Title: Time Makes Space: Emergence of Place Fields in Networks Encoding Temporally Continuous Sensory Experiences
Venue: NeurIPS 2024
Accepted: yes
Keywords: Place Cells/Fields

Recurrent Neural Networks

Episodic Memory

Hippocampus
Abstract: The vertebrate hippocampus is thought to use recurrent connectivity in area CA3 to support episodic memory recall from partial cues. This brain area also contains place cells, whose location-selective firing fields implement maps supporting spatial memory. Here we show that place cells emerge in networks trained to remember temporally continuous sensory episodes. We model CA3 as a recurrent autoencoder that recalls and reconstructs sensory experiences from noisy and partially occluded observations by agents traversing simulated arenas. The agents move in realistic trajectories modeled from rodents and environments are modeled as continuously varying, high-dimensional, sensory experience maps (spatially smoothed Gaussian random fields). Training our autoencoder to accurately pattern-complete and reconstruct sensory experiences with a constraint on total activity causes spatially localized firing fields, i.e., place cells, to emerge in the encoding layer. The emergent place fields reproduce key aspects of hippocampal phenomenology: a) remapping (maintenance of and reversion to distinct learned maps in different environments), implemented via repositioning of experience manifolds in the network’s hidden layer, b) orthogonality of spatial representations in different arenas, c) robust place field emergence in differently shaped rooms, with single units showing multiple place fields in large or complex spaces, and (d) slow representational drift of place fields.  We argue that these results arise because continuous traversal of space makes sensory experience temporally continuous. We make testable predictions: a) rapidly changing sensory context will disrupt place fields, b) place fields will form even if recurrent connections are blocked, but reversion to previously learned representations upon remapping will be abolished, c) the dimension of temporally smooth experience sets the dimensionality of place fields, including during virtual navigation of abstract spaces.

Time Makes Space: Emergence of Place Fields in Networks Encoding Temporally Continuous Sensory Experiences

Abstract

The vertebrate hippocampus is believed to use recurrent connectivity in area CA3 to support episodic memory recall from partial cues. This brain area also contains place cells, whose location-selective firing fields implement maps supporting spatial memory. Here we show that place cells emerge in networks trained to remember temporally continuous sensory episodes. We model CA3 as a recurrent autoencoder that recalls and reconstructs sensory experiences from noisy and partially occluded observations by agents traversing simulated arenas. The agents move in realistic trajectories modeled from rodents and environments are modeled as continuously varying, high-dimensional, sensory experience maps (spatially smoothed Gaussian random fields). Training our autoencoder to accurately pattern-complete and reconstruct sensory experiences with a constraint on total activity causes spatially localized firing fields, i.e., place cells, to emerge in the encoding layer. The emergent place fields reproduce key aspects of hippocampal phenomenology: a) remapping (maintenance of and reversion to distinct learned maps in different environments), implemented via repositioning of experience manifolds in the network's hidden layer, b) orthogonality of spatial representations in different arenas, c) robust place field emergence in differently shaped rooms, with single units showing multiple place fields in large or complex spaces, and d) slow representational drift of place fields. We argue that these results arise because continuous traversal of space makes sensory experience temporally continuous. We make testable predictions: a) rapidly changing sensory context will disrupt place fields, b) place fields will form even if recurrent connections are blocked, but reversion to previously learned representations upon remapping will be abolished, c) the dimension of temporally smooth experience sets the dimensionality of place fields, including during virtual navigation of abstract spaces. Code for our experiments is available at 1 .

1 Introduction

The hippocampus is a brain region that plays a critical role in both spatial navigation [1, 2, 3] and episodic memory [4, 5, 6, 7, 8]. Researchers have therefore sought to understand the neural

substrates of these forms of memory in the hippocampus, as well as the extent to which these roles are interrelated [9, 10, 11, 12]. A key role is played by place cells - so named because they fire in specific spatial locations within an environment [13]. Place cells have spatially constrained firing fields, and 'remap' firing patterns in response to significant contextual changes (especially in hippocampal subregion CA3) [14, 15, 16, 17, 18, 19], including motion to a new environment [20] and modified behavioral context or sensory cues [21, 22]. After remapping, they form almost orthogonal representations [21, 23]. These findings suggest that CA3 place cell network may play a key role in maintaining both positional and contextual information [19, 24], while also supporting a large capacity for memory storage [25]. Meanwhile, others have suggested that hippocampal CA3 is a pattern completion and separation device [26, 27, 28, 29] that supports the storage and retrieval of episodic memories from partial cues [30, 7, 29]. This claim is supported by the extensive recurrent collaterals in CA3 [31, 32, 7], which could allow it to act as an autoassociative network retrieving a complete memory fron partial cues [33, 34, 7, 29].

Prior studies reconciling the spatial and episodic memory perspectives on CA3 propose that hippocampus associates sensory cues with spatial information [35, 36, 37, 38]. In this view, given partial sensory signals, CA3 recalls and reconstructs associated spatial information. Benna and Fusi [39] proposed the hippocampus as a memory compression device, contrasting and memorizing differences between multiple visits to a room, and showed that autoencoders with sparsity constraints develop place-like representations in the network encoding layer. Likewise [40] suggests that spatial awareness results from processing sequences of sensory inputs, and in a learning framework based on Hidden Markov Models, observed the emergence of place-like patterns. Furthermore, [41] trained an RNN on visual observations conditioned on the agent's direction to predict near-future observations and also found localized spatial representations. However, several questions remain. What signals contribute to spatial information? How are memories from multiple visits compared? Do such frameworks reproduce the phenomenology of place cells, including remapping and reversion across rooms during realistic navigation to create orthogonal representations?

Here, we propose that sensory cues weakly modulated by spatial locations collectively create spatial information, and that auto-associating these signals during spatial traversal elicits emergence of place-like patterns. We test this idea by simulating an artificial agent that receives partial and noisy sensory observations while traversing simulated rooms. We model CA3 as a recurrent autoencoder (RAE), which tries to reconstruct complete sensory experiences given partial and noisy observations at each location. We find that place-like firing patterns closely resembling rodent hippocampal place cells emerge in the encoding layer of this RAE. This emergence does not require explicit sparsity constraints (unlike [39]) and is robust across a wide range of environmental geometries, numbers of encoding units, and dimensions of sensory cues. We demonstrate that the pattern-completion objective encourages encoding units to prioritize temporally stable components of perceived experiences, naturally forming place-like representations. We also find that learned recurrent connections reflect expected variations of sensory experience, and thus enable single cells to form distinct representations of sensory experiences at similar locations in different environments. This mechanism allows our emergent place cells to remap and revert spatial representations when agents move between multiple unfamiliar and familiar environments, resembling place cells in the brain [42, 43, 22]. Finally, similar to place cells in CA3, our emergent place units form uncorrelated representations for different rooms and maintain these representations over an extended period.

