Time Makes Space: Emergence of Place Fields in Networks Encoding Temporally Continuous Sensory Experiences
Authors: Zhaoze Wang
Ronald W Di Tullio
Spencer Rooke
Vijay Balasubramanian
Venue: NeurIPS 2024 poster (2024)
Keywords: Place Cells/Fields
Recurrent Neural Networks
Episodic Memory
Hippocampus
Primary area: neuroscience_and_cognitive_science
TL;DR: We model the CA3 region as a recurrent autoencoder that reconstructs sensory experiences from partial observations in simulated environments, and observed emergence of place fields reproducing key aspects of hippocampal phenomenology.

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
Zhaoze Wang Ronald W. Di Tullio
Spencer Rooke
Vijay Balasubramanian
Department of Computer and Information Science, Neuroscience, and *hhysics, University of Pennsylvania; RRddolf Peierls Centre for Theoretical Physics, University of Oxford; and SSnnta Fe Institute
Equal contribution
zhaoze@ seas. wee.ssuennneeee edu srooke @ sas. uas.upenneddu
ron. ron.w. w.i.wliiuulloooeeemmmmm gmail.com vijay @ wwwsseepsssssssnneeeeee
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 con- tains place cells, whose location-selective firing fields implement maps supporting spatial memory. Here we show that place cells emerge networks trained remember temporally continuous sensory episodes. We model CA3 recur- rent autoencoder that recalls and reconstructs sensory experiences from noisy and partially occluded observations by agents traversing simulated arenas. The agents move realistic trajectories modeled from rodents and environments are modeled as continuously varying, high- digensimensionll, sensory experience maps (spa- tially smoothed Gaussian random fields). Training our autoencoder to accurately nattem-complett and reconstruct sensory experiences with constraint total activity causes spatially localized firing fields, i.e., place cells, to emerge 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 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 rever- sion 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 abstract spaces. Code for our experiments is available a
Introduction
The hippocampus is brain region that plays critical role in both spatial navigation
and episodic memory 4 5 g. Researchers have therefore sought to understand the neural
https://2hhsozewwngg github. httpg//ggg///////p/t////ttaaaaaa
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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substrates of these forms of memory in the hippocampus, as well as the extent to which these roles are interrelated p TO [2). key role is played by place cells so named because they
fire in specific spatial locations within an environment [3]. Place cells have spatially constrained
firing fields, and "remap" firing patterns in response to significant contextual changes (especially
in hippocampal subregion CA3)
[4 15
T6 17 T8 19]. including motion to a new environment
[20] and modified behavioral context or sensory cues [21 22 After remapping, they form almost
orthogonal representations 22 23 These findings suggest that CA3 place cell network may play key role in maintaining both positional and contextual information [9 241, while also supporting a large capacity for memory storage 22 Meanwhile, others have suggested that hippocampal CA3 is a pattern completion and separation device 226 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 [1 32 77, which could allow it to act as an autoassociative network retrieving a
complete memory fron partial cues 33
29
Prior studies reconciling the spatial and episodic memory perspectives on CA3 propose that hip- pocampus associates sensory cues with spatial information [35
37 38) In this view, given 36
partial sensory signals, CA3 recalls and reconstructs associated spatial information. Benna and Fusi (39] proposed the hippocampus
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 artificial agent that receives partial and noisy sensory observations while traversing simulated rooms. We model CA3 as a recurrent autocncoder (RAE), which tries 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-coplltion objective encourages encoding units to prioritize temporally stable components of perceived experiences, naturally forming plaee-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
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 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.
Method
2.1 Episodic memory during spatial traversal
We first construct 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 dimensional experience vector (EV), a point in abstract space of possible experiences E. An
collectively constituting high-

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Figure 1: (i) Example trajectory of an artificial agent in 2D room in actual space A. (ii Each room is defined by unique set weakly spatial modulated (WSM) signals representing location- dependent sensory cues. Within room, WSM rate map is defined by F where 2 is a 2D Gaussian random field. W and are the dimensions the room. A room is defined by its WSM set, i.e., = [Fi, P2.... FD] R IR Dx xH b. Training schematic of An artificial agent explores room(s) defined by a unique set of WSM signals, as depicted in panel a. Agents receive location-specifie sensory experience vectors ex.y - R[; 2; y). where ez,y E IR_ The agent's 's trajectory within trial is thereby converted into a sequence of experience vectors. At every training step, we randomly sample Noathh segments of T, seconds from episodic memories within To second window. These segments form stack of memories used to train the RAE. Every EV in this stack is randomly masked occlude between T'mnn to maas % of the signal with added Gaussian noise The RAE is trained to reconstruct complete, noiseless experience vectors. The sampling window shifted forward by At after each step until the end of the trial.
g(o), F R RW*H x
RAE.
agent experiences this world through a temporal sequence "events". Each event produces short sequence of EVs 'segment' of episodic memory. A single event of bounded duration should trace brief, continuous trajectory in the experience space E. Formally, let E {eo, Ci..... er) represent the segment of episodic memory generated by a single event, where each e, E R (for t = 0, T') denotes an EV at time t, D is the dimension of the input experience space, and T 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, there exists non non-zero correlation coefficient, p(e,, C+41). During spatial navigation, we expect the environment experiences. We therefore model EVs in fixed
to be temporally stable, with rrcation-depenee room weakly spatial modulated (WSM) signals (Fig. [ defining 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 pattern completion and separation
We then construct simple network model of CA3 for recalling and pattern-completin 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 [7] enabling association of similar patterns and separation of dissimilar ones (37 28 29]
Accordingly, we model CA3 as recurrent autoencoder (RAE). In view of previous research that observed emergence of grid-like patterns recurrent neural networks (RNNs) trained for navigation
48 49 50] we implemented our RAE as a continuous time RNN. Input projections denoted as 77 represent pathways entering the hippocampus (Fig. [p). The hidden layer units use ReLU non-linearity and contain recurrent connections W emulating non-linear responses in CA3 neurons and their recurrent collaterals. The network then uses post-synaptic connections Wout representing CA3's projection to other brain regions to decode hidden unit states. All weight matrices Win W" and Wout are initialized to zero mean uniform distribution (Suppl. Sec. []. this formulation, both direct and disynaptic inhibition, the latter via interneurons, represented negative weights.

