CNS*2026 Halifax

Computational neuroscience relies on gradient descent (GD) for training artificial neural network (ANN) models of the brain. The advantage of GD is that it is effective at learning difficult tasks. However, it produces ANNs that are a poor phenomenological fit to biology, making them less relevant as models of the brain. Specifically, it violates Dale’s law, by allowing synapses to change from excitatory to inhibitory, and leads to synaptic weights that are not log-normally distributed, contradicting experimental data. Here, starting from first principles of optimization theory, I will present an alternative learning algorithm, exponentiated gradient (EG), that respects Dale’s Law and produces log-normal weights, without losing the power of learning with gradients. We show that in biologically relevant settings EG outperforms GD, including learning from sparsely relevant signals and dealing with synaptic pruning. Altogether, our results show that EG is a superior learning algorithm for modelling the brain with ANNs.

Benjamin S. Sipes^*1, Ashish Raj<sup>1

1</sup>Department of Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, CA, United States

^*Email: [email protected]

Introduction
Diffusion MRI (dMRI) tractography estimates the brain's white matter structural connectivity (SC) in vivo, but it cannot resolve the directionality of white matter pathways. Yet, much recent work has shown that genes and gene co-expression maps relate to SC across species [1-4]. Here we test whether gene co-expression gradients can infer connection directionality from undirected structural connectivity using the brain’s structure–function relationship.

Methods
We introduce asymmetry to SC (C) via a similarity transform with a node-level gauge parameterized by genetic gradients: C̃=ACA^-1, where A=diag(e^{Ga}), with G=[g_1,...,g_k] genetic gradient vectors and a=[a_1,...,a_k]^T gradient weights. We learn gradient weights by fitting a higher order network diffusion (HONeD) model of the SC graph Laplacian, ℒ=I-C̃D_{in}^-1, f(ℒ)=-κI-βℒ+ξℒ^2, to the residual of the Lyapunov equation, f(ℒ)^TΣ+Σf(ℒ)+I [5,6], with stationary covariance (Σ) estimated from functional neuroimaging. We compared our model's performance to ground truth directionality in three species: C. elegans, mouse, and macaque [7-10]. We then ran our model on 770 HCP subjects [11,12]. Public datasets supplied gene expression [13-17].

Results
Model-predicted directionality significantly correlated with ground-truth directed edges in all three species. Our model predicted neuron-to-neuron synaptic directionality in C. elegans (r=0.56, p<10^-253) and tracer-based directionality in mouse (r=0.57, p<10^-37) and macaque (r=0.46, p<10^-44) (Fig.1a-b). The optimal numbers of genetic gradients was also different in each species (C. elegans: k=3; Mouse: k=5; Macaque: k=1). We found that humans had optimal test-retest reliability when using k=5 genetic gradients (ICC=0.46). Human predicted degree asymmetry suggests that the hippocampus and posterior cingulate are network sources while temporal poles are network sinks (Fig.1c).

Discussion
Although white matter pathways exhibit directionality, estimating their orientation has largely been restricted to tracer-based experiments and a small number of specialized imaging methods. Our results suggest that gene gradients combined with structure–function modeling provide a biologically grounded framework for inferring directed structural connectivity across species, supporting the idea that molecular gradients may encode directional biases in large-scale brain networks. Estimating human SC directionality is valuable not only for basic neuroscience, but also for evaluating circuit-level models of brain function and for studying diseases such as Alzheimer’s, Parkinson’s, and ALS that may propagate along structural pathways [18].

Figure 1. (a) Model-estimated directionality parameters (e^{Ga}) for the three non-human species: C. elegans (top), Mouse (middle), Macaque (bottom). In the C. elegans plot, each dot represents a single neuron. (b) Scatter plots comparing empirical to predicted skew edges with Pearson correlations listed at the top left (all p<10^{-37}). (c) Predicted human overall degree asymmetry for 414 brain regions.​

Farzad Karimi^*1,2, Javier G. Orlandi<sup>1,2

1</sup>Department of Physics and Astronomy, University of Calgary, Calgary, Canada
² Hotchkiss Brain Institute, University of Calgary, AB, Canada

^*Email: [email protected]

Introduction
Recent technological advances allowing us to simultaneously record across thousands of neurons have revealed the presence of distributed representations across the brain [1]. However, the network processes and information pathways that create these distributed representations are still poorly understood. To identify these distributed representations, we measured shared information across brain areas, by introducing a new directed connectivity measure, Reduced Rank Connectivity (RRC). RRC is defined through communication subspaces between neural areas, and by comparing these subspaces we can measure the extent of distributed signals across the brain.

