Frontiers in Computational Neuroscience

The -Bonacci weighted sequence space {ell}(,) is introduced for [&ge;] 2, 1 [&le;] < {infty}, and > 0). It is proved to be a Banach space which is isometrically isomorphic to {ell}, with an unconditional Schauder basis. The space is also reflexive and uniformly convex. Its strict inclusion chain, continuous dual, and asymptotic truncation estimate of order - / are also established. Based on this framework, Scaled &#119898-BonacciNet is proposed as a lightweight CNN that rescales Fibonacci-Net channels using the dominant &#119898-Bonacci root and employs depth wise separable convolutions. Tribonacci-Net achieved 96.09% accuracy and a 0.9581 macro F1-score on the 15-class Brain MRI dataset using 0.85 million parameters and 0.366 GFLOPs. Pentanacci-Net attained 95.87% accuracy on the 44-class dataset while reducing parameters and FLOPs by 47.10% and 44.48%, respectively. On the CKD ultrasound dataset, Hexanacci-Net achieved 83.75% accuracy and a 0.7941 macro F1-score, with corresponding reductions of 50.37% and 45.10%. These findings support dominant-root scaling as a structured approach to lightweight CNN design.

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation for training neural networks. EP typically relies on free and nudged dynamical phases: during the free phase, the network relaxes toward an equilibrium state, whereas during nudging, the output state is perturbed toward a target using a teaching signal. However, it remains unclear whether the brain has access to such explicit target signals. Inspired by Attention-Gated Brain Propagation (BrainProp), a reward-based learning framework proposed by Pozzi et al. (2020), we introduce a reward-based variant of EP that replaces full target-based nudging with a selected-output binary reward signal. The proposed method updates the network using only the chosen class and whether that choice is correct, without directly revealing the full target vector. We evaluate the method on MNIST, Fashion-MNIST, and CIFAR-10 using both multilayer perceptrons and convolutional neural networks. The proposed reward-based EP achieves performance close to that of conventional EP across all three datasets, although it generally converges more slowly during the early stages of training. Generalization-gap analyses show similar behavior for the two methods on MNIST and Fashion-MNIST, while reward-based EP exhibits a smaller training-test accuracy gap during later training on CIFAR-10. We further investigate the effect of the exploration probability used during stochastic class selection and find that moderate exploration can provide small performance improvements, although its effect is dataset-dependent. These results demonstrate that EP can learn effectively from sparse, action-specific reward feedback rather than a complete supervised target.

Equilibrium Propagation (EP) is a biologically motivated alternative to backpropagation but requires free and nudged equilibrium phases, raising questions about the biological plausibility of phase-separated learning. We introduce Neuromodulated Equilibrium Learning (NEL), a single-equilibrium reward-based framework inspired by Attention-Gated Brain Propagation and neuromodulatory signaling. After reaching a free equilibrium, NEL propagates a reward-dependent modulatory signal derived from the selected action through reciprocal feedback connections to drive local synaptic updates, eliminating both the reward-nudged equilibrium and contrastive update. We evaluate NEL on MNIST, Fashion-MNIST, and CIFAR-10 using multilayer perceptrons and convolutional networks. NEL approaches reward-based Equilibrium Propagation (REP) in shallow architectures, with gaps of 0.67 and 1.20 percentage points on MNIST and one-hidden-layer Fashion-MNIST, while larger gaps emerge in deeper and convolutional networks. A direct cost feedback control using the full supervised output error does not systematically improve over NEL, indicating that sparse reward information alone does not explain the remaining gap to REP. These results show that effective reward-driven learning can arise from a single free equilibrium while motivating further investigation of the computations provided by reward-nudged dynamics.

Biological neural systems learn new behaviors while retaining earlier ones, whereas sequentially trained artificial networks often overwrite parameters and forget previously learned behaviors. We introduce the Context-modulated Synaptic-states Recurrent Neural Network (CoSyn-RNN), a new continual-learning model inspired by heterogeneous synaptic states and neuromodulatory control. CoSyn-RNN combines sparse recurrent allocation with a discrete protection rule: after each task, recurrent neurons whose synaptic weights cross a fixed threshold form a task-specific neuron group, and their associated parameters enter a protected state during later learning. A neuron-specific gain and a task-cued mask over a fixed base readout control how recurrent activity contributes to behavior. Across various task sequences consisting of many cognitive tasks, training and validation losses and accuracies were maintained throughout learning. The protection rule produced modular, task-ordered recurrent structure compatible with forward reuse of earlier computations. Pairwise recruitment measurements further defined minimum- and maximum-cost curricula that produced markedly different final recurrent structures and different remaining capacity for future learning. Thus, CoSyn-RNN provides a biologically inspired model in which protected synaptic states, sparse allocation, and context-dependent modulation support continual learning.