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During each trial, agents sampled from the unique set of WSM signals that defined that environment. (Fig. [ & ii), while moving trajectories that imitated rodents (random walks with low-probability We discretized each T; trial into di timesteps during which agents received location-specifie local EVs with elements randomly masked imitate factors limiting observation like occlusion and partial attention. We concatenated timesteps sampled from a decaying distribution (Suppl. Sec. [.2) recent experiences (Fig. [T) into "episodic bouts' and trained the RAE 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 mean- srraned error (MSE) objective function for pattern completion and an MSE constraint on the total hidden layer firing rates to enforce realistic firing rates.
changes of direction and speed, see Suppl. Sec. T
extended history. We use
After trial ends, we "record" from the network by letting the agent run freely the trial room while gathering firing patterns of units within the network (Suppl. Sec. [ 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. See 2.1 [51]
Results
3.1 Emergence of place-like patterns
Fig. 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 100% of the hidden units
active with average firing rates above threshold of H.I 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 WSM imputs (0.29 + 0.01; mean = SD). Thus, place-like like cells emerge from dynamics of the task and network structure. The parameters we used in our experiments are in Suppl. Sec. [.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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Figure 2: Firing maps of 40 randomly selected units in a trial room. A majority demonstrate clear Mike firing patterns. Subplot labels indicate the mean and max firing statistics of each unit in Hz. The spatial information content is indicated the last column of subplot labels.
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. WSM signals are spatio-temporally continuous, so smooth motions between adjacent locations generate smooth motions in EE Thus an agent's s exploration generates a set trajectories in that are unique to each environment and the agent's 's paths. The set of possible trajectories the agent could take together defines surface in EE,

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the experience manifold (EM) of an environment. This manifold has the dimension of the space of accessible sensory experiences. Thus, an agent in 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 activation boundary (AB), an dimensional plane dividing the experience space E. This boundary occurs at input loci where the neuron transitions from inactive active. More generally, the distance of an input e to neuron's 's activation boundary determines the response firing rate, regardless of the activation function. For example, in Fig. 3 & C, an animal traversing ID track traces an EM within a 2D experience space. The EM is encoded by two neurons, N1 (Fig. I.i) and N2 (Fig. Biiii,, with the indicated ABs. As an animal moves from locl loc2, its perceived experience moves along EM and intersects NI's activation boundary. This motion causes NI's firing rate to gradually increase then decrease (Fig.B3 B.).) In contrast, N2's activation boundary is roughly perpendicular to the same EM, motion from Tocl and loc2 will change neuron N2's firing rate monotonically (Fig. B..v..
Our autoencoder linearly decodes sensory experience from the hidden unit activations as è Lies T W where j indexes hidden units, Wout is the output weight vector and S are units that fire at the given location. If the firing rate of unit increases monotonically as an agent moves along the EM, the angle between è and the experience encoded by unit i, Wout 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 discriminating locations. Thus, the most useful units for reconstructing sensory experience will have activation boundaries segmenting the EM like N1 1 in Fig. 3
Expecience Space
NI
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Optinell Encediag
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Figure a. room is defined by unique set of WSM signals describing expected sensory experience at every location. The set of WSM signals converts a room to hyperplane in experience space. b. Illustration of animal moving from locl loc2 in 1D track. c. & iii) Illustration of two neurons N1 and N2 intersecting the experience manifold EM corresponds to the ID track. ii & iv) Corresponding firing rates the animal moves from loel to loc2. d. EMI and EM2 are two experience manifolds corresponding to two rooms. The optimal encoding neuron for EMI may be temporarily inhibited through recurrent connections when entering a new room, then reactivated upon returning to the previous room.
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 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 é; = r; Woo! 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 Wout to remove the unit from the reconstruction. Consider the location of peak firing of unit whose
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planar activation boundary intersects the curved EM as in Fig. Bbi. 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. 3 & d). Assuming that the component of the experience vector that 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, population of such units, each tuned to part of the temporally continuous variation of experience, will exhibit place-fielde 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, Le., input projections. So when an animal reenters a familiar room, both the room's '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 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 familiar room could still induce change, as is observed experimentally 16 24
3.3 Place cell remapping 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. $311 by simulating agents exploring two rooms over three sessions in sequence R1-R2-R1, where RI and R2 are rooms defined by unique WSM signals. After training in each room, we recorded hidden layer firing patterns. The results were labeled TIRI, T2R2, and T3R1, representing the Trial (T) and Room (R), respectively.
We selected active hidden units (mean firing threshold 2 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 TIRI (upper row of Figs. 4.. 4p). 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 (p). The correlation matrix showed low spatial correlation in firing fields between TIRI and T2R2. By contrast, the correlation matrix of TIR1 and T3R1 showed significantly higher diagonal values, indicating reversion of place fields a familiar enclosure.
We then tested the mechanism of reversion. To do so, we calculated reorganization score s of the input projections (W*R) and recurrent connections (W"S) across trials (see Suppl. Sec. (.2). Transitioning from TIRI to T2R2, we observed substantial reorganization of W (s 0.564) but only minor alterations in input projections W (s 0.1)... Between T2R2 and T3R1, W also exhibits small changes (s= 0.141), whereas W continues to show a higher reorganization of == 0.430. This observation is consistent with experimental results indicating that synapses between hippocampal neurons in the same region update at 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 IE. 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. 4e) is encoded by some neurons, similar to what we described in Fig. 33. Then, moving between rooms R1 and R2 (blue and orange planes in Fig. 4 induces two potential remapping scenarios: (a) Neurons encoding volumetric region intersect with only one room's 's manifold activating in R1 and remaining inactive in R2 (magenta region), and vice versa for R2 (cyan region), (b) Both manifolds intersect given region (red cube in Fig. [D), 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 partial remapping).

