When and Where: A Model Hippocampal Network Unifies Formation of Time Cells and Place Cells
Authors: Qiaorong S. Yu, Zhaoze Wang, Vijay Balasubramanian
Organizations: Department of Psychology, New York University, New York, NY, USA · Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA, USA · Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA
Hippocampal place and time cells encode spatial and temporal aspects of experience. Both have the same neural substrate, but have been modeled as having different functions and mechanistic origins, place cells as continuous attractors, and time cells as leaky integrators. Here, we show that both types emerge from two dynamical regimes of a single recurrent network (RNN) modeling hippocampal CA3 as a predictive autoencoder. The network receives simulated, partially occluded experience vectors" containing spatial patterns (location-specific activity sampled during environmental traversal) and/or temporal patterns (correlated activity pairs separated by void" intervals), and is trained to reconstruct missing input. During spatial navigation, the network generates stable attractor-like place fields. But trained on temporally structured inputs, the network produces sequentially broadened fields, recapitulating time cells. By varying spatio-temporal input patterning, we observe hidden units transition smoothly between time cell-like and place cell-like representations. These results suggest a shared origin, but task-driven difference, between place and time cells.
Figures & tables
Figure 1: A : A circular track and the corresponding sampling source of each spatial channel. B : The sampling source for each temporal channel when two temporal events occur. C : Continuous time recurrent neural network (CTRNN) model of hippocampal area CA3.
Parameters
Descriptions
Values
N
Number of hidden layer nodes
512
D
Number of sensory channels
100
T
Duration of memory segments
Time Task: 20s
Space, Spacetime Task: 10s
B
Batch size
64
Win∈RD×N
Initial distribution of the input layer
U(−D,D)
Table 1: Network Parameters.
Figure 2: A : Time Task : the experiment simulates an agent that remains stationary while receiving temporal cues at two time points. Through repeated training, the CTRNN learns to predict the time interval between the two events. i : Experimental paradigm. ii : Temporal firing map. iii : Temporal correlation of the firing field. Red dots denote neurons whose firing fields broaden over time, whereas blue dots denote neurons whose firing fields become narrower over time. In the simulation, neurons whose peak firing occurs closer to the second temporal event tend to exhibit sharper temporal tuning, suggesting that temporal resolution increases as the temporal event approaches. This anomaly is also observed in [ 12 ] . B : The agent performs free spatial exploration in a square arena and the network only receives spatially tuned signals. i : The sampling source of each spatial channel. ii : Place cell-like firing rate maps emerge in the hidden layer of the network.
Figure 3: A : Space Task : the experiment simulates an agent running clockwise on a circular track for two laps. The agent samples spatial information throughout the traversal. The CTRNN is trained to reconstruct the entire sensory experience. i : Experimental paradigm. ii : Spatial firing maps. iii : Sum of the spatial firing map. iv : Spatial firing map. B : Spacetime Task : the experiment simulates an agent running clockwise on a looped track. In the first lap, the mouse samples spatial information, while in the second lap, it is unable to access spatial cues. The CTRNN is trained to predict the spatial information in the second lap based on the first lap cues. i : Experimental paradigm. ii : Temporal firing map and correlation between the firing time and the firing width during the first (left column) and second (right column) laps. iii : Spatial firing map in the first lap. iv : Spatial firing map in the second lap.
Figure 4: A : Gradually increasing the duration of temporal events. i & ii : Task design. The duration of the temporal events is increased across trials, leading to a progressive shortening of the intermediate interval ( Z ). iii : Neuron heatmaps across five consecutive trials, showing how firing patterns broaden and become more sequential as Z shortens. iv : Number of time cells in the intermediate interval ( Z ) across trials, and number of time cells within each of the two temporal events across trials. B : Gradually reducing the duration of exposure to spatial sensory input. i & ii : Task design. A mouse runs on a circular track while the duration of spatial input is reduced, with the underlying spatial trajectory kept fixed. iii : Trial-by-trial neuron heatmaps showing the gradual emergence of temporal coding. iv : Number of place cells across trials as the duration of spatial input is reduced. v : Number of time cells and place cells in the two windows where spatial input is provided, and in the intermediate interval where spatial input is absent.
Figure 5: A : Task design. The agent runs on a circular track for two laps. A temporal cue is presented in each lap, while spatial information is provided only during the first lap. The numbers of temporal and spatial channels are varied across trials. B : Numbers of temporal and spatial channels in each trial, ranging from fully temporal input (Trial 1) to fully spatial input (Trial 5). C : Number of detected place cells in each trial. The number of place cells decreases as spatial channels are removed and temporal channels are increased. D : Population activity sorted by peak firing time. As temporal information becomes more dominant, the activity gradually shifts from place-cell-like spatial tuning to time-cell-like firing patterns. E : Correlation between firing-field width and peak firing time across trials. The correlation increases as temporal channels increase, reflecting broader firing fields and a gradual transition toward temporal coding.
Figure 6: A : Proposed recurrent weight matrix with forward excitation, backward inhibition, and strong local inhibition, together with the trained recurrent weight matrix from the time task. B : Sequential activity generated using the idealized recurrent weight matrix in panel A while performing the time task, showing broadened firing fields over time. C : The temporal correlation of firing fields using the idealised recurrent weight matrix in panel A. D : Comparison between the idealised Wrc that generates time cells (blue), the trained Wrc from the time task (red), and the trained Wrc from the space task (green). i : Average sorted recurrent connectivities. ii : Eigenvalue spectra. The left panel shows the full eigenvalue spectra of the idealised and trained Wrc of both time task and space task, while the right panel shows the eigenvalue spectra outside the unit circle of the idealized and trained Wrc of the time task only. iii : Singular value spectra. E : Schematic illustrating how time and place representations arise from reconstructing missing segments of a trajectory in a high-dimensional representational space. F : Distance between embedding trajectories reconstructed by the RNN when sensory input is missing and the corresponding ground-truth embeddings in representational space.
School of physics and Electronic Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China · Teaching Department, Jiangsu University Jingjiang College, Zhenjiang 212028, Jiangsu, China
School of Psychological and Cognitive Sciences, Peking University · IDG/McGovern Institute for Brain Research, Peking University · Peking-Tsinghua Center for Life Sciences, Academy for Advanced Interdisciplinary Studies, Peking University +2