Decision-making requires accumulation of evidence over time, yet exactly how neural circuits implement this computation remains debated. Classical models posit that evidence accumulation is realized by ramping neural activity, whereas recent experimental findings suggest an alternative mechanism in which neural activity remains largely silent before abruptly transitioning into an active decision state. This mechanism leaves a fundamental question unanswered: how is evidence accumulated during the neural activity-silent period? To address this question, we trained excitatory-inhibitory recurrent neural networks (RNNs) with short-term synaptic plasticity (STP) on a reaction-time decision task. We found that after training, the networks learned to leverage STP to make decisions in an activity-silent manner. Choice-tuning analysis revealed a clear functional organization of the network, and connection-pruning analysis uncovered the coupling between choice-selective excitatory and inhibitory neural groups. Guided by the architecture of trained RNNs, we constructed a minimal neural circuit model, in which evidence accumulates in facilitated synaptic efficacy that progressively reshapes the circuit's phase portrait, eventually driving the network state across the stability boundary and triggering a rapid transition to a choice state. We further compared activity before a choice between the theoretical STP and Static models to examine the potential energy benefit of activity-silent decision-making. Together, our results suggest STP as a mechanism for evidence accumulation in activity-silent decision-making and offer insights into the design of energy-efficient artificial neural networks.

This paper introduces a sensorimotor learning framework for a corticocerebellar network, grounded in the perspective of population dynamics. Using an optimal control theory approach, the cerebellum model enhances preparatory activity through premotor input, allowing the motor cortex to reach the desired initial conditions for movement more efficiently. Unlike traditional motor learning approaches that focus on acquiring new skills, this paradigm emphasizes automatization of already executable behaviors through repetition driven by intrinsic motivation. The proposed model is evaluated using a center-out reaching task, demonstrating that the role of the cerebellum is to shorten the preparatory period required for the successful execution of the movement. These findings suggest that corticocerebellar interactions play a crucial role in optimizing motor preparation, offering insight into the neural mechanisms underlying movement efficiency.

We present a network model that enables a navigating agent to shape the spatial and temporal structure of its paths through its environment. The model is inspired by the insect fan-shaped body. In it, a recurrent neural network receives an input that encodes an agent's velocity vector. Meanwhile, network activity determines the setpoint of a control loop that influences this velocity vector through motor outputs. The network thus guides future movement using memory of past movement. We illustrate how the network's dynamics determine the trajectory features it extracts to produce the setpoint. We then relate the joint dynamics of network activity and the agent's velocity vector to the structure of the resulting paths. This network can produce paths suitable for different forms of exploration. It can also stabilize movements initiated by lower-level systems. Our analyses illustrate how recurrent neural dynamics and memory can shape behavior when embedded in closed loops.

We have studied the emergence of slow relaxation oscillations in next generation neural mass models with spike frequency adaptation. Relaxation oscillations connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale the higher is the complexity (number of peaks) displayed by the relaxation oscillations. In particular, a chaos-induced spike-adding mechanism regulates the increase in the number of peaks. In analogy to what found in the Hidmarsh-Rose neuron model, two different types of chaotic behaviors have been identified: Population Spiking and Population Bursting Chaos. The increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Indeed, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength. HighlightsO_LISpike Frequency Adaptation (SFA) promotes the emergence of Slow Relaxation Oscillations C_LIO_LISpike-adding mechanisms, controlled by SFA, lead to Relaxation Oscillations of increasing complexity C_LIO_LITwo types of chaotic behaviours: Population Spiking and Population Bursting Chaos C_LIO_LISFA regulates Up and Down States durations and their correlation C_LI

Serotonergic psychedelics, such as LSD, psilocybin, and DMT, have strong effects on human brain activity, yet their mechanisms of action are only partially understood. Here, we present a biophysically-based mean-field model that integrates cellular and network-level details to simulate the effects of these compounds at different spatial scales. By incorporating the brain-wide distribution of 5-HT2A receptors, our model mechanistically links receptor activation through reducing leak membrane potassium conductances, based on electrophysiological data. Our simulations reveal that this microscopic perturbation leads to the emergence of a brain state characterised by asynchronous irregular dynamics with increased firing rates and alterations in spectral power, in particular reduction of alpha-frequency bands, consistent with empirical findings. This change in dynamics is accompanied by an increase in spontaneous complexity, as quantified by the Lempel-Ziv complexity index, as observed experimentally. Furthermore, our model accurately replicates experimental findings regarding the Perturbational Complexity Index (PCI), demonstrating that PCI does not increase significantly by psychedelic drug administration. This crucial dissociation, where spontaneous complexity and spectral power are affected while perturbational complexity is preserved, highlights the distinct neurophysiological substrates underlying different metrics in psychedelic states. Our multiscale model provides a robust, mechanistic framework for understanding how psychedelics modulate global brain activity.

