A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
Authors: Yi Xie
Jaedong Hwang
Carlos D Brody
David W. Tank
Ila R Fiete
Venue: ICML 2025 poster (2025)
Keywords: place cell
grid cell
neuroscience
Primary area: applications->neuroscience_cognitive_science
TL;DR: We propose a multi-region brain model revealing conjunctive tuning in grid cells and sensory inputs as crucial for spatial decision-making and hippocampal cognitive maps, offering insights into the interactions underlying cognitive functions.

Abstract: Brains excel at robust decision-making and data-efficient learning. Understanding the architectures and dynamics underlying these capabilities can inform inductive biases for deep learning. We present a multi-region brain model that explores the normative role of structured memory circuits in a spatially embedded binary decision-making task from neuroscience.
We counterfactually compare the learning performance and neural representations of reinforcement learning (RL) agents with brain models of different interaction architectures between grid and place cells in the entorhinal cortex and hippocampus, coupled with an action-selection cortical recurrent neural network. We demonstrate that a specific architecture--where grid cells receive and jointly encode self-movement velocity signals and decision evidence increments--optimizes learning efficiency while best reproducing experimental observations relative to alternative architectures.
Our findings thus suggest brain-inspired structured architectures for efficient RL. Importantly, the models make novel, testable predictions about organization and information flow within the entorhinal-hippocampal-neocortical circuit: we predict that grid cells must conjunctively encode position and evidence for effective spatial decision-making, directly motivating new neurophysiological experiments.

A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
Yi Xie 12
Jaedong Hwang' Carlos Brody 23 David Tank? 2
Ila Fiete
Abstract
mann et al., 2022) and deeper architectures (Dosovitskiy et al., 2021; He et al., 2016; Jiang et al., 2023). frequently emphasizing scale over the efficiency driven by biologi- cally inspired models (Banino et al., 2018). To bridge this gap, insights from neuroscience can inform more efficient architectures by studying how biological systems process in- formation make robust and adaptive decisions in dynamic and uncertain environments. The brain contains specialized circuits including the hippocampal circuit (HPC), a key set of brain areas critical for spatial, contextual, and associa- tive learning and memory (O' Keefe, 1978; Dostrovsky & O' Oeeeefe, 1971; Squire, 1992; Scoville & Milner, 1957). Meanwhile, cortical and subcortical regions play a central role in evidence accumulation and decision-making (Pinto et al., 2019; IBL et al., 2023).
Brains excel at robust decision-man making and data- efficient learning. Understanding the architectures and dynamics underlying these capabilities can inform inductive biases for deep learning. We present a multi-region brain model that explores the normative role of structured memory circuits in a spatially embedded binary decision-making task from neuroscience. We counterfactually com- pare the learning performance and neural repre- sentations of reinforcement learning (RL) agents with brain models of different interaction archi- tectures between grid and place cells in the en- torhinal cortex and hippocampus, coupled with action-selection cortical recurrent neural net- work. We demonstrate that a specific architecture- where grid cells receive and jointly encode self- movement velocity signals and decision evidence increments-optimize learning efficiency while best reproducing experimental observations rela- tive alternative architectures. Our findings thus suggest brain- brain-inspired structured architectures for efficient RL. Importantly, the models make novel, testable predictions about organization and infor- mation flow within the hhippoaapplippp neocortical circuit: we predict that grid cells must conjunctively encode position and evidence for effective spatial decision-matee making, directly moti- vating new neurophysiological experiments."
Brain-scale neural recordings at cellular resolution, which are only recently possible, open a window into how brain regions interact with each other to perform complex tasks. Here we focus on the accumulating tower task, a widely adopted, interpretable benchmark in neuroscience for prob- ing multi-region brain interactions underlying spatially em- bedded evidence accumulation and decision-making (Pinto et al., 2019; 2022; Nieh et al., 2021; Brown et al., 2024).
In the task, mice navigate an immersive virtual reality cor- ridor, where they are stochastically presented with visual towers on both sides. At the end of the corridor, they must turn left or right depending on which side has more towers (see Figure 1D). This task requires integrating evidence: computing the difference in the total number of towers on each side ("accumulated evidence"). Task standardization enables reproducible experiments, and these in turn inform theoretical models (Lee et al., 2024; Karniol-Tambont et al., 2024) that generate testable predictions about behavior and neural dynamics. We focus on this task build a multi- system brain model spanning memory, integration, spatial navigation, and decision circuits.
1. Introduction
Deep learning has advanced through the adoption of larger datasets (Lin et al., 2014; Russakovsky al., 2015; Schuh-
"See project page at https: / /mi nzsiure, gi thub. / mult wwwrreennnbrrrreeeee arbrin-mmdeell m/ Massachusetts Institute of Technology. Cambridge, MA, USA "Princeton Neuroscience Insti- tute, Princeton University, Princeton, NJ, USA 'Howard Hughes Medical Institute, USA. Correspondence to: Yi Xie <evay- ixie@ princeton.edu>> lla Fiete <fiete mii..duu>
During the task, the dorsal CA1 region of the hippocampus encodes conjunctive cognitive maps of both the animal's location and accumulated evidence. Place fields in this region are tuned not only to spatial position but also to task-relevant accumulated evidence, meaning that individual neurons fire selectively based on both variables (Nieh et al.,
Proceedings of the 4nnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
2021).
ings illuminate how the brain may coordinate computations across its many substructures to flexibly and efficiently tackle complex challenges.
This finding is intriguing given that the task does not ex- plicitly require spatial information for decision-making- the correct choice depends only on the relative frequency of tow- ers on each side. It raises several key questions: Why does the hippocampus, typically associated with spatial naviga- tion and episodic memory, represent accumulated evidence in this task? Does this suggest that the hippocampus has broader functional role in spatially embedded decision- making tasks, even when spatial information is unnecessary for the decision? Furthermore, why are spatial and evi- dence representations jointly encoded in the hippocampus? These questions point to the potential involvement of the hippocampus in coordinating computations across multiple brain regions during decision-making.
The contributions of this paper are four-fold:
We propose and demonstrate a multi-region brain model framework that counterfactually tests the compu- tational roles of entorhinal hiipaaalaappooaaaa-aaaaaa -eccorttccl in- teractions during spatially embedded decision- decision-making tasks. Our framework makes novel experimentally verifiable predictions for neuroscience.
The model enables systematic exploration of how neu- ral computations shape cognitive capabilities, offering a tool to guide and interpret future neuroscience exper- iments.
Decision-making tasks are often modeled within reinforce- ment learning (RL.) framework (Gershman & Niv, 2015; Gershman & Daw, 2017). While these models excel in task- level performance, they often overlook structured neural architectures and dynamics observed in biological systems. For instance, deep RL approaches applied to the accumulat- ing tower task (Mochizuki-Frreemall et al., 2023; Lee al., 2024) focus on optimizing performance post-training but fail to capture the distributed computations across brain regions and do not explain how natural systems perform efficient and robust learning.
We predict that conjunctive position-evidence tuning in grid cells is essential to the emergence of experi- mentally observed conjunctive position- ceitiinneviieene hip- pocampal representations (Nich et al., 2021).
Finally, we demonstrate that conjunctive grid cell tun- ing and non-grid sensory inputs to the hippocampus are critical for learning spatially embedded contexts (model M5).
2. Related Works
To address these gaps, we developed a multi-region brain model that incorporates an architecturally and dynamically prestructured circuit model of the hippocampal-entorhing system, Vector Hippocampal Scaffolded Heteroassociative Memory (Vector-HaSH) (Chandra et al., 2025). Our model extends HeSH by integrating it with cortical and sub- cortical regions, abstracted as a recurrent neural network (RNN) (Elman, 1990) to serve as the RL decision decision-making actor. This integration enables the model to function as a biologically grounded RL solver, leveraging structured memory circuits to support spatially embedded decision- making. Inspired by the vision for autonomous machine intelligence outlined in LeCun (2022), we demonstrate that integrating structured, aadtentadddressable associative mem- ory with neural representations is a promising approach for efficient task learning and navigation. Specifically, our work highlights the essential role of structured coding schemes, such as grid cells, in forming world models (cognitive maps) that support efficient tookino.
2.1. Biological Evidence and Gaps on Entorhinal- Hipoamaa-iiiiiommmaaaaooorreee Interactions
Hippocampal place cells (HPC), which encode spatial loca- tions through their activity patterns (Dostrovsky & O'Keefe, 1971), form the basis of the cognitive map theory (O" Keefe, 1978; Fenton, 2015; Moser & Moser, 2016). This theory provides foundational framework for understanding how flexible and intelligent behaviors arise from coordinated neu- ronal populations (Fenton, 2024). Cognitive maps not only enable flexible spatial navigation but also support memory organization and the construction of coherent narratives of personal experiences (O' Keefe, 1978; Tolman, 1948; Whit- tington et al., 2022; Fenton, 2024). Furthermore, the HPC's ability to encode internal cognitive variables, such as accu- mulated evidence and task-relevant information, highlights its broader role as a model system for studying internally generated cognition (Bostock et al., 1991; Nieh et al., 2021; Ólafsdóttir et al., 2015; Tavares et al., 2015).
We apply this framework to the accumulating tower task and test counterfactual scenarios in which the entorhinal- hippocampal networks receive different inputs. Our model generates normative predictions about tuning in grid cells, the role of entorhinal-hippe hhippiiaa---ppppaappllll networks, and the con- ditions that give rise to efficient learning and performance of spatially embedded decision-mant making tasks. These find-
Interactions between the HPC and the entorhinal cortex (EC) are well documented crucial for navigation (Me- Naughton et al., 1996; O' Keefe, 1978) and declarative mem- ory (Scoville & Milner, 1957; Squire, 1992). Within the me- dial entorhinal cortex (MEC), grid cells (Hafting et al., 2005) provide a spatial metric through their periodic, hexagonal firing fields (Krupic et al., 2012). These grid cells, along
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
with hippocampal place cells, form the building blocks of neural systems that support both physical navigation and abstract cognitive functions. Recent hypotheses propose that memory and planning mechanisms evolved from pro- cesses originally adapted for physical navigation, suggesting a shared computational framework for navigating both phys- ical and mental spaces (Buzsáki & Moser, 2013). Moreover, hippocampal prefroonal interactions have been shown to play significant role in higher-order cognitive functions, in- cluding decision-making and planning (Eichenbaum, 2017; Preston& & Fichenbaum, 2013). These established interac- tions inform the design of our multi-region model to uncover neural mechanisms underlying cognition.
models of the brain (Sacramento al., 2018; Whittington & Bogacz, 2017), mimicking representational transforma- tions in primate perceptual systems (Bashivan et al., 2019; Kell et al.. 2018). These models often exhibit classic behav- ioral and neurophysiological phenomena when trained on tasks similar to those performed by animals (Banino et al., 2018; Pospisil et al., 2018; Wang et al., 2018). Comple- mentarily, Yamins & DiCarlo (2016) demonstrated corre- lations between artificial neural network (ANN) represen- tations and neuronal activity in the monkey visual cortex during image classification tasks, informing the design of brain-like ANNs (Kubilius et al., 2019; Zhuang et al., 2021), Such -rain-inspired approaches provide value to both neu- roscience and machine learning. For example, while navi- gation is fundamental for humans, it remains challenging for ANNs (Mirowski al., 2017). Leveraging grid cell-like representations, critical for mammalian navigation, Banino et al. (2018) developed deep RL agent with navigation abilities resembling those of primates.
Recent advances in experimental techniques, such as large- scale neural recordings (Jun et al., 2017: Steinmetz et al., 2021), have made it possible to investigate how thousands of neurons across multiple brain regions coordinate to function coherently (Bondy et al., 2024). However, despite these ad- vances, understanding the mechanistic roles and interactions of individual brain regions in cognition remains a challenge. Our theoretical work bridges this gap by providing inter- pretable, mechanistic model "testbeds" that complement experimental findings and generate testable predictions to guide future investigations.
