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.
Experimental evidence indicates that intrinsic temporal dynamics operating across multiple time scales are closely associated with the emergence of periodic spatial activity of increasing complexity. However, how information encoded in grid-like firing patterns for path integration is processed across these intrinsic time scales remains unclear. To address this question, we introduce adaptive time scales through a leak term in recurrent neural networks (RNNs), forming leaky RNNs discretized from the continuous attractors of firing rate models. Our results demonstrate that leaky RNNs substantially enhance the emergence of well-defined and highly regular hexagonal firing patterns. Compared with vanilla RNNs lacking a leak term, the trained leaky RNNs produce more accurate position estimates while generating reliable grid-cell-like representations. Furthermore, under identical noise conditions, leaky RNNs consistently exhibit more stable dynamics and better-defined grid structures. The learned dynamics also give rise to stable torus attractors with a clear central hole, supporting robust and regular grid-like activity. Overall, the dynamic leak acts as a low-pass filtering mechanism that protects recurrent neural circuitry from noise, stabilizes network dynamics, and improves path-integration accuracy in recurrent neural networks.
Yanlin Zhang, Yan Zhang, Muhua Zheng +1
School of physics and Electronic Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China · Teaching Department, Jiangsu University Jingjiang College, Zhenjiang 212028, Jiangsu, China
Neural correlates of spatial cognitive map are well documented, yet exactly how neural circuits perform spatial navigation in complex environments - e.g., reaching a goal while avoiding obstacles - remains largely unclear. Here, we show that a hippocampal network with appropriate recurrent connections can naturally achieve optimal goal-directed navigation via its relaxation dynamics. Specifically, we consider that the recurrent weights between the neurons represent the transition probabilities between spatial locations encoded by neurons; obstacles such as walls and blocked corridors are therefore reflected by the vanishing of connection weights. This connection pattern can be learned in the hippocampus via behavioral-timescale synaptic plasticity (BTSP) while the animal is exploring the environment. When a goal signal is presented, the network dynamics will relax into an activity field representing the goal location. We prove that this field is mathematically equivalent to the desirability field of a Linearly-solvable Markov Decision Process (LMDP), and the local log-gradient of the field indicates the navigation direction. Both theoretical analyses and simulations demonstrate that this recurrent network dynamics-mediated navigation is efficient and robust in environments with complex obstacle layouts. Moreover, only low-rank updates of the network's connection pattern are needed when the environment has local changes. We hope this study offers insight into a general circuit principle for planning in abstract rational maps in the brain beyond spatial navigation.
Yuhang He, Junfeng Zuo, Tianhao Chu +1
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
Biological neural networks (like the hippocampus) can internally generate "replay" resembling stimulus-driven activity. Recent computational models of replay use noisy recurrent neural networks (RNNs) trained to path-integrate. Replay in these networks has been described as Langevin sampling, but new modifiers of noisy RNN replay have surpassed this description. We re-examine noisy RNN replay as sampling to understand or improve it in three ways: (1) Under simple assumptions, we prove that the gradients replay activity should follow are time-varying and difficult to estimate, but readily motivate the use of hidden state leakage in RNNs for replay. (2) We confirm that hidden state adaptation (negative feedback) encourages exploration in replay, but show that it incurs non-Markov sampling that also slows replay. (3) We propose the first model of temporally compressed replay in noisy path-integrating RNNs through hidden state momentum, connect it to underdamped Langevin sampling, and show that, together with adaptation, it counters slowness while maintaining exploration. We verify our findings via path-integration of 2D triangular and T-maze paths and of high-dimensional paths of synthetic rat place cell activity.
Josue Casco-Rodriguez, Nanda H. Krishna, Richard G. Baraniuk
Department of Electrical and Computer Engineering, Rice University, USA · Mila - Quebec AI Institute & Université de Montréal, Canada