1 Introduction

Context fear conditioning has for some time been a very active area of research. In part, this has been because it is thought that the mechanisms the hippocampus uses to create representations of recently encountered contexts to which fear can then become associated are similar to those it uses to form representations of life experiences during the establishment of episodic memories. Thus, context fear learning provides a convenient laboratory model of certain aspects of episodic memory. The study of context fear learning is also of great interest because of its relevance to understanding and potentially treating pathologies of fear and anxiety.

It is widely believed that the initial creation of contextual fear and episodic memories is the result of very rapidly developed synaptic alterations in the hippocampus and paleo- and neo-cortical circuitry with which the hippocampus interacts, but that over extended periods of time (weeks in rodents and months and years in humans) the information initially stored in the hippocampus-related circuitry becomes recoded and stored in neocortical circuitry through some sort of off-line neural “replay” activity (e.g., Nakashiba et al., 2009; Schwindel and McNaughton, 2011; Buzsáki, 2015; Squire et al., 2015; Pfeiffer, 2020). The content of these largely cortical “systems consolidated” or “remote” memories is thought not to be quite the same as that of the new memories generated at the time of encoding. Whereas new memories are thought to be relatively raw snapshots of the encoded experience or context, allowing recollection of many specific details, systems-consolidated memories are thought to have become integrated into the overall knowledge structure of the individual and to become more generic with many details of the originally experienced context (or event) often, though perhaps not always (as in some highly emotional memories) (e.g., Brown and Kulik, 1977), being lost (e.g., Nadel and Moscovitch, 1997; Moscovitch et al., 2005; Wiltgen and Silva, 2007; Wang et al., 2009; Nadel et al., 2012).

New context fear memories have been studied much more than remote ones, presumably because they are easier to study. However, most of an individual’s memories will ultimately become remote, and it will be remote memories that mostly underlie fear pathologies. So, a full understanding of remote episodic and fear memories is badly needed. Fortunately, information about remote context fear is growing (e.g., Frankland et al., 2004; Frankland and Bontempi, 2005; Wiltgen et al., 2010; Vetere et al., 2011; Kitamura et al., 2017; Tonegawa et al., 2018; Takehara-Nishiuchi, 2021).

The purpose of this study is to extend to remote fear a recent neuro-computational model of context fear learning, BACON (BAyesian CONtext Fear Algorithm) (Krasne et al., 2015), that has been quite successful in explaining and predicting aspects of recently learned context fear and to see how it deals with the increasingly substantial experimental findings on remote context fear memory. BACON and an extension of it that deals specifically with extinction (BaconX) (Krasne et al., 2021) are simplifications of Marr’s Theory of Archicortex (Marr, 1971) and its descendants (e.g., Skaggs and McNaughton, 1992; O’Reilly and McClelland, 1994; Treves and Rolls, 1994; Hasselmo et al., 1996; Hasselmo, 2006; Neunuebel and Knierim, 2014) with an added feature: Representation formation and synaptic strength changes in the hippocampus-cortex circuit, as well as conditioning of fear to these representations in the amygdala, are controlled by Bayesian estimates of how confident an individual can be that the context it recalls really is the one it is currently in. With this addition to Marr’s ideas, BACON can simulate a wide range of context fear phenomenology, including the immediate shock deficit (Fanselow, 1986; Landeira-Fernandez et al., 2006), the gradualness of the onset of expressed fear during exposure to a feared context (Fanselow, 1982; Lester and Fanselow, 1986; Wiltgen et al., 2006; Bae et al., 2015; Lingawi et al., 2018), and false conditioning (Rudy and Oreilly, 1999; Rudy et al., 2020). It has also provided a basis for explaining seeming contradictions in experiments on the effects of DG suppression during encoding and recall (Bernier et al., 2017), and it has provided plausible explanations for a number of non-intuitive effects of conditioning that were carried out at short intervals after placement in a context (Zinn et al., 2020). Moreover, it abolishes the so-called “tradeoff between pattern separation and completion” (O’Reilly and McClelland, 1994; O'Reilly and Rudy, 2001) that arises in the absence of some reasonable mechanism to control when new representations should and should not be created. It has even led to a plausible hypothesis about the basis for known sex differences in context fear conditioning (Trott et al., 2022).

We call the extension of BACON to remote memory BaconREM. Before getting into details, we sketch below the main assumptions we have made and what seem to us to be the most important findings that have followed.

1.1 Sketch of assumptions and notable findings

The BACON models all start with a simplified version of Marr’s theory of hippocampal function, which supposes that animals form sparse multicellular hippocampal representations of newly encountered contexts (Marr, 1971; Krasne et al., 2015). The neurons comprising those representations become associated with each other as the result of Hebbian plasticity in the recurrent loops of the hippocampal CA3 region and become associated with cortically represented attributes of the contexts via Hebbian mechanisms at synapses between cortical and hippocampal neurons. Because of these associations, on future occasions observation of a sufficient subset of a context’s attributes activates the full hippocampal representation, which in turn reactivates a cortical version of all of the context’s known attributes.

The BACON models then add the assumption that animals evaluate the correctness of the active hippocampal representation by comparing the attributes of the current context that they are observing with the attributes they recall of the active representation; the metric of correctness is the Bayesian weight of evidence (Kass and Rafter, 1995) that they are in fact in the place they remember, which we refer to as “BRep.” They then use this evaluation to decide whether the context is a new one, in which case a new representation must be created or is in fact valid, in which case newly observed features of the context can become associated with the existing hippocampal representation (“updating”).