Our model predicts that: (1) Rapidly varying sensory experience across space will disrupt place field formation; (2) Disrupting CA3 recurrent connections will not disrupt place fields, but will reduce the speed of formation of new spatial representations and prevent reversion to previous configurations upon re-entry of familiar rooms; (3) The temporally smooth components of sensory experience sets the dimensionality of place fields for animals traversing physical or abstract spaces.

2 Method

2.1 Episodic memory during spatial traversal

Wefirst construct a framework for modeling episodic memory, then predict behavior during navigation. First, assume that the hippocampus continuously receives inputs from other cortical areas such as the entorhinal cortex, prefrontal cortex, and thalamus [44, 45, 7, 1], collectively constituting a highdimensional experience vector (EV), a point in an abstract space of possible experiences E . An

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agent experiences this world through a temporal sequence of 'events'. Each event produces a short sequence of EVs - a 'segment' of episodic memory. A single event of bounded duration should trace a brief, continuous trajectory in the experience space E . Formally, let E = { e 0 , e 1 , . . . , e T } represent the segment of episodic memory generated by a single event, where each e t ∈ R D (for t = 0 , 1 , . . . , T ) denotes an EV at time t , D is the dimension of the input experience space, and T is the duration of this episode in discrete time steps. We take each time step to represent 50 ms in real-time. The sequence is continuous such that for any t and t +1 , where 0 ≤ t < T , there exists a non-zero correlation coefficient, ρ ( e t , e t +1 ) . During spatial navigation, we expect the environment to be temporally stable, with location-dependent experiences. We therefore model EVs in a fixed room as weakly spatial modulated (WSM) signals (Fig. 1), defining a manifold in the experience space E . In this view, episodic memories of traversal of an environment sample the WSM manifold that defines it.

2.2 Recurrent Autoencoder (RAE) as a model of pattern completion and separation

We then construct a simple network model of CA3 for recalling and pattern-completing arbitrary experience vectors. We train the network on EVs generated by an artificial agent exploring varied environments. We design the network following classical theories of CA3 for episodic memory storage, which suggest that recurrent collaterals of CA3 [46, 31, 32, 17, 29] develop attractor dynamics [47] enabling association of similar patterns and separation of dissimilar ones [37, 28, 29]. Accordingly, we model CA3 as a recurrent autoencoder (RAE). In view of previous research that observed emergence of grid-like patterns in recurrent neural networks (RNNs) trained for navigation [48, 49, 50], we implemented our RAE as a continuous-time RNN. Input projections denoted as W in represent pathways entering the hippocampus (Fig. 1b). The hidden layer units use a ReLU non-linearity and contain recurrent connections W rc , emulating non-linear responses in CA3 neurons and their recurrent collaterals. The network then uses post-synaptic connections W out representing CA3's projection to other brain regions to decode hidden unit states. All weight matrices W in , W rc , and W out are initialized to a zero mean uniform distribution (Suppl. Sec. 1). In this formulation, both direct and disynaptic inhibition, the latter via interneurons, are represented as negative weights.

During each trial, agents sampled from the unique set of WSM signals that defined that environment. (Fig. 1a.i & ii), while moving in trajectories that imitated rodents (random walks with low-probability changes of direction and speed, see Suppl. Sec. 1). We discretized each T t trial into dt timesteps during which agents received location-specific local EVs with elements randomly masked to imitate factors limiting observation like occlusion and partial attention. We concatenated timesteps sampled from a decaying distribution (Suppl. Sec. 1.2) of recent experiences (Fig. 1b) into 'episodic bouts' and trained the RAE on these bouts. We added pre- and post-activation noise to the hidden layer to simulate variability inherent to sensory processing. The use of episodic bouts serves to encourage input/output projections to update in consideration of events from a more extended history. We use a mean-squared error (MSE) objective function for pattern completion and an MSE constraint on the total hidden layer firing rates to enforce realistic firing rates.

After a trial ends, we 'record" from the network by letting the agent run freely in the trial room while gathering firing patterns of units within the network (Suppl. Sec. 1). During this recording block, we pause RAE updates so no additional learning occurs. We analyze the recorded firing patterns in the same way as experimentally recorded place cells, by projecting onto 2D room maps for visualization (Suppl. Sec. 1.3) and calculating the Spatial Information Content (SIC, see Suppl. Sec 2.1) [51].

3 Results

3.1 Emergence of place-like patterns

Fig. 2 displays firing profiles of 40 random hidden units, with their spatial information content indicated above. A significant number of cells display strong place-like firing patterns. For example, consider a typical choice of training and constraint parameters (Suppl. Sec. 1.2), for which ∼ 10% of the hidden units are active with average firing rates above a threshold of 0.1 Hz. We find in these cases that ∼ 80% of the active hidden units have SIC greater than 5, which is 20 times the SIC of the WSMinputs (0.29 ± 0.01; mean ± SD). Thus, place-like cells emerge from dynamics of the task and network structure. The parameters we used in our experiments are in Suppl. Sec. 1.2, while we also verified that their precise values do not impact the emergence of place fields (Suppl. Sec. 4.2).

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0.18 |3.49 |44.11

0.18 | 2.84 |33.36

0.63 |2.23 | 0.80

0.19 | 2.27 | 20.66

0.16 |1.64 |6.42

0.38 |4.23 | 16.51

0.19 | 2.11 | 11.85

0.14 | 3.76 |30.94

0.48 |3.07 |3.52

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0.12  2.61 | 17.04

0.15 |3.06| 45.92

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0.20 | 2.82| 16.73

0.11 | 2.70 | 50.08

0.55 |4.61 |6.14

0.14 | 4.41 |31.92

0.20 |3.40 |39.33

0.17 |3.62 |29.30

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0.49 |3.04 |2.26

0.11 |3.76 | 78.19

0.11 |4.50 | 81.33

0.12 | 4.24 | 45.15

0.14 |3.05 | 44.48

0.14 |3.00 | 52.94

0.12 |3.04 | 39.60

0.17| 2.73  26.66

0.14 | 5.67 | 72.96

0.21 |4.04 |13.20

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0.13 |2.60 | 28.23

0.12 | 6.15| 68.41

0.11 | 7.14 | 123.51

0.15 |3.48 |33.88

0.11| 4.50 | 65.30

0.15 |5.26 |33.71

0.11 | 4.02 | 47.88

0.12 | 6.55 | 73.96

0.20 |1.87 | 7.69

3.2 Place field emergence reflects temporally continuous changes in sensory experiences

We describe environments through weakly spatially modulated (WSM) sensory experience profiles that translate physical locations to points in experience space, E . WSMsignals are spatio-temporally continuous, so smooth motions between adjacent locations generate smooth motions in E . Thus an agent's exploration generates a set of trajectories in E that are unique to each environment and the agent's paths. The set of possible trajectories the agent could take together defines a surface in E ,

the experience manifold (EM) of an environment. This manifold has the dimension of the space of accessible sensory experiences. Thus, an agent in a 2D room generates a 2D experience manifold.

