We first review the key experimental results in Chettih et al., 2024. Black-capped chickadees were placed in a laboratory arena comprised of a grid of identical sites. Each site had a perch to land on and a hidden compartment, covered by a flap, where a seed could be hidden. Chickadees were allowed to behave freely in this environment and collect sunflower seeds from feeders. A chickadee often visited sites without interacting with the hidden compartment (Figure 1A) but, at other times, the chickadee cached a seed into the compartment, or retrieved a previously cached seed (Figure 1B). Previous experiments demonstrated that chickadees remember the precise sites of their caches in this behavioral paradigm (Applegate and Aronov, 2022).

Chettih et al., 2024 recorded hippocampal population activity during these behaviors. When chickadees visited sites, place cells were observed, similar to those previously found in birds and mammals (Payne et al., 2021; Figure 1C). Place cells did not change their spatial tuning after a cache. Instead, during caching and retrieval, neurons transiently displayed memory-related activity. During caching, neurons fired sparsely, with individual neurons producing large activity bursts for a small subset of caches at seemingly random locations (Figure 1D). These bursts occurred in both place cells and non-place cells, with the location of cache bursts unrelated to a neuron’s place tuning. At the population level, activity during a cache consisted of both typical place activity and a cache-specific component orthogonal to the place code, termed a “barcode”. Strikingly, barcode activity for a particular cache reactivated during later retrieval of that cache. These findings were evident when examining the correlation between population activity vectors for visits, caches, and retrievals at different sites. When comparing two visits, the correlation profile decayed smoothly with distance, as expected from place tuning (Figure 1E). When comparing caching with retrieval, a similar smooth decay was observed for most distances, indicating the presence of place tuning. However, there was a substantial boost in correlation for caches and retrievals at the exact same site (Figure 1F). This site-specific boost resulted from reactivation of the cache barcode during subsequent retrieval.

Barcode activity during caching and retrieval, which are moments of memory formation and recall, suggests a mechanism supporting episodic memory. We hypothesize that the hippocampus generates a sparse, high-dimensional pattern of activity transiently during the formation of each memory, and that this serves as a unique index to which the contents of the memory are bound. Reactivation of the barcode at a later time drives the recall of the associated memory contents. In the food caching behavior studied by Chettih et al., 2024, the contents of memory include the location (‘where’) and presence of a seed (‘what’). Below, we implement this hypothesis in a computational model.

We model the hippocampus as a recurrent neural network (RNN; Alvarez and Squire, 1994; Tsodyks, 1999; Hopfield, 1982) and propose that recurrent dynamics can generate barcodes from place inputs (Figure 2A). As in experiments, the model’s population activity during a cache should exhibit both place and barcode activity components. The network receives place inputs termed p→\begin{document}$\vec{p}$\end{document} which are spatially correlated as follows. Each neuron in the RNN receives inputs that are maximal at one location in the environment and decay with distance from that location, causing the neuron to have a single place field centered at that location. Across neurons, place fields uniformly span the environment. The firing rate activity of RNN units is denoted as x→\begin{document}$\vec{x}$\end{document}. The recurrent weights of the model are given by J\begin{document}$J$\end{document}, and the RNN activity x→\begin{document}$\vec{x}$\end{document} follows standard dynamics equations:(1)x→=ReLU(v→)\begin{document}$$\displaystyle \newcommand{\pat}[1]{} \vec{x} = ReLU(\vec{v})$$\end{document}(2)dv→dt=−g(x→)v→+Jx→+p→\begin{document}$$\displaystyle \newcommand{\pat}[1]{} \frac{d\vec{v}}{dt} = -g(\vec{x})\vec{v} + J\vec{x} + \vec{p}$$\end{document}

where v→\begin{document}$\vec{v}$\end{document} is the voltage signal of the RNN units and g(⋅)\begin{document}$g(\cdot)$\end{document} is a leak rate that depends on the average activity of the full network, representing a form of global shunting inhibition that normalizes network activity to prevent runaway excitation from recurrent dynamics. In our simulations, we simplify the task by using a 1D circular environment binned into 100 discrete spatial ‘states’. We set the spatial correlation length scale of place inputs such that the smallest distance between cache sites in the experiments of Chettih et al., 2024 is equal to 8 of these states (see Methods for more details).