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Figure 4: a-b. Firing profiles of hidden units that fire (mean firing threashold-O.I 10 Hz) in all three trials and have a place score greater than 5. Upper row: Comparison of T1R1 and T2R2. Lower row: TIRI T3RI. We select cells that fire in all three trials and construct maps of the difference in the binarized firing fields for different rooms (R1 - R2) to compare their locations of firing. The firing fields are binarized by thresholding at 20% of the maximum firing rate of each unit. b. Pearson correlations of the firing fields sorted using hierarchical clustering for visual clarity. c. Illustration of experience manifolds from two rooms. Moving from room RI R2: the encoding units for the magenta region cease firing while those for the cyan one start firing. The encoding units for the red volume fire in both rooms. However, the EMs of RI and R2 might intersect at different angles or correspond to different spatial locations, thereby undergoing global/rate remapping.
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 21). Thus, tested whether our network can also encode large number of rooms in orthogonal representations. To do so, we expanded our training protocol to include 20 unique rooms. We call complete visit of all 20 rooms "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 still exceeds the experience sampling window size of minutes (see Fig. I caption), ensuring a period in which the RAE receives experiences exclusively from one room.
single room while training. This trial duration
After each trial, we replicated analyses in 21 to compare hidden layer population coding vectors in different rooms. For each room, employed a 5 x 5 cm binning window to discretize each 100 x 100 em firing rate map across all 1000 hidden units, resulting in a population vector with dimensions N x W H 1000 x 20 x 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 (1 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 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 compared to different rooms, consistently 23 We also observed that the correlation between population vectors from consecutive visits the same room quickly stabilizes, exceeding 0.8 after the third cycle (Fig. These results combine to suggest that our network is capable of stably encoding a large number of rooms in orthogonal representations.
with experiments 21
18 16
We also observed gradual drifts 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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Figure 5: a-b. Colored lines data from different trial rooms. a. Change in Pearson correlation of population vectors for the same room across consecutive cycles. 1 compares two subsequent cycles. b. Pearson correlation of population vectors from various cycles compared with the final cycle for different rooms, Cycle is excluded because the place fields are not fully formed. As the cycle number increases, the correlation coefficients also increase.
place cells in the brain have representational drift reflecting continuous learning processes [33 We propose that drifts in our network also reflect incremental learning of more efficient ways to encode multiple rooms. To explore, firing patterns) during the first few moments of reintroduction to familiar room. During early cycles, such the third cycle, reintroduction fields (Pearson correlation r = 0.35 when the agent enters familiar room). During the final cycle, cycle 30, the fields immediately reverted 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
measured the amount of reversion (Pearson correlation with previous
familiar room results in a delayed reversion of the place
3.5 Robust emergence of place fields and multiple place fields larger rooms.
While primarily tested our network in Im x Im square rooms, we have confirmed that place fields robustly emerge 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. 44. 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 RAE. To do so, we had our agent explore an environment that contained two rooms connected by a tunnel and trained our RAE the resulting experiences (Fig. (b). Mirroring experimental results, some units in the hidden layer of our RAE developed more than one firing center.
Predictions
Our theory generates several testable predictions. First, we predict that rapid changes sensory and contextual experiences within an environment will disrupt and destabilize place fields. This prediction emerges from the results of Sec. 3.2 where showed that neurons would orient their firing patterns to encode the most varying direction of experience vectors (EVs) at adjacent physical locations. If EV' 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 effectively learn temporal variance adjacent locations, leading 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/cootexttual experience change. We anticipate negative correlation that place cell stability decreases as more aspects 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

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Figure 6: a. Example hidden unit firing maps from a model trained in two connected Im x Im square rooms. The rooms are connected by 20cm 10cm tunnel. b-c To test whether the agent could generate 3D place fields, we assume the agent is able to travel freely in 3D spaces similar to its movement in 2D rooms. We increased the number of WSM channels 1000 to increase experience specificity in 3D enclosures. b. Placing artificial agents in 3D rooms defined by 3D WSM signals, we observed an emergence of 3D place fields. Locations where neurons fire above 65% max firing rate are densely plotted. 1% of the remaining locations are randomly selected and plotted to indicate neurons firing these locations. Warmer colors indicate higher firing rates.
a familiar room, a prediction testable by silencing recurrent hippocampal connections. Third, it is known that deforming room by stretching 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 trajectory dependent shifts in their locations driven by interaction with border cells 663 [44]. Grid cells provide one important class of inputs to the hippocampus, and experience manifold. Our model predicts the corresponding statistics of partial remapping of place fields when the familiar but deformed room is revisited.
expect that the changed grid cell input will correspondingly deform the
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
animal moves through space whether physical abstract. To substantiate, we simulated an agent in 3D rooms and trained our RAF, similar to Sec, 3.1 We observed the emergence of 31D place fields (Fig- (b). This prediction is indirectly confirmed by Grieves 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 Constantinescu al. [66], 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
our study, we tested how episodic and spatial memory, as implemented in the hippocampus, could be interrelated and complementary. To do so, we constructed recurrent autoencoder (RAF) 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 previous encounters. We