Methods
We analyzed Neuropixels recordings from the Allen Institute from 54 mice performing a go/no-go visual change detection task, focusing on six visual cortical areas (V1, LM, AL, RL, AM, PM), as well as the thalamus (LP) and hippocampus (CA1), across two sessions: active behavior and passive replay [2]. To estimate shared information, we applied Reduced Rank Regression (RRR) [3], which predicts target activity from a low-dimensional subspace of a source population. We define the total predictable target activity as a new connectivity measure, called RRC, and distances between subspaces quantify the similarity of shared information across neural areas.

Results
We applied RRR to cortical and subcortical areas to analyze information flow across all area pairs combinations. We showed that model performance, defined as the squared correlation between predicted and test data, saturated with only a few predictive dimensions. These results identify low-dimensional communication subspaces between neural areas (Fig. 1a). We observed consistent shared information across the visual cortex, while predictability was lower for subcortical areas (Fig. 1b). Connectivity computed using RRR differed significantly from structural connectivity [4] (Fig. 1c). Our results also show that RRC is modulated by the animal’s engagement with the task (active vs. passive).

Discussion
Using RRR on multi-area cortical recordings, we identified robust shared information across visual areas during a discrimination task. RRR performance provides a connectivity measure that captures predictive subspaces rather than coarse averages. The results suggest the presence of low-dimensional communication subspaces between neural areas. Cortical areas can be more easily predicted by their own activity than subcortical areas through these communication subspaces during visual processing. RRC differed from structural connectivity and was modulated by behavioral state.

Figure 1. Low-dimensional communication subspaces define RRC. (a) Prediction performance vs. rank; saturation defines optimal number of ranks and RRC. (b) Average RRC across animals; cortical areas are more predictable than subc

Alexandra Busch^*,1,2,3, Roberto Budzinski^2,4, Lyle Muller^1,2,3
1 Department of Mathematics, Western University, London ON, Canada
2 Fields Lab for Network Computation, Fields Lab, Toronto ON, Canada
3 Western Institute for Neuroscience, Western University, London ON, Canada
4  Department of Neuroscience, University of Lethbridge, Lethbridge AB, Canada
* Email: [email protected]

Introduction
Recent technological advances now allow simultaneously recording the activity of thousands of neurons while animals engage in cognitive tasks. These datasets can offer an unprecedented window into how the brain computes in real time, but they also challenge existing analytical frameworks. There has been increasing interest in the possibility that coordinated patterns of spikes, such as sequences, may contribute to neural computation [1-3]. However, in contrast to the many methods available for analyzing firing rates, mathematical tools capable of systematically probing spike-time structure at the scale of these next-generation datasets remain limited.

Methods
We introduce a decomposition operator for population spike patterns, termed the multi-sample Discrete Helix Transform (ms-DHT). We derive a generalized inner product that allows the ms-DHT to operate directly on patterns of discrete spikes across thousands of neurons without smoothing. The ms-DHT decomposes these spike patterns into a fixed, interpretable basis, mapping each input pattern to a unique vector that captures the occurrence and timing of every spike (Fig.1). In this representation, distances between spike patterns reduces to the Euclidean distance between their ms-DHT outputs. This distance is invariant to neuron ordering and allows detecting repeating structure ranging from simple spike sequences to complex population motifs.

Results
We demonstrate several applications of the ms-DHT to large-scale datasets. Notably, in dual Utah array recordings from the prefrontal cortex of a macaque monkey performing a virtual reality working memory task, the ms-DHT reveals structured spike motifs that predict specific behavioural errors on single trials - before they occur. Further, applications to spiking network simulations with 10,000 neurons demonstrate that the transform operates effectively at the scale of next-generation neural recordings.