3. Methods
3.1. Antortinaa-hipcccaaa-Avvoorrrr Spatial Decision Model
Our multi-region brain model integrates cortical circuit, abstracted into an action- oetion-selection RNN policy, with pre- structured eutorhinal-hippocappaa circuit inspired by Chan- dra et al. (2025), which incorporates bidirectional compu- tations between grid cells and place cells to associate, en- code, and learn environmental information. As shown in Chandra et al. (2025) and Fig 1A (purple and orange), the entortinal-hiipooeen
2.2. Models of Entorhinal-- Interactions
Prominent models of entorhinal- hippocampal interactions include the Tolman-Eichenbaun Machine (TEM) (Whit- tington et al., 2020), statistical generative model, and Vector-HaSH (Chandra et al., 2025), a biologically realis- tic, mechanistic model. Vector-Hase separates fixed- fixed-point dynamics for pattern completion from content encoding, leveraging grid-cell scaffolds to prevent catastrophic forget- ting and memory capacity cliffs. Unlike generative models, it provides high-capacity, generalizable framework for spatial and non-spatial memory, making it well-suited to studying episodic and spatial representations.
memory seaffold features bipar- tite architecture comprising hidden (hippocampal) and label (grid cell) layers. The scaffold's design is based on estab- lished and inferred recurrent connectivity patterns between the MEC and HPC (Witter & Groenewegen, 1984; Amaral & Witter, 1989; Witter & Amaral, 1991; Witter et al., 2017) and among grid cells in the MEC (Burak Fiete, 2009).
In contrast to data-driven approaches. such as inferring brdin-wide interactions with constrained RNNs (Perich et al., 2020) or disentangling shared and private latent variables across regions (Koukuntla et al., 2024), our mechanistic model provides interpretable hypotheses about entorhinal- hippocampal interactions. By integrating Vector-HaSH with multi-region dynamics, our approach bridges experimental findings with theoretical predictions, advancing understand- ing of distributed neural computations.
Connections from grid cells the hippocampus (Whg) are fixed and random, while connections from the hippocam- pus to grid cells (W gh)) are set through associative learn- ing and remain fixed thereafter. Connections between the HPC and non-grid lateral entorhinal cortex (LEC) (Wha he and W..) are learned bidirectionally through associative learning. The grid cell layer operates as a k-hot modular vector, constrained by local recurrent inhibition, where k reflects the number of one-hot grid modules. Each module has a unique periodicity, and velocity inputs (e.g., position and evidence) drive the phase progression of each module within its 2D representational space (i.e., a 2D torus).
2.3. Bidirectional Insights Between Deep Learning and Neuroscience
Machine learning-based frameworks are increasingly ap- plied in neuroscience studies (Richards et al., 2019). For instance, deep neural networks have emerged as plausible
We build upon the architecture proposed by Chandra et al. (2025) (Fig 1A), termed Vector-HaSH++ (Fig IB). Unlike the
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
A
foedionntio aneeaatto plasss
B
Proposed muiti-regional model M5
Vector-HaSH
anl oelss (HEC)
N
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pos
grld cells
ppspocaricse
[5]
distal CA3)
hippocampus
(6)
RNN
[2]
[5]
DOIT gidd
MLP
Non-grid sensory (EC)
sensory
C
D
Exampla: An agent moves 3 positions forward, encounters evi, value -1, +1. Joint grid representation:
Reinforcement learning scheme with proposed model M5
axts posttive direction pariodicity indicator
Position Axis (+1, +1,+1)
Dacision region
Evidence Axis (+1,
Delay
patls integ Alion
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Module 1 (N. Ax) encodes pos. & evi.
Module 2 (0, As) encodes pos. & evi.
Module 3 Ag)) encodes pos. &
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Position
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Start
Position velocity
Evidence velecity (#right #loft)
-1,+1)
MLP
(b, x.) encodes pos.
Module (x)) encodes pos.
Module (g) encodes evi.
Figure 1. Task schematies. (A) Schematic of Vector-HaSE (Chandra et al., 2025), the basis of our model architecture. (B) Schematic of the Vector-HaSHa circuit, which we propose to model and investigate the neural computation process for spatially embedded decision- making tasks. The numbers in parentheses are the order of computation. (C) Schematic of grid cell code, for specitic example of agent moving positions forward while encountering evidence value +1, 1. and +1. Here, we assume the grid state is initialized at the top left corner, but the coding scheme is invariant regardless of the initial state. joint grid representation (top) utilizes both of the grid module 2D space for both task variables, position and accumulated evidence, yielding a wiggling activation pattern (red arrows). A disjoint grid representation (bottom) encodes task variables in separate modules, such that each grid module only fires along one axis (red arrows). The periodicity of cach module is indicated by dashed gray arrows, as the representation space of grid module is effectively a 2D torus. (D) Schematic of the RL setup in which an agent navigates a virtual T-maze with towers appearing both sides, and reward given when it turns to the side with more towers in the end. The agent has some field of view ahead, and the visual sensory information communicated HPC through MEC and/or non-grid LEC. The HPC code is then mapped by an RNN policy (cortex) to select an action. The action updates the agent's 's position, which updates the sensory input and then the grid states. This process repeats until task termination.
original VeSHor-HaSH, Vector-HaSH+ provides flexibility in hippocampal readouts, allowing them to receive projections from both grid cells and non-grid sensory inputs simultane- ously or from just one source (Fig IB, orange and green). Grid states are updated by task-relevant velocity inputs, ei- ther across all modules or selectively along specific axes in some modules (see Fig 1C and Appendix A.1). A multi- layer perceptron (MLP) processes sensory inputs extract evidence velocity (Fig IB, yellow), which informs grid cell updates. Similar to Hwang al. (2023); Wang al. (2024), the resulting hippocampal vector is the input to the RNN policy, which is trained using RL policy gradient method to make action decisions (see Fig ID and Appendix A.3 for a detailed step-by- by-step procedure).
biologically (Preston & Eichenbaum, 2013; Eichenbaum, 2017; Canto al., 2008), model the hippocampal vector as the primary cortical input for simplicity. This simplifi- cation assumes the hippocampal vector alone is sufficient for learning the task, while allowing us to test hypotheses about conjunctive hippocampal representations observed in Nieh et (2021), providing a foundation for further inves- tigations. For instance, future studies could evaluate the computational benefits of various combinations of (MEC, HPC, LEC) inputs to the cortex in enabling generalization and efficient learning.
3.2. Model Setup
We describe the model formally in the context of the ac- cumulating tower task. As the agent navigates in space
While the MEC, HPC, and LEC all interact with the cortex

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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
at time i, it processes sensory information from the left and right visual fields, St and Sn. which is projected through the dorsal visual stream to downstream processing regions. This results in a sensory vector in LEC modeled by ((() = Wn. (1) + W. fre(t), representing a weighted integration of the two fields that can be used for further com- putations. We assume a simple concatenation of (1) and (t))), but this setup provides flexibility for modeling abla- tion studies, e.g., simulating the effects of optogenetically inhibiting one hemisphere. The downstream computation includes velocity prediction that updates grid cell states and projection into HPC.
Table I. Overview of how model variants correspoon to alternative hypotheses of neural coding and information flow based on evi- dence source. Our final model. M5, is marked with *.
Models of hypotheses (Source of Evidence)
Not grid cells
grid cells
Not sensory sensory
M1
M3 M4, M5*
M2
Table 2. Summary of the neural coding and information flow in each model variant. Our final model, M5, is marked with *.
Following Chandra et al. (2025), the MEC layer of the model contains A one-hot grid cell modules, each is a binary-valued periodic function on a 2D discretized hexagonal lattice space with periodicity X. Thus, each module state is a vector of dimension À x The module states are concatenated to form collective grid state ÿ E {0, 13%,, where the vector length N₂ Σm A-M-
Model
Grid cell code
Place cell code
MLP input
RNN input
MD
M0+
& Mpox & Mars
M1
pos.
M2
pos.
M3
joint pos. & evi.
M4
disjoint pos. & evi. juint pos. evi.
&
The grid cell state is updated through continuous attrac- tor recurrence dynamics (Burak & Fiete, 2009), where a module-wise winner-take-all mechanism, [. shifts each grid module based on position and evidence velocity signals v(t) informed by s(t). We model the velocity esti- mation as an MLP (Rosenblatt, 1958) that processes sensory inputs for simplicity, representing form of visual-vestibula integration (DeAngelis & Angelaki, 2012). Following Chan- dra et al. (2025), we assume this process occurs externally to the antorhinal-hippocampal circuit. This simplification does not affect our results and is beyond the scope of this framework.
where H is Nr, x &Npatts matrix with N Npatts hippocampal states, each of length No. and S is No x N matrix with columns as the encoded sensory inputs of length N..
We modeled variants with recurrence in the HPC layer (namely, the CA3 recurrence (Sammons et al., 2024)) in Appendix F, which does not alter the conclusions in the main paper. The hippocampal state h in Eqn 2 (or Eqn 3) is the readout of the entorhinal hippocampal circuit to the cor- tex (under the modeling rationale explained in Section 3.1), which is an action-selection RNN policy trained through policy gradient under reinforcement learning. Please re- fer to Appendix A.3 for what one step of the agent in the environment entails among the involved brain regions.
The grid cell state update at time f is thus formalized
g(t + 1) = caN(g(t) v(t)].
(1)
The full implementation of CAN[]] is provided in Ap- pendix A.5.
4. Alternative Multi-Region Interaction Hypotheses
The grid cell layer and the non-grid sensory layer project onto the HPC layer, such that the hippocampal activities are
Nieh et al. (2021) observed conjunctive coding of both accu- mulated evidence (cognitive variable) and position (physical variable) in the hippocampus when mice perform the accu- mulating tower task, suggesting that the hippocampus also performs general computation, rather than merely respond- ing to features of external stimulus such as space (O' Keefe & Burgess, 1996). This discovery highlights the need for mechanistic modeling at an appropriate scale to explore how interactions across multiple brain regions contribute to internally generated cognition. Such processes enable individuals to flexibly navigate spaces and organize, relate, and integrate experiences, objects, and events.
Timix (l + 1) ReLU hss 5(() + W hg H(L + 1)]- (2)
We also test the variants of hippocampal coding, in which only the grid cell layer projects onto the HPC layer, such that the hippocampal activities are
Fronmix (t + 1) = ReL.U[Wng hg 7(1 + 1)]-
The connectivity between the HPC layer and the EC layer is updated in both cases as pseudo-inverse (+) learned het- eroassociative weights,
(4) We use the accumulating tower task as a minimal framework to hypothesize three potential mechanisms underlying the conjunctive HPC code of physical and cognitive variables:
Wh ha HS*
W.. m SH
(5)
5

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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Makingg
flxed random flxed
plastic (Hobb-like) information flow position axds
p2s
accum, evi. axis
RNN
RNN
sensory
MLP
sensory
sensory
MO
M
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pcs
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pos
disjoint
pos
Joint
RNN
RNN
RNN
MLP
consory
MLP
sensory
MLP
sensory
M3
M4
M5*
Figure Model schematics. Counterfactual models of hypotheses on neural code and information flow, as detailed Tables and
Grid cells encode position, aligning with the prevailing view (Moser et al., 2008), and the conjunctive encoding in the HPC arises from sensory input provided by non- grid LECC neurons (M2).
5. Results
5.1. Joint Integration Model Induces Efficient Learning
We compare the performance of different model variants in terms of cumulative success rate and exploration effi- ciency during training (Fig 3). Additionally, as shown in Appendices G and H, our findings remain consistent after tuning the learning rate or matching the number of param- eters in MO and M0+ to that of M5. Our results show that agents fail solve the task when grid cells do not encode evidence (Fig 3A, orange and green), highlighting the impor- tance of MEC in integrating cognitive variables. Moreover, RNN-only baselines (MO and MO+, in blue and black, re- spectively), with the same number of neurons as M1-M5, perform poorly even when supplied with positional and velocity information (MO+, in black), suggesting that the EC-HPC network critical for temporal integration. Addi- tionally, models with jointly tuned grid cells (red and brown) learn efficiently than those with disjointly tuned grid cells (purple). This phenomenon lacks immediately clear computational explanation, which we investigate in Sec- tion 5.2.
