2.1 EC3 persistent activity as a substrate for selective persistence

We first asked what kind of memory substrate is needed before selective readout and transfer can be considered. For the present model, the substrate should support three separable operations: writing new information, keeping relevant information across a delay, and forgetting information when it becomes irrelevant. We therefore begin with EC3 persistent activity [13] as a minimal substrate for selective persistence in simple maintenance tasks such as the CS+ task [4] and the Near/far task [6].

EC3 persistent activity provides a useful biological motivation for modeling write, maintain, and release-like operations. Some EC3 cue-tuned neurons respond to multiple landmark stimuli with different response strengths, thereby encoding external information [22]. EC3 neurons can also exhibit switch-like persistent activity, with firing rates resembling stochastic on/off states. Although such activity is variable, it can encode task-relevant information, including cue and reward locations, even early in learning [15]. These observations motivate a simple modeling assumption: depending on its input, an EC3 subgroup can enter regimes that favor writing new information, maintaining stored information, or releasing information that is no longer needed.

We therefore describe each EC3 subgroup by the fraction of active cells, r(t). This fraction changes according to the input I(t) through two transition probabilities: an on-to-off probability p₁₀(I) and an off-to-on probability p₀₁(I) (Fig 2A and 2B). At the population level, r(t) follows a first-order ODE that converges to a stable fixed point with time constant when I is fixed (see Methods). As I increases, the model passes through three functional regimes: keep, forget, and write (Fig 2D). The resulting activation and maintenance dynamics are qualitatively similar to EC3 persistent activity reported in [15] (Fig 2B and 2E). Unlike a purely discrete Markov-chain implementation, this population-level formulation can be trained by back-propagation.

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Fig 2. Single-lamellar model learns to maintain information.

(A) EC3 0/1 state transition. (B) Simulated EC3 activity shows stochastic on/off dynamics. Top, activity of a simulated EC3 neuron in response to a pulse input at (45, 55), black indicates on state. Bottom, mean neuron rate across trials (shadow = SEM), similar to [15]. (C) Workflow of the single-lamellar model, forming a re-entrant loop. (D) EC3 output governed by P₀₁, P₁₀, , based on EC3 input. Shadowed areas highlight stages of information processing. (E) Sensory stimulus generates different EC3 subgroup activity. This subgroup only receives cue A stimulus in the sensory input area (cue zone, shadowed area). Red and blue curves, mean rate of EC3 subgroup. (F) CA1 neuron model. Left, semantic CA1 neuron structure. Right, semantic input and output of CA1 neuron. EC3 drives the CA1 apical tuft and CA3 drives CA1 basal dendrites, producing splitter-cell-like activity in the model [29]. (G) Training accuracy of Near/far task (shadow = SEM). Performance (y-axis) quantifies per-time-step lick/no-lick accuracy within the task-relevant zones. (H) The model develops place-cell-like and splitter-cell-like activity patterns. Red line indicates x = y. (I) CA1 activity by trial type. Left, firing rate. Red arrows indicate representative cells shown on right, which show qualitatively similar response profiles to those reported in [29]. (J) Agent actions during Near/far task training. Left and middle, raster plots of the “lick” action; yellow pixels denote lick behavior, and black pixels denote no-lick behavior. Right, accuracy curve.

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2.2 A re-entrant loop enables selective readout and self-gating

The EC3 population model provides a substrate for temporary information maintenance. The next question is how stored information should influence behavior only at the appropriate time and place. This requires a selective read function [23] and a feedback pathway that can regulate the subsequent state of the memory substrate.

EC3 input to distal or apical CA1 dendrites is strongly attenuated before reaching the soma, and therefore has limited ability to drive somatic spiking on its own. However, distal EC3 input can be amplified when paired with CA3 input onto basal dendrites, a process often described as dendritic gating [24]. In the present model, CA3 provides a positional or temporal scaffold for CA1 readout, whereas EC3 provides contextual information. CA1 therefore combines positional and contextual inputs to form task-dependent representations [25] (Fig 2F). Furthermore, CA1 readout can determine behavioral actions through a linear transformation. The purpose of the single-lamellar model is not to explain every feature of CA1 activity, but to isolate the minimal circuit computation by which retained information becomes selectively readable and behaviorally useful.