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demonstrated that networks concurrently minimizing average firing rate and reconstruction error naturally develop place-like responses. These responses create 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 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 remap- ping, 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 unified "sensory spatial" framework, which leverages the fact that particular combinations of sensory experiences tend happen at partic- ular 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 use the input to our network. We accordingly propose that these inputs are the primary drivers 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 encode them more efficiently, enabling immediate remapping without learning/rewiring recurrent connections.
Our study provides simple yet powerful framework that reproduces a substantial part of the phenomenology of place cells. 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 IR01MH125544.1 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
Training details
1.1
Simulated trials and the artificial agent
An artificial agent explores simulated room(s) defined by fixed WSM signals, as defined Section
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 trajectory with random small drifts representing animal's exploration interest: 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 (5 1) cm/s normal distribution, and the drift direction is randomly chosen from N AT0,, 0.05) rad/s.
2.2
1.2 Training Recurrent Autoencoder (RAE)
The simulated artificial agent gathers experience vectors along its trajectory. We train the RAE on Is 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 & seconds away from the current time step, the probability of it being sampled is:
T T3
+ B
P(()
Σ/=
j
+
T,
Where T, is the width of the sampling window, a and 0.5.
Our RAE contains three layers: The first and the third layers represent the signals being projected 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, governed by the following continuous-time equation:
dv.
= v. W'v)(v.) + Winh of + +b++ - + n.
(2)
dt
Here fx) is an activation function and governs the decay. Win is the connection matrix to the hidden layer, simulating pathways entering the hippocampus. Wre is the recurrent connectivity matrix emulating CA3 recurrent collaterals. The vector b is firing bias term and v, denotes Gaussian pre-activation noise. The variable v, models neural activation potentials. Setting ? discrete- time gives:
dt and adapting
Vi+1 = v. Av. = (1- (1 +
h, + W'' +b M
(3)
h = f
(4)
Here we have replaced f (v:) in equation hidden layer neurons Hertz (Hz) and &, the post-activation noise.
2 with equation (4) where h, is the state vector of the
The network trained with mean-squared error without strict spanseness constraints. function is:
The loss
D.T.B Σ (bar. ed..))² 2 d.e.b
N
TBB
L D.T.
Amse
Air N
Σ
Σ t.b
Tnab
(5)
D is the dimension of the Experience Vector (EV), T measures timesteps within memory segment, B indicates the number batches, and counts nodes in the hidden layer. The term éd,,, the d-th entry of the reconstructed EV at timestep / in batch b, while ed,,. is the equivalent entry of the ground truth. The second component of the loss, Tn,th denotes the firing rate of the n-th neuron at time within batch b. Unless otherwise stated, set Xmae 0 and A 200 for our experiments.
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Table 1: Network parameters
Parameter
Description
Value
hidden
# hidden layer nodes
1000
InputLayer
Distribution of the input layer
u(-vk, vk), where A in fentures
HiddenLayer
Distribution of the hidden layer
u(-vk, v k), where
hidden
Outputl.ayer dt
Distribution of the output layer Time resolution Time constant
u(-vk ((-vk, v k), where K n_hidden
50 ms
500
de Optimizer learning rate
Decaying factor
0.1
Network optimizer
Adam
The learning rate RAE
0.0005
Amse
Coefficient for the mean-squared
pattern completion error
Afr
Coefficient for the mean-squared
200
hidden layer firing rates
Table 2: Training parameters
Parameter
Description
Value
Nootch warmup_duratee duration
Number of episodic memory in each 'bout'
500 300 s
The duration of experience vector before the first trial room (see Fig. [p)
ratio
The percentage we use to randomly occlude an arbitrary experience vector
U(rmin; [
Tmin = 0 & mmaz = 0.2
The exponential coefficient in equation (1)
3
The constant term equation (1)
0.05
spatial resolution
How each meter in the real-world is converted into pixels in our simulated rooms Width of the sampling window (see Fig. caption)
1 cm/pixel
Tw
300
T.
Length each episodic memory The step size of how much move the sampling window forward
ss
Al
1
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, conducted 20-minute trials repeated 20 times. Importantly, the obtained spatial maps are robust to both the duration and the number of tests since paused parameter updates during testing.
During these tests, we recorded the firing rate apost-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.
Measurements and metrics
2.1 Spatial information content
We used the Spatial Information Content (SIC) 51 measured in bits to measure the strength of cell's plaee-like property terms of spatial selectivity We discretize firing rate maps into M 30cm x 30cm bins. Each bin has a firing rate and associated probability pm of the cell firing. The spatial
16

---

information content (SIC) is computed as:
M Σ Pm
SIC
((m)
logg2
I'm
where r is the average firing rate across bins. Bins with I'm = O are skipped in the sum (to avoid divergences in the log), but are included in the computation of the average rate
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:
Wolld
W
||
Here, Wold and Wnew represent synaptic weight matrices before and after adaptation, respectively.
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 firing rate map from single unit into 20 x 20 grid by averaging the rates within each bin to obtain a population coding vector for room. To compute the similarity between two population vectors, X and Y, Alme et al. 21 used the mean dot product:
N.W.H Σ J.J.
Xij.KYij.
N
H
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 normalized measure of similarity for Fig. i 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 calculated as:
ENW N-W-R H (X, - XY YY
N-W-H (X, 14-Xy -Xx x)V
E N.WW YY-
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 more comprehensive comparison. Suppl. Fig. 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 slightly decreased correlation score, due to the incomplete formation of place fields.
As the simulated agent travels through multiple rooms over increasing number of cycles, we observe that place cells, while reverting to their previous locations upon reentering 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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CM
1.0
0.8
0.6
0.4
0.2
Figure Cross correlation of 600 recorded trials. Each pixel represents a comparison of two trials. During each cycle, the sequence in which the agent explores the 20 rooms is shuffled. We re-organize the room sequence when plotting the cross-correlation between trials to ease visualization. The periodic lines indicate strong correlation of spatial representations generated when the animals entered the same room, even in different cycles.
CS
ON
Figure 2: Illustration place field drift across multiple visits to the same room over 30 cycles.
4 Additional results
4.1 Pattern completion results of RAE
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 average firing rate each location each output channel. This process is similar to the method used to gather firing profiles from the hidden layer. In Suppl. Fig. 3
18

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we plot 20 randomly selected WSM cells and their reconstructed values. All outputs accurately reflect the sensory changes appearing the original WSM signals.
STANT
Las
HOT PAR
18 1I1
1210 nal LA
18:9 (6:00
Figure 3: Example pattern completed WSM signals and their corresponding ground truths. a. 20 randomly selected WSM signals reconstructed by the RAE and plotted on the 2D space map. b. The ground truth values corresponding to the WSM cells in panel a.
4.2 Robustness to parameter variations
have verified that the emergence of place cells consistent across different environment shapes, for example triangles (Suppl. Fig. 4a) and circles (Suppl. Fig, Fb). In both cases, the hidden layer generated place-like patterns similar to those in the square rooms we used our experiment.
IMC
4222 C349
LEAEI
(428
ILLT (AAR
BLIZ BUMY)
B.E. (ATN F4A2
ERAMET DUAT
IKES 11.%
Traik
CMADNT T.SEE STAR
ERONNT SWA SIC
(rens AAl
mree Ereas ISM"
Eeetal STC
FREEN' ISE
a
b
Figure 4: a. Example of emerged place-like patterns in a triangular room. b. Example of emerged place-like patterns in a circular room.
While we fixed the parameter values during our experiments to enhance reproducibility. we also verified that place cell emergence robust 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 place units, identified by Spatial Information Content (SIC) 5; (3) the average SIC across all active units.
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Percetngt Necuee
of Nearees
12
200 duration
Pureatage of Neuratss
Perrestage ot Ntammn
Persantge of Neamaa
Active NCCC
56 Active
Action
5o FC
600
WSM mas
WSM digma
unoccluded, ratio %
Ave-IC
150
85 65
10
84
08 06
80 66
Arther
SIU
3.55
hiddlen
100
Figure 5: a-i. Impact of varying specific parameters, with others held constant at the default values, on place cell emergence. All experiments conducted in single trial room. Evaluation of hidden layer firing rate maps included three metrics: percentage of active cells (max_fr 0.1 Hz) among all hidden units, percentage of place cells (max__r 0.1 Hz and SIC 5) among all hidden units, and average SIC across active units. a. Duration of episodic memory segments. b. Total trial duration. c. Coefficient of firing rate loss. d. Warmup trial length (the recall length also to the same value). e. Maximum firing rate for each WSM channel. Sigma value for smoothing WSM signals. Ratio of unoccluded experience. We randomly preserve fraction of the experience and train the RAE to recall the masked part, where the fraction is drawn uniformly in the interval [r [mmins T mazz] Here we vary the bounds on this interval. h. Effects of pre-activation and post-activation noise. i. Co-varying the number of hidden units and the number of WSM cells (dimension of EV).
20