When a hippocampally represented context is fear conditioned, synapses of the representation neurons (or projections of them) on amygdala fear-evoking cells undergo Hebbian potentiation (Fanselow, 1982, 1990, 2000; Young et al., 1994; McDonald, 1998; Fanselow and Gale, 2000; Bauer et al., 2001; Blair et al., 2001; Rudy et al., 2004; Stote and Fanselow, 2004; Zelikowsky et al., 2014), but the extent to which this happens depends on the weight of evidence that the active hippocampal representation really is that of the context the subject is in.

In extending the BACON model to deal with remote memory, we make three main assumptions:

(1) Over time, the hippocampal representations of recently encoded contexts get replaced by cortical versions. Whereas the hippocampal representations are thought to be composed of small sets of hippocampal cells, each of which may also be part of other representations (a “distributed” code), we suppose that their cortical versions are single or small groups of cells that are dedicated to representing just one single context (a “localist” or “non-distributed” code –see Bowers (2009), Riesenhuber and Glezer (2017), and Roy (2017) for discussions relevant to the biological plausibility of localist coding). There is some evidence that the cortical cells that compose the remote version of a contextual representation get selected very soon after the hippocampal representation is created, though their connections to cells representing contextual attributes and to fear-evoking cells develop more slowly during the extended process of systems consolidation (Kitamura et al., 2017), and our model assumes this to be the case. We suppose that cortical remote representation cells, like hippocampal ones, directly or indirectly innervate amygdala fear-evoking cells via Hebbian synapses, but they do so via a different pathway (Tayler et al., 2013; Kitamura et al., 2017); therefore, for recently conditioned fear to become remote, potentiation must be transferred from synapses in the pathway to the amygdala from the hippocampus to ones in the pathway from the cortex.

(2) It is widely believed that systems consolidation depends on hippocampal information sent to the cortex during hippocampal replay events (e.g., Nakashiba et al., 2009; Schwindel and McNaughton, 2011; Buzsáki, 2015; Squire et al., 2015; de Sousa et al., 2019; Pfeiffer, 2020). Consistent with this, though hippocampus-lesioned animals can form some sort of (presumably cortical) contextual representations and be context fear conditioned (Wiltgen et al., 2006; Zelikowsky et al., 2013; Ramanathan et al., 2018) due to some sort of cortical recovery of function (Fanselow, 2010) that becomes operative when hippocampal mechanisms are not available, such conditioned responses never become remote and are fairly rapidly forgotten (Zelikowsky et al., 2012). These facts have led us to construct BaconREM so that the hippocampus and the information about a context that is encoded within its circuitry are essential for systems consolidation to occur. Furthermore, if new information about a context is learned (“updating”), then the model postulates that the hippocampal circuitry initially stores it just as it does with entirely new learning, and the systems consolidation process is again utilized to make appropriate cortical revisions. However, once a given systems consolidation episode (whether following new learning or updating) is complete, the attribute-hippocampal cell associations and the CA3-CA3 associations that constitute the representation are no longer utilized, and they are erased or over-written so that they do not interfere with new learning. Although the recurrent collateral and attribute associations of a representation are abandoned, cortical remote representation cells form permanent associations with the CA3 cells of their hippocampal progenitors that make possible generalizations between remotely and recently represented contexts.

(3) It is thought from various perspectives that cortical systems consolidated memories are integrated into an individual’s overall cortical knowledge structure in such a way that the memories are more generic, schematic, or gist-like than hippocampally stored new ones, with details of the original situations to at least some extent being lost (e.g., McClelland et al., 1995, 2020, Nadel and Moscovitch, 1997, Wiltgen and Silva, 2007, Winocur et al., 2007, Wang et al., 2009, Wiltgen et al., 2010, Nadel et al., 2012). An important manifestation of this in the kinds of experiments being considered here is that contextual fear tends to generalize much more broadly after systems consolidation than it did before, a phenomenon that we refer to as “hyper-generalization.” Considering just how the integration of cortical knowledge comes about is beyond the scope of this project. However, we wished our model to incorporate the idea that a given memory has both generic aspects that it shares with other memories and ones specific to particular events or contexts. To do this in as simple a way as possible, we supposed that as an animal experiences many situations, it (somehow) comes to recognize attribute commonalities between them and places them into classes or categories, all of whose members share those common attributes. If a new situation is seen to have enough of the attributes of a known category for that category to be identified, then the individual can assume that the context has all of the category’s known attributes, as well as whatever attributes it has actually observed in the situation. We thus let each of our contexts be in a category and have two kinds of attributes, “Categorical” and “Particular”. Categorical attributes are the same for all contexts in a given category, while Particular attributes are specific to an individual context. Thus, all forests have trees and other common categorical attributes, but any given forest has particular kinds of trees, terrain, etc. However, all rat testing chambers (at least of a given kind, i.e., in a given category) are small boxes without a view of the outside, but particular chambers differ in floor textures, odors, lighting, or whatever. If, during the systems consolidation process, BaconREM finds that it knows enough about a context and about the category to which the context belongs to reliably identify the category, all pre-existing knowledge about the category—all of its known categorical attributes—gets added to the set of attributes associated with the context’s cortical representation even though many of these attributes have never been observed to belong to this specific context. On the other hand, a number of the attributes that are associated with the context’s hippocampal representation but are not known to be categorical are lost to the cortical version, much as is thought to happen in real animals.