Discussion
The ms-DHT provides a flexible framework for analyzing large-scale spike patterns. By decomposing spiking activity onto a fixed, interpretable basis using a generalized inner product, the ms-DHT produces unique descriptions of population activity even when neurons emit variable numbers of spikes—a setting that has posed a central challenge for analytical approaches. The resulting representation supports multiple analyses, including clustering and decoding of full spike patterns, detecting repeating substructure through specific helix contributions, and sliding-window analyses that trace the temporal evolution of spike patterns across long recordings.

FIgure 1. Decomposing spike patterns. The ms-DHT maps a spike pattern (a) to a unique complex-valued vector (b). Each component encodes the strength (amplitude) and timing (phase) of a basis sub-pattern. (c) Distances between spike patterns reduce to Euclidean distances between ms-DHT outputs, which are invariant to neuron order, ensuring behaviourally relevant clusters do not depend on neuron order.​

References
[1] Xie, W., Wittig, J. H., Chapeton, J. I., El-Kalliny, M., Jackson, S. N., Inati, S. K., & Zaghloul, K. A. (2024). Neuronal sequences in population bursts encode information in human cortex. Nature, 635(8040), 935–942. https://doi.org/10.1038/s41586-024-08075-8
[2] Chettih, S. N., Mackevicius, E. L., Hale, S., & Aronov, D. (2024). Barcoding of episodic memories in the hippocampus of a food-caching bird. Cell, 187(8), 1922–1935.e20. https://doi.org/10.1016/j.cell.2024.02.032
[3] Busch, A., Roussy, M., Martinez-Trujillo, J. C., et al. (2024). Neuronal activation sequences in lateral prefrontal cortex encode visuospatial working memory during virtual navigation. Nature Communications, 15, 4471. https://doi.org/10.1038/s41467-024-48664-9

Acknowledgments
This work was supported by NSERC, CFREF, NIH, Neuronex NSF, and Canada Research Chairs Program. A.B. gratefully acknowledges a BrainsCAN studentship and NSERC CGS-D. 

Cecilia Romaro*¹, Matei Coldea², William W. Lytton^3,4, and Robert A. McDougal^1,5,6,7,8
1 Department of Biostatistics, Yale School of Public Health, New Haven, CT, United States
2 Yale College, Yale University, New Haven, CT, United States
3 Department of Physiology and Pharmacology & Neurology, SUNY Downstate Health Sciences University, Brooklyn, New York
4 Department of Neurology, Kings County Hospital Center, Brooklyn, New York
5 Department of Biomedical Informatics and Data Science, Yale School of Medicine, New Haven, CT, United States
6 Program in Computational Biology and Bioinformatics, Yale University, New Haven, CT, United States
7 Wu Tsai Institute, Yale University, New Haven, CT, United States
8 Interdepartmental Neuroscience Program, Yale University, New Haven, CT, United States
* Email: [email protected]

Introduction
Just as neuron morphology influences spiking behavior and thus network interactions, so too does the 3D placement of spines affect interaction between spines [1] and thus cellular behavior. However fine spine details are not visible under the optical microscopy used for reconstructing neuron morphology and full-cell scanning electron microscopy (SEM) images are generally not feasible due to size constraints. To address these challenges, we developed a tool for the NEURON simulator [2] for importing and editing an SEM reconstruction of a portion of a dendrite, selecting spines, rotating them, and inserting them into a full-cell reconstruction for simulation, using our experimental support for reaction-diffusion multigridding in NEURON.

Methods
SEM images may be segmented to identify each spine using standard segmentation software then exported to a TIFF stack. We estimate key electrical properties: approximately equivalent length, diameter, volume, and surface area. Our tool loads the image stack and identifies the voxels forming each spine-dendrite boundary so that we can preserve the connection location after transformations. PySide6 is used to provide a graphical interface allowing spines to be selected and manipulated into position; this can also be done programmatically. An algorithm adds/removes voxels to connect the spine cleanly. Transformed spines can be exported to text files for easy editing, enabling iterative refinement.