We initialize the recurrent weights from a random Gaussian distribution J∼N(μNx,σ2Nx)\begin{document}$J\sim\mathcal{N}(\frac{\mu}{N_{x}},\frac{\sigma^{2}}{N_{x}})$\end{document}, where Nx\begin{document}$N_{x}$\end{document} is the number of RNN neurons and μ<0\begin{document}$\mu \lt 0$\end{document}, reflecting global subtractive inhibition that encourages sparse network activity to match experimental findings Chettih et al., 2024. We first consider network activity before any learning-related changes. For the range of parameters we use, the network is in a chaotic state with a roughly constant overall level of activity but fluctuations in the activities of individual units. From an initial state of 0, we run recurrent dynamics until this steady-state level of overall activity has been achieved (Figure 2—figure supplement 1A, B). The chaotic recurrent dynamics induced by the random weights (Sompolinsky et al., 1988) effectively scrambles incoming place inputs. We demonstrate this by measuring the correlation of RNN activity across different locations and plotting this correlation as a function of distance (Figure 2B). Place inputs show a smoothly decaying correlation curve. At low values of σ\begin{document}$\sigma$\end{document}, the network is primarily input-driven, showing a smoothly decaying correlation matching inputs. At high values of σ\begin{document}$\sigma$\end{document}, recurrence is so strong that it entirely eliminates the spatial correlation of nearby sites: activity at each state is decorrelated from activity at all other states.

Interestingly, at an intermediate level of σ=7\begin{document}$\sigma=7$\end{document}, the network retains elements from both high and low recurrence regimes (Figure 2B). The network exhibits a smoothly decaying correlation curve reflecting its inputs, but each state’s activity also contains a strong decorrelated component, apparent in the large drop in correlations for nearby but non-identical sites. This intermediate network regime closely resembles spatial correlation profiles observed during caching (Chettih et al., 2024; Figure 1F). The smoothly decaying component is caused by the place code, whereas the sharp peak at zero distance – reflecting barcode activity – is caused by the recurrent dynamics. We thus construct networks using intermediate σ\begin{document}$\sigma$\end{document} values, which allow for the coexistence of place code and barcode components in population activity.

A key result from Chettih et al., 2024 is that the hippocampus exhibits both place code and barcode activity during caching and retrieval, but only place activity during visits. We propose that this effect can result from a network in which recurrent strength is flexibly modulated. In a low-recurrence condition, the network produces the place code, whereas in a high-recurrence condition, the same network produces a combination of place code and barcode activity. To simulate this in our model, we modify equation 2 to(3)dv→dt=−g(x→)v→+rJx→+p→\begin{document}$$\displaystyle \newcommand{\pat}[1]{} \frac{d\vec{v}}{dt} = -g(\vec{x})\vec{v} + rJ\vec{x} + \vec{p}$$\end{document}

where the newly included r∈{0,1}\begin{document}$r\in\{0,1\}$\end{document} scales recurrent strength such that the network may be in a feedforward (r=0\begin{document}$r=0$\end{document}) or recurrent regime (r=1\begin{document}$r=1$\end{document}). During visits, we assume the network is operating with low recurrent strength (r=0\begin{document}$r=0$\end{document}). As a result, the activity in the RNN exhibits the spatial profile of its place inputs. We verify this is the case by visualizing early and late RNN activity given a place input (Figure 2C). With low recurrence, early and late RNN activity have similar spatial profiles, and late activity patterns for nearby states are highly correlated (Figure 2E). In contrast, when recurrence is enabled (r=1\begin{document}$r=1$\end{document}), network activity is sparse with a heavy tail of a few strongly active neurons and is decorrelated between nearby states (Figure 2D and F). These changes match experimental observations of excitatory neurons during food caching (Chettih et al., 2024).

