longitudinal gradients of CA3 fiber distribution, clear in the rat, are much more subtle in the nonhuman primate brain23. The implication is that in primates, the CA3 network operates even more as a single network than in rodents.

10A fundamental property of the autoassociation model of the CA3 recurrent collateral network is that the recall can be symmetric, that is, the whole of the memory can be retrieved from any part. For example, in an object-place autoassociation memory, an object could be recalled from a place retrieval cue, and vice versa.

3.2. Continuous, spatial, patterns and CA3 representations

  • 24 Kesner and Rolls, 2015; Rolls, 2008, 2016.

11The fact that spatial patterns, which imply continuous representations of space such as those provided by spatial view cells in primates and place cells in rodents, are represented in the hippocampus, has led to the application of continuous attractor models to help understand hippocampal function. This has been necessary because space is inherently continuous, because the firing of place and spatial view cells is approximately Gaussian as a function of the distance away from the preferred spatial location, because these cells have spatially overlapping fields, and because the theory is that these cells in CA3 are connected by Hebb-modifiable synapses24.

  • 25 Amari, 1977; Battaglia and Treves, 1998; Rolls, 2016; Rolls and Stringer, 2005; Stringer and Rolls, (...)
  • 26 Rolls, 2008.
  • 27 Rolls, 2016.

12A continuous attractor neural network (CANN) can maintain the firing of its neurons to represent any location along a continuous physical dimension such as spatial position, head direction, etc.25. It uses excitatory recurrent collateral connections between the neurons (as are present in CA3) to reflect the distance between the neurons in the state space of the animal (e.g. place or spatial view). These networks can maintain the bubble of neural activity constant for long periods wherever it has started to represent the current state (spatial view, place, etc.) of the animal, and are likely to be involved in many aspects of spatial processing and memory, including spatial vision26. Global inhibition is used to keep the number of neurons in a bubble or packet of actively firing neurons relatively constant, and to help to ensure that there is only one activity packet. Continuous attractor networks can be thought of as very similar to autoassociation or discrete attractor networks27, and have the same architecture, as illustrated in Fig. 3. The main difference is that the patterns stored in a CANN are continuous patterns, with each neuron having broadly tuned firing which decreases with for example a Gaussian function as the distance from the optimal firing location of the neuron is varied, and with different neurons having tuning that overlaps throughout the space. Such tuning is illustrated in Fig. 4. For comparison, autoassociation networks normally have discrete (separate) patterns (each pattern implemented by the firing of a particular subset of the neurons), with no continuous distribution of the patterns throughout the space (see Fig. 4). A consequent difference is that the CANN can maintain its firing at any location in the trained continuous space, whereas a discrete attractor or autoassociation network moves its population of active neurons towards one of the previously learned attractor states, and thus implements the recall of a particular previously learned pattern from an incomplete or noisy (distorted) version of one of the previously learned patterns.

Figure 4

Figure 4

The types of firing patterns stored in continuous attractor networks are illustrated for the patterns present on neurons 1-1000 for Memory 1 (when the firing is that produced when the spatial state represented is that at location 300), and for Memory 2 (when the firing is that produced when the spatial state represented is that of location 500). The continuous nature of the spatial representation results from the fact that each neuron has a Gaussian firing rate that peaks at its optimal location. This particular mixed network also contains discrete representations that consist of discrete subsets of active binary firing rate neurons in the 1001-1500 range. The firing of the latter neurons can be thought of as representing the discrete events that occur at the location. Continuous attractor networks by definition contain only continuous representations, but this particular network can store mixed continuous and discrete representations, and is illustrated to show the difference of the firing patterns normally stored in separate continuous attractor and discrete attractor networks. For this particular mixed network, during learning, Memory 1 is stored in the synaptic weights, then Memory 2, etc., and each memory contains a part that is continuously distributed to represent physical space, and a part that represents a discrete event or object.

All rights reserved

  • 28 Stringer et al., 2002b.

13So far we have said that the neurons in the continuous attractor network are connected to one another by synaptic weights wij that are a simple function, for example Gaussian, of the distance between the states of the agent in the physical world (e.g. place, spatial view, etc.) represented by the neurons. In many simulations, the weights are set by formula so that they have these appropriate Gaussian values. However, Stringer, Trappenberg, Rolls and de Araujo28 showed how the appropriate synaptic weights could be set up by learning. They started with the fact that since the neurons have broad tuning that may be Gaussian in shape, nearby neurons in the state space will have overlapping spatial fields, and will thus be co-active to a degree that depends on the distance between them. They postulated that therefore the synaptic weights could be set up by associative learning based on the co-activity of the neurons produced by external stimuli as the animal moved in the state space. For example, during learning, spatial view cells are forced to fire by visual cues in the environment that produce Gaussian firing as a function of the spatial view, from an optimal spatial view for each neuron. The learning rule is simply that the weights wij from spatial view neuron j with firing rate to spatial view neuron i with firing rate are updated according to an associative (Hebb) rule that is consistent with findings from long-term potentiation

where δwij is the change of synaptic weight and k is the learning rate constant. During the learning phase, the firing rate of each spatial view neuron i might be the following Gaussian function of the distance of the spatial view from the optimal firing view of the neuron