As will be detailed in the Results section, this model emulates a number of well-established experimental findings and makes predictions that, as far as we know, have never been tested. However, we think perhaps the most important insight it has provided is an alternative interpretation for the well-known finding that hyper-generalization of remote fear can be largely abolished, and hippocampal dependence can be re-established by a “reminder” exposure to the feared context. This has been taken to mean that at least some of the contextual details encoded in the hippocampus at the time of original learning remain in the hippocampus even after systems consolidation is complete and that they again become accessible as a result of the reminder stimulus. However, such a conclusion is contrary to the spirit of the Marr-derived theory of hippocampal function on which BACON is based and for which there is much evidence. Since hippocampal contextual representations in Marr-type models, are distributed, a given neuron that is part of one representation may eventually also become part of others; therefore, confusion between one context and another would become rampant if too many contexts were encoded. Thus, it is of critical importance that BaconREM, which postulates that old memories are always removed from the hippocampus, simulates the ability of “reminder” exposures to abolish hyper-generalization of remote context fear memories and their return to hippocampal dependence. It does this not because the “reminder” exposures somehow make information still residing in the hippocampus more accessible but rather because they cause new learning (or relearning) about the context’s attributes (updating), which adds information that improves discriminability. There is a return to hippocampal dependence because the new learning must then be integrated with existing cortical knowledge, and this requires information about recently observed attributes that are associated with the hippocampal representation.

2 Methods

The present model, BaconREM, which is designed to simulate experiments on remote context fear, is based on the previously published model, BACON (Krasne et al., 2015), which dealt only with recent learning. BaconREM deals with recent learning in the same way as did BACON. Extinction of recent fear, which was treated in a separate model (BaconX, Krasne et al., 2021), was, for simplicity, not incorporated in BaconREM, but the approach would have been the same as that in BaconX, and some expected differences between the extinction of recent and remote context fear are considered in our Discussion section.

2.1 Parameters

The values of important BaconREM parameters are listed in Table 1. Not listed are the values of some relatively minor parameters, which are the same as those used in BACON.

Table 1. Parameter values and definitions of parameters and abbreviations.

The number of cells listed at the top of the table is approximately 1/100 of rat estimates (see O’Reilly and McClelland, 1994; Treves and Rolls, 1994). An exception is Ndg, which had to be made closer to the biological value (1/10 -th of it) to get biologically plausible results for some simulations. Parameters specifically relevant to systems consolidation, listed separately below the above, were chosen so that the model would simulate known properties of remote context fear as studied in rodents. In particular, the ceiling on the proportion of attributes not known to be categorical (κ) must be relatively low, and the proportion of attributes that are particulars (πptc) must be substantial to get sufficient hyper-generalization and to simulate the Reminder Effect (see parameter-space graphs at the URL given in the Model Availability section). The overlap of unrelated contexts in the table is approximately equal to expected values for randomly chosen sets of attributes given the number of attributes involved.

2.2 Parameters for particular experiments simulated

In all simulations of the Results section, conditioning sessions were 76 computational intervals long, with the US being given at interval 75 (as explained in the Results section, a computational interval occurs whenever a new attribute of the BaconREM’s current context is observed). The duration of all test sessions was 95 intervals.

Except for the simulation in which generalization to a context in a different category than that of the conditioned one was tested, OcatAB = 1. Categories were made different by letting OcatAB = 0.2.

For most of the simulations, the proportion of overlap of particular attributes is OptcAB = 0.6. However, for the simulation just mentioned, OptcAB was set equal to 0.75 so that the hypo-generalization effect would be obvious. For the simulation of the same figure in which a long pre-exposure was given to the to-be-conditioned context, OptcAB = 0.8 so that the generalization in the recent case would not be negligible.

Pre-exposure to context B in the simulation showing failure of hyper-generalization when the test context is familiar (Simulation I) was 76 intervals. In the simulation that was designed to show that hyper-generalization fails to occur when the conditioned context is extremely well-known, pre-exposure to context B was 98 intervals.

2.3 Evaluating the degree of confidence in an active representation’s correctness (or “validity”)

As explained in the Results section, the mode of operation of the model during each computational interval is determined by the degree of confidence in the currently active representation’s correctness. The degree of confidence in a representation’s validity is indexed by the Bayesian weight of evidence (Kass and Rafter, 1995; Krasne et al., 2015), which we refer to as “BRep.” Suppose that after having observed a number “Zcur” of a current context’s attributes, BaconREM were to activate a representation associated with a number “Zrec” of recalled attributes and that there was a number “Zcom” of matches between the recalled and current set. Then, BaconREM would compute the probability of getting this number of matches if the recalled context was in fact the current one and also if the current context was just some random place and then calculate the log of the ratio of these probabilities. This is the Bayesian weight of evidence (BRep) that the recalled and current contexts are the same. If BRep is large and positive, BaconREM probably really is in the recalled context; if it is large and negative, it is probably somewhere else, and if BRep is near zero, there was not enough information to make a good decision. It should be noted that the greater Zcur or Zrec, the greater will be BRep if the representation is valid and the more negative it will be if it is not. Our model postulates that BRep is calculated by some extra-hippocampal circuitry (we conjecture pre-frontal). For the simulations of this study, BRep was based on expected values of Zrec and Zcom, given Bacon’s prior experience, assuming that attributes are sampled at random without replacement during a contextual visit.