We visualized neural activity during visits (r=0\begin{document}$r=0$\end{document}) and caches (r=1\begin{document}$r=1$\end{document}). During visits, RNN units display ordinary place tuning (Figure 2G, Figure 2—figure supplement 1C). We also simulated spikes for all units at each location and visualized this as a matrix where units were sorted by the preferred location of their inputs (Figure 2H). This matrix exhibits a diagonal structure reflecting strong spatial correlations. During caches, single neurons develop sparse, scrambled spatial responses relative to their place tuning (Figure 2I, Figure 2—figure supplement 1C). Accordingly, simulated spikes across the population have greater random, off-diagonal components during caching than during visits. Thus, recurrence in a randomly connected RNN is a simple and effective mechanism to generate barcode signals from spatially correlated inputs. We alternatively considered a feedforward mechanism to generate barcodes, in which barcodes are computed by a separate feedforward pathway (Figure 2—figure supplement 2). We found the feedforward mechanism required an unreasonably large number of neurons and sparsity levels to match the decorrelation level of the recurrent mechanism.

Having suggested a mechanism for the generation of barcode representations, we next propose how such a representation can be leveraged for memory storage in a network model. In our food-caching task, we assume that the contents of a memory include the location of the cache and the identity of a food item within the cache. Thus, we add an additional input source besides spatial location into our model – an input s\begin{document}$s$\end{document} representing the presence of a seed (Figure 3A). The ‘seed’ input projects randomly onto the RNN neurons. During caching, both place inputs and seed inputs arrive into the RNN, matching experimental findings (Chettih et al., 2024). This causes a mixed response in the network: one component of the response (place activity) is spatially tuned, another component (seed activity) indicates the presence of a seed and does not vary with location, and the third component (barcode activity) is generated by recurrent dynamics interacting with these inputs.

To store memories, we assume the RNN undergoes Hebbian learning after some fixed time point during the r=1\begin{document}$r=1$\end{document} recurrent dynamics (Figure 3A). At this time, the synapse j→i\begin{document}$j\rightarrow i$\end{document} changes by an amount(4)ΔJij∝xixj−βxi\begin{document}$$\displaystyle \newcommand{\pat}[1]{} \Delta J_{ij} \propto x_i x_j - \beta x_i$$\end{document}

where β>0\begin{document}$\beta \gt 0$\end{document} provides an overall inhibition of the stored pattern. This term helps to prevent network activity from collapsing to previously stored attractors. Memory storage works as follows, following the experimentally observed sequence in Chettih et al., 2024: place inputs arrive into the RNN, recurrent dynamics generate a random barcode, seed inputs are activated, and then Hebbian learning binds a particular pattern of barcode activity to place- and seed-related activity. In this way, fixed-point attractors are formed corresponding to a conjunction of a barcode and memory content.

Memory recall in our network follows typical pattern completion dynamics, with recurrence strength set to r=1\begin{document}$r=1$\end{document} as for caches. As an example, consider a scenario in which an animal has already formed a memory at some location l\begin{document}$l$\end{document}, resulting in the storage of an attractor a→\begin{document}$\vec{a}$\end{document} into the RNN. The attractor a→\begin{document}$\vec{a}$\end{document} can be thought of as a linear combination of place input-driven activity p(l)\begin{document}$p(l)$\end{document}, seed input-driven activity s\begin{document}$s$\end{document}, and a recurrent-driven barcode component b\begin{document}$b$\end{document}. Later, the animal returns to the same location and attempts recall (i.e. sets r=1\begin{document}$r=1$\end{document}, Figure 3B). Place inputs for location l\begin{document}$l$\end{document} drive RNN activity towards p(l)\begin{document}$p(l)$\end{document}, which is partially correlated with attractor a→\begin{document}$\vec{a}$\end{document}, and the recurrent dynamics cause network activity to converge onto attractor a→\begin{document}$\vec{a}$\end{document}. In this way, barcode activity b\begin{document}$b$\end{document} is reactivated as part of attractor a→\begin{document}$\vec{a}$\end{document}, along with the place and seed components stored in the attractor state p(l)\begin{document}$p(l)$\end{document} and s\begin{document}$s$\end{document}. The seed input can also affect recall, as discussed in the following section.