First consider neurons without recurrent connections. Given n -dimensional inputs, each neuron's input projection and ReLU non-linear firing rate collectively define an activation boundary (AB), an n -1 dimensional plane dividing the experience space E . This boundary occurs at input loci where the neuron transitions from inactive to active. More generally, the distance of an input e to a neuron's activation boundary determines the response firing rate, regardless of the activation function. For example, in Fig. 3b & c, an animal traversing a 1D track traces an EM within a 2D experience space. The EM is encoded by two neurons, N 1 (Fig. 3c.i) and N 2 (Fig. 3c.iii), with the indicated ABs. As an animal moves from loc 1 to loc 2 , its perceived experience moves along EM and intersects N 1 's activation boundary. This motion causes N 1 's firing rate to gradually increase then decrease (Fig. 3c.ii). In contrast, N 2 's activation boundary is roughly perpendicular to the same EM, motion from loc 1 and loc 2 will change neuron N 2 's firing rate monotonically (Fig. 3c.iv).

Our autoencoder linearly decodes sensory experience from the hidden unit activations as ˆ e = ∑ j ∈ S r j W out j where j indexes hidden units, W out j is the output weight vector and S are units that fire at the given location. If the firing rate of a unit i increases monotonically as an agent moves along the EM, the angle between ˆ e and the experience encoded by unit i , W out i , will decrease monotonically as this unit dominates. This will cause the reconstructed experience at many locations to be dominated by a single vector which cannot generally be correct. On the other hand, if the activation boundary for a unit is exactly parallel to an EM, it will have the same firing rate everywhere and will not contribute to discriminating locations. Thus, the most useful units for reconstructing sensory experience will have activation boundaries segmenting the EM like N 1 in Fig. 3c.i.

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This argument implies that training should rotate activation boundaries of some hidden units to segment the generally nonlinear experience manifold (EM). To simultaneously encode similar but differently positioned EMs (Fig 3d), in networks without recurrent connections, neurons would require substantial rewiring of input projections W in . Recurrence helps reallocate the contributions to reconstructed sensory experience, so that the largest contributions are made by units whose activation boundaries segment the EM. This switching of encoding neurons obviates the need for input projection rewiring.

We can also see from this reasoning why place-like units develop in the hidden layers. A given hidden unit contributes ˆ e i = r i W out i to the reconstructed experience. As we explained above, only hidden units whose activation boundaries segment the EM are useful for reconstructing experience, so learning will either rotate activation boundaries to segment the EM, or adapt output weights W out i to remove the unit from the reconstruction. Consider the location of peak firing of a unit whose

planar activation boundary intersects the curved EM as in Fig. 3c.i. Because of the continuity of the EM, adjacent locations will produce similar experiences. The region of space where the unit fires will correspond to the part of the EM that is segmented by the activation boundary (indicated by ' + ' in Fig. 3c & d). Assuming that the component of the experience vector that is orthogonal to the activation boundary varies approximately isotropically in space, the intersection locus of the activation boundary with the EM will be approximately circular when projected back to the environment. Thus, a population of such units, each tuned to part of the temporally continuous variation of experience, will exhibit place-field-like activation regions.

Critically, as we argued, the presence of recurrent inhibitory connections enables units that are most useful in one room to remain silent in other rooms. Recurrent inhibitory connections allow neurons to do this without altering their activation boundaries, i.e., input projections . So when an animal reenters a familiar room, both the room's EM and input projections to each neuron will remain relatively stable, while the recurrent connections reactive the most useful neurons in this familiar room. This combination ensures that individual neurons have stable place fields within a particular room while maintaining flexibility in the network to encode multiple rooms. This stability occurs because the relative positions of the EM of a familiar room and the activation boundaries of the encoding neurons remain unchanged. Thus radical changes to experiences within a familiar room could still induce change, as is observed experimentally [16, 24].

3.3 Place cell remapping as EM repositioning

We then tested whether our networks support place cell remapping across rooms and reversion within familiar rooms. To do so, we extended our experiment in Sec. 3.1 by simulating agents exploring two rooms over three sessions in a sequence R1-R2-R1, where R1 and R2 are rooms defined by unique WSMsignals. After training in each room, we recorded hidden layer firing patterns. The results were labeled T1R1, T2R2, and T3R1, representing the Trial (T) and Room (R), respectively.

We selected active hidden units (mean firing threshold ≥ 0.1 Hz) across trials with SIC above 5 (more than 20x the SIC of the WSM signal) for comparison. T2R2 demonstrates significant remapping in hidden nodes as compared to T1R1 (upper row of Figs. 4a, 4b). Hidden nodes displayed both global and partial remapping with many nodes displaying global remapping including: in the given example, ceasing to fire (n=39), beginning to fire (n=94), or consistently firing in both rooms (n=130). We also observed place firing fields reverting to their original locations, upon returning to room 1 (T3R1) (Figs. 4a,4b, lower rows). These results mirror observations in rodent hippocampus CA3 [18, 20, 21]. To quantify, we calculated pairwise Pearson correlations of firing fields for the selected hidden layer units (Fig. 4b). The correlation matrix showed low spatial correlation in firing fields between T1R1 and T2R2. By contrast, the correlation matrix of T1R1 and T3R1 showed significantly higher diagonal values, indicating reversion of place fields in a familiar enclosure.

We then tested the mechanism of reversion. To do so, we calculated a reorganization score s of the input projections ( W in ) and recurrent connections ( W rc ) across trials (see Suppl. Sec. 2.2). Transitioning from T1R1 to T2R2, we observed a substantial reorganization of W rc ( s = 0.564) but only minor alterations in input projections W in ( s = 0.169). Between T2R2 and T3R1, W in also exhibits small changes ( s = 0.141), whereas W rc continues to show a higher reorganization of s = 0.430. This observation is consistent with experimental results indicating that synapses between hippocampal neurons in the same region update at a much faster rate than synapses coming from neurons projecting to the hippocampus or across hippocampal regions [52], and confirms that in our model remapping and reversion are driven by reorganization of recurrent connections.

In our framework, different rooms might correspond to differently positioned experience manifolds (EMs) in E . We suppose the network has sufficient capacity to encode every EV in experience space E , and thus every volumetric region in E (small cubes in Fig. 4c) is encoded by some neurons, similar to what we described in Fig. 3b. Then, moving between rooms R1 and R2 (blue and orange planes in Fig. 4c) induces two potential remapping scenarios: (a) Neurons encoding a volumetric region intersect with only one room's manifold - activating in R1 and remaining inactive in R2 (magenta region), and vice versa for R2 (cyan region), (b) Both manifolds intersect a given region (red cube in Fig. 4c), and will activate in different physical locations for each room (shifting firing centers). Alternatively, intersections at similar locations from different angles or positional shifts can cause neurons to adjust their firing rates or alter their patterns (rate changes or partial remapping).