2.4 Model availability

A functional version of BaconREM is available at URL https://www.dropbox.com/scl/fo/edt5unutlzuvr9ghmk88t/h?rlkey=epin8ax8qmsefbr0zjf5zn4jz&dl=0.

3 Results 3.1 The model

BaconREM is an extension of the BACON model (Krasne et al., 2015), which adds a capacity to develop remote context representations and remote context fear. BaconREM’s treatment of newly created contextual representations, which are hippocampal, and of conditioning to them is the same as in BACON and is incorporated in the following.

3.1.1 New (hippocampal) representations

As in BACON, the attributes of a context are represented cortically by entorhinal cortex-like cells, each of which we think of as coding for a contextual attribute. There are “Nctx” possible attributes, “Natr” of which fully characterize a context [note: the number of attributes of each context (Natr) is one-tenth the total number of representable attributes (Nctx)] (see Table 1 for values and definitions of all parameters as well as definitions of variable names). In BaconREM, each context belongs, as explained in the Introduction section, to a category, and its attributes are of two types, “categorical,” which are the same for all contexts in a given category, and “particular,” which are specific to a specific context. The Natr attributes of a context are composed of “Ncat“categorical attributes and “Nptc” particular ones; for our simulations, we let Ncat be 20 and Nptc 80. It should be noted that a given attribute might well be categorical for one context but particular for another.

Cortical attribute cells come in homologous pairs. One member projects to the hippocampus, as illustrated in Figure 1A, and is activated when BaconREM observes the attribute for which that cell codes. We refer to these as “Current” or “Cur” cells (they were called ECin cells in previous articles). The other member of the pair is innervated by the hippocampus and is activated when the attribute for which it codes is recalled. We call these “Recalled” or “Rec” cells (these were previously called ECout cells).

Figure 1. BaconREM representations. Hippocampal (A) and Cortical (B) representation cells for an illustrative context are colored red and starred. Not indicated in the figure, each Cur cell innervates a random subset of DG cells, while each Rec cell is innervated by all hippocampal CA3 cells, as well as all cortical Context and Category cells, via Hebbian synapses that are ineffective in a naive individual. Amygdala fear-causing cells are innervated by all CA3 cells and all potential Context cells via initially ineffective Hebbian synapses. The particular and current cells representing the attributes of this context are indicated by the brackets at the top of the figure. Synapses that have been made functional by Hebbian potentiation resulting from either representation formation or systems consolidation of this illustrative context are indicated by black arrowheads, with sets of cells making similar connections encircled. Cur and DG cells that might be firing during a visit to the context (depending on what attributes the individual had noticed on this occasion) are green, and cells activated when the red representation cells fire are colored orange. Synapses of the dashed cyan and blue pathways on amygdala cells would be the ones potentiated if a US were to occur when the representation was active. Note that fear conditioned to the hippocampal version would be expressed even if the cortical version were active because of the permanent pathway from the cortical representation to the CA3 cells of its hippocampal progenitor and conversely. “Via CA1” notes that in real animals, this pathway is not directly from CA3; however, CA1 has been omitted in the BACON models because various simplifications made it irrelevant.

As explained in the Introduction section, before systems consolidation, a context’s representation is hippocampal and distributed. Such a representation is portrayed by the red-starred cells in Figure 1A. There is always a fixed number (“K”) of cells in a hippocampal representation, which is only a small proportion of the number of cells available to form such representations. The Cur cells that code for attributes project to the dentate gyrus (DG). Each DG cell is innervated by a random subset of Cur cells (of size “F,” about half Natr in number), and it itself innervates a single CA3 cell partner via an innately effective synapse (a simplification of the biological situation where each DG cell innervates a small number of CA3 cells via synapses that are plastic in some way, but not Hebbian, as discussed by Krasne et al., 2015). When a representation is created, the K DG cells most richly innervated by the active Cur cells fire and drive their CA3 partners. This leads to the Hebbian potentiation of the synapses between the active Cur and DG cells, between the active CA3 cells and the Rec homologs of active Cur cells, and between one active CA3 cell and another in the recurrent collateral circuitry. Once these potentiations have occurred, the observation of a moderate fraction of the attributes of a familiar context will cause all K CA3 cells of its representation to be activated, and thereby, the Rec cells coding for all of the context’s known attributes (which in a real animal would presumably lead to a conscious recollection of the context).

CA3 hippocampal cells also project to the amygdala (a simplification of the biological case where this projection is indirect), where their synapses on fear-evoking cells become potentiated if a CA3 cell is active when a US occurs, thereby causing conditioning.

In rodents, the K cells composing a representation have been suggested to be on the order of about half a percent of the set of cells available to form such representations, and this is also the case in BaconREM. Because K is such a small proportion of the available cells (i.e., the representation is “sparse”), hippocampal representation overlap is usually very modest even when two contexts have quite similar sets of attributes (i.e., there is considerable “pattern separation” at the level of hippocampal representation cells). The exact degree of overlap will be discussed further when we consider generalization mechanisms.