As an initial test of memory function in our model, we analyzed the activity patterns that are stored and recalled in the model. We simulated caching at different sites in the arena and extracted the population activity that is stored via Hebbian learning (Figure 3C, left). We then simulated retrieval as an event in which the animal returns to the same site and runs memory recall dynamics (r=1\begin{document}$r=1$\end{document}) in the RNN. Population activity during retrieval closely matches activity during caching and is substantially decorrelated from activity during visits (Figure 3C). To compare our model with the empirical results reproduced in 1E,F, we ran in silico experiments with caches and retrievals at varying sites in the circular arena. We simulated Poisson-generated spikes drawn from our network’s underlying rates to match the intrinsic variability in empirical data (see Methods). We find that population activity in the RNN is more strongly correlated between caches and retrievals at the same site than two visits to a site that are not seed related (r=0\begin{document}$r=0$\end{document}; Figure 3D). In addition, cache-retrieval correlations for non-identical sites rapidly drop to the level of visit-visit correlations because barcodes are orthogonal even for nearby sites. These correlation profiles closely resemble those observed in Chettih et al., 2024 (compare Figure 3D and Figure 1E, F).

What are the computational benefits of barcode-mediated memory storage? We designed two behavioral tasks for our model that quantify complementary aspects of memory performance. In both tasks, we simulate a sequence of three caches in the circular arena. We then test the model’s performance during memory recall (i.e. r=1\begin{document}$r=1$\end{document}) using two distinct tasks. The ‘Cache Presence’ task requires the network to identify the presence or absence of a cached seed at the current location (Figure 4A). By evaluating the model on this task using different spacings between caches, we can measure the spatial precision of memory, that is how far apart two caches must be to prevent interference between their associated memories. The ‘Cache Location’ task requires the network to identify the cache nearest to the current location by reactivating place activity corresponding to that cache location (Figure 4B). This task measures the robustness of recall and requires attractor dynamics to accurately retrieve memories from potentially distant locations. Together, these questions probe the ability of the memory system to be both specific (pattern separation) and searchable (pattern completion).

To enable readout from the model, we add an output layer containing place and seed units. During memory formation, these units receive a copy of place and seed inputs, respectively, and undergo Hebbian plasticity (equation 4 with β=0\begin{document}$\beta=0$\end{document}) with RNN units. This enables the RNN to reactivate a copy of the inputs that were provided during memory formation. We measure the activity of the seed output to determine cache presence, and we measure place outputs to determine cache location. We note that other readout mechanisms would likely function similarly – for example, plastic feedback connectivity from recurrent onto input units. The output layer used here is not intended to correspond to a specific brain region, but simply to provide a window into what could be read out easily from network activity by downstream neural circuits.

We first show model performance on a single example of the Cache Presence and Cache Location tasks, where caches are made at the locations 20%, 35%, and 70% of the way around the circular track. For the Cache Presence task, we evaluate the model at each spatial location and plot the activity of the seed output (Figure 4C). After the first cache, we see that the seed output is only high at states around the vicinity of the first cache (Figure 4C, top). The false positive rate is not zero since the states around the cache also have high output. However, the width of this false positive area is less than the distance between two sites in the arena used in Chettih et al., 2024, indicating that the model is able to identify caches at the spatial resolution observed in chickadee behavior in these experiments. After a second cache, the seed output correctly reports seeds in the areas around the two caches (Figure 4C, middle). Importantly, the network separates the caches from each other, correctly identifying the absence of a seed at a position between the two caches. This behavior is maintained after the addition of the final third cache (Figure 4C, bottom).

For the Cache Location task, we examine the place outputs (Figure 4D, ‘Narrow Search’). When the current position is near a cache, the network correctly outputs a place field for the location of the nearest cache. However, an animal relying on memory to guide behavior may need to recall cache locations even when far away from a cache. To enable increased search radius, we make use of the seed input, which can bias network activity towards all memory patterns previously associated with this input. Activating the seed input greatly increases the range of current positions over which cache memories are retrieved (Figure 4D, ‘Broad Search’). Critically, this does not cause interference between memories. For example, as the current position moves from the location of cache 1 to cache 2, place outputs discretely jump from one cache location to the other, corresponding to correct selection of the nearest cache location. The search radius during recall can thus be flexibly adjusted according to task demands, allowing the trade-off between pattern completion and pattern separation to be dynamically regulated by simple scaling of a network input.