With 302 neurons and a rigorously characterized connectome, the nematode Caenorhabditis elegans represents a powerful model organism to study the fundamental roles of neuronal circuits in behavior. However, despite the breadth of research, many questions remain unanswered regarding how these organisms are able to successfully navigate their environment. Here, we present a biologically grounded dynamical circuit model for the investigation of sensory-guided behavior during C. elegans chemotaxis. Our mathematical model consists of the chemosensory neuron AWA, interneurons RIM and RIA, motor neurons, including SMDs and RMDs, and body wall muscles that provide proprioceptive feedback through stretch receptors. After optimization with an evolutionary algorithm, the model locomotes effectively toward a chemical attractant, realistically capturing nematode chemotactic behavior. Chemotaxis is ensured by sharp turns, which resemble the omega turns of living nematodes, as a key emergent property of the model. The sharp turning behavior is triggered by decreases in the concentration of the attractant. These result in reduced AWA activity, which in turn triggers disinhibition of RIM and subsequent changes in RIA oscillations. The ensuing coordinated changes in downstream motor neurons activity patterns produce sharp turns, which correct the nematodes path, so that the model worm heads toward the attractant, and remains at its proximity, after it reaches the gradient peak. The proposed framework, along with its emergent dynamics, provides new insights into the minimum requirements for C. elegans circuitry to display major features of its chemotactic behavior, including omega turns. In parallel, it generates experimentally testable hypotheses with respect to the participating neuronal elements.

Astrocytes actively regulate synaptic transmission and neuronal excitability, yet their role in orchestrating macroscopic cortical network regimes and slow-wave oscillations remains an active area of reasearch. This study investigates how bidirectional neuron astrocyte interactions shape emergent population dynamics using a computational network model of excitatory and inhibitory neurons coupled to an astrocyte. The results identify astrocytic feedback topology, rather than astrocytic coupling strength alone, as a key determinant of emergent cortical network dynamics. By systematically dissecting pathway-specific connectivity, it has been shown that the neuronal population driving astrocytic activation and the neuronal population receiving gliotransmission jointly determine whether the network occupies asynchronous irregular (AI), synchronous irregular (SI), synchronous regular(SR), asynchronous regular(AR) or quiescent regimes.Directing gliotransmission selectively onto excitatory neurons consistently promotes population synchrony regardless of the population influencing astrocytic dynamics, whereas selective modulation of inhibitory interneurons induces network quiescence via strong suppression. Under dual-target gliotransmission, network synchrony is dictated by the population driving astrocytic dynamics: excitatory-only drive promotes synchrony, while combined or inhibitory-specific drive preserves asynchronous states. Furthermore, the model reveals that astrocytic signaling kinetics provide an additional temporal control mechanism that regulates the frequency and persistence of self sustained up states.

Electrical stimulation of brain activity has emerged as a key therapeutic intervention for neurological diseases. The success of these approaches relies on precisely tuned stimulation parameters. A major challenge is that these parameters should ideally be adjusted in real-time based on changes in brain activity. Closed-loop controllers address this challenge by monitoring brain activity and adapting stimulation according to ongoing changes in neural dynamics. While machine learning has been helpful in this context, closed-loop controllers typically do not adapt in real-time to fluctuations in brain activity. Here, we propose a novel framework based on reservoir computing to train a closed-loop, real-time neural controller. This approach, termed CLEAR-FORCE, trains the output weights of a recurrent network based on a combination of target signals and feedback from brain activity. Two series of simulations were performed, where the controller was successful at (1) inducing neural oscillations in a population of spiking neurons and (2) suppressing pathological oscillations. This framework provides a promising avenue for the implementation of neural controllers in low-powered, real-time, and adaptive hardware that harnesses machine learning for the personalized treatment of brain disorders.

Deep Brain Stimulation (DBS) is an established clinical treatment for a variety of neurological disorders, including Parkinsons Disease where it has been shown to reduce motor symptoms as well as disrupt pathological beta oscillations in the basal ganglia. The mechanisms of action of DBS on the collective activity of neuronal circuits is not fully understood. We use a recurrently-connected excitatory-inhbitory network based on the Brunel network architecture that can produce activity in a variety of states. Using a model of DBS that can reproduce observed effects such as antidromic activation, local somatic suppression, and axonal activation, we characterize the effect of stimulation across the entire parameter space of the network. We show that the effects of stimulation are dependent on the baseline state of the network, with the level of beta suppression dependent on the level of inhibition and the external drive. Specifically, networks with higher inhibition and lower drive show greater disruption of beta oscillations. We further show that networks in different states are preferentially sensitive to different frequencies of stimulation, suggesting that alternative protocols to the clinically standard high-frequency stimulation may have therapeutic efficacy.