3.1.2 Remote (cortical) representations

When contextual representations in BaconREM become remote, they are no longer distributed. They are composed of cortical cells that represent just one context. Such a representation is portrayed by the red-starred cell in Figure 1B. Cortical context representation cells, like hippocampal ones, innervate Rec cells, and they also innervate a set of Category cells that innervate and are innervated by Rec cells. As discussed below, categories that are known become represented by a category cell dedicated to representing that category, and the synapses of that cell to and from the Rec cells that represent the category’s known attributes become potentiated. When, during systems consolidation, a context is recognized as belonging to a known category, the synapse of that context’s cortical representation cell on the cell representing that category becomes potentiated so that thereafter, when the context cell fires, it drives the category cell and in turn the Rec cells of all the category’s known attributes. Cortical representation cells also innervate and are innervated by the cells of their hippocampal progenitor. As explained below, these connections serve to allow the generalization of fear between hippocampally and cortically represented contexts. Finally, similar to their hippocampal counterparts, cortical representation cells also innervate the amygdala via Hebbian synapses.

As the result of all these connections, observation of suitable sets of contextual attributes will tend to cause recall of all of the known attributes of a context’s category along with some of its particular attributes and may evoke fear if appropriate conditioning has occurred.

3.1.3 The computational cycle—Decision and Execution

While BaconREM is in a context, it observes (“samples”) the context’s attributes in random order (without replacement), discovering a new one about every half second. The attributes sampled are held in a working memory for the duration of the session. As each new attribute is observed, BaconREM carries out a computational cycle consisting of a Decision phase and an Execution phase.

3.1.3.1 The Decision phase

The purpose of this phase is to activate the representation for which the evidence is best. To do this, the Bayesian weight of evidence (“BRep”) is computed (as described in the Methods section) for each of Bacon’s current cortical representations and for whichever hippocampal representation the current set of attributes activates.

It should be noted that the computed BRep values, which depend on the number of attributes that have been observed (“Zcur”) and the number associated with the representation (“Zrec”), are a highly non-linear, and often non-monotonic, function of these variables. Figure 2A portrays the relationship between these variables. The Bayesian mathematics is such that the more one knows about a context, the less sampling of the current context is needed to decide whether it is or is not the hypothesized place, and conversely. It is important to keep in mind that as BaconREM samples contextual attributes in a new context that is similar to, but not the same as, a known one, it can become quite confident that it is in the known place (i.e., very high BRep) before it “realizes” that this is really somewhere different (i.e., before BRep goes very negative). These features are illustrated in the figure and are discussed more fully by Krasne et al. (2015); they lead to some interesting predictions that we will discuss.

Figure 2. BRep as a function of Zcur and Zrec, and thresholds for execution. (A) Red curves: Expected BRep values as a function of Zcur for three different values of Zrec when BaconREM is actually in the context it recalls (Context A). Dashed curves: BRep values when in a context whose attributes overlap those of the recalled context by 90% (blue) or 50% (green). (B) The BRep values at which various actions are executed (not to scale).

3.1.3.2 The execution phase

The winning representation is maximally activated causing several possible, not mutually exclusive actions that depend on the representation’s BRep value:

i. A new representation may be created: If the BRep value of the winner is sufficiently negative (specifically, BRep is less than the negative parameter Bnew) and there is no close runner-up (i.e., BRep of the winner is an amount δ greater than that of the runner-up), then a new representation is created.

ii. Conscious recollection of the context may occur: If the winner is not rejected, the active representation cell activates the Rec cells of all the attributes associated with the representation, presumably causing conscious recollection of the attributes for which they code.

iii. A US may cause conditioning of fear to the active representation (as spelled out in Figure 3). The extent to which a US will cause conditioning of contextual fear, the “Conditionability” (Cnd), depends on how confident BaconREM is as to the identity of the context it is in Figure 3, Eq. 1. If the representation is hippocampal, the weight of each of the CA3 cell’s synapses on amygdala fear-evoking cells is increased by an amount Cnd∙α (where we refer to α as the ‘learning rate parameter”) (Eq. 2), and since the representation consists of K CA3 cells, the cumulative weight increase is K∙Cnd∙α. If the representation is cortical and composed of only one cell, we assume that conditioning should produce the same excitation of amygdala fear-evoking cells as if it were hippocampal (for a comparable conditionability), and thus, we make the weight increase due to a US the same as the cumulative increase that occurs in the hippocampal case (i.e., K∙Cnd∙α – Figure 3, Eq. 3).

iv. If fear has previously been conditioned to the winner, its expression depends on BRep. Expressed fear is proportional to BRep with a proportionality constant we call the Fear Expression Factor (Fef) (Eq. 8).

v. The attributes associated with an active representation may be updated during visits to a known context. If Bacon’s stay in a context has just terminated and Bacon is sufficiently confident that the activated representation was valid (i.e., BRep > Badd), then the observed attributes of the known context not already associated with its representation will become so. This is referred to as “updating.”