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3.4 Storage capacity and the orthogonality of spatial representations

Studies of episodic and spatial memory suggest that CA3 can memorize and discriminate a large number of experiences [18, 21]. Thus, we tested whether our network can also encode a large number of rooms in orthogonal representations. To do so, we expanded our training protocol to include 20 unique rooms. We call a complete visit of all 20 rooms a "cycle" and trained the RAE for 30 cycles, with the room sequence shuffled in each cycle. We reduced the time the agent spent in each room to 10 minutes (12000 timesteps) to avoid overfitting to a single room while training. This trial duration still exceeds the experience sampling window size of 5 minutes (see Fig. 1 caption), ensuring a period in which the RAE receives experiences exclusively from one room.

After each trial, we replicated analyses in [21] to compare hidden layer population coding vectors in different rooms. For each room, we employed a 5 × 5 cm binning window to discretize each 100 × 100 cm firing rate map across all 1000 hidden units, resulting in a population vector with dimensions N × W × H = 1000 × 20 × 20 . We compared the similarity between any two population vectors by their Pearson correlation coefficients (Suppl. Sec. 3.1).

We compared the correlation between rooms from cycle 2 and cycle 3, a scenario similar to the experiments in [21]. The mean correlation between different rooms is 0 . 164 ± 0 . 029 , and that of the same rooms is about 0 . 55 greater, 0 . 710 ± 0 . 097 . The corresponding experimental values reported in [21] are also different by about 0 . 57 : 0 . 08 ± 0 . 005 and 0 . 65 ± 0 . 02 , respectively. Note that we should not expect precisely the same values of the correlation because the precise setups of the environments and experiments are different. For example, we have many trial rooms in our in silico study, while there are only 2 rooms in [21]. Furthermore, our network contains 1000 units while Alme et al. recorded only 342 neurons [21]. Overall, we find that the population vectors of familiar rooms have significantly higher correlations as compared to different rooms, consistently with experiments [21, 18, 16, 19, 23]. We also observed that the correlation between population vectors from consecutive visits to the same room quickly stabilizes, exceeding 0.8 after the third cycle (Fig. 5a). These results combine to suggest that our network is capable of stably encoding a large number of rooms in orthogonal representations.

We also observed gradual drifts in the generated place fields as well as a slow decrease across cycles in correlation with the initial representations, in parallel with recent experiments suggesting that

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place cells in the brain have representational drift reflecting continuous learning processes [53]. We propose that drifts in our network also reflect incremental learning of more efficient ways to encode multiple rooms. To explore, we measured the amount of reversion (Pearson correlation with previous firing patterns) during the first few moments of reintroduction to a familiar room. During early cycles, such as the third cycle, reintroduction to a familiar room results in a delayed reversion of the place fields (Pearson correlation r = 0 . 35 when the agent enters a familiar room). During the final cycle, cycle 30, the fields immediately reverted to their original patterns upon reentry ( r = 0 . 92 ), supporting our proposal. Additional comparisons, including plots of place field drifts, appear in Suppl. Sec. 3.2.

3.5 Robust emergence of place fields and multiple place fields in larger rooms.

While we primarily tested our network in 1m × 1m square rooms, we have confirmed that place fields robustly emerge in environments of various shapes (Suppl. Sec. 4). We also found that emergence of place fields is robust to the dimension of the experience vectors and the number of hidden units (Suppl. Sec. 4). There is experimental evidence that place cells can develop multiple place field centers in larger enclosures [54, 55]. We tested whether this phenomenon occurred within our RAE. To do so, we had our agent explore an environment that contained two rooms connected by a tunnel and trained our RAE on the resulting experiences (Fig. 6a). Mirroring experimental results, some units in the hidden layer of our RAE developed more than one firing center.

4 Predictions

Our theory generates several testable predictions. First, we predict that rapid changes to sensory and contextual experiences within an environment will disrupt and destabilize place fields. This prediction emerges from the results of Sec. 3.2, where we showed that neurons would orient their firing patterns to encode the most varying direction of experience vectors (EVs) at adjacent physical locations. If EVs at neighboring locations exhibit substantial variations over short durations of time, there is no consistent, most varying direction of the EVs. Accordingly, it is impossible for place cells to effectively learn temporal variance at adjacent locations, leading to an interruption in the formation of place cells. This prediction can be readily tested in VR setups as well as in specially constructed physical environments. Spatial information or other metrics of place cell stability should be measured as a function of sensory/contextual experience change. We anticipate a negative correlation that place cell stability decreases as more aspects of the experience are changed. Secondly, expanding on our hypothesis from Sec. 3.1, which suggests that recurrent connections facilitate reversion of place fields, we propose that the absence of recurrent connections will not disrupt formation of place fields, but will prevent them from reverting to previous representations upon re-entry into

b

a familiar room, a prediction testable by silencing of recurrent hippocampal connections. Third, it is known that deforming a room by stretching or shrinking it changes the firing fields of grid cells [56, 57, 58, 59] and correspondingly affects human behavior [60], possibly because grid fields depend on path integration [61, 62], and there are trajectory dependent shifts in their locations driven by interaction with border cells [63, 64]. Grid cells provide one important class of inputs to the hippocampus, and so we expect that the changed grid cell input will correspondingly deform the experience manifold. Our model predicts the corresponding statistics of partial remapping of place fields when the familiar but deformed room is revisited.

We also predict that the dimensionality of place fields is determined by the dimension in which temporally stable experiences change smoothly. As outlined in Sec. 3.2, place cells in our network prioritize encoding the most variable component within a localized region. The dimensionality of emergent place cells is therefore set by the projection of this encoded component onto the experience manifold (EM), and will be defined by the number of independent components of experience that change smoothly as an animal moves through a space-whether physical or abstract. To substantiate, we simulated an agent in 3D rooms and trained our RAE, similar to Sec. 3.1. We observed the emergence of 3D place fields (Fig. 6b). This prediction is indirectly confirmed by Grieves et al. [65], who observed 3D place cells in rodents navigating a lattice maze, a 3D environment that where rodents explore volumetrically. To test in physical spaces, VR setups with parametrically controlled sensory inputs could be employed. For abstract space, the prediction could be tested following procedures similar to the bird-deformation space used in Constantinescu et al. [66], or by placing rodents in 1D or 2D tracks while gradually changing auditory/olfactory signals within the enclosure or varying visual cues displayed on walls. We predict these continuous changes along the abstract dimension will extend previously generated place cells to higher dimensions.