Grid cells co-tune to both position and evidence. phenomenon that has not been extensively investigated experimentally to the best of our knowledge. The LEC pathway neither necessary nor relevant (M3).
Grid cells co-tune to both position and evidence, and the EC pathway contributes to the formation of the conjunctive hippocampal code (M4, M5).
Notably, there are two possible mechanisms for grid cell tuning of accumulated evidence and position:
Joint Integration Model:
Grid cell modules each en- code combination of evidence and position by lever- aging their 2D toroidal attractor network. This implies the simultaneous representation of spatial and cogni- tive variables within the same grid modules (M3 M5, see Fig 1C top).
Interestingly, when sensory information is projected to the hippocampus (M4, M5), the learning performance becomes more variable relative M3 (Fig 3A), possibly because mixing place codes with sensory signals complicates the representation. However, including sensory information in HPC increases exploration efficiency (brown in Fig 3B), presumably because it captures the nuances in the envi- ronment-such as wall positioss-complmmen the rigid information encoded by grid cells. In support of this view, M3, a variant of M5 without sensory projections, requires longer navigation times (red in Fig 3B). Please refer to Appendix A. for implementation details.
Disjoint Integration Model: Individual grid cell mod- ules each encode distinct task variables. Specifically, some grid cell modules exclusively encode position, while others exclusively encode evidence (M4, see Fig 1C bottom).
Our framework provides a systematic approach evaluate the proposed hypotheses shown in Tables 1 and 2, and Fig This evaluation includes (a) quantitative analyses of learn- ing performance and behavioral outcomes (Section 5. and (b) qualitative alignment with experimental findings (Sec- tion 5.2). Furthermore, we hypothesize the roles individ- ual brain regions in spatially embedded decision- preiiion-mmainn tasks by analyzing neural representations (Section 5.3).
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
B
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Figure 3. Learning performance measured by cumulative success rate and exploration efficiency over the course of training for all model variants. We present the mean and standard deviation of these metries across three trials. Baselines are indicated by dashed gray lines. In (A), using window size of 5, 000 episodes, we observe efficient learning in models with jointly tuned grid cells (M3, in red; M5, in brown). In (B), with a window size 10, 000 episodes, M5 demonstrates its ability to effectively leverage spatial information, navigating the maze more quickly (hrown). For clarity, data from the first 100 episodes are excluded due initial instability.
5.2. Joint Integration Model Predicts Evidence-Posithee Co-Tuning in Grid Cells
Disjoint code model
As shown among simulated hypotheses, joint tuning of po- sition and evidence in the MEC promotes efficient learning, while the sensory pathway enhances efficient navigation. Here, we further analyze the relationship between grid cell computations and place cell firing patterns. Our results re- veal that model variants capable of efficient task learning exhibit firing fields closely resembling the experimental ob- servations in Nieh et (2021). This aligmment makes clear prediction that the conjunctive grid cell representa- tions give rise the joint encoding of spatial and cognitive variables in the HPC.
Posilion
Joint code model
Position
Evidence
Figure 4. Place cell tuning during the task. The schematic plot (left, adapted from Nich et al. (2021)), and the firing fields of selective hippocampal neurons models (right, top) (right, bottom). The firing field of each hippocampal cell is de- termined by averaging smoothed neural activity across trials and normalizing within the cell. See Appendix C for raw firing fields without smoothing and Appendix for smoothing details using 01, T2 1. In Nich et al. (2021), since hippocampal cells have conjunctive code of evidence (E) and position (Y), smaller firing fields effectively partition the evidence dimension in the E Y space. Notably, only models with jointly tuned grid cells exhibit conjunctive place fields in the E. F Y space (right, hottom).
5.2.1. JOINT INTEGR ATION MODEL EXHIBITS EXPERIMENTALLY ALIGNED HPC FIELDS
Nich et al. (2021) demonstrated experimentally that individ- ual CA1 neurons encode both position and accumulated evi- dence. This interdependence implies that trials leading the same final decision would evoke distinct hippocampal firing sequences, the agent traverses different tower/evidence configurations (Fig 4, left). Consequently, smaller firing fields would partition the evidence dimension within the Evidence (E) x Position (Y) space of hippocampal activity.
5.2.2. JOINT INTEGRATION MODEL EXHIBITS BOTH
We found that joint integration models (M5 in Fig 4, bottom right; M3 in Appendix C) successfully replicate the E Y place fields observed by Nieh et al. (2021). In contrast, models lacking joint integration, such M4 (Fig 4, top right), fail to reproduce this behavior, instead exhibiting stripe-like firing patterns indicative of independent repre- sentations of position and evidence. additionally demonstrate that smoothing hippocampal activ- ity reveals more localized and stereotyped tuning, consistent with experimental observations.
FIELDS EVIDENCE FIELDS
Here, we demonstrate that only the joint integration model aligns perfectly with the experimental findings, strongly supporting its role in governing the neural computations un- derlying place cell behaviors described in Nieh et al. (2021). In this model, grid cells jointly encode evidence and posi- tion, enabling the HPC to create integrated maps.
Appendix I, we
Only joint integration models exhibit choice-specific neu- rons Nich et al. (2021) observed that CA1 neurons exhibit choice-specific place cell sequences when sorted by their
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A Multi- Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
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Figure 5. Choice-specific place cell sequences & evidence fields. Only models with conjunctive grid code exhibit choice-specific place cell sequences observed in Nich et al. (2021). Activation is averaged and normalized in each cell. We compare results from (1) Nieh et al. (2021), (2) disjoint integration model M4, and (3) joint integration model M5, respectively. (A) "chicc--ppciffe place cell sequences. Cells are categorized into ftt-choicc-preferring (top), right-choice-prfeente
(middle), and non-preferring (boltom) based on the significance of mutual information; within each row, cells are sorted by peak activities the respective neurons of preferred choices. (B) Firing fields of place cells in accumulated evidence space, sorted by the positions of peak activities.
peak activity positions. To ensure a fair comparison, we analyze our models using the same approach, computing the mutual information (see Appendix B) between each cell's activity and the agent's position during left- and right-choice trials, and comparing these results to a shuffled dataset for their significance. Our analysis illustrates that only joint in- tegration models (M3, M5) have a subset of place cells that are choice-specte speccccc under this metric (Fig 5, A3; Fig 9, B), closely matching experimental observations (Fig 5, A1). In contrast, the disjoint integration model does not exhibit choice-specific place cell sequences (Fig 5, A2).
ables form visually separable clusters in low-dimensional principal component (PC) space. The presence of such low- dimensional representations would provide insight into the functional roles of specific brain regions and the computa- tional strategies employed by different model variants.
We showed that only the joint integration model with an activated LEC pathway (M5) exhibits distinct, visually sep- arable clusters of hippocampal activity in PC space for both position (Fig 6, B1) and local evidence velocity (#R-#L towers at a position, Fig B2). This contrasts sharply with other model variants (Figs 6, A1, A2, and Appendix E). Interestingly, we did not observe separability in accumu- lated evidence within the first three PCs of hippocampal activity. This is counterintuitive, given that grid cells en- code and communicate accumulated evidence to the HPC. Since hippocampal neurons are projection neurons (Fox Ranck Jr, 1975; 1981), the source and encoding mecha- nism of local evidence velocity in the HPC warrant further investigation. Future studies could analyze existing exper- imental data to validate the predicted hippocampal role in representing local evidence velocity and conduct ablation studies using the proposed model to understand the under- lying mechanisms. Together, these findings underscore the importance of sensory inputs from the LEC in generating cohesive, -iw-eeenniional representations of task variables in the hippocampus, which are critical for efficient learning and spatial navigation (Fig 3).
Place cells form firing fields in evidence space Similarly, we measure the mutual information between accumulated evidence and the neural activity of each place cell. As ex- pected, when grid cells encode evidence, place cells then form firing fields in evidence space, spanning small seg- ments of evidence values, consistent with Fig 4, left. Con- versely, place cells fail to form evidence fields in models MI and M2, where evidence information is either absent or originates from the LEC instead of MEC (see Appendix D).
5.3. Only Joint Integration Model With Activated EC Pathway Exhibits Well-Separated Low-Dimenne Dimensional Co-representation of Task Variables
We performed Principal Component Analysis (PCA) on hip- pocampal and cortical activities to assess whether task vari-
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A
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Figure 6. Separability of hippocampal (column 1, 2) and cortical representations (column 3, 4) in low-dimensional PC space in M4 (row A) and M5 (row B). Joint grid cell code with activated EC-HPC pathway (M5) uniquely Icads to separable, low-dimensional hippocampal representations when colored by position (B1) and local evidence velocity (#R-#L per position, B2). We did not observe other separable task variables in the first PCs of hippocampal activities in all variants (Appendix E). We observe the separability of actions in hippocampal and cortical activities in PC space in both M4 and M5 (columns 3 and 4). The gray lines indicate the trace of temporal trajectories.
6. Discussion
ablating models M1-M5 to test the computational roles of CA3 recurrence and other mechanisms. Concurrently, we are collecting neurophysiological data to directly test our falsifiable predictions and assess whether CA3 recurrence further refines hippocampal place cell tuning.
Our work predicts that grid cells jointly encode spatial and task-relevant information, and that this conjunctive coding, along with LEC sensory input to the hippocampus, facili- tates efficient decision-making in spatial contexts. More- over, our findings indicate that conjunctive grid coding is essential for replicating experimental results observed in Nich et al. (2021), offering new insight into the prevailing view that grid cells primarily support spatial representa- tions (Moser et al., 2008).
Taken together, our findings demonstrate that conjunctive grid coding is fundamental to spatially embedded decision- making, supporting the hypothesis (Buzsáki & Moser, 2013) that spatial and cognitive processes are deeply intercon- nected within the brain's 's navigation and memory systems More broadly, neural algorithms that support path inte- gration and spatial navigation may be repurposed for ab- stract cognitive functions, suggesting that the hippocampal- entorhinal network facilitates both physical navigation and decision-making based on internal cognitive states.
We derive this prediction by proposing and testing counter- factual neural codes and information flow in variants of our multi-region brain models, which integrate a prestructured entorhinal- hippooaaappppp circuit (Chandra et al., 2025) with cortical action-selecting recurrent neural network (RNN). These models evaluated based their task performance and hippocampal representations in the accumulating tower task (Nieh et al., 2021), formulated as RI. problem.
In conclusion, we presented a comprehensive testhed for exploring how the pappocampal-entorhinall-aaa work integrates physical and cognitive information to build flexible neural representations that facilitate learning, decision and navigation. This framework provides foundation for future wet lab studies to test clear, falsifi- able predictions while minimizing reliance on invasive and resource-intensive animal experiments, offering a platform to investigate the links between physical navigation and ab- stract cognitive processes. Furthermore, highlights the mutual benefits of integrating machine learning and neuro- science in advancing our understanding of neural phenom- ena and guiding future research. This synergy underscores the transformative potential of neuro-inspired artificial intel- ligence.
net-
While the CA3 region of the hippocampus is known to ex- hibit recurrent dynamics (Sammons et al., 2024), we follow Chandra et al. (2025) in assuming, based on anatomical evidence (Donato et al., 2017), that structured, input-driven coding in the MEC plays primary role, as it matures first and drives the development of hippocampal circuits. In Appendix F. we test variants of models M2 and M4 incor- porating CA3 recurrence and find that this modification neither reproduces the experimentally observed conjunctive hippocampal code in Nieh et al. (2021) nor alters the con- clusions drawn in the main paper. Building on these results, future studies could extend our framework by systematically
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
Acknowledgments
brain activity during accumulation of sensory evidence and decision commitment. bioRxiv, pp. 1024-08, 2024.
lla Fiete supported by the Office of Naval Research, the Howard Hughes Medical Institute (HHMI, and NIH (9M4H)))9904)). Carlos Brody and David Tank are sup- ported by NIH (U19NS132720). We are grateful to Dr. Sarthak Chandra, Dr. Manuel Schottdorf, and the BRAIN CoGS community for their many insightful discussions. We appreciate the constructive feedback received during our presentations preliminary results at the 2024 Conference on Cognitive Computational Neuroscience and the 2025 Society for Neuroscience annual meeting.