Results
We present our graphical tool, examples of relevant data sets, and simulation results. The graphical tool allows visualization of both the loaded SEM data and the placed spines after transformations. The simulations leverage our previous work, allowing a synaptic source (e.g., of IP3) to be placed at a precise 3D location within a spine. We validate the multigrid simulation by comparing to a single unified 3D simulation and contrast it to simplified geometry approximations, illustrating their similarities and differences. In particular, our tool allows toggling between the two representations.

Discussion
Support for imported spine morphologies brings NEURON a step closer to capturing the intricacies of the human brain. The same tool described here can also directly be used for incorporating SEM data of a dendrite as well. It is not feasible to simulate full cells and networks at this level of detail, nor is that necessarily desirable -- simpler models are often more useful for insights -- but our approach allows us to explore localized behavior in detail in a multiscale context with full cell and network simulations. This tool can give us insight on which details model when and allow us to explore detailed biological questions of synaptic plasticity or the role of morphological changes in disease.

References

1. Huertas, M. A., Newton, A. J., McDougal, R. A., Sacktor, T. C., & Shouval, H. Z. (2022). Conditions for synaptic specificity during the maintenance phase of synaptic plasticity. Eneuro, 9(3). https://doi.org/10.1523/ENEURO.0064-22.2022

2. Hines, M. L., & Carnevale, N. T. (1997). The NEURON simulation environment. Neural computation, 9(6), 1179-1209. https://doi.org/10.1162/neco.1997.9.6.1179

Acknowledgments
This research was funded by the National Institute of Mental Health, National Institutes of Health, grant number R01 MH086638. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Brett J. Kagan^*1, David Hogan¹, Andrew Doherty¹,  Boon Kien Khoo¹,  Johnson Zhou¹,  Richard Salib¹,  James Stewart¹,  Kiaran Lawson¹,  Alon Loeffler¹,
¹Cortical Labs, Melbourne, Australia
² The University of Melbourne, Department of Biochemistry and Pharmacology, Parkville, Melbourne, 3000, Australia

^*Email:[email protected]


Introduction
Neural cultures are increasingly explored to understand the computational properties of neural systems due to the controllability and modifiability of these systems. However, BNNs can only be explored reliably as reliable information-processing systems if inputs are delivered in a temporally and structurally consistent manner. In practice, this requires stimulation with precisely controlled structure, microsecond-scale timing, multi-channel synchronization, and the ability to observe and respond to neural activity in real-time. Existing approaches depend on either depend on low-level hardware mechanisms, imposing prohibitive complexity for rapid iteration, or they sacrifice temporal and structural control, undermining consistency.

Methods
To resolve this problem. We developed a bespoke but scalable system (the CL1)¹ that coupled with a easy to use Application Programming Interface ( CL API)² to  enables real-time, sub-millisecond closed-loop interactions with neural cultures. The system itself provides real-time closed-loop electrophysiology with integrated life support. For the API design approach, the CL API provides users with precise stimulation semantics, transactional admission, deterministic ordering, and explicit synchronization guarantees. This contract is presented through a declarative Python interface, enabling non-expert programmers to express complex stimulation and closed-loop behavior without managing low-level scheduling or hardware details.

Results
The result is a scalable device for interacting with in-vitro neural cell cultures via electrophysiology in a closed-loop real-time environment coupled with an integrated life-support system. The devices are server rack stackable, generating up to 6TB of neural activity data per server rack per day, allowing detailed analysis of electrophysiological data, where each unit can run its own embodied environment. This allows an unparalleled investigation of nearly fully controllable neural systems to explore their dynamics in depth. The flexibility of the Cl1 means that information processing and computation in neural cultures can be explored in many ways, including as reservoir computing, in robotics⁴, or via games such "Pong"⁵ or “Doom”.

Discussion
The CL1 system coupled with the CL API offers a scalable system for exploring computational dynamics of biological neural networks. Aside from being possible to set up in traditional cell culture laboratories, these systems can be accessed remotely via the cloud where the cell culture methods are managed either by a dedicated company or by partner laboratory groups. This provides a tool for computational neuroscientists, who might otherwise not be able to access these neural cultures, to explore research questions at scale, with precision, and with rapid iteration loops. It is proposed that this availability will allow computational neuroscientists to be able to explore the dynamics of biological neural systems in way never possible before.