5 Discussion

In our study, we tested how episodic and spatial memory, as implemented in the hippocampus, could be interrelated and complementary. To do so, we constructed a recurrent autoencoder (RAE) model of CA3 that received partial and noisy sensory inputs while an agent traversing an environment attempted to reconstruct the complete sensory experience at each location based on previous encounters. We

demonstrated that networks concurrently minimizing average firing rate and reconstruction error naturally develop place-like responses. These responses create a continuous landscape of attractor basins (Suppl. Sec. 4.3), enabling robust recall of spatial experience at any location. We found that the emergent place-like units display remapping resembling experiments [21, 17, 18, 29], including cells that only fire in some environments while turning off in others, and other that change their firing location in novel environments while reverting in familiar arenas. Our network also generates orthogonal spatial representations for multiple rooms similarly to place cells in the brain.

Our findings both reinforce and reframe previous theories of place cell generation, place cell remapping, and CA3 function. Previous works have discussed how sensory or contextual information could be multiplexed with purely spatial information [29, 23]. While both types of information can be encoded in the CA3 place cell network, our theory suggests a unified 'sensory as spatial' framework, which leverages the fact that particular combinations of sensory experiences tend to happen at particular locations and that sensory experiences tend to change smoothly over time. Neurally, these facts are embodied in the numerous weakly spatially modulated cells seen as inputs to the hippocampus [67] and which we use as the input to our network. We accordingly propose that these inputs are the primary drivers of place cell generation.

In our model, neurons that capture more input variance contribute more to pattern completion, and reorganization of recurrent connections serves to maximize their role. This suggests that individual cells will remap to form unique representations for similar sensory experiences encountered in different environments since the trajectory of those experiences and the expected variation of these experiences will differ across rooms. At a network level, this difference is reflected in reorganization of recurrent connections across environments, along with minimal input projection adaptation. These input projections also allow experience trajectories to remain stable in familiar environments, allowing cells to revert to prior firing locations upon return to a familiar arena. Finally, our findings indicate that if a network repeatedly navigates between multiple rooms, it could gradually learn to encode them more efficiently, enabling immediate remapping without learning/rewiring recurrent connections.

Our study provides a simple yet powerful framework that reproduces a substantial part of the phenomenology of place cells. It would be interesting to statistically compare our emergent place cells with rodent hippocampus data especially if we can also accumulate 'natural experience statistics' from multi-modal sensors attached to navigating physical agents.

Acknowledgments: We thank Dori Derdikman, Genela Morris, and Shai Abramson for many illuminating discussions in the course of this work, which was supported by NIH CRCNS grant 1R01MH125544-01 and in part by the NSF and DoD OUSD (R&E) under Agreement PHY-2229929 (The NSF AI Institute for Artificial and Natural Intelligence). VB was supported in part by the Eastman Professorship at Balliol College, Oxford. We are also grateful to Pratik Chaudhari for his insightful suggestions on designing the RAE and analyzing its dynamics.

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Supplemental Materials

1 Training details

1.1 Simulated trials and the artificial agent

An artificial agent explores simulated room(s) defined by fixed WSM signals, as defined in Section 2.2. The agent updates its behavior and samples sensory experience every 50ms. To realistically model rodent movement trajectories, we simulate a random walk, where artificial agents explore the room in a trajectory with random small drifts representing an animal's exploration interest: at every timestep, the agent randomly changes its movement speed and direction with a small probability, 0.2 and 0.3, respectively. The change in speed is randomly chosen from an N (5 , 1) cm/s normal distribution, and the drift direction is randomly chosen from N (0 , 0 . 05) rad/s.

1.2 Training Recurrent Autoencoder (RAE)

The simulated artificial agent gathers experience vectors along its trajectory. We train the RAE on 1s experience segments with a batch size of 500, sampled from a 300s 'decaying' distribution of recent events to encourage the network update in consideration of an extended history of events. For an event that is t seconds away from the current time step, the probability of it being sampled is:

Where T s is the width of the sampling window, α = 3 and β = 0 . 5 .

Our RAE contains three layers: The first and the third layers represent the signals being projected to and read out from CA3, respectively. The hidden layer, being fully connected by recurrent connections, corresponds to CA3. The hidden-layer states, which model activation potentials of neurons, are governed by the following continuous-time equation:

Here f ( x ) is an activation function and τ governs the decay. W in is the connection matrix to the hidden layer, simulating pathways entering the hippocampus. W rc is the recurrent connectivity matrix emulating CA3 recurrent collaterals. The vector b is a firing bias term and η t denotes Gaussian pre-activation noise. The variable v t models neural activation potentials. Setting γ = dt τ and adapting to discrete- time gives:

Here we have replaced f ( v t ) in equation (2) with equation (4), where h t is the state vector of the hidden layer neurons in Hertz (Hz) and ξ t is the post-activation noise.

The network is trained with mean-squared error without strict sparseness constraints. The loss function is:

D is the dimension of the Experience Vector (EV), T measures timesteps within a memory segment, B indicates the number of batches, and N counts nodes in the hidden layer. The term ˆ e d,t,b is the d -th entry of the reconstructed EV at timestep t in batch b , while e d,t,b is the equivalent entry of the ground truth. The second component of the loss, r n,t,b , denotes the firing rate of the n -th neuron at time t within batch b . Unless otherwise stated, we set λ mse = 0 and λ fr = 200 for our experiments.

1.3 Testing RAE and visualizing hidden layer firing profiles

After training in each trial, we paused parameter updates and 'recorded" the network response at every location in the room. The network continued to receive batches of partially occluded experiences with added noise, generated by a random traveling agent, as detailed in the main text. To ensure sufficient data at every location and to average out effects of random occlusions and noise, we conducted 20-minute trials repeated 20 times. Importantly, the obtained spatial maps are robust to both the duration and the number of tests since we paused parameter updates during testing.

During these tests, we recorded the firing rate (post-activation value) of each hidden layer unit at every location. We then averaged the unit's responses at each location across all previous visits. We repeated this process for all locations and hidden layer units to obtain spatial maps after.

2 Measurements and metrics

2.1 Spatial information content

We used the Spatial Information Content (SIC) [51] measured in bits to measure the strength of a cell's place-like property in terms of its spatial selectivity We discretize firing rate maps into M 30cm × 30cm bins. Each bin has a firing rate and associated probability p m of the cell firing. The spatial

information content (SIC) is computed as:

where ¯ r is the average firing rate across bins. Bins with r m = 0 are skipped in the sum (to avoid divergences in the log), but are included in the computation of the average rate ¯ r .

2.2 Synapse reorganization score

We quantify synaptic adaptation as the ratio of the Frobenius norm of the change in the weight matrix to the Frobenius norm of the weight matrix prior to update:

Here, W old and W new represent synaptic weight matrices before and after adaptation, respectively.