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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. 5)) (2) The number of place cells decreases slowly as trial duration increases. This decrease 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. (p)) (3) As Arr increases, increases the recall length increases, stabilizing once the recall duration exceeds 200 seconds. (see Fig. 5 (5) Neither the maximum firing rate of WSM signals nor the sigma value affects the emergence of PFs. (see Fig- 5 & ) (6) Place fields only emerge when the number of WSM signals exceeds 100, aligning with our hypothesis the main text that the emergence of place fields requires large number of WSM signals. We observed in 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.
active cells become place cells. (4) The number of place cells and active cells
4.3 Attractor landscape of the RAE model of place cells
Classical thcories 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 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.
A31 K701R
21T 14
2115 1011
201
r
Figure 6: Example of neuronal responses at convergence points. For each location, we sample its specific EV, pause synaptic updates, and test the network by fixing this EV until convergence. Neuron states at each location are recorded upon convergence.
Attractor basins 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:
V (vv.) = (1 a)v; - f(v.) + Winn
(6)
where we removed the bias and noise terms to simplify the calculation. As we show below, the network state update function contraction, and if inputs are held constant, the network will converge stable state. Given this property, can plot the attractor landscape of our RAE
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network by testing the network with location-specifie 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 convergence will also result in 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., Vi,j E (0, we have e; ej = =*), where T is the length of the input sequence. We would like prove the network update function is contraction, i.c. the network will converge to a fixed state. We work with the network update function:
V++1 = (vv)) = (1 - avv, + a [Wve)(vv) + w
To show that the network will converge fixed state, first show that the network update function a contraction. To do so, we need to show Vi,j E [), i $ j. if ((v,) - +vv))l < kl[v, v:ll. where & < 1.
Suppose v, V; = u, then
2(v,) = (vv, + = (t </ W
(8)
((v,) - (vv:) -1--a
+ [ - -- aW~ [/(v, u f(v:)]
a)v, (wre +
w
(9)
By the triangle inequality and submultiplicatiiity. [ - ((v))l s (1-a)]lul + [l| + f(v:)l
(10)
Furthermore, if the activation function is bounded and is Lipschitz continuous on real numbers, Lipschitz constant L exists such that [V, + u) f[(v)]] is bounded by L.||u|]] Thus,
[ (v:))l < [ +
(11)
= a1 a + ail W [ [] u|| = k||u||
The update function is a contraction mapping if k = (1 a) + a||WTS|| < 1. Therefore, ||Wre] < L-1 to ensure & 1. The Lipschitz constant
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 real numbers and the metric, the state-space is complete. By the Banach fixed-point theorem, iteratively applying this transformation will converge fixed point v in the state space.
using the distance function as
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Justification: There are two claims in the abstract: Training autoencoder to pattern- complete 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 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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Reviews:
[{"review_id": "lhxhyLiwPj", "reviewer": "Reviewer_hM85", "summary": "This 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.", "questions": "I'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?", "limitations": "I 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.", "rating": 8, "confidence": 5, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "This 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.", "weaknesses": "More 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.?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank reviewer hM85 for their time and suggestions, and are happy that they liked the paper. We will address the reviewer’s comments one-by-one:\n\n\n>A more 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?\n\nWe thank the reviewer’s endorsement of Figure 3. We have generated a more elaborate plot of Figure 3. However, the attached PDF does not have enough space for us to include an additional figure. We will add this new plot and the corresponding discussion to the supplemental materials.\n\nEssentially, the examples for suboptimal and optimal coding will be similar to Figure 3b but broken into two separate plots. The case of suboptimal coding would be when neuron N1 encodes experience manifold E2, while the optimal encoding would be when neuron N1 encodes E1.\n\n\n>It 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 buffers, different levels of noise, a form of input different than the WSM, etc.?\n\nWe thank the reviewer for this comment and agree that this paper will benefit from indicating how different parameters affect the results. We addressed this suggestion in the global response, where we provided an additional figure with an discussion of how these parameters impact the emergent PF. In short, the history buffer won’t affect the PF emergence after passing a threshold value (approx. 200 seconds); The noise also doesn’t impact the PF emergence until the noise is too high and the pattern becomes undecipherable.\n\nAs for different forms of WSM signals, we have varied max_fr and sigma values when we generate WSM signals, and none of them disrupt PF emergence. Additionally, we verified the feasibility of using WSM signals to represent sensory experience, especially for visual signals. In one of our parallel studies, we tested responses to visual stimuli at different spatial locations in VR-simulated rooms. We captured images at different locations in these rooms and passed them through several network models of visual systems. The features generated by these models consistently produce WSM fields. These WSM fields, when used to train our RAE, consistently produce place cells.\n\n\n>I'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\nYes, we also agree on the presence of many redundant solutions. We hypothesize that neurons that capture more variance within a localized region could encode this place's information more efficiently. As proposed in section 2.3, only a few neurons may be efficient in capturing this variance. Therefore, within a region, as long as these few selective neurons remain efficient in capturing the variance of the experience manifold (i.e., their input projections remain stable), there could be many ways to inhibit the non-critical neurons.\n\n\n>I 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.\n\nWe thank the reviewer for pointing us to this relevant research. We have included a wider comparison to other models in the global rebuttal and will include this in the main text if accepted. Specifically regarding comparing [1] with our model, given that the observation of the next step and observation of the current time step could be very similar, our model best corresponds to the next-step architecture in their setup. The most significant difference is that the agent’s observation in Levenstein et al. is conditioned on the direction of the agent. However, this detail could be reconciled by considering non-observing directions in Levenstein et al. as experiences being occluded in our setup. We were also excited to see somewhat similar place-like units emerge in this relevant research.\n\n**Reference**\n\n[1] Levenstein et al. Sequential predictive learning is a unifying theory for hippocampal representation and replay. 2024.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "eXyQpEZiN6", "reviewer": "Reviewer_6VUu", "summary": "This 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.", "questions": "- 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?", "limitations": "The 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).", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- 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.", "weaknesses": "- 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?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank reviewer 6VUu for their time and suggestions.\n\n>Limited quantitative comparison with actual neural data from rodent studies.\n\nWe thank the reviewer for their suggestions. We addressed this in the global response.\n\n>Reliance on simplifying assumptions about sensory input structure.\n\n>WSM signals lacks a clear definition.