EC5 provides a plausible candidate pathway for closing this loop in the present abstraction. EC5 also shows persistent activity but behaves more like a numerical integrator [26], i.e., its firing rate changes only when sufficiently strong excitatory or inhibitory input is given. Combined with the known hippocampal-entorhinal connectivity, this motivates the EC3-CA1-EC5-EC3 re-entrant loop in our model. Specifically, information retained in EC3 is selectively read out by CA1, integrated by EC5, and then fed back to regulate the next EC3 state–namely, whether a subgroup should write new information, maintain the current content, or release it. In this sense, the loop is self-gating: the circuit not only stores information, but also helps determine how that stored information should evolve over time.

This re-entrant architecture defines the single-lamellar model. The model receives sensory input through EC3 and positional or temporal input through CA3, and outputs the current behavioral decision (Fig 2C). It performs well in the CS+ and Near/far tasks (Fig 2G), where performance is quantified as lick/no-lick accuracy within the reward-relevant evaluation zones. Furthermore, the single-lamellar model develops splitter-cell-like task-relevant activity at the cellular level [27–29]. These splitter-like units collectively covered much of the track, with individual units active at distinct spatial locations (Fig 2H and 2I), and provided task-relevant information that could be read out for behavioral choice in the model. Note that fewer CA1 cells exhibit activity in the distal region, consistent with a distributed coding mechanism where the behavioral output is supported by a compact task-relevant subpopulation rather than broad population activation. For visualization, we selected the three CA1 units with the most pronounced cue-dependent differences (Fig 2I). Such strongly modulated cells frequently appear near the end of the track, where behavioral decisions occur. These examples demonstrate that, after learning, different CA1 units develop distinct spatial–contextual tuning and that the same location can evoke different activity patterns across trials, both of which support correct performance in this implementation.

The model also contains CA1 units without clear trial-type tuning. These units may provide additional positional or temporal signals for downstream readout and feedback in the model. In short, the single-lamellar model enables CA1 to selectively read out information held by EC3 populations, thereby guiding the behavior decision, while simultaneously enabling EC5 to integrate and guide the information maintaining process in EC3. Additionally, by analyzing the agent’s behavior (“lick” or “not lick”), we find that the single-lamellar model shows a staged behavioral progression that qualitatively resembles reported rodent behavior (Fig 2J). At the beginning of training, the agent licks broadly across the track. After a short training period, it licks at both reward sites, and eventually develops selective licking at the cue-appropriate reward site [6].

Importantly, localized CA1 fields are not imposed by a fixed CA3 → CA1 mapping. They emerge from random initial weights through training in the full EC3–CA1–EC5–EC3 loop. To test whether this localized tuning depends on a Gaussian CA3 template, we replaced the original Gaussian-like CA3 input with non-Gaussian rectangular-wave position bases; representative CA1 cells still developed localized Gaussian-like responses after learning (S1 Fig). This result suggests that localized and behaviorally useful CA1-like readout is shaped by circuit constraints and task demands in the model. The upstream generation of CA3 spatial fields is not modeled here; CA3 is treated as a simplified scaffold used to isolate the computation of interest.

These results should therefore be read as a proof of principle for the self-gating mechanism, not as a full model of hippocampal representation. The single-lamellar circuit is intentionally minimal: it isolates how the EC3–CA1–EC5–EC3 loop can turn retained information into selective CA1 readout and behaviorally useful gating. This minimal circuit then serves as the building block for the multi-lamellar model.

2.3 Combined self-gating across lamellae supports more complex task structure

The single-lamellar model captures key aspects of selective maintenance in simple tasks, but many tasks require more than retaining sensory details. Such tasks also require the circuit to extract internal task variables, such as order [8], accumulated evidence [9], or lap count [10], from similar sensory inputs. This motivates the second design step of GATE: repeating the same self-gating loop across lamellae so that different layers can operate at different representational scales.

To capture externally and internally driven information, we build a multi-lamellar model (Fig 3A). Externally driven information (sensory input) acts as input into the dorsal EC3, and the CA1 readout in ventral lamella guides the actions. In each lamella i, reads out information from . , a linear transformation of , is then provides input to in the next lamella, where it is combined with local feedback. Thus, sensory information enters through dorsal EC3, whereas behavioral output is read from the ventral CA1 population.