Figure 3. Innervation and plastic properties of amygdala fear-causing cells [inhibitory circuitry responsible for extinction, considered in the BaconX model of Krasne et al. (2021), is omitted here]. Neuron F at the center of the figure is an amygdala fear-causing cell. Activations (i.e., firing rates which are between 0 and a maximum of 1) are denoted by the variable A: The activation of the j-th CA3 cell is denoted Ahipp(j), that of a cortical context representing cell as Acort, and that of an amygdala fear causing cell as AF. The weights of synapses on the amygdala cell are denoted by W, and the changes in weights that result from an unconditioned stimulus that depolarizes the amygdala cell are indicated by ΔW. The value of the learning rate parameter α and other parameters are given in Table 1. The postsynaptic conductances of F cells resulting from representation cell activity are indicated by g, the values of which are given as a proportion of the amygdala cell’s leakage conductance. The value of g for the hippocampal input is given by Eqn. 4 and for the cortical input by Eqn. 5. The depolarization V resulting from input is given as a function of g and the excitatory equilibrium potential E (Eq. 6). The depolarization of amygdala cells is converted to a firing rate by the Linsig (“linear sigmoid”) function of V and E (Eq. 7). The Linsig function, Linsig(x|thrs, mxat), rises linearly from zero as a function of x, starting when x = xthresh and plateauing at unity when x = mxat. The fear that is expressed is equal to the activation of the amygdala cell multiplied by a Fear Expression Factor (Fef), which is defined as FefBRep=LinsigBRep|0,BmxF .

If the representation is hippocampal, all newly observed attributes will be added to those already associated with the representation (the details of this process are described in Krasne et al., 2015).

If the representation is cortical, then, as detailed below, the hippocampal representation again becomes the active one, and all of the known attributes, including the newly discovered ones and the known attributes of the context’s category (if the category has been identified), become associated with it, and the process of systems consolidation is repeated (note that we do not refer to this repetition of the systems consolidation process as “reconsolidation” to avoid confusion with the protein synthesis-dependent “reconsolidation” that is often needed following the recall of previously established learning).

3.1.4 The development of remote representations

The systems consolidation process, which is presumed to operate when the brain is not occupied with current activities, must do a number of things:

(1) Select the cortical cell(s) that will comprise the representation. In actuality, the details of this would probably depend on the then-existing cortical knowledge structure and the attributes of the hippocampal representation that is being systems-consolidated. However, we merely assume that representation cells are chosen at random from unused cells of a pre-existing pool designated for that purpose.

(2) Associate appropriate contextual attributes with the representation. The attributes of the current context that has become associated with the new hippocampal representation must be compared to the known attributes of known categories, and if a match is found, the matching representation must become associated with the developing cortical representation; this in effect associates the known attributes of the category with the cortical representation. Then, a limited subset of the hippocampal representation’s associated attributes that are not known to be categorical must also become associated with the cortical representation.

(3) Associate the CA3 cells of the hippocampal representation with the cortical one. As will be explained when we discuss generalization, mechanisms must be put in place to make possible generalization between recent and remote representations. The approach we use to do this requires that the CA3 cells of a cortical representation’s hippocampal precursor become permanently associated with the cortical representation.

(4) Transfer fear that has become conditioned to the hippocampal representation to its cortical version. Fear that was conditioned when the hippocampal representation was active and became associated with it must be transferred to the cortical representation.

(5) Upgrade the cortical categorical knowledge structure. The attribute information associated with the context’s hippocampal representation must be used, in conjunction with previously accumulated cortical information, to upgrade the cortical knowledge structure itself. The systems consolidation process presumably attempts to use attribute commonalities between the observed attributes of contexts to try to discover new categories and to add further attributes to existing ones. We do not attempt to model how this is done here, but we assume that it is a potentially time-consuming process that may significantly increase the amount of time needed for the completion of the systems consolidation episode.

We define several stages of systems consolidation (Figure 4) during which the above things are done, as well as an updating procedure that repeats the systems consolidation process to incorporate new attribute information into existing cortical representations.

Figure 4. Representation stages. Stage I: The selection of a cell that will become the cortical representation (Item 1 of the remote representation development process as described in the text) is thought to be done very soon after the creation of the hippocampal representation (Kitamura et al., 2017). Once a cell has been selected, an appropriate category (if any) must become associated with it (item 2). Doing this is computationally very similar to the necessarily rapid steps carried out during each computational interval, so we suppose it occurs rapidly. Additionally, the CA3 cells of the hippocampal representation become associated with the cortical representation (item 3 above). As explained, when we consider the generalization of fear between contexts with recent and remote representations, these connections between cortical representation cells and the CA3 cells of their hippocampal precursors only function during the execution phases of a computational cycle and so do not influence the outcome of the representation competition of the decision phase. Once a cortical representation cell is chosen, an appropriate category cell, if any, must become associated with it, along with a limited number of attribute cells for attributes that are not known to be part of the context’s category. This process begins by comparing the context’s known attributes with those of each known category and computing for each the weight of evidence that the context belongs to that category. If the BRep value for the category whose weight of evidence is greatest exceeds a parameter we call Bcat, that category cell becomes associated with the context representing cell. This in effect associates all the known attributes of the category with the context to which it belongs. Then, a random subset of other attributes associated with the hippocampal representation also becomes associated with the cortical representation. BaconREM does not at this point know whether any given such attribute is categorical or particular, so we refer to them as Unclassified attributes or Unc’s, but given the parameters we have used, they will usually be mostly particulars. The size of the set of Unc’s that gets associated with the developing cortical representation is thought to be small, and we usually cap it to a proportion κ of Nptc, setting κ to 0.3 (Table 1) for the simulations done here. However, if the context’s category cannot be determined, we suppose it would be expedient to remember more of its attributes so that it will be more likely to be recognizable in the future and its category more likely to be discoverable at a later time. So, if a category cannot be determined, the ceiling for Unc retention is set to a value κo, which is larger than κ and taken as 0.8 for all our simulations. Although it is thought that the amount of context-specific information that becomes remote is limited, it is also thought that considerable detail may sometimes be retained, for example, when highly emotional memories become remote (e.g., Brown and Kulik, 1977). We have not incorporated emotion into our model, but it does seem to us that there are some especially familiar contexts for which we hold many details in more or less permanent memory. We, therefore, have designed BaconREM so that when a very great amount has been learned about a particular context, memory for more of its unclassified attributes (which will usually be mostly particulars) is allowed to become remote [we consider in the Discussion section, the possibility that some detail memory might be retained hippocampally rather than cortically]. Figure 5 shows the ceiling that Bacon places on its remote memory of non-categorical attributes as a function of the total amount that is known about the context. For our simulations, we have set the parameter ϵ, which determines how the ceiling on Uncs that becomes remote increases as a function of the total amount known, to 20 (bold curve of Figure 5). The type of circuit that is produced by the systems consolidation process is illustrated in Figure 6B. Stage II: Variable, potentially long period during which we hypothesize categories are being revised. Stage III: Systems consolidation process has gone as far as it can with available information, and hippocampal representation is abandoned.