Bostock, E., Muller, R. U., and Kubic, J. L. Experience- dependent modifications of hippocampal place cell firing. Hippocampus, 1():1193-205 1991.
Brown, L. S., Cho, J. R., Bolkan, S. S., Nieh, E. H., Schottdorf, M., Tank, D. W., Brody, C. D.. Witten, I. B., and Goldman, M. S. Neural circuit models for evi- dence accumulation through choice-selective sequences. bioRxiv, 2024. doi: 1111101/2023.00.01.5555
Burak, Y. and Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLoS computational biology, 5(2)e1000221, 2009.
Impact Statement
This work advances both machine learning and neuroscience by presenting a biologically plausible multi-region brain model as computational framework for studying decision- making in spatial contexts in mammals. The model is testbed for hypothesis generation, offering an efficient way to explore neural mechanisms, such as the role of conjunc- tive coding in hippocampallentoohinaa circuits, that are dif- ficult to measure experimentally. By reducing the need for invasive or rssource-intensin experiments, our approach has the potential to accelerate neuroscience discovery while minimizing unnecessary animal studies. Additionally, the structured neural architectures studied in this work may in- form the design of more robust and interpretable machine learning systems that leverage biological principles for real- world decision-man making tasks.
Buzsáki, G. and Moser, E. I. Memory, navigation and theta rhythm in the hippocampal-entorhinad system. Nature neuroscience, 16(2):130-138, 2013.
Canto, C. B., Wouterlood, F. G., and Witter, M. P. What does the anatomical organization of the entorhinal cortex tell us? Neural plasticity, (1:38(1) 2008
Chandra, S., Sharma, S., Chaudhuri, R., and Ficte, I. Episodic and associative memory from spatial scaffolds in the hippocampus. Nature, pp. 1-13, 2025.
DeAngelis, G. C. and Angelaki, D. E. Visual-vestibular integration for self-motion perception. In Murray, M. and Wallace, M. (eds.), The Neural Bases of Multisensory Processes, chapter 31. CRC Press/Taylor & Francis, Boca Raton, FL, 2012.
This work contributes to advancing the fundamental under- standing of the brain and bridging the gap between neuro- science and machine learning. We do not foresee significant negative societal impacts from this research.
Donato, F., Jacobsen, R. I., Moser, M.-B., and Moser, E. I. Stellate cells drive maturation of the entorhinal- hippocampal circuit. Science, (55(6330) 2017.
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Appendix
A. Experimental Details
A.I. Model
For models MI-M5, we use three grid modules with periodicities of 7, 8, and 11, esulting in grid cell layer dimension of N₂ 234 (= 7 + 8 + 11?). We simulate 800 hippocampal cells. Both the MLP and RNN models have learning rate of 0.0005 and hidden size of 32. The RNN consists of leaky units with a 0.025.
The grid coding scheme is hand-designed to test the counterfactual of joint versus disjoint coding, as illustrated in Fig. IC. In general, velocity inputs update the phases of each grid module via path integration, following the Vector-HaSH implementation from Chandra et al. (2025). Evidence velocity for the grid cell modules is computed as the difference between the number of towers on the right and the number on the left at the current position. This is predicted through an MLP based on the current field of view (sensory inputs). Positional velocity, in contrast, represented as either 0 (stationary) or +1 (forward movement), without an MLP, as backward movement is not task-relevant (Nich et al. (2021), behavioral training). While an MLP could be used for positional velocity, we opted for simplified approach since this modification does not affect the results.
For the two standalone RNN baselines (MO and M0+), we scale up the hidden size to 32 + N₂ + Nrp + NN = 1076 to match the total number of neurons used in M1-M5. The input to these RNN baselines consists of sensory information. The MO+ variant additionally incorporates positional velocity (whether the agent has moved) and evidence velocity (predicted by an MLP with the same setup as in MI-M5). We use a learning rate of 0.0001 with gradient clipping to maximum norm of 1. This adjustment was necessary because the large standalone RNNs failed to train with the 0.0005 learning rate used in MI-M5 due to learning instabilities (e.g., exploding or vanishing gradients). To address this, we conducted hyperparameter search and selected the settings that produced the best performance.
A.2. Environment
The accumulating tower task consists of agent navigating T-maze with towers positioned on both sides (Fig. 1C). The agent must decide which direction to turn at the end of the corridor, aiming to turn toward the side with more towers to receive reward. The maze is divided into distinct regions: a start region (9% of the total length) with no towers, a cue region (61%) containing towers, and a delay and decision region (the remaining portion) without towers. This structure aligns approximately with the division used in Nieh et al. (2021). Each episode presents a unique configuration of towers, requiring the agent to traverse the corridor step by step before reaching the T-junction and making a decision. The left and right sides of the maze are encoded as vectors, where a value of 1 represents a tower, 0 indicates an empty position, and 1 denotes areas outside the maze. The agent has limited field of view that allows it to perceive a certain number of positions ahead.
In each episode, the rewarded side (i.e., the side with more towers) is chosen uniformly at random, with the number of towers on that side, Treward. is sampled from Uniform(1, [1, K), where K is the maximum allowable number of towers. The non non-rewarded side contains strictly fewer towers, with its count znon-reward drawn from Uniform(O, xooward) At each step, the agent can take one of three possible actions: left (0), rith (1), or forward rd (2). Before reaching the T-junction, the agent receives small reward of 0.01 for moving forward and a penalty of -0.001 for any other action. Once the end of the maze, it receives a reward of 10 for making the correct turn, reward for choosing the wrong direction, and penalty of -1 for attempting to move forward and colliding with the wall. The episode ends when the agent turns or reaches the maximum number of decision attempts, the latter incurring an additional penalty of -5. For this study, we set the maze sequence length to 20, dividing the start, cue, delay, and decision regions into segments of length {1, 12, 6, 1), respectively. The agent has field of view spanning five positions. Training is conducted using the REINFORCE algorithm (policy gradient) (Sutton et al., 1999) until convergence.
A.3. Single step in the task
Each step in the accumulating tower task follows a structured sequence (Fig. 1C). First, the agent perceives sensory information from its field of view. This information processed by an MIP,, which extracts an estimate of evidence velocity. The evidence velocity, along with position velocity, is then used to update the grid cell state through path integration. The updated grid representation is projected onto the hippocampal layer, alongside the non-grid sensory input, forming the
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
agent's internal state representation. The hippocampal code is then passed the cortical RNN policy, which selects an action-movinng left, right, forward. Once an action is executed, the agent's position is updated accordingly. This new position brings in fresh sensory input, which is implicidly processed by the grid cell subnetwork to update the grid state. The updated grid state, along with the newly perceived sensory information, is then used to refine the hippocampal representation. This iterative process continues, with the agent repeatedly updating its internal representations and selecting actions, until it reaches the T-junction and makes a final turning decision. The agent's 's behavior is governed by the reward scheme outlined in Appendix A.2.
A.4. Further details on the biological grounding of Vector-HaSH
While the relevant biological groundings of Vector-HaSHs are inherited from and addressed in Chandra et al. (2025), we include summary below on how the model enforces sparsity and spatial selectivity place cells for completeness.
Sparsity As described in the main text, the projection matrix Wng from grid cells to hippocampal (HPC) units is drawn from standard Gaussian distribution, consistent with classical random projection models (see Methods, Chandra et al. (2025)). Due to the symmetry of the distribution, each entry has zero mean, and hence half the activations are expected to be subthreshold. Moreover, each grid module encodes its position using one-hot representation, enforcing input sparsity via inductive bias. Nonlinear gating through ReLU is applied to h (Eqns. 2, 3), further ensuring that only a sparse subset of HPC units are active for given input. Importantly, the number of unique grid states (II: A?) is much smaller than the total number of possible HPC activation patterns (2 As result, only very small subset of HPC units are active for any given grid code, which enforces a highly sparse representation in the hippocampus.
Selectivity To ensure spatial selectivity, each sensory state is associated with a specific grid state. This is implemented by updating the weights W.. and Wsh sh during training, such that the sensory input strongly modulates only a small subset of HPC units. Consequently, each sensory state drives a selective hippocampal code via its associated grid representation, thereby grounding place field formation in both sensory and grid input pathways.
A.5. Continuous-attracton (CAN) update rule in Vector-HaSH
For completeness, here we make explicit the equations that govern the CAN () update used in Eqn. 1 (Burak & Fiete, 2009; Chandra et al., 2025) of the main text. Let g(t) E {0, 1),², denote the concatenated grid-code vector at time t and v(() E {-1,- + the 1-D velocity signal. The CAN step is a velocity-dependent cyclic shift of each grid module, implemented by a block-diagonal shift matrix M(u(t)):
g(t + = CAN(g(t) v(t) M(e(t) 9(t)
(6)
For illustration, consider two one iree-imensional grid modules of periods A = 3 and 222 = 4 (N, = 7). A rightward velocity v = +1 is realized by the block-diagonal matrix U:
Example with two modules (A1 3, A22 4)
0
0
0
0
1 0
M(+1) U
where S
1
S.
S.
1
1
0
0
0 0
leftward step (v = 1) is obtained with M(-1) UT.
Formal definition Let A be the periodicity of module and X₁ = Et / d (with X, = 0) the cumulative offset. For indices i belonging to the same module (Xa-1 i < Xx) we set
f1, 1, if ((-Xx-1) mod dR = (i+ mod AE.
Mij(o)
0, otherwise.
All mross- blocks are zero, making M(U) block-diagonal.
Extension to 2-D For two-dimensional fcetor-HaSHt we apply the same 1-D rule independently to the x- and y-components and construct the full 2-D shift via Kronecker product of the corresponding 1-D shift matrices.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
B. Mutual information
B.1. Mutual information analysis
We follow the mutual information analysis in Nich et al. (2021). Here we reiterate this procedure for completeness. For each neuron, we evaluate the mutual information metric defined in Skaggs al. (1992),
Max) I 1= f log2 logg p(x)dd,
in which 7 is the mutual information rate of the neuron in bits per section, x is the spatial location (or accumulated evidence) of the agent, A(r) is the mean firing rate of the neuron at location (accumulated evidence) x, p(z) is the probability density of the agent occupying location (accumulated evidence) x and = J. ((x)p(z)dz is the overall mean firing activity the neuron.
B.2. Scatterplots of mutual information
A1
M1
A2
M2
A3
M3
A4
M4
A5
M5
EXRx
EXR,
EX Rx
EXR.
EX
0
EXY
EXY
EXY
2
EXY
ExY
A1
A2
A3
A4
A5
R Y
RXY Y
XXY
XXY
X
RE
0
EXY
EXY
EXY
ExY
EXY
Figure 7. Scatterplots of the hippocampal mutual information in E x Ry space versus E x Y space (top row), and scatterplots of mutual information in Rg space versus E Y space (bottom row). We show data for all model variants MI to E respectively. We observe evidence and position interact to provide meaningful information in M3. M4, and M5 (when grid cells co-tune position and evidence). while MI and M2 rely on information of position (when grid cells tune evidence only, and there either no some sensory information projected into the hippocampus). Here, Ry is randomized position, generated by randomly sampling from distribution corresponds to the non-randomized E value Rg Y variables. More details of the procedure are described in the Mutual Information Analysis section of Nieh et al. (2021).
the order of panel
cell. similar procedure performed generating the
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
C. Hippocampal firing fields within E x Y space in model variants
A
Example ExY fields in M1
Position
Position
Position
Evidence
Evidence
Evidence
B
Example ExY fields in M2
19
19.