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Fig 3. Multi-lamellar model supports simulated working-memory tasks.

(A) Schematic of the multi-lamellar model. (B) Evaluation accuracy in task Lap, Sequence, and Evidence. Shadow area indicates SEM. (C) Delay-active cell activity in the Trace task, sorted by maximum activity location, qualitatively similar to [31]. CS, conditional stimulus zone (black bar); US, unconditional stimulus zone (brown bar). (D) Cell representation in Lap task. Orange boxes and dashed arrows indicate representative cells on left, similar to [10]. (E) Evidence-cell activity in the Evidence task, qualitatively similar to [9] (F) Representative cell activity transitions during training, illustrating switching-like patterns similar to [33]. (G) Linear decoder accuracy of cue versus action in error evaluation trials across three layers. Retrospective coding was observed across layers, whereas prospective coding was mainly observed in the ventral layer in this model. (H) Cue-identity decoding accuracy based on CA1 population activity from dorsal, intermediate, and ventral lamellae in the CS1234 task. Dashed green line indicates chance accuracy. Gray shading, cue zone; blue shading, action zone. Ventral-like CA1 shows reduced cue-identity decoding at the action zone, qualitatively similar to [4]. (I) Dorsal (left), intermediate (middle), and ventral (right) CA1 population representations in the CS1234 task. Top, MDS results show that cues with the same task outcome (CS1+ and CS2 + ; CS3- and CS4-) become closer. Bottom, representative neuronal activity in different cue trials. (J) Model neural manifold moves toward the task-relevant topology during training in the Near/far task. 20 trials are grouped as one session. Trials start from the black cross and proceed clockwise. Note that the representation gradually decorrelates at the action zone (black arrow), resembling the split-ring-like manifold reported in [6].

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The multi-lamellar model supports the simulated tasks shown in Fig 3B. In addition to splitter-cell-like and place-cell-like activity, it develops lap-cell-like activity in the Lap task [10], evidence-cell-like activity in the Evidence task [9], and delay-active-like activity in the Trace task [30,31] (Fig 3C, 3D and 3E).

During training, model units also undergo representational transitions resembling tuning changes [6]. Some initially silent units become splitter-cell-like or place-cell-like, whereas some place-cell-like units later become silent (Fig 3F). These switching-like changes are qualitatively similar to rapid representational changes reported in rodent neurons [32,33].

To investigate the presence of retrospective and prospective splitter cells in the model, we adopted the definitions provided by [3] and [5]. We trained the model on a Near/far task, where decisions were made at a single time point near the end of the trajectory, and naturally occurring errors were observed in 41 evaluation trials (Fig 3G). For each CA1 unit, we used its firing-rate profile across the trajectory as the feature vector and trained two separate linear classifiers: one to decode cue identity and the other to decode the chosen action. Cells were classified as retrospective-like if cue decoding was significant and exceeded action decoding, and as prospective-like if action decoding was significant and exceeded cue decoding. The results revealed a predominant presence of retrospective cells in the dorsal and intermediate layers: (i) Dorsal CA1: 39 retrospective cells and 1 prospective cell; (ii) Intermediate CA1: 36 retrospective cells and 0 prospective cells; (iii) Ventral CA1: 7 retrospective cells and 7 prospective cells.

This analysis indicates that, in this model, CA1 activity is primarily retrospective-like, consistent with its working-memory design. The ventral lamella showed a higher proportion of prospective-like cells, which we interpret as a model prediction, rather than as a pattern already established in the experimental literature.

Beyond the single-cell level, we next asked what kind of information is preserved in the population code of each lamella. In Fig 3H, the decoder was trained to predict cue identity (CS1–CS4), rather than behavioral output [4]. Thus, this analysis does not quantify splitter-like activity or action readout, but instead measures how much stimulus-specific information is retained in each lamellar population along the trajectory.