Figure 5. Number of unclassified attributes (“Unc’s”) associated with a remote representation. There is a ceiling on the number of (Unc) attributes that are transferred to the cortical version of a representation when the representation becomes remote. This ceiling as a proportion of Nptc is given by ceiling=κ+1−κ.Zrec/Natrϵ (Eq. 9) where Zrec is the number of attributes associated with the hippocampal representation. For the simulations of this study, we have let κ = 0.3 and ϵ = 20. For these parameters, the ceiling is essentially κ unless a great deal is known about the context. However, if the category of a context cannot be determined, the ceiling is set to a fixed high value кo, which we have set to 0.8 for our simulations.

3.1.4.1 Stage I

This is the period that begins directly after the creation of a new hippocampal representation, during which the hippocampal representation is controlling behavior, and the information in it is being used to associate attributes of the context with a cortical representation cell, as detailed in Figure 4.

3.1.4.2 Stage II

Whereas we believe that construction of a cortical representation should be relatively fast, in published experiments on rodents, fear has been found to remain hippocampally dependent and continue to have generalization properties consistent with hippocampal mediation (i.e., does not show the hyper-generalization associated with cortical representations) for a quite variable period ranging from 1 and 2 weeks to well over a month (Kim and Fanselow, 1992; Maren et al., 1997; Anagnostaras et al., 1999; Wiltgen et al., 2010) and sometimes much longer in humans (Reed and Squire, 1998). Thus, there appears to be an extended period after we believe the cortical version of a representation should have been constructed during which the hippocampal representation is still operational and fear conditioned during Stage I is still associated with it. We call this period “Stage II.”

Since contextual fear remains hippocampus-dependent, we presume that even though the cortical representation may be operational, fear that has been conditioned to the hippocampus representation does not actually get copied to it until the end of Stage II. We postulate that during this period, the hippocampal and cortical representations compete for activation but that the hippocampal representation usually wins because the values of Ncat and Nptc that we have chosen to simulate known findings are such that the hippocampal representation usually has more attribute information than its cortical descendant and thus a higher BRep value. Moreover, as discussed below, the model predicts that given these assumptions, there should be circumstances under which the cortical rather than the hippocampal representation wins during Stage II.

We postulate that the hippocampal representation remains intact even after the construction of its cortical descendant so that attribute information associated with it (but not transferred to the cortical version) can contribute to upgrading the cortical categorical knowledge structure itself (item 5 above). We conjecture that animals use commonalities between contexts to try to discover new categories and add further attributes to existing ones. This is computationally much more difficult than merely recognizing membership in an existing category, and there is a substantial cognitive science literature concerned with this problem (e.g., Gluck and Bower, 1988; McClelland, 1994; Love et al., 2004; Ashby and Maddox, 2005; Ashby and Maddox, 2011; Carvalho and Goldstone, 2022). Proposing a theory of it and building it into BaconREM is well beyond the scope of this article. We merely suppose that it occurs and may take considerable time; it continues until it has gone as far as it can with available information. We would expect its duration to depend on what old and current information is available and, therefore, to be quite variable.

3.1.4.3 Stage III

When Stage II is finished and fear-producing potentiation has been copied from the hippocampal-amygdala pathway to the cortical representation cell-amygdala pathway, the contextual attribute information of the hippocampal representation is no longer needed for the updating process. We postulate that the representation’s attribute and fear associations, as well as its CA3 recurrent collateral potentiations (but not the associations of the hippocampal representation’s CA3 cells with the cortical representation), are then erased or become subject to being over-written so that the hippocampal circuitry is available to form new representations without interference from old ones (see further below and in the Discussion section). We refer to the post-Stage II period, during which the hippocampal representation is no longer activatable, and its cortical descendant is by default always the one used as Stage III.

3.1.4.4 Fear conditioning and expression in the three stages

Fear becomes conditioned to whichever representation is active at the time of a suitable unconditional stimulus: This will be to the hippocampal representation in Stage I, the cortical representation in Stage III, and whichever version of the representation is active during Stage II.