Position
Position
Position
Evidence
Evidence
Evidence
C
Example ExY fields in M3
Posttion
Position
Position
0
Evidence
Evidence
Evidence
D
Example ExY fields in M4
19
19
Position 19
Position
Position
0s
Evidence
Evidence
Evidence
E
Example ExY fields in M5
19
15
19
Positonn
Position
Position
Evidence
Evidence
Evidence
Figure Example hippocampal firing fields space (A), (B), (C), (D), (E), We observe that the firing fields of MI and M2 (A, B) do not depend evidence with stripe patterns. M2 firing fields occasionally have some amount of gradient, potential artifact of sensory injection, similar firing fields M4 (D. E). (C) firing fields exhibit conjoint tuning position and evidence and have apparent gradient artifacts.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Secision-Making
D. Hippocampal evidence and place fields in model variants
A1
A2
A3
B
L-choice
R-choice Cue period
Nomolized averge actiitty
Normalized overgge sctiviyy
Normal zed averige.ativityy
Cue period
Delay
Delay
Left
100
100
100
Neuron preference
200
Neuron
Neuron
Neuron
Right
500
49
None
Evidence
Evidence
Position
Position
Figure 9. Hippocampal firing fields evidence (A) and in space (B), for M1 (AI), M2 (A2), and M3 (A3, B). We see MI and M2 do not have firing fields in evidence (A1, A2), while M3 does (A3). Furthermore, M3 contains choice-specific place fields (B) similar M4 (Fig 5, A3), implying that joint tuning of position and evidence in grid cells key to forming a conjoint hippocampal map.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Makingg
E. HPC and RNN PC representation in model variants
A1 Place (M1): position
A2
Place cells [M1]; local velocity (*R-0L)
A3
Place cells (M1); action
A4
RNN states (M1): action
B1
Place cells (M2):
B2
Place cells (M2): velocity
B3
action
B4
(#R-PL)
2
PC3
C1
Place cells [M3]:
C2
Place cells (M3); local valocity (AR-aL)
C3
(M3): action
C4
states (M3): action
Figure 10. Low-dimensional representation of hippocampal and RNN activities PC space, shown for MI (row A), M2 (row B), M3 (row C). We show the representations colored according to selective task variables, specifically position, local evidence velocity, and action, in which M4 shows clear separation (in correspondence to Fig 6). Other variables visualized HPC and RNN activity PC space include accumulated evidence, position changes, left-/right-choice trials, total evidence of the trial, and ground truth action; we observe no visual separation.
A1
B1
C1
D1
E1
M1
M2
M3
M4
M5'
Cum, Eoo
Cim Vir. Exctiieed
Onm VIA Scolured
A2
Number of PCS
B2
Number PCS
C2
Number of PCS
D2
Number of PCS
E2
Number of PCS
Place calls (M1))
Place cells (M2)
Place cells (M31)
Place colls (M4):
Place cells (MS+))
PC3
P33
PC3
P3
PC2
PC2
PC2
PC
PC2
PCL
PC1
PC1
Figure 11. Cumulative variance explained percentage of hippocampal (orange) and RNN (blue) activities, by the number of principle components (PCs), and low -iwddimenioonal representations of hippocampal activities in PC space, colored by accumulated evidence, shown for MI (column A), M2 (column B), M3 (column C), M4 (column D), and MS (column E). The first two PCs MS explained the most amount of variance in hippocampal representations (68%) in comparison to other model variants. We do not observe any visual separability of accumulated evidence in the PC space of the first three PCs, as shown the second row.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
F. Effect of CA3 Recurrence in M2 & M4
In this section, we demonstrate in M2 and M4, as proof of concept, that the inclusion of CA3 recurrent connectivity the HPC layer does not affect the general conclusions presented in the main paper. Specifically, the inclusion of CA3 recurrence in M2 or M4 does not induce the experimentally observed place cell phenomena (Nich al., 2021), producing similar results as if recurrence was absent (see Figs 4, 4, 7, 8, and 9).
To model CA3 recurrence, we incorporate additional recurrent connections within the HPC layer, W ah. updated through hebbian-like associative learning using (t) and hmix (t + 1), analogous to the learning update for Whs and Wah sh (see Eqns. and 5). The activity of mixed hippocampal cells is then described by:
mimix (1 + 1) = ReLU s(() + Whg Ø(l + 1) W /imix (4)]
(8)
The rest of the setup remains consistent with Appendix A.I. The above changes would be the same for models with Phonmix (t) and Anommix (t + 1).
As shown in Fig. 12, the inclusion of the recurrent integration of positional information from MEC and sensory information from non-grid EC does not result in the emergence of conjunctive place cells in M2. Similarly, Fig. 13 shows that the lack of conjunctive place cells in M4 persists when the grid cell modules encode position and evidence disjointly.
These findings confirm that the recurrent integration HPC alone does not induce conjunctive coding, underscoring the critical role of joint integration of position and evidence in grid cells for producing co-tuned place cells.
A
Example ExY fields in M2 with CA3 recurrence
C
Place cell evi. fields under M2 w/ CA3 recurrence
Normalized average activity
Position
Position
Position
100
Evidence
Evidence
Evidence
300
B1
B2
Neuron
9
9
500
Ex Ry
Re Y
700
0
-5
ExY
E Y
Evidence
Figure 12. Analysis of hippocampal code in M2 with CA3 recurrence. (A) Example hippocampal firing fields in E Y space. (B) Scatterplots of the hippocampal mutual information in M2 with CA3 recurrence when only the position is randomized (B1), 1, and when only the evidence randomized. The model shows higher mutual information in position only. See the caption of Fig B.2 for implementation details. (C) Hippocampal firing fields in evidence in M2 with CA3 recurrence.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
A
Example ExY fields in M4 with CA3 recurrence
19
19
Positon
Position
Position
-5
0 Evidence
-5
Evidence
Evidence
B1
B2
C
Place cell evi. fields under w/ CA3 recurrence
E Ry
REX
Normalized average activity
EXY
EXY
100
Place fields under M4 w/ CA3 recurrence
D
L-choice trials
R-choice trials
Cue period Delay
Cue period Delay
300
Neuron
Neuron preference Left
500
Right
700
-5
0 Evidence
None
100
Position
Position
Figure 13.. Analysis of hippocampal code in M4 with CA3 recurrence.(A) Example hippocampal firing fields in Y space. (B) Scatterplots of the hippocampal mutual information in M4 with CA3 recurrence when only the position is randomized (B 1), and when only the evidence is randomized. The model shows higher mutual information both position and evidence, consistent with the case when the recurrence is not considered (Fig B.2, column D). See the caption of Fig B.2 for implementation details. (C) Hippocampal firing fields evidence in M4 with CA3 recurrence. We observe evidence fields. (D) Hippocampal firing fields space. We do not observe choice-specifis place fields shown in Nieh et al. (2021) after considering the CA3 recurrence in M4.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
G. Learning Performance Under Hyperparameter Tuning
To evaluate the impact of hyperparameter choices on model learning, we conducted a sweep over learning rates (LR) for all models, including [5e-5, 1e-4, 5e-4, 1e- 1e-3]. except when specific learning rate was already selected in the main text, in which case we retained without sweeping to ensure consistency with the main text. The performance curves with hyperparameter tuning results visualized in Fig. 14.
Table 3 reports the mean final success rate and average exploration time (measured at the last 100 episodes across three independent trials), formatted as: success [8] = standard deviation / steps per episode + standard deviation. The best-performing metrics for each model are highlighted in bold.
Table success rate standard deviation and mean exploration time + standard deviation across trials over the last 100 out 17400 episodes. Only the best success rate and lowest exploration time per model are in bold. The maximum number of steps allowed per episode is 200 steps. Our final model, M5, fairly robust to learning rates as shown.
LR
MO
M
M1
M2
M3
M4
M5
Success (%)
19.33
72.00=4497
49.33+2.7
50.33+4.19
95.67=2.05
93.67
95.00=1.63
5e-5
Steps/ep.
31.23
27.94.1.220
24.77.0..6
21.33
28.9110..
26.09 11.6
25.71 1:0700
Success (%)
68.67:15:46
81.67::4.03
47.33
49.00#3.56
97.00=2.45
99.33=
99.00=
1e-4
Steps/ep.
1..22:11.6
22.95.1.118
23.974081
23.01 #0.66
1.48
25.52
27.65
Success (%)
8.00
0.00.10.00
51.33
49.001..45
9..33
76.67116.53
97.00
5e-4
Steps/ep.
193.48+9.22
200.00+0.000
23.31+0038
29, 19.14
23.34=0077
28.02#6.18
19.70=0.22
Success (%)
0.00
12.33
51.67
51.67.4.11
67.33
13.33
90.00
1e-3
Steps/ep.
200.00
193.36.19.99
25.81
24.86+2.11
33.7 13349
28.79 44.02
30.74
Across models, we observe that the chosen hyperparameters in the main text (le-4 for MO and MO; 5e-4 for M1-M5) generally yielded near-optimal performance. For M4, LR of le-4 mitigated instability noted in the main paper's Fig. 3. This updated choice is applied to generate Fig. 14.
Conclusion Although learning rate tuning helped stabilize M4, none of these modifications altered the qualitative conclusions or key claims presented in the main paper. Section 5.1 observations regarding learning efficiency and rapid exploration in M5 remain unchanged.
A
B
Cum, success rate in training
Steps spent per episode in training
Cumulative Success Rate (96)
100
Exploration Time (steps/episood
MO: RNN w/ sensory sensory.
90
40
pos. vel. & evi. vel.
80
35-
pos. only g, nonmix p pos. only 9,
M3: joint nonmix
M4: disjoint mix
60
25
M5: joint mix p
Randem chance in
20
Expected #steps in
100
17400
100
17300
Episode
Episode
Figure 14. Updated Fig. 3 with optimized learning rate for each model, with a change using a learning rate of 1e-4 4 for M4. The rest remains consistent with Fig. 3, and this does not alter claims made in the paper. The moving average setup is same as Fig. 3. including the window sizes used (5, 000 for A and 10, 000 for B) and the exclusion of the first 100 episodes.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
H. Results for Controlling Trainable Parameter Count in RNN Baselines
Here we provide additional ablations of the RNN baselines (MO and M0+) to address whether the later-onset performance of MO and M0+ might simply reflect a larger number of weights to optimize. We conclude that the performance RNN baselines with the same number of parameters M5, with or without additional velocity input, does not alter the conclusions drawn in the main paper.
Parameter formula For a vanilla RNN with input dimension I, hidden dimension H, and output dimension O, the total number of back-prop-trainable parameters, including biases, is
#params
(TH HH H)
= H² + H(I+0+1) + O. (9)
input & recurrent weights hidden bios
output weights output bias
Matching MO or MO+ M5
Model M5 (with an RNN of input size = 800, hidden size HM = 32, output size = 3)
contains
#params A15 26 755.
Solving Eq. (9) for H with mini Mp 10 and mini MO-
12, well as the same O = 3 yields
Mmini-Mo 2 158,
Hmini-Mo+ s 157,
so that the mini versions of MO and MO+ have the same order of trainable parameters as M5.
Control experiment We trained these mini- mini-models for three independent trials (learning rate 10-5). Figure 15 shows their learning curves alongside the original MO/M0+ and M5. The qualitative conclusion of the main paper is unchanged: even when parameter counts are matched, MO and MO+ still lag behind M5 in both learning speed and final performance.
A
Cum. success rate in training
Steps spent per episode training
Cumulative Success Rate (%)
100
Exploration Time steps/eplsode
45
80
mini-MO+: RNN sensory
mini-M0: RNN w/ sensory
80
35
MO: RNN w/ sensory
MO+: RNN sensory. pos. vel. & evi. vel.
70
30
M5: joint g, mix
60
25
Random chance In Expected #steps in
50
20
100
17400
100
17400
Episode
Episode
Figure 15. Parameter count alone does explain performance differences. Learning curves for parameter-matchhd mini-MO and MOni-MO+ (red and orange), compared with the original MO (blue), MU+ (black), and M5 (brown). (A) Cumulative success rate during training. (B) Steps spent per episode (exploration time). The plotting setup and color conventions match Fig.