We next systematically quantified model performance on these tasks. For these analyses, we binarized the seed output as being above or below a threshold (Figure 4—figure supplement 1A, B). When caches are sufficiently spaced, memory recall is near perfect (Figure 4—figure supplement 1A, B). This led us to evaluate the resolution of the model’s memory as caches become more closely spaced. We decreased the distance between cache 1 and 2 to identify the minimum distance where caches are separable, that is where the model correctly indicates the absence of a cache at a midpoint between caches 1 and 2. Figure 4E shows this correct reject rate as a function of the distance from each cache and the seed input strength. With low seed input (e.g. s=0\begin{document}$s=0$\end{document}), the correct reject rate is high when the current location is one site distance away from caches 1 and 2. In other words, if a cache is made at site 1 and site 3, our model recognizes that site 2 remains empty. This precision matches the single-site resolution measured by behavioral experiments in this arena (Applegate and Aronov, 2022). As expected, performance on the Cache Presence task decreases with greater seed input strengths, as these are suited to searching over a broad spatial range.

For the Cache Location task, we measure the probability that the model outputs the location of the nearest cache. We plot this probability as a function of distance from the current location to the nearest cache (Figure 4F). The model is able to correctly recall cache locations with almost perfect accuracy when it is near a cache. Performance drops sharply with distance when the seed input is low, but is substantially recovered by increasing the seed input strength. Critically, even when the search radius is broad enough to include multiple caches, attractor dynamics encourage selection of the single closest cache location rather than blending memories. Thus, the seed input strength provides a flexible search radius during the recall process. Low values of s\begin{document}$s$\end{document} are more suitable for detecting the presence or absence of a seed near the current location, while high values of s\begin{document}$s$\end{document} are more suitable for finding remote caches. The complementary demands of the Cache Presence and Cache Location tasks demonstrate the utility of a flexible search radius within one memory system.

We further examined how model hyperparameters affected performance on these tasks. We find that the plasticity bias β\begin{document}$\beta$\end{document} is needed to prevent erroneous memory recall at sites without caches (Figure 4—figure supplement 1E-H). Without this, recall specificity is poor and model performance suffers on the Cache Presence task. We also verified that our model is robust to the order in which caches were made (Figure 4—figure supplement 1C, D). We found that adding noise to the network’s temporal dynamics had little effect on memory recall performance (Figure 4—figure supplement 2A). However, large static noise vectors added to the network’s input and initial state decreased the overall probability of memory recall, but not its spatial profile (Figure 4—figure supplement 2B). Finally, we extended our model to work with random, spatially correlated inputs, rather than receiving place cell-like inputs (Figure 4—figure supplement 3). This shows that our results apply regardless of the specific format of spatial inputs, which are experimentally undetermined.

We have shown that a barcode-mediated memory system is precise yet allows flexible, content-based retrieval. Below we identify the specific contributions of place and of barcode activity by ablating either of these components in our model. To ablate barcodes (‘Place Code Only’ in Figure 5), we initialize our model without the random recurrent weights that produce chaotic dynamics. This is akin to running caching dynamics in ‘visit mode’, that is r=0\begin{document}$r=0$\end{document} in Figure 2. To ablate place activity (‘Barcode Only’ in Figure 5), we eliminate spatial correlations in the network inputs. This is akin to having place fields with extremely narrow precision, rather than a spatially smooth place code. We test both ablated models on the three-cache tasks from above and compare their performance to our full model.

The Place Code Only model directly binds memory contents of place and seed. This causes cache memories for nearby locations, where the place code is correlated, to interfere with each other. Interference is clearly visible in the performance on the Cache Presence task (Figure 5A, left). The seed output of the place code only network is high across a wide area including caches 1 and 2 and the empty locations between them. Indeed, this network is unable to identify the absence of a cache at locations between caches 1 and 2, even with a substantial distance between them (Figure 5C). Furthermore, the memories for caches 1 and 2 sometimes appear to suppress memory for a distant cache 3. Further evidence of interference is apparent in the Cache Location task, where the network merges caches 1 and 2 and entirely fails to signal the cache at location 3 (Figure 5B, left). This network has a low true negative rate, and often a single cache dominates the output (Figure 5—figure supplement 1A, D). Accordingly, the network is able to signal the location of a cache, but this location is often not the nearest cache (Figure 5D). Intuitively, without barcodes, the network is unable to distinguish individual memories at nearby spatial locations. Without this barcode-mediated competition, it forms a single agglomerated memory that is inflexibly recalled.