  • 29 Stringer et al., 2002b.

where s is the difference between the spatial view x (in degrees) of the agent and the spatial view xi for neuron i, and σ is the standard deviation. Stringer, Trappenberg, Rolls and de Araujo29 showed that, after training at all positions in the space, the synaptic connections develop strengths that are an almost Gaussian function of the distance between the cells in the space. This shows how cells such as spatial view cells could be associated together in CA3 to form a continuous attractor network.

3.3. Combined continuous and discrete memory representations in the same (e.g. CA3) network, and episodic memory

  • 30 Rolls et al., 2002.

14Space is continuous, and object representations are discrete. If these representations are to be combined in an object-place memory, for example, then we need to understand the operation of networks that combine these representations. It has now been shown that attractor networks can store both continuous patterns and discrete patterns (as illustrated in Fig. 4), and can thus be used to store for example the location in (continuous, physical) space (e.g. the place “out there” in a room represented by spatial view cells) where an object (a discrete item) is present30.

3.4. Idiothetic update by path integration

  • 31 Kesner and Rolls, 2015; Rolls, 2016; Rolls and Stringer, 2005; Stringer and Rolls, 2002; Stringer e (...)
  • 32 Giocomo et al., 2011; Zilli, 2012.
  • 33 Stringer et al., 2005.
  • 34 Stringer et al., 2005.

15We have considered how spatial representations could be stored in continuous attractor networks, and how the activity can be maintained at any location in the state space in a form of short-term memory when the external (e.g. visual) input is removed. However, many networks with spatial representations in the brain can be updated by internal, self-motion (i.e. idiothetic) cues, even when there is no external (e.g. visual) input. Path integration can be implemented in recurrent attractor networks as described elsewhere for hippocampal CA331 and for the entorhinal cortex32. In our approach, the movement signal, in this case eye position and head direction, are used as inputs to the spatial view continuous attractor network, with the appropriate synaptic strengths set up by self-organizing learning33. The effect is that there can be a steady trajectory through the space of spatial views, and potentially remembered spatial views, produced by head and eye movements34.

4. The theory of ars memoriae

4.1. The theory

16Building on the above evidence, I now describe a theory, which uses the above components, of how it is that attaching items to different parts of a remembered but familiar scene provides a good strategy to remember the order of the items.

  • 35 Stringer et al., 2005.

17An essential feature of the proposal comes from the way in which a smooth continuous trajectory through a space can be produced by a small input that pushes one through the space, in the way described above for spatial view cells35. Because the spatial view fields have overlapping approximately Gaussian receptive fields, when the pushing input moves one in a certain direction, say left to right, across the scene, the firing of a set of spatial view cells for one view in the scene automatically recruits the next set of spatial view cells for the next view in the scene. Thus, the continuous attractor network effectively embodies the structure of the space, that is, the order of the different views in the scene, because cells that represent the same view in the space (even though not topologically together in the CANN) have strong synaptic connections between one another, and fairly strong connections only with other neurons in the network that represent nearby views in the scene. That is the effect of the learning mechanism described above. Therefore, as we move from one part of the scene to another, the CANN automatically looks up the next adjacent spatial view. Thus the order of the spatial views is implicit in the structure of the CANN. Which spatial view is next to another is what is encoded in the CANN, which effectively represents the distances between the spatial views in the strengths of the synapses between the neurons.

18The proposal is that ars memoriae takes advantage of this spatial structure and order, with a different item or object associated with each spatial view in the scene, in exactly the way that our research indicates for object-place associations in hippocampal CA3. Thus, as the person sweeps from one spatial view in a scene to another, the correct items are recalled in the correct order.

  • 36 Stringer et al., 2005.
  • 37 Robertson et al., 1998.

19This sweeping in a continuous trajectory through a CANN state space can be produced by eye and head movements, which can move the bubble of activity from one place to another36. We have shown that this can occur for some hippocampal cells in the primate, when the eyes and/or head move in conditions when the views themselves cannot be seen, so that effectively a remembered position in the spatial view space is being recalled37. The only difference is that for ars memoriae, it is possible that the eyes and head do not actually have to be moved (though they may move!), and that one just thinks of moving across the scene to the next position in the spatial view space.