\n\nHere, WSMs simulate processed sensory information entering the hippocampus. They should be location-dependent, and the response magnitude should decrease as distance to the stimuli increases. Thus, the most important property of using WSMs is that they should be smooth. This smoothness can be guaranteed if the Gaussian kernel used to generate the WSM signals has a standard deviation ($\\sigma$) greater than the body length ($l_a$) of the modeled animal.\n\nWe verified the validity of using GRFs as models for WSMs in a parallel study but have not included it here to maintain the focus of this paper. Specifically, we tested responses to visual stimuli at different spatial locations in VR-simulated rooms. We capture images at different locations in these rooms and pass them through several network models of visual systems. The features generated by these models consistently produce WSM fields.\n\n>Insufficient exploration of network parameter dependencies.\n\nWe resolved this point in the global response and provided a summary figure in the corresponding pdf.\n\n>Publicly available code for verification and extension of the work.\n\nWe completely agree that publicly available code greatly accelerates neuroscience and AI research. In fact, the RAE used in this project builds on a general-purpose RNN for neurostimulation we have previously published on PyPI and GitHub. All parameters in this study directly match those in our package. We will point readers to this code. The code for simulating rodent movement and generating WSM cells is also part of an extensive rodent simulation project we plan to release on PyPI after we wrap up our current work.\n\nAgain we are happy to release our code, including the parts for simulating rodent movement and WSM cells. However, anonymizing the entire RNN package without breaking its integrity is challenging, and we're concerned about potentially violating the double-blind requirement. We'll add a link to our GitHub repository once the reviewing process is over.\n\n>Lack of formal theoretical analysis to explain the emergence of place fields.\n\nWe agree that this work would benefit from a formal theoretical analysis. This work is primarily inspired by previous studies where grid cells emerge in networks that reconstruct locations from sequences of movement-modulated signals. Here, in contrast to the movement-modulated signals required for grid cell emergence, we suggest the encoding spatial modulated signals gives rise to place-like patterns. In the present work we aimed to both explain this emergence and provide a comprehensive replication of place cell phenomenology in a computational RNN framework. There is not enough space to include the formal mathematical framework that we are separately working on.\n\n\n>Inadequate positioning within existing frameworks\n\nWe thank the reviewer for pointing us to this. We have included a more detailed comparison with these models in the global response.\n\n\n>Section structure could be improved for clarity\n\nWe thank the reviewer for this suggestion. We employ our current style which derives from theoretical physics, in an effort to incrementally introduce conceptual ideas and provide corresponding experimental verifications immediately afterward. We agree that the clarity of the paper could benefit from dividing Section 2 into two parts, as this aligns better with the NeurIPS-style convention and enhances the paper's structure. We will split section 2 at approximately line 119.\n\n\n>Robustness to network architecture and hyperparameters?\n\nWe have verified that PFs consistently and robustly emerge across a wide range of parameters. We have also provided the details in the global response.\n\n\n>Statistical comparison with experimental data\n\nWe attempted to conduct a more rigorous statistical comparison. The primary challenge is that the precise hippocampal stimuli of place cells are unknown, making it hard to conduct such a comparison in the absence of aligned stimuli. Additionally, in our model, place cell properties, such as their width and firing rate, can be parametrically adjusted. We could use this to fit the statistics of experimental datasets. But that requires examination of data for many animals and different experimental settings. There is insufficient space here for such a substantive analysis, and we therefore postpone it to a separate effort. We have included a more detailed explanation in the global response.\n\n>Relation to theta precession and grid cells\n\nGiven that both WSM signals and grid cells are found in the MEC, which projects into the hippocampus, it's plausible that grid cells might act as a specific type of WSM signal. The WSM signals we focus on primarily come from sensory observations, which vary constantly and might not always be available. Grid cells, on the other hand, are hypothesized to be generated from integrating movement modulated signals and may provide robust input for hippocampal place cells. This idea is also supported by [1] which shows that path integrating velocity to produce place cells generates grid cells in intermediate layers. Regarding theta precession, we consider it primarily as a separate process that consolidates hippocampal memory and thus is not directly related to our model. That said, theta rhythms may cause events that happen together to compress into a single memory, similar to our training protocol which composes recent events into single memories.\n\n[1] Sorscher et al. A unified theory for the origin of grid cells through the lens of pattern formation. NeurIPS 2019.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vDuLW6uMOO", "reviewer": "Reviewer_KNH2", "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.", "questions": "How does your approach relate to path integration?\n\nDo you expect to see place cells in the absence of visual inputs? \n\nWhat exactly are the inputs to the place cells? Can those pixel-level visual inputs preprocessed with some sensory processing modules?\n\nDo 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.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "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. \n\nThe 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. \n\nThe interaction between sensory inputs and velocity integration seems to be missing.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank reviewer KNH2 for their time and suggestions. We will resolve the reviewer’s comments in turns:\n\n\n>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.\n\nWe thank the reviewer’s suggestion. We employ our current style in an effort to incrementally introduce conceptual ideas and provide corresponding experimental verifications immediately afterward. We agree that the clarity of the paper would benefit from dividing Section 2 into two parts, as this aligns better with the NeurIPS-style convention and enhances the paper's structure.  We will split section 2 at approximately line 119.\n\n\n>The interaction between sensory inputs and velocity integration seems to be missing.\n\n>How does your approach relate to path integration?\n\nThis question can be interpreted in two ways, and we address both to ensure clarity:\n\n1. \"Why is the velocity/path integration feature not discussed in the context of place cells?\": Velocity integration is typically hypothesized to be a functionality of grid cells in the MEC, as cited in references [1-3]. The velocity and other vestibular signals necessary for the grid system's emergence [2, 3] do not directly project into the hippocampus, where place cells are primarily located. This is why the discussion does not extend to place cells in this context.\n2. \"Since WSM signals, grid cells, head direction cells, and border cells are reported in the same region (i.e., MEC), how would they interact with each other?\": This issue requires further investigation as responses in the MEC are typically multimodal. We emphasize the \"spatially modulated\" nature of our system's inputs, contrasting with the \"movement modulated (MM)\" signals involved in the grid systems [2, 3]. We design the input to our system under the hypothesis that while both place cells and grid cells are suggested to encode locations, they differ in their phenomenologies due to the nature of their inputs — one being movement-modulated and the other spatially modulated. Thus, we believe that keeping MM signals separate from the SM signals will better reflect the hypothesis.\n\nRegarding the relationship to path integration, which is typically hypothesized to be the function of grid cells rather than place cells, we suggest the place cells do not support this functionality.\n\n\n>Do you expect to see place cells in the absence of visual inputs?\n\n>What exactly are the inputs to the place cells? Can those pixel-level visual inputs preprocessed with some sensory processing modules?