3 Orthogonal spatial representations

3.1 Measurement of orthogonality

To measure how generated place-like patterns form representations of different rooms, and to what extent these representations are orthogonal, we adopted a methodology similar to that proposed by Alme et al. [21]. At the end of each trial, we converted the 100 × 100 cm firing rate map from a single unit into a 20 × 20 grid by averaging the rates within each bin to obtain a population coding vector for a room. To compute the similarity between two population vectors, X and Y , Alme et al. [21] used the mean dot product:

Here N is the number of units, and W and H are the bin dimensions in width and height, respectively. The dot product involves the population vector of a room as a whole. However, to provide a normalized measure of similarity for Fig. 5 in our main paper, we adopted the Pearson correlation. Pearson correlation also uses the population vector of a room as a whole, but normalizes the data to reduce the dominance of highly active units. Thus, the similarity between X and Y is calculated as:

3.2 Drifting place fields and orthogonal representations

To test whether the generated representations can be used to construct cognitive maps for different enclosures, and whether these maps can be maintained over an extended period, we placed the agent in 20 rooms for 30 cycles, resulting in 600 recordings. In the main text, we compared how spatial representations in the last cycle compared to representations from previous cycles. Here, we offer a more comprehensive comparison. Suppl. Fig. 1 presents the cross-comparison of all 600 recordings, showing that recordings from the same room remain correlated even many cycles apart. Only recordings from cycle 1 show a slightly decreased correlation score, due to the incomplete formation of place fields.

As the simulated agent travels through multiple rooms over an increasing number of cycles, we observe that place cells, while reverting to their previous locations upon reentering a familiar room, may exhibit slight shifts in their locations. As the number of cycles between two trials of a single room increases, this discrepancy becomes increasingly pronounced, manifesting as a place field drift. Figure 2 depicts the drift of six randomly selected hidden layer units across 30 cycles in Room 1.

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4 Additional results

4.1 Pattern completion results of RAE

We train the RAE to reconstruct the complete, noiseless experiences from partial and noisy sensory inputs. To examine pattern-completion performance, we pause training after each trial to record the reconstructed values and compute the average firing rate at each location for each output channel. This process is similar to the method used to gather firing profiles from the hidden layer. In Suppl. Fig. 3,

we plot 20 randomly selected WSM cells and their reconstructed values. All outputs accurately reflect the sensory changes appearing in the original WSM signals.

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10.74 | 13.17 | 7.14

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10.47 | 14.85 | 2.70

10.85 | 15.91 | 8.26

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10.55 | 13.44 | 6.86

9.96 14.43 3.39

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9.24 | 13.37 | 6.84

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4.2 Robustness to parameter variations

We have verified that the emergence of place cells is consistent across different environment shapes, for example triangles (Suppl. Fig. 4a) and circles (Suppl. Fig. 4b). In both cases, the hidden layer generated place-like patterns similar to those in the square rooms we used in our experiment.

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0.14 | 1.59 | 16.57

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While we fixed the parameter values during our experiments to enhance reproducibility, we also verified that place cell emergence is robust to parameter changes and does not require specific values. To quantify, we evaluated the firing maps of hidden layer units using three metrics: (1) the percentage of active units, defined as units with a maximum firing rate > 0.1 Hz; (2) the percentage of place units, identified by a Spatial Information Content (SIC) > 5; (3) the average SIC across all active units.

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15.0

12.5

30

10.0

60

20

7.5

50

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2.5

30

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.20.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

upper bound

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upper bound

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noise

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56

S0

-44

-18

54

-42

70

17

52

40

0.1

16

38

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36

10°0

14

48

34

13

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0.050.1

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10S0°0100

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Figure 5 shows that: (1) Increasing the duration of each episodic memory segment slightly reduces the number of place cells, as longer episodes likely involve multiple locations, decreasing spatial specificity. Despite this, the majority of active cells continue to exhibit place-like characteristics. (see Fig. 5a). (2) The number of place cells decreases slowly as trial duration increases. This decrease is due to the optimizer forcing the network to encode WSMs more efficiently after the MSE loss stops decreasing. This optimized encoding is thus overfitted to one single room and requires individual cells to fire at unrealistic rates, which are unlikely to occur in biological systems (see Fig. 5b) (3) As λ fr increases, all active cells become place cells. (4) The number of place cells and active cells increases as the recall length increases, stabilizing once the recall duration exceeds 200 seconds. (see Fig. 5d) (5) Neither the maximum firing rate of WSM signals nor the sigma value affects the emergence of PFs. (see Fig. 5e & 5f) (6) Place fields only emerge when the number of WSM signals exceeds 100, aligning with our hypothesis in the main text that the emergence of place fields requires a large number of WSM signals. We observed in our experiments that the number of hidden units required for PF emergence increases as the dimension of the experience vector (EV), i.e., the number of WSM signals, increases. This is likely because increasing the dimensionality of experience will increase the amount of information that must to be stored, and thereby require more hidden units. We leave exploration of the best ratio between input and hidden units for future work. Overall, our main finding is that the emergence of place fields is robust under a wide range of parameters.

4.3 Attractor landscape of the RAE model of place cells

Classical theories of CA3 episodic memory storage suggest that the recurrent connections establish attractor dynamics [29, 30, 28, 68]. Each attractor basin can be either a singular fixed point or a collection of points in the network's state space. Nearby network states evolve autonomously toward these attractors [47]. The attractor network theory of episodic memory also accounts for spatial memory storage, where each place-cell firing field corresponds to an attractor basin. Therefore, we also examined the attractor landscape of our RAE.