4.2. Forgetting the previous day’s items, and producing a new order for different items

  • 38 Kondo et al., 2009.
  • 39 Kesner and Rolls, 2015; Rolls, 1989a, 2013.
  • 40 Rolls and Treves, 1994; Treves and Rolls, 1991, 1994.
  • 41 Amit, 1989; Hopfield, 1982.
  • 42 Rolls, 2016.

20The CA3 network is a single network, in that the recurrent collaterals reach throughout the CA3 region, and make synaptic contacts with other CA3 neurons in all parts of the CA3 region38. This architecture enables any object to be associated with any spatial view/place39. However, the capacity of an autoassociation net is limited, mainly by the number of recurrent collaterals onto any one CA3 neuron. We have shown that with a sparse representation, the number of memories that can be stored is in the order of the number of recurrent collateral connections onto any one neuron40, which is in the order of 12,000 in the rat. If the limit on the capacity of an attractor network is exceeded, then the ability to recall memories from the network will be very degraded41. For this reason, and given that new episodic memories are being formed, some form of forgetting is required in the hippocampus, and there are several possible mechanisms42.

  • 43 Nadal et al., 1986.
  • 44 Parisi, 1986.
  • 45 Rolls, 2008, 2016.

21One mechanism is decay of synaptic strength. The simple forgetting mechanism is just an exponential decay of the synaptic value back to its baseline, which may be exponential in time or in the number of learning changes incurred43. Another form of forgetting is implemented by setting limits to the range allowed for each synaptic strength or weight44. A third mechanism for forgetting is overwriting of previously stored memories, which will happen as a result of heterosynaptic long-term depression. If a postsynaptic neuron is activated during the formation of a new memory, then any inactive synaptic inputs, from other memories, will become weaker, an effect termed heterosynaptic long-term depression, and this will tend to weaken previously stored memories, and thus gradual forgetting of old memories occurs45.

  • 46 Cicero, 55 BC; Yates, 1992.

22These neural mechanisms contribute to allowing new items for a different speech or occasion to be added onto a well-memorized scene, which was used in the practice of ars memoriae46. This is my scientific theory of ars memoriae.

5. Discussion

23The power of the mechanism described here, underlying ars memoriae (the art of memory), is the fact that space is inherently continuous. When mapped onto a continuous attractor network in a brain region such as the hippocampus, where there are spatial view neurons with approximately Gaussian receptive fields, the proximity of different views of a spatial scene is represented by the strengths of the synaptic weights between the neurons. Thus, when the bubble or packet of neuronal activity in the CANN moves, whether by idiothetic (self-motion) input, or by moving in thought from one view of a scene in say a clockwise direction, then the next adjacent view in the scene is automatically retrieved from the network. In this way, a set of views can be recalled in the correct order. If each view is associated with a different discrete item (e.g. an object or thought), then the items are retrieved in the correct order, and none of them are forgotten. It is this order inherent in the spatial representation in the brain that helps to provide the system with its power. The items themselves have no order, for each item or object is represented just by a randomly chosen set of neurons, that is, by a discrete representation in which each item is uncorrelated with the other items, as illustrated in Fig. 4.

  • 47 Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1997; Rolls et al., 1998.

24The mechanism as described was implemented with spatial view cells with Gaussian receptive fields. The exact shape of the receptive field does not matter, provided that it has a peak at the centre of the view field, and a decreasing firing rate as one moves away from the view at which a neuron has its peak firing rate. The reason is that the continuous attractor network learns proximity in its synaptic strengths by an overlap of firing, and the exact shape of the overlap does not matter. The view fields of spatial view neurons do have the required properties47.

  • 48 Andersen et al., 2007; Hartley et al., 2014; OKeefe, 1990; O’Keefe and Dostrovsky, 1971.
  • 49 Kesner and Rolls, 2015; Rolls, 1989a, 1990, 1996, 2016; Rolls and Kesner, 2006; Rolls and Treves, 1 (...)