The multi-lamellar model shows a representational gradient along the DV axis. In the CS1234 task, dCA1 retains more cue-identity information, whereas vCA1 shows reduced cue-identity decoding at the action zone while preserving information relevant to behavioral outcome (Fig 3H). MDS of CA1 population activity showed a similar lamellar difference (Fig 3I). For all tasks except the Lap task, neuronal activity was reset to zero at the beginning of each trial in the revised implementation. These results are qualitatively consistent with selected aspects of rodent hippocampal population coding reported in [4]. To visualize how neural representations evolve during learning, we also applied uniform manifold approximation and projection (UMAP) to CA1 population activity in the CS1234 task [34]. Each population vector was reduced to a point in 3-D space (Fig 3J). In the model, the neural manifold gradually moved toward a task-relevant topology during learning, qualitatively resembling physiological results in [6].

Taken together, these simulations support the model-level hypothesis that repeated self-gating loops can organize information from more local cue-bound coding toward broader task-related structure, which may facilitate later adaptation to related tasks.

2.4 Structure-preserving transfer accelerates relearning

We next asked whether GATE can reuse learned representations when part of the task setting changes but the underlying task structure is preserved. We use “generalization” in this restricted sense: accelerated relearning under constrained perturbations, rather than a full model of hippocampal remapping. To test this, we modified task settings in four ways (Fig 4A): (1) replacing the EC3 input with entirely new sensory coding, corresponding to novel cue types [6]; (2) shuffling all CA3 place fields (or time fields) to perturb the positional scaffold [35]; (3) altering the action requirements, such as replacing a CS + - task with Near/far; and (4) changing task parameters, such as modifying the lap cycle count while preserving the task’s internal logic. Across all conditions, the model relearned faster after prior training (Fig 4B and 4C), consistent with faster adaptation after related cue changes in rodents [4,6].

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Fig 4. Structure-preserving transfer boosts relearning.

(A) Scheme of four generalization experiments. PF, place field. (B) GATE requires fewer epochs across repeated generalization rounds. Left, Type 1 generalization; right, Type 2 generalization. Top, representative loss curves (loss values above 0.4 are omitted for clarity). Middle, number of epochs required for the classification loss to reach 0.01; training was stopped after 300 epochs if the criterion was not reached. Bottom, splitness-index correlations across generalization rounds. (C) Representative loss curve in Type 3 (left) and 4 (right) generalization. (D) Place fields remain largely stable during Type 1 generalization. Left, two representative neuronal activity profiles. Right, neuronal activity correlation between training and generalization, or between training and shuffle controls. (E) Task-related representations are partially preserved during generalization. Left, scatter plot of splitness during training versus generalization, or training versus shuffle control; red line indicates x = y. Right, splitness correlation between training and the first or second generalization in dCA1 and intermediate CA1 (iCA1), illustrating lamella-dependent differences in task-related modulation. (F) Splitness correlations across training and repeated generalization. Correlations of single-cell splitness were computed between training and the first generalization, and between the first and second generalizations, to assess the stability of task-relevant representations across constrained perturbations. (G) Number of epochs required to reach the loss criterion (cross-entropy < 0.1) in the 40-step Near/far benchmark. In all bar plots, n = 30; two-sided Mann–Whitney U-tests with Holm–Bonferroni correction for multiple comparisons; *P < 0.05, **P < 0.01, ***P < 0.001, n.s., not significant.

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Under this interpretation, the representation analyses in Fig 4 test which components of the learned code are reused. When EC3 sensory coding is replaced while CA3 positional input is kept fixed, stable CA1 place fields are expected (Fig 4D); the purpose of this analysis is to test whether spatial representations can be reused without catastrophic rewriting while cue-related components are relearned.

When CA3 fields are shuffled, the purpose is complementary: to ask whether task-related modulation can still be partially preserved after the spatial scaffold is changed. We examine a task-relevant representation using a splitness index to quantify each cell’s ability to encode distinct task-related information (Fig 4E). The results reveal a partial stability of splitness, suggesting that task-related modulation can be retained to some extent after positional reshuffling. Notably, intermediate CA1 shows stronger inheritance of these representations than dorsal CA1 in this benchmark, suggesting lamella-dependent differences in representation inheritance (Fig 4F).