mean|max|SIC

0.15 3.59  23.87

mean|max |SIC

0.32  6.3134.09

mean|max|SIC

0.12  2.11 21.65

0.29 5.00  24.36

mean|max|SIC

0.10 2.05  25.34

mean|max|SIC

mean|max|SIC

0.37  4.86 14.69

mean|max |SIC

0.25 3.34 11.62

mean|max|SIC

0.17 3.42  29.49

mean|max|SIC

0.12  1.77  15.94

0.10 1.9714.72

mean|max|SIC

mean|max|SIC

0.17 3.56 39.12

mean|max |SIC

0.16 3.19 31.17

mean|max|SIC

0.65|2.301.33

mean|max|SIC

0.17 6.36  40.30

mean|maxSIC

0.29 4.63 29.23

mean|max|SIC

0.27 3.57  11.94

x

0.15 6.48 |46.30

mean|max|SIC

0.13  4.39 45.31

mean|max|SIC

0.335.2318.03

mean|max|SIC

0.17| 4.87| 50.52

mean|max|SIC

meanmax |SIC

mean|max |SIC

meanmax |SIC

mean|max |SIC

meanmax|SIC

meanmax |SIC

mean|max|SIC

0.23 2.49 8.17

0.315.36 25.04

0.218.23 91.61

0.12 2.71 40.05

0.146.5158.38

0.12 3.87 44.88

0.246.28 34.68

0.13 2.29 23.41

0.12  2.77| 42.14

0.101.9018.02

meanmax|SIC

mean|max|SIC

mean|max|SIC

meanmax|SIC

mean|max|SIC

meanmaxSIC

mean|max|SIC

mean|max|SIC

mean|max|SIC

mean|max|SIC

0.135.2547.78

0.195.2848.74

0.2111.1241.68

0.318.1032.62

0.152.90 17.85

0.193.7522.75

0.224.0722.66

0.214.1424.59

0.16 5.10 56.86

0.11|4.84 92.07

mean|max|SIC

0.24 5.10 38.09

mean|max|SIC

0.18  3.02 25.06

mean|max|SIC

0.31 3.29 12.92

0.15  5.67 52.09

mean|max |SIC

0.19  7.88  58.23

mean|max|SIC

mean|max|SIC

0.17  5.77  63.17

mean|max|SIC

0.383.55 7.35

mean|max|SIC

0.17 |3.51  27.90

mean|max|SIC

0.15  2.38  22.89

0.312.303.81

mean|max|SIC

Attractor basins are locations where the network state becomes stable or dynamically stable. We thus examined how the network evolves when presented with a constant input. For this analysis, we simplified the network update function by removing the noise and bias terms:

where we removed the bias and noise terms to simplify the calculation. As we show below, the network state update function is a contraction, and if inputs are held constant, the network will converge to a stable state. Given this property, we can plot the attractor landscape of our RAE

network by testing the network with location-specific EVs, and waiting for convergence to the attractor at each point.

As depicted in Suppl. Fig. 6, individual units maintain place-like patterns after the network has converged. This single-unit level continuous response at convergence will also result in a continuous landscape after the network converges. Thus, our network also aligns with the classical attractor theory of place cells.

̸

Proof. If the input to the RNN is fixed (i.e., ∀ i, j ∈ [0 , T ] , i = j , we have e i = e j = e ∗ ), where T is the length of the input sequence. We would like to prove the network update function is a contraction, i.e., the network will converge to a fixed state. We work with the network update function:

̸

To show that the network will converge to a fixed state, we first show that the network update function is a contraction. To do so, we need to show ∀ i, j ∈ [0 , T ] , i = j , if ∥ Φ( v j ) -Φ( v i ) ∥ < k ∥ v j -v i ∥ , where k < 1 .

Suppose v j -v i = u , then

By the triangle inequality and submultiplicativity,

Furthermore, if the activation function is bounded and is Lipschitz continuous on real numbers, a Lipschitz constant L exists such that ∥ f ( v i + u ) -f ( v i ) ∥ is bounded by L ∥ u ∥ . Thus,

The update function is a contraction mapping if k = (1 -α ) + α ∥ W rc ∥ L < 1 . Therefore, ∥ W rc ∥ < L -1 to ensure k < 1 . The Lipschitz constant is L = 0 . 25 for sigmoid activation, L = 0 . 5 for tanh activation, and L = 1 for the positive part of ReLU activation.

Because the neuronal activation potentials are real numbers and we are using the distance function as the metric, the state-space is complete. By the Banach fixed-point theorem, iteratively applying this transformation will converge to a fixed point v ∗ in the state space.

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Justification: There are two claims in the abstract: 1) Training our autoencoder to patterncomplete and reconstruct sensory experiences with a constraint on total activity causes place cells to emerge in the encoding layer. 2) The emergent place fields reproduce key aspects of hippocampal phenomenology, including remapping, orthogonality of spatial representations in different rooms, robust place field emergence in differently shaped rooms, and slow representational drift of place fields. Both our conceptual framework and the results supporting the claims made in the abstract have been reported in the paper.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper shows that place cells can emerge in networks that autoencode temporally continuous sensory episodes based on spatially smoothed Gaussian random fields. The obtained place fields reproduce the disputed idea of remapping, the established fact that such spatial representations are uncorrelated, and a slow representational drift. The model implements “experience manifolds” in the network’s hidden layer and weakly spatially modulated (WSM) rate maps, which are interesting concepts that deserve more analysis. Also, dimensionality of the environment seems to be non-problematic, although also here a comparison to observations in biological experiments would be desirable.\n\nSTRENGTHS:\nThe paper introduces useful concepts such as experience manifolds or weakly spatially modulated (WSM) rate maps that may be useful in the further study of hippocampal function, although at the moment the ideas play a role only in the context of modeling, and the experience manifolds seem to be here merely metaphorical (although a similar analysis tool has been used in other instances of population codes). It is very good that clear prediction have been made, and that model is well describe (suppl. material).\n\nWEAKNESSES:\nMain problems with the paper are the lack of strong quantitative evidence and the realizability of the model by biologically relativistic neural networks of a size comparable to CA3 (or much smaller considering that a mammal typically works with environmental information of much higher complexity. On the level of the current model, it could be discussed what model features are essential for what feature of the result. For more detail see Questions below.\n\nQUESTIONS:\nAlthough it is possible to model CA3 as a recurrent autoencoder to show how place cells can emerge, can we really say that CA3 **is** an autoencoder or that it is its function to represent place fields?\n\nWould it be possible to reach the level where a quantitative comparison to experimental data becomes possible or is this difficult due to the ongoing discussion of what characteristics can be extracted from experimental data towards a meaningfully comparison? \n\nCan affirmative statements like “closely resembles results of experiments” (l295), “consistent with experimental results” (l203) be given more evidence? \n\nThe numbers given (l232) are said to be “mirroring experiments with rodent CA3 place cells”, but isn't the absence of certain correlations both in the simulations and in the biological experiments rather weak evidence for the proposed model? Can any remainder correlations be compared?\n\nThe fit in [47, Fig. 2A] is quite bold and does not represent the underlying mechanism, so that it is not exactly a good standard for comparison (l239). Would it nevertheless be useful to mention any quantitative agreement with even some interpretation of the biological data?\n\nThe “experimental evidence that place cells can develop multiple place field” (l252) was never really “strong”. Would it be possible to consider more recent studies, so that a delicate analysis might be enabled to show whether the experimental observations are “mirrored” by the simulations?\n\nCan the bias in the literature be changed from classical papers towards more recent modeling approaches so that these are sufficiently discussed? It is not needed to do this here comprehensively, but the paper would gain from some comparison with other approaches as would the theory of spatial representations in mammals.\n\nIt remains unclear why not the weakly spatially modulated (WSM) rate maps (or any other non-local representation of spatial information) can provide a similar autoencoding property and what specifically is necessary for the formation of roundish place fields. This question can be asked for most models that show place field emergence, so that here also theoretically not much progress is achieved, and it could seems that without the specifically designed noise of sigma=12cm (which is not varied here and not listed in the parameter tables in the appendix) the results may have been less realistic, while the diversity of realistic place fields in not achieved in the proposed model nor is it evaluated in comparison to biological data.\n\nLIMITATIONS:\nThe current version is limited in regards to the discussion of experimental finding, the effect of some of the model parameters, and of the realization of model by biologically more realistic neural networks. Other limitation and some open questions are addressed well in the paper.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-11"}

comments: SUMMARY:
The paper explores the emergence of place cells in neural networks by simulating the hippocampal area CA3, specifically when trained to recall and reconstruct temporally continuous sensory experiences encountered during navigation in simulated environments. The authors model this area as a recurrent autoencoder that operates on sensory inputs from simulated agents moving through environments with varying sensory landscapes. The results show place cells that resemble those recorded in the hippocampus.