Additional learning-rate sweeps We further trained the mini-models under alternative learning rates 31e-3,5e 5e -, 53. The supplementary results (see Fig. 16) likewise show no qualitative change, reinforcing that parameter count alone does not explain the performance gap.
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
A1
B1
Cum, success rate in training
Steps spent per episode in training
Cumulative Success Rate (96
100
45
Exploration Time (steps/eplson)
LR=1e-3
90
40
mini-M0+: RNN w/ sensory
mini MO: RNN w/ sensory
MO: RNN w/ sensory
MO+: RNN w/ sensory.
30
pos. vel. & evi. vel.
MS: joint g. mix
60
25
Random chance in A Expected #steps
20
100
17400
100
17400
Episode
Episode
A2
B2
Cum. success rate in training
Steps spent episode in training
Cumulative Success Rate (%)
100
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45
LR=5e-4
40
mini-M0+: RNN w/ sensory
mini-MO: RNN w/ sensory
80
35
MO: RNN w/ sensory
MD+: RNN w/ sensory. pos. vel. evi. vel.
30
M5: joint g,
25
Random chance A
Expected #steps
50
20
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17400
Episode
Episode
A3
B3
Cum. success rate In training
Steps spent episode in training
Curulative Success Rate (96)
100
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45
LR=5e-5
40
mini-MO+: RNN w/ sensory
mini-MO: RNN sensory
80
35
MO: RNN w/ sensory
M0+: RNN w/ sensory, pos. vel. evi. vel.
70
30
M5: joint g,
60
25
Random chance A
Expected #steps
50
100
17400
Episode
Episode
Figure 16. Mini-models consistently underperform across learning rates. Additional learning curves for serameter-matched mini-MO and mini-MO+ trained with varying learning rates. (A) Cumulative success and (B) exploration time for mini-MO and mini-MO+ (red and orange), which have approximately the same number of trainable parameters as M5 (brown). Original MO and M0+ (blue and black) shown for comparison. The plotting format and color scheme follow Fig. 3. Each corresponds to different learning used for the mini-models, indicated above the legend: 1c-3 (top), 5c-4 4 (middle), and 5e-5 (bottom).
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A Multi-Region Brain Model to Elucidate the Role of Hippocampus in Spatially Embedded Decision-Making
I. Effect of smoothing on HPC tuning visualization
Here we provide additional clarification and visual evidence regarding the appearance conjunctive tuning in the hippocam- pus neurons, particularly in models M4 and M5.
It noted that the tuning curves shown in Fig. 4 appear weaker and more diffuse than those observed in Nich al. (2021). However, here show that this difference can largely be attributed to differences in preprocessing and visualization- particularly the use of smoothing.
Smoothing improves the appearance of conjunctive tuning Smoothing neural data is a fairly standard procedure empirically, which is done in both Nieh et (2021) and Chandra al. (2025). When we apply smoothing procedures, the tuning curves become substantially more localized and stereotyped. Specifically, we follow the 2-stage filtering process described in Nieh et al. (2021):
1. Apply ID Gaussian filter with standard deviation 01.
2. Threshold the result by zeroing all values below fixed multiple of the standard deviation across time.
3. Apply second ID Gaussian filter with d2.
We show examples of tuning curves after smoothing in selected HPC units from models M4 and M5 in Fig. 17. As anticipated, smoothing reveals structure that is otherwise obscured, making the tuning appear more consistent with findings reported in experimental work, such as Nich et al. (2021).
2
Neuron A
Neuron
Neuron A
Neuron B
19
19
Position
M5
E4
42
0
Neuron C
Neuron
Neuron
19
19
19
19
00
M4
Positio
04
Evidence
Figure 17. Smoothing enhances visualization of conjunctive tuning. Tuning curves from selected hippocampal neurons in M5 (top row) (bottom row) after applying a two-stage smoothing and thresholding procedure. Each row shows two example neurons (A, B in M5; C, D in M4), with each neuron visualized under 1, then two different levels of secondary smoothing: 1 (left two columns) and du = 2 (right two columns). Increased d2 leads to more diffuse but still conjunctive tuning. Smoothing reveals structure that is less apparent in raw activity and produces hippocampal fields more consistent with experimental observations.
Relation to overall findings While smoothing improves the interpretability of individual neuron tuning curves, our broader conclusions regarding conjunctive representations are supported by quantitative measures such as mutual information (Appendix. B.2) and the presence of both place fields and evidence fields in HPC (Figs 5, 9). Thus, the visual appearance of raw tuning curves does not reflect a fundamental limitation of the model, but rather a visualization artifact that can be addressed through appropriate preprocessing.
25


Reviews:
[{"review_id": "SpuvfRWkVf", "reviewer": "Reviewer_c3tv", "summary": "This paper aims at providing a mechanistic characterisation of how sensory and abstract (task-dependent) information is encoded and transmitted across different brain regions, including the hippocampus (HPC), medial and lateral entorhinal cortex (mEC and lEC), and the cortical circuity. The authors specifically focus on explaining the data reported in Nieh et al., 2021, which is an decision-making task based on sensory evidence accumulation under the spatial context. The model is largely based on the existing Vector-HASH+ model (Chandra et al., 2025), but with the additional cortex component (represented by an RNN) that takes in the hippocampus readout and map into actions. Several variants of the baseline Vector-HASH model are proposed, underlying different candidate intra- and inter-circuitry mechanisms. The authors then trained the models on the abstracted version of the towering task from Nieh et al., 2021, and show that post-training, the place cells indeed exhibit selectivity with respect to spatial location and sensory evidence. They also show that the sensory and task information are only well-separated in one specific circuitry configuration, and making predictions for the mEC-HPC circuitry.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We deeply appreciate the reviewer’s precious time & comprehensive feedback. We sincerely thank them for recognizing the significance & clarity of our work. The reviewer raised questions on the support for our claims, method novelty, and the biological grounding of models. Here we clarify with the relevant content in the paper. **Together with the discussion below, does this address the reviewer’s concerns?**\n\n> The model is largely an adoption of the Vector-HASH+... I do find the neural predictions and hypotheses interesting, but…limited in terms of methodological novelty.\n\nThanks for acknowledging our findings. The architecture is based on Vector-HaSH (VH, Chandra et al., Nature, 2025), but **the “+” part is our original development (lines 215-218)**. We emphasize our application-driven work is among the first to apply VH systematically, with appropriate adaptation (e.g., the “+” part), to understand spatial decision-making w/ experimentally verifiable predictions. Similar studies exist w/ RNNs but lack the necessary bio details in modeling multi-region circuits.\n\n> ...I accredit the authors' mechanistic attempt, but I personally find many claims made in the paper to be ungrounded, and no sufficient ablations exist to support... \n\nOur M1-M5 are ablations of multiple hypothesized multi-region interactions. We refer to VH (Chandra et al., 2025) for the detailed bio grounding as they’ve substantially addressed them. We ensured further claims are supported w/ evidence. We address below the reviewer's specific concern on the sensory criticality claim, but happy to elaborate on other claims if needed:\n\n> The authors make claims about the criticality of sensory inputs from lEC in driving efficient learning and spatial navigation. However, I cannot draw such conclusion from Fig 5. The lack of qualitative comparison with M3…undermines the validility of the authors' claim.\n\nThe sensory criticality claim is made for efficient navigation & low-d representation, **not** for learning. The navigation aspect is evident in Fig 2B (M3 vs M5) & lines 304-314; low-d representation aspect is in Fig 5, w/ M3 in Appendix E, referred to in line 413. Joint grid code is critical to efficient learning (M3 & M5 in Fig 2A, lines 299-303).\n\n> The authors assumes direct projections from lEC and mEC consistutes the firing of place cells. How could the authors enforce sparsity and spatial selectivity in place cells? \n\nRelevant bio groundings are inherited from & addressed in VH (Fig 6 in Chandra et al., 2025), so we didn’t reiterate. We'll include these details in the appendix:\n\n**Sparsity:** Per line 200, $W_{hg}$ is a random projection matrix generated by *standard Gaussian distribution* (Method in Chandra et al. (2025)), so half of the activation is 0 on expectation. The input is sparse as the firing of each grid module is one-hot per model inductive bias (line 208).  ReLU is applied to `h` (eqns 2 & 3) to also enforce sparsity.\n\nThe number of unique grid states ($\\prod \\lambda^2_i$) is much smaller than the number of unique activated HPC states ($2^{N_h}$), so only a small number of HPC cells are >0.\n\n**Selectivity:** Each sensory state is associated w/ a specific grid state by updating $W_{hs}, W_{sh}$, so each sensory state is only associated with certain HPC states.\n\n> …M0 and M0+ models do not yield good performance could due to poor implementation of the recurrent structure. I can imagine a recurrent networks designed for temporal integration…will be able to perform the task whilst not requiring the complicated EC-HPC network...think this is an unfair comparison...\n\nVanilla RNN is fairly powerful & extensively studied, e.g., Yang et al., Nat Neurosci, 2019 & Driscoll et al., Nat Neurosci, 2024 applied RNNs to NeuroGym tasks with temporal components. \n\nAnd, our goal is to assess the added value of the structured EC-HPC networks, not to benchmark arbitrary network classes; changing the recurrent structure of baselines necessitates changing M1-M5’s RNN for fair comparison. This would be unnecessary and defeat the purpose of isolating the inductive bias introduced by EC-HPC circuits.\n\nOur work highlights the utility of leveraging VH as a **hypothesis-generating testbed** to study the entorhinal-hippocampal-cortical network. A task-optimized recurrent structure misses the necessary bio details.\n\n > ...useful to apply the model to other tasks…validity of the model...two-armed bandit...\n\nThe validity of the model is grounded in Chandra et al. (2025), and we emphasize the depth, not breadth, of results since\n1. Our scope is spatially embedded decision-making with phenomena specific to HPC & related circuits. e.g., two-armed bandit task doesn't study the **spatial aspect** of HPC.\n2. The tower task is justified for many reasons noted in lines 36-63, e.g., `we focus on this task to integrate our findings into a larger cohesive narrative that transcends the inherent scope limitations of stand-alone studies on arbitrarily chosen tasks`.", "claims_and_evidence": "The paper is quite well-written, with comprehensive citations to relevant literature. \n\nSome claims made by the authors are ungrounded and questionable, I list them and some general comments/questions below.\n\n- The authors assumes direct projections from lEC and mEC consistutes the firing of place cells. How could the authors enforce sparsity and spatial selectivity in place cells then? I do not see a mechanistic explanation for the necessary occurrence of place fields. I think the missing of inductive biases in constructing the place cells limits the capability of the model for predictions beyond those already presented in Nieh et al. 2021.\n- The fact that M0 and  M0+ models do not yield good performance could due to poor implementation of the recurrent structure. I can imagine a recurrent networks designed for temporal integration (e.g., those used for explaining drift diffusion) will be able to perform the task whilst not requiring the complicated EC-HPC network. I hence think this is an unfair comparison and statement to make.\n- The authors make claims about the criticality of sensory inputs from lEC in driving efficient learning and spatial navigation. However, I cannot draw such conclusion from Figure 5. The lack of qualitative comparison with M3, the model that yields similar performance in the decision making task as the M5 model, undermines the validility of the authors' claim.\n- The model is largely an adoption of the Vector-HASH+ under a simple RL setting. I do find the neural predictions and hypotheses interesting, but the paper is limited in terms of methodological novelty.\n- It would be useful to apply the model to other tasks to substantiate the validity of the model, such as the two-armed bandit task from Mishchanchuk et al., 2024.\n\nOverall, I accredit the authors' mechanistic attempt, but I personally find many claims made in the paper to be ungrounded, and no sufficient ablations exist to support their claims. Adding on the limited methodological novelty in the paper, I am leaning towards rejection. But I am happy to change my mind should the authors provide compelling empirical support for their claims.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "There is not theoretical claims in the paper.", "experimental_designs_or_analyses": "Yes.", "relation_to_broader_scientific_literature": "The paper proposes a mechanistic model for predicting circuitry configurations across multiple brain regions that lead to cognitive behaviours. I think this is a useful application of the Vector-HASH+ model beyond spatial contexts.