For a baseline comparison, we conducted a controlled evaluation between GATE and GRU models trained under identical BP conditions. Both models successfully learned the simplified 30-step Near/far task; however, when the delay was extended to 40 time steps or more, GRUs frequently failed to reach convergence within 100 epochs, consistent with known limitations in gradient propagation across long temporal spans [36]. Fig 4G summarizes the number of epochs required to reach the loss threshold (0.1). Across 30 sessions, GATE required substantially fewer epochs than GRU both during initial learning (mean ± SEM: vs. ) and generalization ( vs. ). Moreover, GRUs showed non-convergence in 63% (19 out of 30) of all 40-step condition sessions, whereas GATE achieved consistent convergence across all runs. These results indicate that, under this controlled benchmark, GATE relearns structurally related but temporally more demanding conditions more efficiently than the GRU baseline.

Accordingly, these results are best interpreted as selective representation inheritance and faster relearning under structure-preserving changes. They do not aim to explain full remapping across arbitrary environments. Within that more specific scope, GATE shows that the same circuit can preserve unaffected components of prior knowledge and update the rest efficiently.

4.1 EC3 setup and external input

Parameters of all methods are listed in Table 1. For simplicity, the agent runs with a constant unit velocity through the whole track, such that x = t.

To keep it clear, we describe the EC3 model at three linked levels. First, EC3 persistent activity is motivated at the single-cell level as stochastic on/off switching. Second, the average behavior of many such cells is written as a population-level ODE, which is the form used for analysis and training. Third, after training, the same population dynamics can be approximated by a discrete Markov realization for simulation. These are not separate models, but three descriptions of the same EC3 memory substrate.

In our model, each cue activates a fixed subset of EC3 subgroups with a short pulse in the cue zone, thereby providing the external signal that can later be written into, maintained within, or released from the EC3 memory substrate. When a task has types of cue, and the j-th cue type is deployed in a training trial, the cue stimulates several EC3 neurons as follows:

(1)

where M is a binary matrix randomly defined before training, so that each cue activates a specific subset of EC3 subgroups; is an indicator function that restricts cue input to the cue zone :

(2)

4.2 EC3 population model

We model EC3 as the memory substrate of the loop. At the single-cell level, persistent activity is motivated as stochastic on/off switching: a cell may switch from off to on, or from on to off, depending on its current input. This single-cell picture provides the biological intuition for the model. For training and analysis, however, we use a population-level description in which each EC3 subgroup is represented by the fraction of active cells, denoted by .

Given (defined below), the probability of transition from on to off is , and the probability of transition from off to on is , where and are nonlinear functions:

(3)

in which , and .

At the population level, these transition probabilities determine the average activity of each EC3 subgroup.

(4)

When is fixed, this ODE converges to a stable point with time constant . In our interpretation, different combinations of and correspond to three functional regimes of the EC3 substrate: writing new information, maintaining currently stored information, and releasing information that is no longer needed.

After training, the same population dynamics can be approximated by a discrete Markov realization (each subgroup is replaced by multiple on/off units with the same input). We use this only as a simulation-level approximation of the trained dynamics, not as a separate model or conceptual contribution.

4.3 Model initialization and inter-trial state transition

At the beginning of training, all neurons are initialized with zero activity. For all tasks except the Lap task, the activity states of EC3, EC5, and CA1 are reset to zero at the beginning of each trial. The only exception is the Lap task, in which information from the previous lap must be retained across successive laps by design. For this reason, cross-trial state continuity is preserved only in the Lap task.

4.4 Hippocampus formation network

The hippocampal-entorhinal loop is implemented so that EC3 provides the memory substrate, CA3 provides positional or temporal gating, CA1 performs selective readout, and EC5 feeds back to regulate the subsequent EC3 state. We now specify these components in turn. The output of the m-th neuron in CA3 is modeled as a Gaussian function on time t:

(5)

where D is the standard deviation and is the center of the place field that covers the whole track. For simplicity, the agent moves at constant speed on a periodic linear track, so that the beginning and end of the track are connected.

The j-th CA1 neuron can be described by the following multi-compartment model:

(6)

where is the basal potential, is the apical potential, and are basal and apical weights, and are learnable inhibitory biases, and C₁ and C₂ are constants. In this formulation, CA3 determines when or where CA1 readout is allowed to occur, whereas EC3 modulates what information is amplified at that moment. When the basal potential is weak, the CA1 output is close to zero; in this sense, CA3 input gates CA1 readout. When is sufficiently strong, acts as a gain factor [50]: the CA1 output is potentiated when is large and depressed when is small. These cellular mechanisms allow CA1-like units in the model to learn task-relevant activity patterns, including place-cell-like and splitter-cell-like responses.