Figure 1. The CL-1 device is scalable desktop device compatible with standard server racks that allows real-time closed-loop interactions with neural cells via an MEA reader. The CL-1 has onboard hardware that interprets simple code via a Python API to allow rapid code development and experimental iterations coupled with a closed-loop perfusion circuit to automatically adjusts gas levels and temperature to​

References
1) Kagan, B. J. (2025). The CL1 as a platform technology to l

Sanjna Kumari^*1 and Rishikesh Narayanan^1
1 Cellular Neurophysiology Laboratory, Molecular Biophysics Unit, Indian Institute of Science, Bengaluru 560012, India
^*Email: [email protected]

Introduction
Granule cells (GCs) in the dentate gyrus (DG) receive grid-like spatial inputs and contextual inputs from the entorhinal cortex, both broadly tuned to multiple spatial locations. Despite this, GCs elicit sparse spatial firing that is confined to single place fields, thus playing a central role in selective routing of spatial information to the hippocampal circuit. The mechanisms behind the transformation of broadly tuned afferent inputs into sparse and location-specific outputs remains unclear. In this study, we ask if there are physiologically relevant plasticity mechanisms that can mediate selective routing of spatial information towards place-cell emergence and spatial remapping, especially when inhibitory synapses are absent.

Methods
We employed morphologically and biophysically realistic models of DG GCs (Kumari & Narayanan, 2024), receiving grid-like and contextual spatial inputs from the entorhinal cortex. We employed a stochastic search paradigm in the plasticity space involving fold-changes in excitatory synaptic strengths, persistent sodium (NaP), hyperpolarization-activated cyclic nucleotide-gated (HCN), and inward rectifier potassium (Kir) conductances. We validated plasticity combinations that achieved one of four functional targets relevant to DG spatial tuning: conversion of silent neurons to place cells, uphold existing place field firing, spatial remapping to a new location, and suppression of spurious place fields to obtain a single place field (Fig 1).

Results
While excitatory synaptic plasticity alone was insufficient to generate valid spatial tuning, conjunctive synaptic and intrinsic plasticity yielded several valid plasticity combinations for all 4 targets (Valid/Total models for 4 targets: 243/142,000, 325/10,000, 139/5,000, 224/50,000). These valid plasticity combinations manifested pronounced heterogeneity across all fold-changes, unveiling plasticity degeneracy where disparate plasticity combinations yielded similar spatial tuning outcomes. Dimensionality reduction analyses revealed low-dimensional structures in intrinsic measurement and parameter spaces of valid models. In contrast, the plasticity space did not manifest strong constraints on plasticity across different components.

Discussion
While inhibitory synaptic inputs have been studied as mechanisms for sculpting spatial tuning, we show that selective routing of information and suppression of off-field firing can be achieved through intrinsic plasticity. Among intrinsic components, we predict the axonal initial segment K_ir conductance as the strongest determinant of spatial selectivity. We demonstrate that disparate combinations of concomitant plasticity in excitatory synaptic and intrinsic conductances can mediate the emergence, refinement, and remapping of place fields. We show that co-dependent plasticity in different neuronal components can enable robust yet flexible spatial representations despite heterogeneities in neuronal composition and plasticity mechanisms.

FIgure 1. Medial and lateral entorhinal cortex inputs impinge on a DG granule cell. Disparate combinations of synaptic and intrinsic plasticity (NaP, HCN, Kir channels) achieved one of four targets: convert silent cell to place cell, uphold existing place field, remap, or suppress spurious firing. Our results show that robust and flexible spatial tuning is achievable through plasticity degeneracy.​References
Kumari, S., & Narayanan, R. (2024). Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells. J Neurophysiol, 132(3), 991-1013. https://doi.org/10.1152/jn.00071.2024

Shujia Liu^{*1, 2}, Bailu Si¹, Michael Herrmann<sup>2

1</sup>School of Systems Science, Beijing Normal University, Beijing, China
² School of Informatics, The University of Edinburgh, Edinburgh, UK

^*Email: [email protected]

Introduction
Most ring attractor models hard-code and phase-biased translation kernels to obtain a stable activity profile (bump) and velocity-driven shifts [1]. This bypasses a key developmental question: Can these stabilizing and translation kernels self-organize, without any pre-set ring topology, from activity statistics under staged multimodal constraints? The Lateral Mammillary Nucleus--Dorsal Tegmental Nucleus (LMN--DTN) loop implicated in head direction system also lacks developmental constraints. Motivated by synfire chain theory [2] we build a plasticity enabled LMN--DTN model and propose: Spontaneous traveling wave statistics plus staged vestibular/visual constraints can drive the emergence of a ring attractor and path integration.