25This is a new theory, and it is new in a number of ways. First, no previous theory has used as a foundation the spatial view cells present in primates. These are an essential component of the theory, for a human can stand in one place, and remember a series of locations in a scene “out there in space”, each one of which is associated with a different object or event. That is an important aspect of ars memoriae, and how it is used, for example to deliver a speech when standing in one place. This function could never be performed by rat place cells48, for the place where the human is located while learning the scene-object associations, or later recalling them, is not changing. Second, no previous theory of ars memoriae that I know of has used a continuous attractor network to help account for the retrieval of the items (objects or events) in the correct order. A continuous attractor network is an important component of the present theory, because it provides for a continuously linked set of spatial locations that is formed in the continuous attractor network. The network, because of the inherent continuity of space, and of the way that spatial proximity operates in a continuous attractor network, results in a continuous trajectory through the state space during recall, automatically (i.e. mechanistically) leading to the items being recalled in the correct order. Thus, the continuous attractor network is an important part of the new theory. Third, an essential component of the theory is that the system, as implicated in the primate hippocampus, is a memory system, in which spatial to object, or time to object, associations are important. These associations are implemented by the firing of primate hippocampal spatial view cells, as shown by object-spatial view neurons and reward-spatial view neurons. Fourth, I know of no other neuroscience theory of ars memoriae based on a fundamental neurophysiological analysis of the relevant properties of neurons involved in memory, and of the computational neuroscience of how these neurons could implement memory49.

26In ars memoriae, an extended argument (or series of points to be made) may be implemented by associating the first set of items with the different views of say a first room in a building, then moving to a second room and associating further items with each view in that room, etc. The theory accounts for that well, for the different rooms are linked of course by their proximity, and the last view in one room can become associated with the first view in a second room, all followed in a systematic order (e.g. left to right, or clockwise) in ars memoriae.

  • 50 Kesner and Rolls, 2015; Rolls, 1989a, 1990, 1996, 2016; Rolls and Kesner, 2006; Rolls and Treves, 1 (...)

27Also, for ars memoriae, a prediction is that it is likely to be useful to utilize scenes that are distant from an observer, for then the views in the scene are linked continuously as one scans steadily across the scene from a single place (from which one might be giving a lecture or speech). A scene with an object in the middle around which the observer walks produces sudden and unsystematic changes in the views and the relations between the views, and is likely to be less efficient for ars memoriae. When analysing the properties of spatial view cells, we did not have a landmark in the middle of the room, because it has no relatively fixed spatial relation to other landmarks when walking around any central landmark. A second prediction is therefore that the neural encoding of such landmarks that do not bear a fixed relation to other landmarks may be different from the continuous attractor mechanism described in this chapter. Such central landmarks (such as Nelson’s column in Trafalgar Square around which one can walk) may be treated more like objects, and associated only transiently with the relatively fixed and distant scene landmarks when viewed from a particular place. The point here is that the relationship of a central landmark in a space does not have a fixed relationship to the distant fixed elements of a scene, as one moves round a central landmark. Indeed, it is part of the theory of hippocampal function that it is best suited to the incorporation of allocentric spatial relations, for then the elements of a scene or a series of places do have a fixed relationship to each other, and can therefore be learned in a continuous attractor network50.

Acknowledgements: Different parts of the research described here were supported by Programme Grants from the Medical Research Council; by a Human Frontier Science program grant; by an EEC BRAIN grant; by the MRC Oxford Interdisciplinary Research Centre in Cognitive Neuroscience; and by the Oxford McDonnell-Pew Centre in Cognitive Neuroscience.

Bibliographie

Amari S. (1977), “Dynamics of pattern formation in lateral-inhibition type neural fields”, Biological Cybernetics, 27 (2), 77-87.

Amit D.J. (1989), Modeling Brain Function, Cambridge University Press, Cambridge.

Andersen P., Morris R.G.M., Amaral D.G., Bliss T.V.P. and O’Keefe J. (2007), The Hippocampus Book, Oxford University Press, London.

Battaglia F.P. and Treves A. (1998), “Attractor neural networks storing multiple space representations: a model for hippocampal place fields”, Physical Review, E 58, 7738-7753.

Cicero M.T. (55 B.C.), De Oratore, II, Rome.

Feigenbaum J.D. and Rolls E.T. (1991), “Allocentric and egocentric spatial information processing in the hippocampal formation of the behaving primate”, Psychobiology, 19, 21-40.

Georges-François P., Rolls E.T. and Robertson R.G. (1999), “Spatial view cells in the primate hippocampus: allocentric view not head direction or eye position or place”, Cerebral Cortex, 9 (3), 197-212.

Giocomo L.M., Moser M.B. and Moser E.I. (2011), “Computational models of grid cells”, Neuron, 71 (4), 589-603.

Hafting T., Fyhn M., Molden S., Moser M.B. and Moser E.I. (2005), “Microstructure of a spatial map in the entorhinal cortex”, Nature, 436, 801-806.

Hartley T., Lever C., Burgess N. and OKeefe J. (2014), “Space in the brain: How the hippocampal formation supports spatial cognition”, Philosophical Transactions of The Royal Society B Biological Sciences, 369 (1635), 20120510.