4.5 EC5 feedback and EC3 state update

EC5 acts as an integrative feedback pathway in the loop. At each step, CA1 output is accumulated in EC5, and the resulting EC5 activity contributes to the next EC3 input. Therefore, EC3 state transitions are not determined by sensory input alone but jointly by current external drive and loop feedback. This is the sense in which the EC3–CA1–EC5–EC3 circuit is self-gating.

The k-th EC5 neuron integrates its CA1 input:

(7)

where is the CA1-to-EC5 weight, is a threshold function that ignores small inputs, and the clip function limits EC5 output to . EC5 output is then transmitted to the EC3 input of the same lamella:

(8)

where is the EC5-to-EC3 feedback weight, is the sensory input, is the dorsoventral transition weight, and is the CA1 output in the previous lamella. The second term is only included when the EC3 neuron belongs to the dorsal lamella, while the third term is only included in other lamellae.

4.6 Retrospective and prospective splitter cell analysis

To distinguish retrospective-like from prospective-like coding, we analyze evaluation trials from the Near/far task under the single-action-point setting, in which the behavioral decision is read out at one predefined position near the end of the trajectory. For each trial, we record the full CA1 activity trace across the trajectory, together with cue identity, chosen action, and trial correctness. Error trials are not artificially introduced, but are the naturally occurring incorrect trials generated during model evaluation.

The analysis is performed at the single-cell level. For each CA1 neuron, the feature vector for one trial is defined as that neuron’s firing-rate profile across the trajectory. Two separate linear classifiers are then trained using correct trials only: one to decode cue identity and the other to decode action. Both classifiers are subsequently tested on the error trials. This design allows us to dissociate whether a neuron primarily reflects the preceding cue or the forthcoming action when the behavioral output is incorrect.

For each neuron, we obtain cue-decoding accuracy and action-decoding accuracy on the error trials. A neuron is classified as retrospective-like if cue decoding is significant and exceeds action decoding, and as prospective-like if action decoding is significant and exceeds cue decoding. Cells with no significant decoding are labeled neutral, whereas cells with significant decoding of both variables but only a small difference between them are labeled ambiguous.

Chance level was estimated with a permutation test rather than assumed directly. For each neuron and decoding target, the training labels were randomly shuffled times, the classifier was retrained, and decoding accuracy on the same error trials was recomputed to form a null distribution. A decoding result was considered significant if it exceeded the permutation-based chance level at p < 0.05, where

(9)

denotes the observed decoding accuracy of neuron i, and denotes the decoding accuracy obtained from the k-th shuffled-label permutation.

4.7 Agent behavior and task performance

Agent behavior is derived from the CA1 output in ventral lamella through a policy matrix :

(10)

where n indexes possible actions, and the action with the larger q value is selected. In our tasks, the agent determines whether to lick the feeding tube at each time step [4], forming a binary classification problem. When reward is available at the feeding tube, the agent should lick; otherwise, it should withhold licking. Given these labels, the model is trained by back-propagation using a weighted cross-entropy loss and the Adam optimizer with learning rate lr. The data are batch-normalized to accelerate training with batch size bs. During generalization, is reset while other weights are retained.

In all of the tasks, task performance quantifies whether the agent correctly performs licking behavior at the appropriate decision step. Specifically, the task is formulated as a binary classification problem, where the model predicts whether a lick should occur (“lick” = 1, “no lick” = 0). For example, in the near/far task, licking should occur only in the corresponding reward zone depending on the cue [6]. Performance was computed as the proportion of correctly predicted lick or no-lick states within the evaluation zone(s) rather than the whole track, providing a model-level analogue of behavioral lick accuracy. In tasks such as the near/far task, this definition implies a chance level of 50%, because one evaluation zone is labeled as “lick” and the other as “no lick” for a given cue. Hence, always licking (or always withholding licking) yields approximately 50% correct responses.

4.8 Splitness index

The splitness index of the j-th CA1 cell is defined as follows:

(11)

where is the mean neuronal output in trials with cue type l, and is a small constant used to prevent division by zero and filter out low-activity neurons.