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A, see above.", "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": "3XZ3Jwwmqg", "reviewer": "Reviewer_gA4b", "summary": "This work is motivated to implement efficient reinforcement learning (RL) inspired by computation in hippocampus. It develops a multi-region brain model that incorporates hippocampal-entorhinal circuit based on the Vector-HaSH model. It shows a structured, content-addressable associative memory with neural representations is biologically grounded efficient RL solver. It proposes with a variants of models from M0 to M5 with different grid cell and place cell coding strategy, and inputs to the MLPs or RNNs. The results demonstrate joint integration model induces efficient learning, and evidence-position co-tuning in grid cells, how this model's results aligned with current experimental evidence.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer’s precious time and comprehensive feedback. We deeply appreciate their generous recognition of the significance of our work. The reviewer shared an interesting insight regarding comparison with advanced AI models, and had a clarifying question on how our setup and findings compare with the biology. Here we address both. **Together with the discussion below, does this address the reviewer’s questions?**\n\n> One major limitation is that the work is mostly biologically driven, as it claims to an efficient brain-inspired reinforcement learning rule, while it does not directly compare with existing models in artificial intelligence sides.\n\nThanks a lot for the insights, and we agree having some comparison with advanced AI models could be quite interesting to see if brain-inspired models could perform SoTA in the standard machine learning benchmark (e.g, image classification, Atari). However, our main focus is to design a biologically-inspired model that can be applied to explain neuroscience experiments. This objective is aligned with previous neuroscience-application studies that only use simple RNNs as baselines published in top ML venues (e.g., Miller et al., NeurIPS, 2023; Valente et al., NeurIPS, 2022).\n\n> Any model designs do not directly follow biological constraints, or findings are not aligned with experimental discoveries?\n\nWe think the biological constraints can be assessed through \n1. the information flow among regions, and \n2. the representation produced by the model. \n\nWhile there are not sufficient neuroscience experiments (to the best of our knowledge) revealing the exact information flow among regions in the context of spatially-embedded decision-making tasks, M1-M5 are all reasonable hypotheses of (1) given the current neuroscientific understanding (elaborated in Section 4). However, as presented in our paper, M1, M2, M4 did not produce experimentally aligned representations (e.g., Figs 4, 8).\n\n---\n\nMiller et al. \"Cognitive model discovery via disentangled RNNs.\" NeurIPS. 2023.\n\nValente et al. \"Extracting computational mechanisms from neural data using low-rank RNNs.\" NeurIPS. 2022.", "claims_and_evidence": "This work is based on existing Vector-Hash model, and extending its studies to a multi-region brain model across entorhinal, hippocampal and neocortical regions, and systematically exploring the role of joint integration and coding strategy to induce efficient learning. It proposes a variant of models to find the one leads to the most efficient learning (number of episodes taken to converge). It also further checks how the finding from models aligned with existing experimental findings, which presents a very solid study.", "methods_and_evaluation_criteria": "The study is conducted with a task-driven perspective, and evaluates with multiple variants of constraints, to finding alignments between experimental phenomenon, which is orthogonal to the data-driven paradigm, and directly fitting the experimental measured the data, which could also ignore critical components. And only one task has been evaluated in the experiment, this framework could potentially extend to more diverse tasks and settings to achieve a more comprehensive study.", "theoretical_claims": "There are no theoretical proofs or claims.", "experimental_designs_or_analyses": "The soundness/validity of experimental designs have been evaluated, systematic explorations are conducted, and results are solid. One major limitation is that the work is mostly biologically driven, as it claims to an efficient brain-inspired reinforcement learning rule, while it does not directly compare with existing models in artificial intelligence sides.", "relation_to_broader_scientific_literature": "This work has covered sufficient amount of literatures and a comprehensive survey. The study is well grounded.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "As described above, this work introduces a systematic exploration of the computation in hippocampus for decision making with a task-driven perspective, and it delivers interesting results on how a joint integration strategy contributes to efficient learning and aligning with existing experimental discovered phenomenons.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "Any model designs do not directly follow biological constraints, or findings are not aligned with experimental discoveries?", "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": {"ethical_review_concerns": "N/A"}}, {"review_id": "hQQjYCulCV", "reviewer": "Reviewer_QCkJ", "summary": "This paper introduces a series of models to investigate how animal brains may solve the accumulating towers task. Beginning with a simple RNN, the authors add model components until they arrive at extensions of the Vector-HaSH model of the hippocampus that also include a cortical model component. The authors now evaluate the models on their ability to solve the accumulating towers task, but also analyze how the added complexity enable to increased model performance. \n\nThe authors predict that only models that include models that allow conjunctive position-evidence tuning in grid cells exhibit the conjunctive position-evidence hippocampal representations that had been identified earlier experiments in mice.\n\n## update after rebuttal\n\nI have no remaining questions for the authors. I applaud that the authors commit to releasing the code for their experiments, and are putting effort into making their code understandable and useful for other researchers.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for their precious time, and their comprehensive feedback. We deeply appreciate their recognition of the significance and clarity of our work. In summary, the reviewer raised an insight regarding the role of hyperparameters, and made additional comments to help us enhance clarity. We share the hyperparameter tuning results and CAN implementation, which are added to the appendix. **Together with the discussion below, does this address the reviewer’s questions?**\n\n> It would be helpful…how hyperparameters for model training were chosen…A few extra sentences in appendix A.1 should be sufficient.\n> how much would tuned hyperparameters have helped for models that used default hyper parameter configurations?\n\nThank you for attention to this detail. M0 and M0+ used a different learning rate due to gradient issues (line 681). We share the result on hyperparameter tuning on learning rate (LR) [0.001, 5e-4, 1e-4, 5e-5] (here’s an anonymous colored version: https://imgur.com/a/Ve7B3Mo). \n\nThe current set of hyperparameters largely ensures fairly optimized performance, except a slower LR of 1e-4 improves M4 instability in Fig 2. **However, none of them changed the claims made in the paper.** The table includes mean [success rate]/[exploration time] +- sem at the terminating episode across 3 trials. The highest success rate and the lowest exploration time are bolded for each model.\n\n| LR      | M0                             | M0+                            | M1                              | M2                              | M3                              | M4                              | M5                              |\n|--------:|:------------------------------:|:------------------------------:|:-------------------------------:|:-------------------------------:|:-------------------------------:|:-------------------------------:|:-------------------------------:|\n|0.00005  |61.69±9.27/27.49±3.05           |**74.13±5.90**/**24.80±0.22**   |49.98±0.24/24.63±0.68            |**50.34±0.78**/**21.80±0.47**    |93.76±1.28/28.88±0.42            |92.73±3.69/**25.23±0.93**        |95.03±0.50/25.94±0.79            |\n|0.0001   |**67.96±5.65**/**26.65±2.41**   |72.54±1.40/25.13±0.60           |49.75±0.20/25.39±0.56            |50.19±0.21/23.33±0.96            |94.59±2.50/29.11±0.17            |**97.35±0.34**/26.53±0.70         |**97.78±0.55**/27.04±0.67         |\n|0.0005   |0.00±0.00/200.00±0.00           |0.00±0.00/199.99±0.02           |49.99±0.55/**22.92±0.04**        |49.79±0.46/27.66±1.77            |**97.62±0.87**/**22.42±0.04**    |72.13±17.06/25.47±4.11           |97.52±2.40/**19.96±0.22**        |\n|0.001    |0.00±0.00/200.00±0.00           |0.00±0.00/200.00±0.00           |**50.18±0.21**/24.64±0.34        |49.95±0.29/26.67±1.84            |83.86±8.77/32.60±1.13            |55.11±7.09/28.14±1.84            |87.23±12.14/27.48±1.29           |\n\nWe also provide **an updated Fig 2** with the optimized LRs. The changes are a LR of 5e-5 for M0+ and 1e-4 for M4. This **doesn’t alter the conclusion** in Section 5.1 regarding M5’s learning efficiency & fast exploration: https://imgur.com/a/U0OVo2H. **We'll include this in the appendix.**\n\n> It would be helpful if the authors could include more equations in the paper, likely in an appendix. For example, the CAN equations...\n\nThank you for pointing this out. We agree that including more equations would enhance the clarity. If accepted, we will include below in the appendix in the camera-ready version. Specifically, we implement $CAN()$ in Eq. (1), based on the Vector-HaSH repo [1]: \n\n$g(t+1) = \\textsf{CAN}[g(t), v(t)] \n = \\mathbf{M} g(t),$\n\nwhere $\\mathbf{M}$ denotes a shift matrix depending on the velocity signal $v$. For simplicity, suppose we have two grid cells with periodicities 3 and 4 and use a single dimension instead of two dimensions (our case). Then, $\\mathbf{M}$ is defined as a shift matrix in each grid module as follows:\n\n$\nM = U = \\begin{bmatrix}\n0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\\\\\n0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\\\\\n1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\\\\\n0 & 0 & 0 & 0 & 1 & 0 & 0 \\\\\\\\\n0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\\\\\n0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\\\\\n0 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\\\\\n\\end{bmatrix}\n$\n\nif $v$ shifts the bump activity to the right, otherwise $U^T$. \n\nFormally, $M_{i,j} = 1$ if $(j - X_{k-1}) \\mod \\lambda_k \\equiv (i + \\text{velocity} - X_{k-1}) \\mod \\lambda_k$, where  $X_{k-1} < i, j < X_k  \\forall i, j, k, X_k = \\sum_{l=1}^{k} \\lambda_l$. Otherwise, $M_{ij} = 0$. \n\n2D Vector-HaSH is a simple extension of this to two-dimensional grid states and velocities.\n\n> code release. \n\nWe appreciate the reviewer’s emphasis on reproducibility and agree accessible code is important for advancing the field. We're finalizing documentation and ensuring the code is well-organized and user-friendly. We remain committed to releasing the full codebase upon acceptance (w/ the camera-ready version).\n\n---\n\n[1] https://github.com/FieteLab/VectorHaSH", "claims_and_evidence": "Yes, the main claims are clearly laid out and supported well.", "methods_and_evaluation_criteria": "Yes, the accumulating towers task is suited well for this investigation.", "theoretical_claims": "There are no theorems or proofs.", "experimental_designs_or_analyses": "The experiments seem sound. \n\nIt would be helpful if the authors could include more information on how hyperparameters for model training were chosen, and how much those hyperparameters affect each of the half-dozen models that the authors built. A few extra sentences in appendix A.1 should be sufficient.\n\nIt would be helpful if the authors could include more equations in the paper, likely in an appendix. For example the CAN equations should be included.", "relation_to_broader_scientific_literature": "This paper uses the Vector HASH method https://www.biorxiv.org/content/10.1101/2023.11.28.568960v2 , a recent and state-of-the-art hippocampal model, as a core component in most of the models investigated. The authors build a series of models and compare their behavior with behavior that was observed in laboratory experiments on mice in earlier work. These models present significant extensions of the Vector HASH method, and advance our understanding of the hippocampus and brain regions that it connects to. \n\nThe paper is particularly exciting because the authors pay close attention to existing neuroscience literature, and marry this with complex but meaningful modeling.", "essential_references_not_discussed": "Relevant literature has been cited.", "other_strengths_and_weaknesses": "Strengths:\n- The paper advances the field of hippocampal modeling by investigating how state-of-the-art existing models of the hippocampus might perform when integrated with other parts of the brain. While the work reviewed here is entirely theoretical (computer models), the work appears to be inspired by recent (2021) measurements taken in brains of mice. The paper’s alignment with existing laboratory measurements on the task that is being investigated (accumulating towers) makes this work particularly exciting. Last: the authors announce in the paper that they are performing experimental work to test hypotheses born out of the models built here. \n- The work presented in the paper is quite comprehensive: the authors investigate half a dozen models, all of which are interesting from a computational neuroscience perspective. \n- The paper is written well: while the paper is dense, it does a good job of conveying the material. The diagrams showing the model architectures make it easy to understand the experimental set-up. \n- The authors highlighted that their work builds on the Vector-HaSH method published earlier. This