\n\nWe sample a set of WSM signals generated by Gaussian Random Fields (GRFs) to train our model (refer to Fig. 1 caption). Essentially, each room corresponds to a set of unique WSM rate maps. At each location, we sample this set of WSM rate maps to generate a high-dimensional embedding to train the model.\n\nThe WSM signals are used to represent a general format of what sensory signals might look like after being processed by their corresponding cortices at various locations within the trial room. We posit that these can be represented by WSMs (GRFs), based on the assumption that the magnitude of any sensory response decreases as the distance to the stimulus increases, regardless of the specific modality.\n\nWe have tested the validity of this assumption in our parallel work. Specifically, we tested responses to visual stimuli at different spatial locations in VR-simulated rooms. We captured images at different locations in these rooms and passed them through several models of visual systems. The features generated by these models consistently produce WSM fields. Therefore, the WSM signals can be regarded, if desired, as processed visual input. But more generally they are intended to represent the full range of inputs from different sensory modalities, pre-processed by diverse cortical modules. So our model will work in the absence of visual inputs, reflecting the fact that place fields are known to have multi-modal inputs and responses.\n\n\n>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)?\n\nYes, we observed such remapping. As mentioned above, we defined each room as a set of WSM rate maps. Therefore moving the wall could be considered as a rotation or flip of a subset of WSM signals while keeping the rest unchanged. We have verified that this will elicit remapping in the emerged place units. We will add a figure panel to the final version of the paper.\n\n**References**\n[1] Yoram Burak, Ila R. Fiete. Accurate path integration in continuous attractor network models of grid cells. 2009. PLoS Comp. Biology.\n\n[2] Chris Cueva & Xue-Xin Wei. Emergence of grid-like representations by training recurrent neural networks to perform spatial localization. ICLR 2018.\n\n[3] Ben Sorscher, Gabriel Mel, Surya Ganguli, Samuel Ocko. A unified theory for the origin of grid cells through the lens of pattern formation. NeurIPS 2019.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JqV8uKG5u9", "reviewer": "Reviewer_kdgt", "summary": "The 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.", "questions": "Although 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.", "limitations": "The 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.", "rating": 3, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The 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).", "weaknesses": "Main 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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank reviewer kdgt for their time and suggestions.\n\n>Can we really say that CA3 is an autoencoder or that it is its function to represent place fields?\n\nThe idea that CA3 functions like an AE directly corresponds to the autoassociative model of CA3 [1-3]. The 'autoencoding' property of the network arises from the fact that the input is a partially masked signal of the target output. We are putting forward the hypothesis that CA3 functions as an AE, and suggest that place cells are naturally produced during pattern completion of memory, while CA3’s core function is not to produce place cells per se.\n\nNote also that that our network functions as a standard continuous time RNN, which are biologically plausible and have been used in many previous studies [4-9].\n\n>Quantitative comparison to experimental data?\n\nWe have listed the challenges for such a comparison in the global response. While a statistical comparison may be possible, the precise stimuli to which place cells respond is unknown, thus complicating the possibility of meaningful interpretations. Secondly, the properties of PFs can be parametrically adjusted by parameters within our framework as we intend our work to be a study of PF emergence. These parameters could be fit to experimental data, but that is a substantial endeavor in its own right and there is not sufficient space to report it in a single paper.\n\n>Can affirmative statements like “closely resembles results of experiments” (l295), “consistent with experimental results” (l203) be given more evidence?\n\nThese statements aim to emphasize that qualitative aspects of the emergent place cells resemble the phenomenology of biological place cells. We emphasize this qualitative similarity as it extends previous research (Fig. 2) while generating many of the experimentally observed features of PFs within a single framework.\n\n>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?\n\nThe correlation we report is higher than what is reported in biological experiments because we used a Pearson correlation, whereas the ref [10] uses the averaged dot product. The averaged dot product for different rooms in our experiments is 5e-4, which compares well with [10]. We will add this information to the final version.\n\n>The fit in [47, Fig. 2A] is quite bold and ... is not exactly a good standard for comparison (l239). \n\nSimilar experiments that have tested a single subject this many times are very sparse. We are currently in conversation with an experimental group to carry out such measurements, but it will take a while to set up the experiment. Additionally, the representational drift which we plotted in Suppl. Fig. 2 is similarly observed in [10] Fig. 3 A.\n\n\n>The “experimental evidence that place cells can develop multiple place field” (l252) was never really “strong”. \n\nA few recent work has reported this. [11] has reported the development of multiple place field centers in dorsal CA1 when an animal is placed in very large environment. [12] indicates that cells with multiple PFs consistently occur in large environments across CA1, CA3, and the dentate gyrus.\n\n\n>Comparison with more recent modeling approaches\n\nWe thank the reviewer for this suggestion. In the global response, we have included a discussion of some recent work. \n\n\n>Why couldn’t the WSM rate maps supports autoencoding?\n\n>Explanation for roundish PFs\n\nThe WSM signals are modeling processed sensory inputs which are not known to have a direct autoencoding property. The idea here is that the hippocampus provides that autoencoding property for the incoming sensory representation. Why do place cells specifically emerge from this autoencoding? As shown in panel c of the attached PDF, place cells emerge as we increase the constraint of the overall firing rate, indicating that they are likely a balance between efficiency and encoding precision. This balanced solution encourages fewer units to encode as much variation as possible within a localized region. When each cell’s encoded pattern is projected onto the experience manifold, the pattern will naturally be roundish and place-like, because of the high-dimensional nature of the projection (l164-l166).\n\n>Theoretically progress achieved?\n\nThe framework we proposed is our theoretical progress. Motivated by numerous prominent computational studies that report the emergence of grid cells when a system processes movement-modulated sensory signals [6-8] to achieve various target functions, we suggest the encoding of spatially modulated sensory information (WSM) with a simultaneous firing rate constraint gives rise to place cells and shapes their phenomenology. \n\n>Why sigma is set fixed to 12cm\n\nWe used sigma=12cm as an example for reproducibility. The value of sigma does not impact PF emergence. We have illustrated this in the attached PDF.\n\n>How to achieve a diversity of place cells\n\nThe sizes and firing rates of our emergent PFs change in response to variations in the firing rates and sigma values of the WSM signals. More diverse place fields could therefore be realized if we take the input signals to be sparse and allow more variation in the number of WSM channels connected to different hidden units. These parameters can be chosen to match hippocampal anatomy and physiology when such data becomes available.\n\n[1] M. Hasselmo & Wyble (1997). Behavioural Brain Research.\n\n[2] J. Guzowski et al. (2004). Neuron.\n\n[3] S. Leutgeb et al. (2007). Science.\n\n[4] G. Yang et al. (2019). Nature Neuroscience.\n\n[5] V. Mante et al. (2013). Nature.\n\n[6] D. Schaeffer et al. (2023). NeurIPS.\n\n[7] B. Sorscher et al. (2019). NeurIPS.\n\n[8] C. Cueva & X. Wei (2018). ICLR.\n\n[9] M. Benna & S. Fusi (2021). PNAS.\n\n[10] K. Almea et al. (2014). PNAS.\n\n[11] J. Harland et al. (2021). Current Biology.\n\n[12] S. Park et al. (2011). PLoS ONE.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We thank all reviewers for your time and valuable comments. We have addressed the common suggestions below and will resolve additional comments in each individual reply.