Hertz J., Krogh A. and Palmer R.G. (1991), An Introduction to the Theory of Neural Computation, Addison-Wesley, Wokingham.

Hopfield J.J. (1982), “Neural networks and physical systems with emergent collective computational abilities”, Proceedings of the National Academy of Science USA, 79, 2554-2558.

Ishizuka N., Weber J. and Amaral D.G. (1990), “Organization of intrahippocampal projections originating from CA3 pyramidal cells in the rat”, The Journal of Comparative Neurology, 295 (4), 580-623.

Jackson M.B. (2013), “Recall of spatial patterns stored in a hippocampal slice by long-term potentiation”, Journal of Neurophysiology, 110 (11), 2511-2519.

Kesner R.P. and Rolls E.T. (2015), “A computational theory of hippocampal function, and tests of the theory: new developments”, Neuroscience & Biobehavioral Reviews, 48, 92-147.

Kondo H., Lavenex P. and Amaral D.G. (2009), “Intrinsic connections of the macaque monkey hippocampal formation: II. CA3 connections”, The Journal of Comparative Neurology, 515 (3), 349-377.

Lynch M.A. (2004), “Long-term potentiation and memory”, Physiological Reviews, 84, 87-136.

Morris R.G. (2003), “Long-term potentiation and memory”, Philosophical Transactions of The Royal Society B Biological Sciences, 358 (1432), 643-647.

Morris R.G., Moser E.I., Riedel G., Martin S.J., Sandin J., Day M. And OCarroll C. (2003), “Elements of a neurobiological theory of the hippocampus: The role of activity-dependent synaptic plasticity in memory”, Philosophical Transactions of The Royal Society B Biological Sciences, 358 (1432), 773-786.

Moser E.I., Moser M.B. and Roudi Y. (2014), “Network mechanisms of grid cells”, Philosophical Transactions of the Royal Society B Biological Sciences, 369, 2012.05.11.

Nadal J.P., Toulouse G., Changeux J.P. and Dehaene S. (1986), “Networks of formal neurons and memory palimpsests”, EPL (Europhysics Letters), 1, 535.

Nakazawa K., McHugh T.J. and Wilson M.A. and Tonegawa S. (2004), “NMDA receptors, place cells and hippocampal spatial memory”, Nature Reviews Neuroscience, 5, 361-372.

Nakazawa K., Sun L.D., Quirk M.C., Rondi-Reig L., Wilson M.A. and Tonegawa S. (2003), “Hippocampal CA3 NMDA receptors are crucial for memory acquisition of one-time experience”, Neuron, 38, 305-315.

OKeefe J. (1990), “A computational theory of the hippocampal cognitive map”, Progress in Brain Research, 83, 301-312.

OKeefe J. and Dostrovsky J. (1971), “The hippocampus as a spatial map: preliminary evidence from unit activity in the freely moving rat”, Brain Research, 34 (1), 171-175.

Parisi G. (1986), “A memory which forgets”, Journal of Physics A: Mathematical and General, 19, L617.

Robertson R.G., Rolls E.T. and Georges-François P. (1998), “Spatial view cells in the primate hippocampus: Effects of removal of view details”, Journal of Neurophysiology, 79 (3), 1145-1156.

Rolls E.T. (1987), “Information representation, processing and storage in the brain: Analysis at the single neuron level”, in: Changeux J.-P. and Konishi M. (Eds.), The Neural and Molecular Bases of Learning, Wiley, Chichester, 503-540.

Rolls E.T. (1989a), “Functions of neuronal networks in the hippocampus and neocortex in memory”, in: Byrne J.H. and Berry W.O. (Eds.), Neural Models of Plasticity: Experimental and Theoretical Approaches, Academic Press, San Diego, 240-265.

Rolls E.T. (1989b), “Parallel distributed processing in the brain: Implications of the functional architecture of neuronal networks in the hippocampus”, in: Morris R.G.M. (Ed.), Parallel Distributed Processing: Implications for Psychology and Neurobiology, Oxford, Oxford University Press, 286-308.

Rolls E.T. (1990), “Theoretical and neurophysiological analysis of the functions of the primate hippocampus in memory”, Cold Spring Harbor Symposia in Quantitative Biology, 55, 995-1006.

Rolls E.T. (1996), “A theory of hippocampal function in memory”, Hippocampus, 6, 601-620.

Rolls E.T. (2008), Memory, Attention, and Decision-Making: A Unifying Computational Neuroscience Approach, Oxford, Oxford University Press.

Rolls E.T. (2013), “A quantitative theory of the functions of the hippocampal CA3 network in memory”, Frontiers in Cellular Neuroscience, 7, 98.

Rolls E.T. (2016), Cerebral Cortex: Principles of Operation. Oxford University Press, Oxford.