Methods
We constructed a rate-based LMN--DTN circuit model with 400 neurons in LMN and two populations of 400 direction--velocity conjunctive cells in DTN. LMN follows leaky integrator dynamics with plastic recurrent excitatory connectivity and a fixed long-range inhibitory kernel. DTN to LMN feedback consists of plastic phase-biased weights gated by the angular velocity input. Training proceeds in functional stages: We first obtain stable traveling wave statistics without external velocity or vision, then update connectivity via STDP-like and structural plasticity, and subsequently introduce long-range inhibition and a visual teacher for representational stabilization and gain

Results
With random sparse connectivity, no external velocity input, and no hand-designed ring topology templates, LMN networks spontaneously produce a stable unidirectional traveling wave under the joint action of dominant refractory-like neuronal dynamics and global inhibition, exhibiting consistent phase progression (Fig. 1A). STDP-like and structural plasticity then consolidate the temporal correlations into locally enhanced recurrent excitation (Fig. 1B); long-range inhibition transforms the traveling wave regime into a phase-selectable single bump state. Visual relearning markedly improves short-term angle tracking, yet cumulative drift persists during pure path integration after removing visual information (Fig. 1C).

Discussion
Our results indicate that stabilizing and translation kernels of ring attractors need not be hard-coded: intrinsic recurrent dynamics can provide a directional temporal scaffold, which activity-dependent plasticity, staged inhibition, and multimodal constraints shape into a stable bump representation and a learnable translation kernel. Although residual drift remains after visual removal, it is structured rather than arbitrary, suggesting that the model captures much of the required computation while revealing imperfections in the learned kernel. This makes the framework useful both as a proof of principle for de

Pablo Sanchez-Martin^*1, Alicia Garrido-Peña¹, Irene Elices¹, Carlos Garcia-Saura¹, Rafael Levi¹, Francisco B. Rodriguez¹, Pablo Varona<sup>1 

1</sup>Grupo de Neurocomputación Biológica (GNB), Department of Computer Engineering, Universidad Autónoma de Madrid, Madrid, Spain

^*Email: [email protected]

Introduction
Rhythmic sequential activity is present in many nervous systems. Neural circuits that generate this activity usually involve intrinsic neuronal variability and different synapse types [1]. Sequential rhythms often require coordination at different time scales to adapt to specific conditions, or to adjust speed and timing to meet functional needs. Previous studies in computational models have assessed how synchronization and excitability can modulate cycle-by-cycle sequential dynamical invariants [2,3]. In this study, we analyzed the interplay among neural synchronization, excitability, and variability to understand how they are related to the sequentiality timing in CPG rhythms.

Methods
We acquired long recordings of pyloric CPG neurons of  Carcinus maenas  and extracted the spike timings from intracellular and extracellular time series followed by calculation of all sequence intervals between the PD neurons and the LP. We used metrics of synchronization between the electrically coupled PDs (Victor-Purpura distance, Euclidean distance), excitability for all three neurons (Spike Density Function -SDF-, average ISIs), and interval variability. We identified dynamical invariants in the form of relationships between specific intervals and the instantaneous period. To find relationships between these metrics, we performed analysis at three time scales: whole experiment, segments inside experiments, and cycle-by-cycle analysis.

Results
We observed a high level of variability for synchronization, excitability, and the intervals in this system. Ranking each experiment for all metrics revealed a relationship between the variability in the period, the neurons’ SDF, and the strength of the dynamical invariant relationship. Segmenting the data, we found that, in addition to these relationships, synchronization in the PD neurons is related to their excitability. We found non-linear relationships between the excitability of all neurons and their period variability and dynamical invariants. Excitability changes in any neuron were related to the other neurons' excitability at each cycle, although other relationships present at larger time scales were not preserved cycle-by-cycle.