If correlations in inputs cause memory interference, why not do away with them entirely? The Barcode Only model shows that this is not a good option. This model performs well on the Cache Presence task (Figure 5A, right, Figure 5—figure supplement 1E-G), correctly identifying the presence of all three caches and the absence of caches in other locations (Figure 5C). However, the Barcode Only model fails on the Cache Location task. The model is unable to recall place fields that are not precisely at its current location (Figure 5B and D). With greater seed input, the model can sometimes recall memories at remote locations, but these are selected randomly with no preference for nearby caches (Figure 5D, Figure 5—figure supplement 1H). Intuitively, the model cannot distinguish nearby and distant caches because it lacks input correlations, which establish the measure of proximity.

In summary, place and barcode activity play complementary roles in our model. Barcode activity functions like an index for individual memories. This function supports discriminability of memories even when memory contents overlap – for example, for two nearby caches with correlated place activity. Barcodes also support selective recall of individual memories in our model via competitive attractor dynamics. However, the discriminability advantage of barcodes is only useful if they can be reactivated during memory recall. Spatially correlated place inputs (and the seed input) allow efficient memory retrieval by defining a measure of proximity in memory contents and support remote memory recall. The presence of both index and content signals in our model allows all of these functions to be performed by the same network, and for the trade-offs between them to be adjusted flexibly.

We have constructed a model of a simple episodic memory, taking inspiration from hippocampal data (Chettih et al., 2024). However, the hippocampus has also been suggested to support functions beyond episodic memory. An especially influential line of prior work proposes that the hippocampus plays a role in generating predictive maps, with evidence from both experiments (including in food-caching birds; Muller and Kubie, 1989; Mehta et al., 2000; Payne et al., 2021; Applegate et al., 2023) and theory (Blum and Abbott, 1996; Stachenfeld et al., 2017; Whittington et al., 2020). This raises the question – is our model consistent with predictive map theories? And if so, how might predictive maps influence episodic memory recall?

Interestingly, prior work has shown that biologically realistic RNNs can generate predictive maps with structured recurrent weights (Fang et al., 2023). Specifically, if recurrent weights encode the transition statistics of an animal’s experience, then predictive map-like activity will arise from the RNN dynamics and can be controlled by recurrent strength (analogous to the value of r\begin{document}$r$\end{document} in equation 3). This prediction via structured recurrent weights invites comparison to the use of random recurrent weights in our model to generate barcodes. Inspired by this connection, we considered whether a single model could generate both predictive and barcode activity via recurrent dynamics. We constructed a hybrid model, in which recurrent weights are a blend of random weights, as above, and structured, predictive weights as in Fang et al., 2023 (Figure 6—figure supplement 1B). We hypothesize that network activity changes from a predictive to a chaotic regime (supporting barcodes) with increasing recurrent strength, that is as we adjust r\begin{document}$r$\end{document} in the range 0<r<1\begin{document}$0 \lt r \lt 1$\end{document}.

We use the same circular arena for our simulations, but with the assumption that animal behavior is biased, that is the animal only moves clockwise (Figure 6A). We visualize population activity at each site, with units sorted by their place field. When recurrent strength is at its lowest (r=0\begin{document}$r=0$\end{document}, Figure 6B) network activity is place-like and reflects the current location of the animal provided in its inputs. When recurrent strength is slightly increased (r=0.3\begin{document}$r=0.3$\end{document}, Figure 6C), the network exhibits predictive activity. That is, neural activity of recurrent units is shifted to reflect an expected future position, relative to the current spatial position encoded in inputs. This is consistent with observations from experimental data collected from the hippocampus of animals with biased movements in a linear track (Wilson and McNaughton, 1993; Mehta et al., 1997; Mehta et al., 2000; Lisman and Redish, 2009). Finally, when recurrent strength is maximal (r=1.0\begin{document}$r=1.0$\end{document}, Figure 6D) we observe barcodes, i.e. sparse activity at random positions relative to inputs. We plot spatial tuning curves of a few example RNN units under low, intermediate, and high recurrent strengths (Figure 6E, Figure 6—figure supplement 1C). Individual units can display typical place fields (blue), skewed predictive place fields (orange), and barcode activity (purple).