enables readers who are familiar with the surrounding literature to instantly situate the paper. \n\nWeaknesses:\n- It would be helpful if the authors could include more equations in their paper. For example, the CAN or Vector-HaSH equations (which have of course been published elsewhere in papers cited by the paper reviewed here) are so central to the paper that they should in my opinion by included in the paper or in the appendix. \n- While the authors promise to release the code for the experiments, they did not include them with the supplementary materials. While authors may be worried about their code getting stolen by reviewers, peer review can inspire improvements to experiment code that benefit the quality of the paper, and make it easier for other research groups to build on the paper, or even just benchmark against the models presented here.", "other_comments_or_suggestions": "-  It would be helpful if the authors could include more equations in their paper. For example, the CAN or Vector-HaSH equations (which have of course been published elsewhere in papers cited by the paper reviewed here) are so central to the paper that they should in my opinion by included in the paper or in the appendix.", "questions_for_authors": "The authors mention on line 682 (Appendix A.1) that different learning rates were used for different model configurations, and that a hyper parameter search was performed for some configurations, while other configurations used common “default” hyper parameter configurations. This made me wonder: how much would tuned hyperparameters have helped for models that used default hyper parameter configurations?", "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": "w5CxMUnsUq", "reviewer": "Reviewer_zdy4", "summary": "This work studies recent neurophysiological results through the use of computational modeling and reinforcement learning. The authors consider several different variants of the model (varying the connectivity and coding properties) and find only certain of these models achieve high performance and similarities to neural activations. The authors' work provides several direct predictions that can be tested with new experiments. More generally, the authors' approach proscribes a framework for studying decision-making embedded in spatial navigation.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for their precious time and comprehensive feedback. We deeply appreciate their recognition of the significance of our work. In summary, the reviewer raised an insightful question regarding experimental v.s. model data comparison to strengthen our claims, and our interpretation of task performance, for which we discuss the implication of M5 for studying lapses. We provide results for when we shrink the number of trainable parameters of baselines to match that of M5, which do not alter our conclusion. We have fixed the typos on our end. **Together with the discussion below, does this address the reviewer’s questions?**\n\n> The authors compute the mutual information…in Fig. 6. could they do the same with the hippocampal data from Nieh et al. (2021) and compare the distributions? Something to make it more quantifiable…would strengthen this claim.\n\nThanks for the insight. We’d like to first refer to Figs S2b, c in Nieh et al., which plot mutual information (M.I.) of hippocampal data, the same as our Fig 6. We share it here for convenience: https://imgur.com/a/acEavag.\n\nThis qualitatively matches the results of M3-M5 in Fig 6, showing models with both position and evidence encoded in grid cells give rise to higher ExY M.I. than when one variable is randomized. This makes sense for M4 because M.I. is not a metric for localization. However, as shown in Fig 4, M4 does not match experiments in having choice-specific neurons. \n\nWe don’t expect a quantitative match in M.I, because \n1. Our environment is discretized;\n2. We don’t have the same level of noisiness as the experiments; \n3. Real neurons exhibit higher redundancy; \n4. The real data is smoothed but we didn’t apply smoothing, hence the scale of M.I. is different. The smoothing also influences the localization in HPC maps.\n\n> M0, M0-star, and M4 all solve the task at around 70% at around by the end of training…subsequent results provide additional support for M3/M5…but discussing this aspect of performance (that the mice did not perform the task as well as M3/M5) is important I think.\n\nIndeed, the lapses phenomenon in mice (low performance) is an important ongoing research direction. \n\nWhile early literature proposed lapses could be due to perceptual noise, more recent work like Ashwood et al., Nat Neurosci., 2022 pointed out that mice might be leveraging different strategies characterized by different states, while Pisupati et al., eLife, 2021 proposed the mice are potentially balancing exploration and exploitation when making mistakes. These statistical models have specific parameters to account for lapses based on their hypotheses and are evaluated based on how well they fit the data. While we find the lapses literature important, we don’t think the low performance of M0, M0+, & M4 would be informative for understanding lapses, as you carefully noted that they are limited in reproducing experimental findings.\n\nWhile studying lapses is beyond our scope, future studies on lapses could leverage M5, validated as being able to reproduce experimental findings. It’d be interesting to investigate what the key ingredients are to observe lapses while preserving the properties we observed. To our knowledge, a mechanistic model for lapses would be fairly novel. **We will include this in our discussion.**\n\n> Could one reason models M0 and M0-star not perform as well until later in training be due to the fact that they have more weights to optimize over? How does the number of training able parameters differ between M0/M0-star and the other models?\n\nThis is a fair point. We focused on an equal number of neurons as a fair baseline for expressivity. Here we found the number of parameters trained by back prop doesn't play a key role: \n\nAssume the total number of parameters in an RNN w/ input size $I$, hidden size $H$, and output size $O$, w/ bias, is $(IH + HH + H) + (HO + O) = H^2 + H(I+O+1) + O,$ then M5 has ~$26,755$ back-prop-trainable parameters. We can apply similar reasoning to M0 and M0+, with $1,172,843$ and $1,174,995$ gradient-trainable parameters. To match M5, M0 would have $H \\approx 158$ and M0+ would have $H \\approx 157$.  \n\nWe ran these mini-models for 3 trials each: the **conclusion in the main paper stays the same**. Plz see the anonymous results here with mini-M0 & mini-M0+ (red and orange, w/ learning rate of 1e-5), in comparison with M5 and original M0 and M0+: https://imgur.com/a/Qr5MmT4 \n\nSupplement: mini models w/ other learning rates, no change of conclusions: https://imgur.com/a/vCD2HRG \n\nWe notice our use of M0-star & M0+ interchangeably; we will use “M0+” consistently.\n\n> Other Comments\n\nThanks! We'll ensure a consistent notation `h`. We’ll modify “lacunae” to gaps and correct the sentence.\n\n---\nAshwood, Zoe C., et al. \"Mice alternate between discrete strategies during perceptual decision-making.\" Nature Neuroscience (2022).\n\nPisupati, Sashank, et al. \"Lapses in perceptual decisions reflect exploration.\" Elife (2021).", "claims_and_evidence": "All claims are supported by some evidence. However, I felt that M3 and M5's conjunctive coding of evidence and position (Figs. 3 and 7) was not convincingly shown. In particular, while it is clear that M1, M2, and M4 do no conjunctively encode evidence and position, the maps of M3 and M5 are not particularly localized (and differ from the maps of Nieh et al. (2021)). The authors compute the mutual information between E x Y and E x RY (and RE x Y) in Fig. 6 - could they do the same with the hippocampal data from Nieh et al. (2021) and compare the distributions? Something to make it more quantifiable how similar the ExY coding is in the model to the hippocampal data would strengthen this claim.", "methods_and_evaluation_criteria": "The methods and evaluation make sense for the problem and were well motivated.", "theoretical_claims": "No theoretical claims were made.", "experimental_designs_or_analyses": "The experimental design and analysis were well done and appeared sound.", "relation_to_broader_scientific_literature": "The paper explores a surprising neurophysiological result that challenges how the field thinks about place cells and their role in spatial navigation and episodic memory. The authors' result, finding that they expect grid cells to jointly encode space and evidence, is itself surprising and motivates greater study of the MEC-hippocampus-cortex circuit. These points were well made by the paper and the Introduction did a nice job of laying out the motivation.", "essential_references_not_discussed": "The authors include all \"essential\" references. However, I do think there are several relevant papers that are worth citing (which, I imagine the authors are familiar with):\n\n1. https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1007796 - The joint encoding of space and evidence reminds me of this work on how grid cells can encode higher dimensional variables. The random projection method discussed by Klukas and co-authors would be interesting to consider in the context of the authors model. \n\n2. https://proceedings.neurips.cc/paper_files/paper/2017/file/5f14615696649541a025d3d0f8e0447f-Paper.pdf - The use of RNN models to generate hypotheses about navigation seems related to the work of  Kanitscheider and Fiete. \n\n3. https://www.cell.com/neuron/fulltext/S0896-6273(11)00609-X (and other time cell related papers) - The idea that hippocampal neurons encode accumulating evidence (and temporal integration) is somewhat reminiscent of hippocampal cells encoding accumulating time.", "other_strengths_and_weaknesses": "**Strengths:**\n1. This paper provides a general framework for testing hypothesis on hippocampal-MEC-cortical interactions. \n2. This paper is able to replicate existing neurophysioloigcal results and leads to new predictions on the role of grid cells that can be experimentally tested.\n3. This paper is generally well written and motivated, and the experiments are well done. \n\n**Weaknesses:**\n1. As noted previously, the major weakness to my mind is that the conjunctive encoding of location and evidence is not convincing from the heat maps alone. Quantifying the extent of this joint encoding would strengthen this claim. \n2. The results in Fig. 2A clearly show that only M3 and M5 are able to optimally perform the task. This has clear implications for building an AI system that can solve the task. But the mice in Nieh et al. (2021) don't perfectly solve the task. Looking at Fig. 1b in Nieh et al. (2021), it seems like the mice are solving the task at around 75% accuracy. M0, M0-star, and M4 all solve the task at around 70% at around by the end of training. I understand that the subsequent results provide additional support for M3/M5 having similarities to the neural recordings, but discussing this aspect of performance (that the mice did not perform the task as well as M3/M5) is important I think. \n3. Models M0 and M0-star have the same number of units as the other models. But one thing that was not clear to me was if they have the same number of trainable weights (since the Vector-Hash model has some fixed weights). Could one reason models M0 and M0-star not perform as well until later in training be due to the fact that they have more weights to optimize over?", "other_comments_or_suggestions": "1. Both $p$ and $h$ are used to reference the hippocampal units (i.e., $W_{pg}$ and $W_{hg}$). \n2. (Very minor) I had not heard of the word \"lacunae\" before. Maybe change it to something more common? \n3. \"theoretical work can leverage this standardized yet rich task and readily test its predictions\" - should this be \"and its predictions can be tested\"?", "questions_for_authors": "1. How does the mutual information distributions (for E x Y) compare between real hippocampal data and the models? \n2. How closely do models M0, M0-star, and M4 perform to the mice in Nieh et al. (2021)? \n3. How does the number of training able parameters differ between M0/M0-star and the other models?", "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:

Meta-review: This paper proposes a biologically grounded multi-region model of the hippocampus and entorhinal cortex integrated with cortical action selection to explain spatially embedded decision-making. It systematically compares circuit architectures using variants of the Vector-HaSH model and generates testable predictions about conjunctive grid cell coding of position and evidence. The authors apply their models to the accumulating towers task and show that a specific architecture, M5, reproduces neural and behavioral patterns observed in experimental studies.

The strengths of the paper lie in its neuroscientific motivation, strong alignment with experimental data, and comprehensive exploration of alternative circuit mechanisms. The authors provide ablations across multiple structured models, quantify neural representations, and respond thoroughly to reviewer concerns—especially regarding mutual information comparisons, parameter counts, and visualization quality. The commitment to code release and detailed clarifications in the rebuttal further demonstrate the authors’ thoughtfulness and rigor.

One reviewer expressed concerns over limited methodological novelty and interpretability of heatmaps, but these are addressed by explaining the adaptation of Vector-HaSH and adding smoothing analyses in the appendix. While the model does not outperform baseline RNNs on complex AI benchmarks, its purpose is hypothesis-driven modeling of biologically plausible decision-making circuits.

Given the paper's careful design, robust empirical evidence, biological relevance, and constructive engagement with reviewer feedback, I recommend acceptance.
Decision: Accept (poster)