In order for the fear evoked by the cortical version of a representation to be the same as that produced by its hippocampal progenitor, we postulate that at the Stage II–III transition, the weight of the cortical representation cell synapse on amygdala fear-causing cell(s) is set equal to the cumulative weights of the K hippocampal representation cells’ synapses on it. However, when control of behavior is returned to the hippocampal representation as part of revising the associations of an existing cortical representation during its updating, fear previously conditioned to the cortical representation remains so and is expressed via the CA3-cortical representation pathway that mediates generalization between cortical and hippocampally mediated conditional fear as described during our consideration of generalization below. Should conditioning occur when a cortical representation is active, the weight of representation-to-amygdala synapses will be as explained in relation to Figure 3 above.

We presume that the development of potentiation of cortical pathway-amygdala synapses during the transfer of fear from a hippocampal representation to its cortical descendant would be an NMDA-dependent process and, therefore, that pharmacological blocking of NMDA-dependent processes within the amygdala during Stage II would prevent previously learned fear from becoming remote (Table 2, Prediction A), though it would not prevent a cortical representation of the context from replacing the hippocampal one.

Table 2. Predictions.

3.1.4.5 Timing of the systems consolidation process

The processing required to associate appropriate attributes with a cortical representation cell is similar to that carried out during each computational cycle, so we would expect Stage I to be relatively brief. However, as said above, we would expect the duration of Stage II to be highly variable and sometimes very lengthy. In fact, as said above, in rodents, the development of hyper-generalization and hippocampus independence, which under the conditions of most experiments indicate the Stage II–III transition, does occur at variable times ranging from as early as 1–2 weeks after representation creation to well over a month. If we assume that the Stage I–II transition usually occurs at a relatively brief and constant time after representation creation, it should occur before the shortest II–III transition and thus at less than 1–2 weeks after representation creation, while the Stage II–III transition occurs at variable times between 1 and 2 weeks and over a month.

3.1.5 Updating a cortical representation

A Stage III representation remains in Stage III indefinitely unless BaconREM is sufficiently confident at the end of a session that an active Stage III representation is valid (i.e., BRep > Badd) so that newly observed (or currently re-observed) attributes can become associated with it. In that case, the representation returns to Stage I with all known attributes, including the newly discovered ones, becoming associated with the reconstructed hippocampal representation, and the process of systems consolidation is then repeated to incorporate the new information into the cortical representation and, if possible, to upgrade the categorical knowledge structure.

Such updating of a cortical representation begins by using its knowledge of the CA3 cells of its hippocampal progenitor to re-establish the CA3-CA3 associations of the representation’s hippocampal version so that it will be able to function during Stage I of the systems consolidation process while the cortical version’s attributes are being revised. Then, all known attributes become associated with the re-established hippocampal representation. These include all currently observed attributes and all cortical representation-associated attributes, including those associated with the cortical category representation if it is known. Then, the hippocampally associated attributes become associated with the existing cortical representation during its initial construction. This completes Stage I of the revision process. During Stage II, when both the hippocampal and cortical versions of a representation are operational, any fear that is associated with a cortical representation gets expressed via the hippocampal representation’s CA3 cells’ connections to the cortical representation cell, as explained below when considering generalization.

It should be noted that when, during updating, a limited set of Unclassified (“Unc”) attributes associated with the hippocampal representation is selected to become associated with the representation’s cortical version, the selection, as during de novo representation formation, is random. Therefore, while updating a cortical representation may cause new information to be added to the representation, some previously known information may be lost.

In so far as the present theory applies generally to episodic memory, as opposed to just fear conditioning, the updating process could well lead to changes over time in memories of recalled events (Loftus, 2005; Yassa and Reagh, 2013).

Since updating, whether of a hippocampal or a cortical representation, involves new, presumably Hebbian learning, we presume that it would be prevented by NMDA receptor blockers affecting those regions where Hebbian potentiation must occur. We will return to this point, which leads to a crucial test of the model, in the Discussion section.

3.1.6 Generalization

The generalization of context fear has been an important area of study that has shaped ideas about the nature of remote memory. Generalization is a complex affair. Generalization of fear from a conditioned context A to an unconditioned context B might occur, or not, for at least three reasons: (1) A and B might be similar enough that B is simply mistaken for A, especially if B is not already familiar (“misidentification”). Such misidentification is responsible for the hyper-generalization of remote contextual fear. (2) Even if A and B are recognized as being different places or situations, similarities between them might cause a subject to suspect that since A is dangerous, so too might be B. (3) Specific to our model, even if B is mistaken for A (i.e., Rep A is activated in context B), the degree to which the known attributes of A and the observed attributes of B overlap will affect BRep and therefore the degree of fear expression.

We will see examples in the simulations described below of all three factors operating. However, we consider now just the situation in which contexts A and B are both known and each activates its appropriate representation.

3.1.6.1 Generalization when one or both representations are hippocampal

If context A and B’s representations are both still hippocampal, fear of conditioned context A will be due to potentiation of the synapses of representation A’s CA3 projection onto fear-activating cells of the amygdala, and generalized fear of context B will be produced by those of B’s representation cells that are also are part of A’s representation and hence already have potentiated synapses on fear-activating cells (Figure 6I). As in all Marr-like models, in which representations are composed of the K CA3/DG pairs most richly innervated by the set of active Cur cells, the overlap of A and B’s hippocampal representations (“OhippAB