Discussion
It is still unclear how robustness and flexibility can be autonomously balanced in neural sequences. Previous works have found evidence that suggests that connectivity asymmetry, i.e., the presence of both slow and fast synapses, could be responsible for the emergence of coordination rules such as sequential dynamical invariants [2, 3]. The LPPDdelay interval and instantaneous period are related cycle-by-cycle, as well as the excitability of all neurons among them. In an intermediate scale, the excitability is non-linearly related to synchronization, variability and strength of the dynamical invariants. In a larger time scale, excitability, variability, and the strength of dynamical invariants are all related, but not synchronization.

References
[1] Selverston, A. I., Rabinovich, M. I., Abarbanel, H. D., Elson, R., Szücs, A., Pinto, R. D., ... & Varona, P. (2000). Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. Journal of Physiology-Paris, 94(5-6), 357-374. 
[2] Berbel, B., Latorre, R., & Varona, P. (2025). Theoretical bases for the relation between excitability, variability and synchronization in sequential neural dynamics. Neurocomputing, 645, 130218. 
[3] Elices, I., Levi, R., Arroyo, D., Rodriguez, F. B., & Varona, P. (2019). Robust dynamical invariants in sequential neural activity. Scientific Reports, 9(1), 9048. 

Acknowledgments
Research funded by grants PID2024-155923NB-I00, PID2023-149669NB-I00 and CPP2023-010818 (MCIN/AEI and ERDF- "A way of making Europe"). 

Roberto Budzinski^1,2,#, Alexandra Busch^2,3,4, Luisa Liboni^2,5, Ján Mináč^2,3, Lyle Muller^2,3,4
1 Department of Neuroscience, University of Lethbridge, Lethbridge AB, Canada
2 Fields Lab for Network Computation, Fields Lab, Toronto ON, Canada
3 Department of Mathematics, Western University, London ON, Canada
4 Western Institute for Neuroscience, Western University, London ON, Canada
5 King's University College at Western University, London ON, Canada
# [email protected]

Introduction
Networks throughout physics and biology use spatiotemporal dynamics for computation [1]. In neural systems, waves of neural activity have recently been shown to shape spiking responses, gate perception, and influence behaviour [2]. However, it remains unclear how network connectivity gives rise to neural dynamics and how these dynamics support computation. To address this question, we introduce a new type of recurrent neural network that admits an exact mathematical solution [3,4], enabling us to directly relate network structure to emergent dynamics and the computations those dynamics perform.

Methods
We introduce a nonlinear recurrent neural network in which each unit is modeled as a complex-valued oscillator. This complex-valued recurrent neural network (cv-RNN) admits a closed-form solution given by an exact propagator. Importantly, this framework introduces a unified matrix representation of the system that encodes the network's connectivity, including connection strengths and delays, and the input. The exact mathematical solution allows us to control the network dynamics, down to the fine-scale pattern of connectivity, allowing us to use the spatiotemporal patterns that emerge for dynamics-based computation in a wide range of tasks [3,4].

Results
We find the cv-RNN can perform a wide range of tasks, including working memory, logic operations, sequence processing, and computer vision, while remaining precise and interpretable mathematically [3,4]. The analytical framework reveals the mechanisms underlying each computation. By exploiting traveling-wave dynamics, the network performs image segmentation and generalizes across different datasets using the same recurrent weights [4]. Further, we create a bio-hybrid version of our cv-RNN, where we leverage patch-clamping techniques to link biological neurons to the recurrent layer, where these neurons can decode the network’s spatiotemporal dynamics and implement computations [3].

Discussion
These results demonstrate that structured spatiotemporal dynamics can serve as a powerful computational substrate in recurrent neural networks. The exact solution links connectivity, input, and emergent dynamics within a unified operator framework. This approach provides a principled way to understand how neural circuits may compute through traveling waves and network dynamics. More broadly, it establishes a general framework for connecting network structure, emergent dynamics, and computation, offering new tools for interpreting biological neural activity and for designing transparent dynamical models in artificial intelligence.