These results suggest that the structured and random components of recurrent connectivity can act somewhat independently of each other, with their relative contributions determined by recurrent strength. We quantify this by measuring the magnitude of the projection of population activity onto the place code, the predictive code, and barcodes as a function of recurrent strength (Figure 6F). At the lowest recurrent strength (r=0\begin{document}$r=0$\end{document}), the population activity is solely concentrated on the place code. As recurrent strength is increased, place coding decreases and predictive activity increases with a peak around r=0.4\begin{document}$r=0.4$\end{document}. Beyond this, both place and predictive activity decrease as barcode activity rises to a peak when r=1.0\begin{document}$r=1.0$\end{document}.

Finally, we explore the functional implications of including predictive maps into our memory model. We first verify that model performance in the previous three-cache tasks is not disrupted by including predictive weights in the model (Figure 6—figure supplement 2). We then examine memory recall of a single cache for a predictive model, assuming a clockwise behavioral bias (Figure 6G). The model exhibits a profound skew: the cache is recalled much earlier on the path leading up to the cache location, at further distance from the cache than on the path after the cache location. This indicates that knowledge of the environment and prior experience, as reflected in predictive place activity, can shape memory recall in our model.

We simulate a caching task in a circular track, similar to Chettih et al., 2024. The track consists of Ns\begin{document}$N_{s}$\end{document} connected states. The goal of this task is to test how well an agent equipped with a memory model can precisely recall the locations where a cache (or memory) has been stored. Specifically, for each simulation, we first choose a set of states C\begin{document}$C$\end{document} that will be the location where caches are made. For each state c∈C\begin{document}$c\in C$\end{document} we assume the agent is currently at state c\begin{document}$c$\end{document} and allow the model to store a memory at that state. We then simulate what the output of the model is if the agent is at any of the other Ns\begin{document}$N_{s}$\end{document} states. We continue this procedure for the remaining states in the list.

In the three-cache task, C={0,m,Ns∗0.7}\begin{document}$C=\{0,m,N_{s}*0.7\}$\end{document}. We sweep over different values of 0<m<Ns∗0.7\begin{document}$0 \lt m \lt N_{s}*0.7$\end{document} to test the effects of site spacing. In the main figures, these three caches are made in increasing order of their location. However, we also randomly shuffle the order of caching in a supplementary figure (Figure 4—figure supplement 1C, D) and do not find any effects on model performance.

To allow comparisons to data in Chettih et al., 2024, we first determine the number of states in our simulation that’s equivalent to the distance between adjacent cache sites in Chettih et al., 2024. To do so, we note that the spatial correlation between population activity at two adjacent cache sites is around 0.75 (when spatial correlation profile is normalized to [0, 1]). We identify the number of states in our simulation such that the normalized correlation between visit activity is also around 0.75. We find that this is around eight states. Thus, we define eight states in our simulation as equivalent to the distance between adjacent cache sites.

We simulate Poisson spikes from our rate network in Figure 2HJ. Specifically, for a unit with rate r\begin{document}$r$\end{document}, we draw spikes from a Poisson distribution with mean and variance r+K\begin{document}$r+K$\end{document}. We set K=0.2\begin{document}$K=0.2$\end{document} to visually match observations from data.

To calculate correlation values as in Figure 3D, we simulated experiments where five sites were randomly chosen for caching and retrieval. To compare model results to the empirical data in 1E,F, which includes intrinsic neural variability, we sampled Poisson-generated spike counts from the rates output by our model. Specifically, for RNN activity ri→\begin{document}$\vec{r_{i}}$\end{document} at location i\begin{document}$i$\end{document}, using the rates at t=100\begin{document}$t=100$\end{document} as elsewhere, we first generate a sample vector of spikes si→∼Poisson(kri→)\begin{document}$\vec{s_{i}}\sim\text{Poisson}(k\vec{r_{i}})$\end{document}. We choose k\begin{document}$k$\end{document} to be 0.2 to match experimental spatial correlation profiles in the ‘visit-visit’ condition. To get the correlation of population activity at locations i,j\begin{document}$i,j$\end{document}, we calculate the population Pearson correlation coefficient between si→\begin{document}$\vec{s_{i}}$\end{document} and sj→\begin{document}$\vec{s_{j}}$\end{document}. To generate Figure 3D, we repeated this simulated experiment 20 times with different random seeds and then pooled over experiments to average correlation values as a function of distance. All values are normalized by the ‘visit-visit’ correlation value at a site distance of 0, to match the analysis of experimental data in Chettih et al., 2024. This is repeated over 20 random seeds.