Rolls E.T. (2017a), “A scientific theory of Ars Memoriae: Spatial view cells in a continuous attractor network with linked items”, Hippocampus, 27, 570-579.

Rolls E.T. (2017b), “The storage and recall of memories in the hippocampo-cortical system”, Cell and Tissue Research, DOI: 10.1007/s00441-017-2744-3.

Rolls E.T. and Kesner R.P. (2006), “A computational theory of hippocampal function, and empirical tests of the theory”, Progress in Neurobiology, 79 (1), 1-48.

Rolls E.T., Miyashita Y., Cahusac P.M.B., Kesner R.P., Niki H., Feigenbaum J. and Bach L. (1989), “Hippocampal neurons in the monkey with activity related to the place in which a stimulus is shown”, The Journal of Neuroscience, 9 (6), 1835-1845.

Rolls E.T. and OMara S.M. (1995), “View-responsive neurons in the primate hippocampal complex”, Hippocampus, 5, 409-424.

Rolls E.T., Robertson R.G. and Georges-François P. (1997), “Spatial view cells in the primate hippocampus”, European Journal of Neuroscience, 9 (8), 1789-1794.

Rolls E.T. and Stringer S.M. (2005), “Spatial view cells in the hippocampus, and their idiothetic update based on place and head direction”, Neural Networks, 18 (9), 1229-1241.

Rolls E.T., Stringer S.M. and Trappenberg T.P. (2002), “A unified model of spatial and episodic memory”, Proceedings of the Royal Society of London B, 269, 1087-1093.

Rolls E.T. and Treves A. (1994), “Neural networks in the brain involved in memory and recall”, Progress in Brain Research, 102, 335-341.

Rolls E.T. and Treves A. (1998), Neural Networks and Brain Function, Oxford, Oxford University Press.

Rolls E.T., Treves A., Robertson R.G., Georges-François P. and Panzeri S. (1998), “Information about spatial view in an ensemble of primate hippocampal cells”, Journal of Neurophysiology, 79 (4), 1797-1813.

Rolls E.T. and Xiang J.-Z. (2005), “Reward-spatial view representations and learning in the hippocampus”, Journal of Neuroscience, 25 (26), 6167-6174.

Rolls E.T. and Xiang J.-Z. (2006), “Spatial view cells in the primate hippocampus, and memory recall”, Reviews in the Neurosciences, 17, 175-200.

Rolls E.T., Xiang J.-Z. and Franco L. (2005), “Object, space and object-space representations in the primate hippocampus”, Journal of Neurophysiology, 94, 833-844.

Stringer S.M. and Rolls E.T. (2002), “Invariant object recognition in the visual system with novel views of 3D objects”, Neural Computation, 14 (11), 2585-2596.

Stringer S.M., Rolls E.T. and Trappenberg T.P. (2004), “Self-organising continuous attractor networks with multiple activity packets, and the representation of space”, Neural Networks, 17 (1), 5-27.

Stringer S.M., Rolls E.T. and Trappenberg T.P. (2005), “Self-organizing continuous attractor network models of hippocampal spatial view cells”, Neurobiology of Learning and Memory, 83 (1), 79-92.

Stringer S.M., Rolls E.T., Trappenberg T.P. and Araujo I.E.T. (2002a), “Self-organizing continuous attractor networks and path integration. Two-dimensional models of place cells”, Network: Computation in Neural Systems, 13, 429-446.

Stringer S.M., Rolls E.T., Trappenberg T.P. and Araujo I.E.T. (2002b), “Self-organizing continuous attractor networks and path integration: One-dimensional models of head direction cells”, Network: Computation in Neural Systems, 13, 217-242.

Treves A. and Rolls E.T. (1991), “What determines the capacity of autoassociative memories in the brain?”, Network, 2, 371-397.

Treves A. and Rolls E.T. (1992), “Computational constraints suggest the need for two distinct input systems to the hippocampal CA3 network”, Hippocampus, 2 (2), 189-199.

Treves A. and Rolls E.T. (1994), “Computational analysis of the role of the hippocampus in memory”, Hippocampus, 4 (3), 374-391.

Wang S.H. and Morris R.G. (2010), “Hippocampal-neocortical interactions in memory formation, consolidation, and reconsolidation”, Annual Review of Psychology, 61, 49-79, C41-44.

Witter M.P. (2007), “Intrinsic and extrinsic wiring of CA3: indications for connectional heterogeneity”, Learning & Memory, 14, 705-713.

Yates F.A. (1992), The Art of Memory, Chicago, University of Chicago Press.