STRENGTHS:
The approach is novel, and the idea of training a network to remember temporally continuous sensory episodes and then characterize its neural representations is a useful contribution. 

The paper conducts empirical evaluations in different types of environments (e.g., rooms with different shapes) and makes several testable predictions.

WEAKNESSES:
The paper is written in a somewhat unusual style with the results following right after the introduction without a separate methods section making it difficult to follow the approach and understand the results. 

The interaction between sensory inputs and velocity integration seems to be missing.

QUESTIONS:
How does your approach relate to path integration?

Do you expect to see place cells in the absence of visual inputs? 

What exactly are the inputs to the place cells? Can those pixel-level visual inputs preprocessed with some sensory processing modules?

Do you observe the remapping and changing shape of the place fields when the environment changes size or the walls move (e.g., O'Keefe & Burges 1996)?

LIMITATIONS:
The authors should address the limitations more explicitly.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-12

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents a novel approach to understanding the emergence of place fields in the hippocampus. The authors propose that place cells can emerge from networks trained to remember temporally continuous sensory episodes, without explicit spatial input. They model the hippocampal CA3 region as a recurrent autoencoder (RAE) that reconstructs complete sensory experiences from partial, noisy observations. The model reproduces key aspects of hippocampal phenomenology, including remapping, orthogonality of spatial representations, and slow representational drift. The paper offers several testable predictions and provides a fresh perspective on the origin of place fields, suggesting that \"time makes space\" in neural representations.\n\nSTRENGTHS:\n- Novel approach: The paper presents an intriguing hypothesis about the emergence of place fields from temporally continuous sensory experiences.\n- Comprehensive modelling: The model reproduces multiple key aspects of hippocampal phenomenology.\n- Testable predictions: The paper offers concrete predictions that could guide future experimental work.\n- Thorough experimentation: The authors conduct a wide range of simulations to test their hypotheses.\n- Biological plausibility: The model is grounded in known hippocampal anatomy and physiology.\n- Effective explanations: The paper employs (impressively) clear (to me) expressions and explanations that enhance its readability and impact.\n\nWEAKNESSES:\n- Limited quantitative comparison with actual neural data from rodent studies.\n- Reliance on simplifying assumptions about sensory input structure (smooth Gaussian random fields).\n- Insufficient exploration of network parameter dependencies.\n- Absence of publicly available code for verification and extension of the work. I read the author’s justification, but this remains a weakness in my point of view.\n- Lack of formal theoretical analysis to explain the emergence of place fields, i.e. a rigorous mathematical framework that provides a deep analytical understanding of why place fields emerge in this model.\n- Inadequate positioning within existing frameworks of sequential data modelling, for example in relation to simple hidden Markov models (HMMs).\n- Although minor, the term \"weakly spatially modulated\" signals, which is important for understanding this work, lacks a clear definition.\n- Also minor, the section structure could be improved for clarity, particularly Section 2 which combines methods and results. How about calling it Experiments?\n\nQUESTIONS:\n- The most important question for me is, how sensitive are your results to changes in network architecture and hyperparameters?\n- How does your model specifically relate to and extend beyond HMM in the context of sequential data modelling?\n- How about my 2 minor points in the weaknesses?\n- Have you considered conducting a more rigorous statistical comparison with experimental rodent data? If so, what challenges did you face?\n- Could you elaborate on how your model might be extended to account for other hippocampal phenomena, such as theta phase precession or grid cells?\n\nLIMITATIONS:\nThe authors have addressed some limitations of their work, particularly regarding the simplifying assumptions of their model. However, they could improve by:\n- Providing a more detailed discussion of the limitations of using smooth Gaussian random fields to model sensory inputs.\n- Addressing potential limitations in the generalizability of their findings to real neural systems.\n- Discussing any computational limitations or scalability issues of their approach.\n- Considering potential negative societal impacts, if any, of their work (e.g., implications for AI systems that might use similar principles).", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis study demonstrates that place cells can develop in networks trained to remember temporally continuous sensory episodes. The model CA3 as a recurrent autoencoder that recalls and reconstructs sensory experiences from noisy and partially occluded observations by agents traversing simulated arenas. The autoencoder training, which included a constraint on total activity, led to the emergence of place cells with spatially localized firing fields. These place cells exhibited key hippocampal characteristics: remapping, orthogonality of spatial representations, robust place field formation in variously shaped rooms, and slow representational drift. The authors present a unique framework of the optimal encoding of the experience space The study suggests that continuous spatial traversal results in temporally continuous sensory experiences, making several testable predictions about place field behavior under different conditions.\n\nSTRENGTHS:\nThis work presents a new perspective on the topic of place cell formation in CA3 during navigation. Their model is clear and well described model. The analysis of their network, combined with the predictions they make regarding hippocampal remapping, make this a relevant work for the field.\n\nWEAKNESSES:\nMore in-depth visualization in figure 3 would be nice, I like this framing of the problem in the text. Maybe show each example (suboptimal encoding, optimal encoding, remapping in a new environment, returning to the original environment) as a figure panel?\nIt would be helpful for the authors to examine which of their assumptions and initializations are critical for the PF emergence they observe. What do your results look like when you use different history buffer, different levels of noise, a form of input different than the WSM, etc.?\n\nQUESTIONS:\nI'm surprised that the units learn (via the recurrent weights) return to their initial positions - especially after changes (albeit small) in the input weights. My naive assumption would be that there are many redundant solutions which could accurately autoencode the experience vectors. Why does the network return to the same solution it initially had?\n\nLIMITATIONS:\nI think this work would greatly benefit from greater comparison to other models of place field/cognitive map formation (in either an autoencoder or predictive learning framework), Levenstein et al. 2024 as a recent example.", "TITLE": "Official Review", "RECOMMENDATION": 8, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 4, "DATE": "2024-07-15"}