References
[1] Ermentrout et al. (2001), "Traveling electrical waves in cortex: insights from phase dynamics and speculation on a computational role”, Neuron 29, 33.
[2] Muller et al. (2018), “Cortical travelling waves: mechanisms and computational principles”, Nature Reviews Neuroscience 19.
[3] Budzinski et al. (2024) “An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network, Communications Physics 7.
[4] Liboni et al. (2025), “Image segmentation with traveling waves in an exactly solvable recurrent neural network”, Proceedings of the National Academy of Sciences 122.
Acknowledgments
​This work was supported by NSERC, CFREF, NIH, Neuronex NSF, and Canada Research Chairs Program.

Adrián Ponce-Alvarez^*1,,2,3 and Germán Sumbre^4
1 Departament de Matemàtiques, Universitat Politècnica de Catalunya, 08028 Barcelona, Spain.
² Institut de Matemàtiques de la UPC - Barcelona Tech (IMTech), Barcelona, Spain.
³ Centre de Recerca Matemàtica, Barcelona, Spain.
⁴ Institut de Biologie de l’ENS (IBENS), Département de biologie, École normale supérieure, CNRS, INSERM, Université PSL, 75005 Paris, France


*Email : [email protected]

Introduction
Neuronal activity shows statistics consistent with a critical point, a regime that maximize information capacity. Yet, the role of different cell types remains largely unexplored. Models [1] and in vitro studies [2] suggest that excitation–inhibition (E/I) balance is key for self-organized criticality, but how E and I dynamics interact during in vivo critical activity is unclear. Similarly, glial cells such as radial astrocytes (RAs) regulate neuronal function [3], but their role in criticality is unknown. Here, we studied how E/I neuronal activity and astrocyte calcium dynamics contribute to criticality by combining transgenic zebrafish with cell-type-specific calcium indicators, a stochastic network, and model inference.

Methods
Spontaneous neuronal activity in the optic tectum (OT) of 10 zebrafish larvae was recorded using light-sheet microscopy. A double-transgenic line expressing GCaMP6f in all neurons and Vglut in glutamatergic neurons identified of E and I cells. Two-photon calcium imaging was performed in 7 larvae expressing GCaMP6f in neurons and RCaMP1b in RAs [3]. OT activity was recorded during spontaneous activity and after mild electrical stimulation, which triggered synchronized Ca²⁺ transients in RAs.
E and I activity was modelled using a stochastic network displaying critical avalanches at a E/I phase transition [1]. The maximum entropy principle mapped neuronal activity onto statistical models [4], quantifying criticality and detecting deviations.

Results
Our results show that neuronal avalanches approached criticality when E and I activity were balanced. Notably, the model accurately captured the observed avalanche statistics and their sensitivity to E/I fluctuations around a critical point defined by balanced excitatory and inhibitory synaptic strengths, where balanced amplification drives network avalanches. Furthermore, we found that RA synchronization shifted tectal neuronal activity away from its spontaneous critical state toward a more ordered regime, with a reduced repertoire of network states and diminished susceptibility to external inputs. These findings demonstrate that glial activity can actively regulate the state of neuronal ensembles, including their proximity to criticality.

Discussion
Extensive research highlights the benefits of E/I balance and critical dynamics. Balanced networks enhance amplification, selectivity, and stability, while critical dynamics optimize information processing. Here, we show that neuronal avalanche statistics and their dependence on spontaneous E/I fluctuations in the zebrafish OT match a model reaching criticality at balanced E and I couplings. Moreover, RA synchronization in the OT reshapes collective neuronal activity, consistent with a shift from spontaneous critical dynamics to a more ordered subcritical regime. Our findings show that radial astrocyte activity can shift the state of neuronal ensembles and modulate their proximity to criticality.

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Acknowledgments
This study was supported by the Project PID2022-137708NB-I00 funded by MICIU/AEI /10.13039/501100011033 and FEDER, UE. A. Ponce-Alvarez was supported by a Ramón y Cajal fellowship (RYC2020-029117-I) funded by MICIU/AEI/10.13039/501100011033 and “ESF Investing in your future”. G. Sumbre was supported by ERC CoG 726280.