The barcode model with prediction differs from the default model in the initialized weight matrix. Specifically, the weight matrix J=B+M\begin{document}$J=B+M$\end{document}, where B\begin{document}$B$\end{document} is the random Gaussian matrix of the default model. M\begin{document}$M$\end{document} is a successor representation-like matrix (Stachenfeld et al., 2017) defined asM=ρ(∑d=0DγdTt)+δ\begin{document}$$\displaystyle \newcommand{\pat}[1]{} M = \rho(\sum_{d=0}^D \gamma^d T^t) + \delta$$\end{document}

where T\begin{document}$T$\end{document} is the transition probability matrix and γ=0.99\begin{document}$\gamma=0.99$\end{document} is a temporal discount factor. We also add a scaling factor ρ=0.075\begin{document}$\rho=0.075$\end{document} and an inhibitory offset δ=−0.015\begin{document}$\delta=-0.015$\end{document} is a 5000-dimensional square matrix, and we truncate the summation at D=300\begin{document}$D=300$\end{document} steps. T\begin{document}$T$\end{document} is defined asTij={1,ifj=i+10,otherwise\begin{document}$$\displaystyle \newcommand{\pat}[1]{} T_{ij} = \begin{cases} 1, & \text{if}\ j=i+1 \\ 0, & \text{otherwise} \end{cases}$$\end{document}

We will construct a feedforward model to generate sparse, decorrelated barcodes (Figure 2—figure supplement 2A). Place inputs to the model are fed through a hidden expansion layer before being compressed again by an output layer to generate the barcode. We first define these layers via the random matrices Wh∈RM,Np\begin{document}$W_{h}\in\mathcal{R}^{M,N_{p}}$\end{document} and Wo∈RNx,M\begin{document}$W_{o}\in\mathcal{R}^{N_{x},M}$\end{document} where Wh∼N(0,1Np)\begin{document}$W_{h}\sim\mathcal{N}(0,\frac{1}{N_{p}})$\end{document} and Wo∼N(0,1M)\begin{document}$W_{o}\sim\mathcal{N}(0,\frac{1}{M})$\end{document}. We make the hidden layer very large: M=20000\begin{document}$M=20000$\end{document}. The activity of the model in the hidden layer is described as:xh→=ReLU⁢(Wh⁢p→-Cθ)\begin{document}$$\displaystyle \vec{x_{h}}=\text{ReLU}(W_{h}\vec{p}-C_{\theta})$$\end{document}

where Cθ\begin{document}$C_{\theta}$\end{document} is a constant chosen such that the proportion of units in xh→\begin{document}$\vec{x_{h}}$\end{document} that are active is θ\begin{document}$\theta$\end{document}. In other words, θ\begin{document}$\theta$\end{document} is a hyperparameter of the model that sets how sparse the hidden layer activity is.

The hidden layer activity is then passed through the output weights to form the barcode activity generated by the feedforward model:x→=ReLU⁢(Wo⁢xh→-C)\begin{document}$$\displaystyle \vec{x}=\text{ReLU}(W_{o}\vec{x_{h}}-C)$$\end{document}

where C\begin{document}$C$\end{document} is a constant chosen such that the sparsity of x→\begin{document}$\vec{x}$\end{document} matches the sparsity of barcodes generated in the default RNN barcode model.

We simulate a version of the model with more realistic and complex place inputs. We generated the input currents to the RNN units according to a 0-mean multivariate Gaussian process. The statistics of the Gaussian process are chosen such that the covariance of the inputs to RNN unit i\begin{document}$i$\end{document} and unit j\begin{document}$j$\end{document} is an exponentially decaying function of their minimum spatial distance d\begin{document}$d$\end{document} around the circular arena: Σij=e−d0.4\begin{document}$\Sigma_{ij}=e^{-\frac{d}{0.4}}$\end{document}. All other details of this alternative model are the same as in the default.

Code is publicly available on https://github.com/chingf/barcodes (copy archived at Fang, 2024).