Zilli E.A. (2012), “Models of grid cell spatial firing published 2005-2011”, Frontiers in Neural Circuits, 6, 16.

Notes

1 Cicero, 55 BC.

2 Yates, 1992.

3 Rolls, 2017a.

4 O’Keefe, 1990; O’Keefe and Dostrovsky, 1971.

5 Hafting et al., 2005; Moser et al., 2014.

6 Feigenbaum and Rolls, 1991; Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1989; Rolls and O’Mara, 1995; Rolls et al., 1997; Rolls et al., 1998; Rolls and Xiang, 2006.

7 Rolls et al., 1998.

8 Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1997; Rolls et al., 1998.

9 Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1997; Rolls et al., 1998.

10 Robertson et al., 1998.

11 Rolls and Xiang, 2006.

12 Rolls et al., 2005.

13 Rolls and Xiang, 2006.

14 Rolls and Xiang, 2005.

15 Kesner and Rolls, 2015; Rolls, 1989a, 1990, 2016; Rolls and Kesner, 2006; Rolls and Treves, 1994; Treves and Rolls, 1994; Rolls, 2017b.

16 Kesner and Rolls, 2015; Rolls, 1987, 1989a, 1989b, 1990, 1996, 2008, 2016; Rolls and Kesner, 2006; Rolls and Stringer, 2005; Rolls et al., 2002; Treves and Rolls, 1992, 1994.

17 Kondo et al., 2009.

18 See Andersen et al., 2007; Jackson, 2013; Lynch, 2004; Morris, 2003; Morris et al., 2003; Nakazawa et al., 2004; Nakazawa et al., 2003; Wang and Morris, 2010.

19 Rolls, 2016; Rolls and Treves, 1998.

20 Hertz et al., 1991; Hopfield, 1982; Rolls, 2008, 2016; Rolls and Treves, 1998; Treves and Rolls, 1991.

21 Rolls, 2016.

22 Ishizuka et al., 1990; Witter, 2007.

23 Kondo et al., 2009.

24 Kesner and Rolls, 2015; Rolls, 2008, 2016.

25 Amari, 1977; Battaglia and Treves, 1998; Rolls, 2016; Rolls and Stringer, 2005; Stringer and Rolls, 2002; Stringer et al., 2004; Stringer et al., 2005; Stringer et al., 2002a; Stringer et al., 2002b.

26 Rolls, 2008.

27 Rolls, 2016.

28 Stringer et al., 2002b.

29 Stringer et al., 2002b.

30 Rolls et al., 2002.

31 Kesner and Rolls, 2015; Rolls, 2016; Rolls and Stringer, 2005; Stringer and Rolls, 2002; Stringer et al., 2004; Stringer et al., 2002a; Stringer et al., 2002b.

32 Giocomo et al., 2011; Zilli, 2012.

33 Stringer et al., 2005.

34 Stringer et al., 2005.

35 Stringer et al., 2005.

36 Stringer et al., 2005.

37 Robertson et al., 1998.

38 Kondo et al., 2009.

39 Kesner and Rolls, 2015; Rolls, 1989a, 2013.

40 Rolls and Treves, 1994; Treves and Rolls, 1991, 1994.

41 Amit, 1989; Hopfield, 1982.

42 Rolls, 2016.

43 Nadal et al., 1986.

44 Parisi, 1986.

45 Rolls, 2008, 2016.

46 Cicero, 55 BC; Yates, 1992.

47 Georges-François et al., 1999; Robertson et al., 1998; Rolls et al., 1997; Rolls et al., 1998.

48 Andersen et al., 2007; Hartley et al., 2014; OKeefe, 1990; O’Keefe and Dostrovsky, 1971.

49 Kesner and Rolls, 2015; Rolls, 1989a, 1990, 1996, 2016; Rolls and Kesner, 2006; Rolls and Treves, 1994; Treves and Rolls, 1994.

50 Kesner and Rolls, 2015; Rolls, 1989a, 1990, 1996, 2016; Rolls and Kesner, 2006; Rolls and Treves, 1994; Treves and Rolls, 1994.