>How might the emergence of place fields (PFs) change in response to different parameter settings?

We thank the reviewers’ for their suggestion to include this information. We have now included a detailed discussion of robustness of our results to parameter variations throughout the attached PDF which we will add to the supplement..

We evaluate 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.

We’d like to highlight a few interpretations: (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 Panel a). (2) The number of place cells decreases as trial duration increases. This decrease is due to the optimizer forcing the network to encode WSM 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 Panel b) (3) As $\lambda_{fr}$ 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 Panel d) (5) Neither the maximum firing rate of WSM signals nor the sigma value affects the emergence of PFs. (see Panels e & f) (6) Place fields only emerge when the number of WSM signals exceeds 100, aligning with our hypothesis that the emergence of place fields requires a larger number of WSM signals (l164-l166). We have also observed that the PF emergence prefers different numbers of hidden units under different numbers of WSM signals. This could likely be due to different optimal encoding strategies under different input vs encoding unit ratios, which could be further explored in future studies. Overall, the emergence of place fields is robust under a wide range of parameters.

>Quantitative comparison with actual neural data from rodent studies.

We thank the reviewers for suggesting comparisons with neural data from rodents. We didn’t include such comparisons in this work for the following reasons:

1. While the firing of place cells is highly correlated to the animal’s location, the precise stimuli leading to place cell formation remain unclear. Even identical trial rooms under different global environments may produce orthogonal population representations. It is hard to quantitatively compare two neuronal responses without knowing if they are responding to the same stimuli.
2. At the population level, developing methods to compare two populations of neuronal response remains an active field of research. Most existing lines of work also require the stimuli to be aligned before the comparison is possible, information that we do not have for extant animal experiments.
3. Most importantly, we designed our experiments parametrically so that most qualitative PF properties and statistics can be varied with parameter adjustments (see above). For instance, the width of the PFs could be adjusted using the sigma of the Gaussian smoothing kernel of WSM signals as well as $\lambda_{fr}$​; the firing rate (FR) of PF could be adjusted with the FR of the WSM signals or the ratio of $\lambda_{mse}$​ and $\lambda_{fr}$​, etc. 

It could be meaningful to fit the statistics of our emergent place fields to different experimental data sets to see how the parameters of our model need to vary to match different animals and experimental settings. However, that requires a comprehensive examination of many datasets, for which there is insufficient space in this submission. We will therefore return to this in a separate effort.

>A more elaborated comparison with recent models of PFs

We thank the reviewers for suggesting this and will include comparison with recent literature in our paper. The two studies most relevant to our work are [1] and [2]. Specifically, [1] trains a model with visual observations conditioned on the agent's direction. Conditioning on agent direction can be realized in our setup by considering non-observed directions as occluded experiences in our setup. Their RNN also develops localized representations when trained to predict observations for the next step or multiple steps ahead. Additionally, our view that place cells may simply be emergent patterns of memory during navigation aligns with [2], which suggests spatial awareness results from processing sequences of sensory inputs. Although they use a different learning framework based on a hidden Markov model, they similarly observed the emergence of place-like patterns. 

On the other hand, our hypothesis extends these recent works, particularly in explaining the key phenomena of remapping and reversion of place fieldss after remapping. In particular, differently from [1,2], our conceptual framework proposes that the RNN acts as an encoder for experience manifolds, elucidating how remapping is a learned process and why such learning is reversible. 

Overall, our hypothesis and observations are consistent with recent efforts to explain PFs, but offering complementary perspectives on the PF emergence and their detailed phenomenology.

[1] Levenstein et al. Sequential predictive learning is a unifying theory for hippocampal representation and replay. 2024.

[2] Raju et al. Space is a latent sequence: Structured sequence learning as a unified theory of representation in the hippocampus. 2024.

Meta-review: The present study presents a novel idea that place cells can emerge by training a network to encode not just spatial locations, but temporal sensory sequences. The trained network model reproduces some characteristics of hippocampal neurons, including remapping, orthogonality of spatial representations, slow representational drift, etc. It is a study of interest to both neuroscience and machine learning communities. Therefore I recommend accepting this paper. Please integrate reviewers' feedback to improve the paper.
Decision: Accept (poster)