Table des illustrations

Titre Figure 1
Légende Examples of the firing of a hippocampal spatial view cell when the monkey was walking around the laboratory. (a) The firing of the cell is indicated by the spots in the outer set of 4 rectangles, each of which represents one of the walls of the room. There is one spot in the outer rectangle for each action potential. The base of the wall is towards the centre of each rectangle. The positions on the walls fixated during the recording sessions are indicated by points in the inner set of 4 rectangles, each of which also represents a wall of the room. The central square is a plan view of the room, with a triangle printed every 250 ms to indicate the position of the monkey, thus showing that many different places were visited during the recording sessions. A spot is printed every 250 ms in the inner rectangles to show that a wide range of spatial locations was viewed. (b) A similar representation of the same 3 recording sessions as in (a), but modified to indicate more fully the range of places when the cell fired at more than 12 spikes/s, to indicate that this is not a place cell, but a spatial view cell. The triangle indicates the current position of the monkey. The same data are shown in the inner and outer rectangles, and each dot represents one action potential. c1–c4 are cups in which food may be found. T1 and T2 are trolleys at fixed positions within the space within which the monkey can walk freely. The four walls of the room are situated 1-3 mm from the 3 × 3 m space in which the monkey can walk, and are part of a rich laboratory environment with windows, door, apparatus etc.
URL http://books.openedition.org/cdf/docannexe/image/5552/img-1.jpg
Fichier image/jpeg, 140k
Titre Figure 2
Légende Forward connections (solid lines) from areas of cerebral association neocortex via the parahippocampal gyrus and perirhinal cortex, and entorhinal cortex, to the hippocampus; and backprojections (dashed lines) via the hippocampal CA1 pyramidal cells, subiculum, and parahippocampal gyrus to the neocortex.There is wide convergence in the forward connections down to the single network implemented in the CA3 pyramidal cells; and wide divergence again in the back projections. Left: block diagram. Right: more detailed representation of some of the principal excitatory neurons in the pathways. Abbreviations: D stands for Deep pyramidal cells. DG: Dentate Granule cells. F: Forward inputs to areas of the association cortex from preceding cortical areas in the hierarchy. mf: mossy fibres. PHG: parahippocampal gyrus and perirhinal cortex. pp: perforant path. rc: recurrent collateral of the CA3 hippocampal pyramidal cells. S: Superficial pyramidal cells. 2: pyramidal cells in layer 2 of the entorhinal cortex. 3: pyramidal cells in layer 3 of the entorhinal cortex. The thick lines above the cell bodies represent the dendrites.
URL http://books.openedition.org/cdf/docannexe/image/5552/img-2.jpg
Fichier image/jpeg, 140k
Titre Figure 3
Légende The architecture of a continuous attractor neural network (CANN). The architecture is the same as that of a discrete attractor neural network. During learning, external inputs ei with Gaussian spatial fields force the output neurons to fire with rates ri, the recurrent collaterals produce the same rates rj as the presynaptic inputs to the neurons, and the synapses wij become associatively modified. Many different inputs, each corresponding to a different spatial representation, are applied during learning, and the synapses between every pair of neurons come to represent the distance between the positions represented by each pair of neurons. The neurons shown are excitatory, and inhibitory neurons maintain the average firing so that some of the neurons that correspond to one part of the space are firing, and keep one another firing by the excitatory synaptic connections between them, to provide a packet or bubble of neuronal activity, as illustrated in Fig. 4. Because of the Gaussian spatial response profile of each neuron, the space defined is continuous. Thus, as the space is traversed from one end to the other, the bubble of activity moves continuously through the space.
URL http://books.openedition.org/cdf/docannexe/image/5552/img-3.jpg
Fichier image/jpeg, 92k
Titre Figure 4
Légende The types of firing patterns stored in continuous attractor networks are illustrated for the patterns present on neurons 1-1000 for Memory 1 (when the firing is that produced when the spatial state represented is that at location 300), and for Memory 2 (when the firing is that produced when the spatial state represented is that of location 500). The continuous nature of the spatial representation results from the fact that each neuron has a Gaussian firing rate that peaks at its optimal location. This particular mixed network also contains discrete representations that consist of discrete subsets of active binary firing rate neurons in the 1001-1500 range. The firing of the latter neurons can be thought of as representing the discrete events that occur at the location. Continuous attractor networks by definition contain only continuous representations, but this particular network can store mixed continuous and discrete representations, and is illustrated to show the difference of the firing patterns normally stored in separate continuous attractor and discrete attractor networks. For this particular mixed network, during learning, Memory 1 is stored in the synaptic weights, then Memory 2, etc., and each memory contains a part that is continuously distributed to represent physical space, and a part that represents a discrete event or object.
URL http://books.openedition.org/cdf/docannexe/image/5552/img-4.jpg
Fichier image/jpeg, 132k
URL http://books.openedition.org/cdf/docannexe/image/5552/img-5.png
Fichier image/png, 4,4k
URL http://books.openedition.org/cdf/docannexe/image/5552/img-6.png
Fichier image/png, 4,4k

Auteur

Oxford Centre for Computational Neuroscience, Oxford, UK and University of Warwick, Department of Computer Science, Coventry, UK

© Collège de France, 2018

Conditions d’utilisation : http://www.openedition.org/6540