The precise mechanism through which Deep Brain Stimulation (DBS) mitigates freezing episodes in Parkinsons disease remains unknown. We modelled Parkinsonian freezing using a model of the basal ganglia that adopts a Dynamic Neural Field network for simultaneous action selection (selecting which action is executed) and specification (resolving the continuous parameters governing how that action is performed). Action selection success was based on whether activation surpassed a threshold. The model robustly differentiated healthy and dopamine-depleted (Parkinsonian) conditions, producing stable action selection under healthy dopamine and impaired, freeze-prone dynamics following depletion. We then modelled DBS as a scaled reduction in afferent drive to the subthalamic nucleus and globus pallidus internus. While this formulation has succeeded in previous computational work, it did not yield consistent restoration of action selection within our framework, motivating future investigation of alternative DBS formulations.

How transient neural representations become integrated and stable enough to function as internal neural models remains incompletely understood. Grounded in efficient coding, Bayesian and predictive frameworks, recurrent and attractor dynamics, neural state-space models, and systems neuroscience, the Principle of Representation Integration for Stable Models (PRISM) proposes five operations: extraction, compression, integration, stabilization, and prediction/action. Here we developed PRISM-M, a minimal nine-equation recurrent dynamical realization with an explicit contraction condition (0 < J < 1), to examine whether these operations can generate persistent, context-sensitive, and prospectively informative model states. Seven simulation analyses showed persistent but revisable trajectories and a 0.209 context-dependent shift in the event-period model state. A 60 x 60 parameter sweep identified 719 rigid, 2,344 adaptive, and 537 high-gain trajectories within this structurally contractive parameter space, and the same regimes were recovered across 1,000 randomized environments. Perturbations of extraction, integration, and stabilization altered model trajectories, whereas the scalar compression perturbation had a small effect. The full PRISM state predicted the next model state more accurately than the model-state-only baseline (RMSE 0.0186 versus 0.0218), while performing similarly to an unconstrained ARX model. In the BART dataset, spatial fMRI states were distinguishable in 155 participants (69.7% accuracy; 33.3% chance), and inflation-related activity was modestly associated with pumping behavior in the 99 participants with matched behavioral data ({beta} = 0.198, P = 0.040). PRISM-M provides a constrained, testable framework centered on four operational signatures of model-like organization structured representation, contextual integration, persistence or reconstructability, and prospective relevance.

Competitive spiking networks can form sensory representations through local synaptic plasticity and lateral inhibition. A canonical example is the Diehl-Cook architecture, in which Poisson-encoded sensory inputs drive excitatory neurons through spike-timing-dependent plasticity (STDP), while a separate inhibitory population imposes competition between excitatory units. In most implementations this competitive circuit is fixed, although inhibitory synapses are plastic in cortical circuits and contribute to excitation-inhibition balance. It therefore remains unclear under which conditions biologically motivated inhibitory plasticity can replace fixed lateral competition without disrupting representation learning. Here we study this question in a competitive STDP network trained on MNIST. We compare fixed inhibition with a Vogels-style inhibitory STDP rule, slow homeostatic inhibition, and a budget-constrained slow homeostatic rule that conserves the total inhibitory input received by each excitatory neuron. A fixed-inhibition operating-point map showed that stability depends on the dynamical regime: 56% of tested fixed-inhibition runs completed training, whereas stronger inhibition at higher input gain produced runaway activity. The reference regime g = 2.0, wIE = 10.0, selected for subsequent comparisons, combined complete stability across replicate initializations with high classification performance (84.3 {+/-} 0.6% after 30,000 training examples). In this regime, the budget-constrained rule was stable in all replicate runs when its inhibitory budget matched the fixed-inhibition reference (BI = 3990), reaching 83.5 {+/-} 0.6% accuracy with firing-rate and inhibitory-conductance statistics close to fixed inhibition, whereas a mismatched budget (BI = 7980) produced runaway activity in every replicate. Parameter maps showed that Vogels-derived iSTDP was broadly but not uniformly stable (90% runs completed), while slow homeostatic inhibition was even more broadly stable (96%). Budget-constrained stability depended strongly on the conserved budget, i.e., low and matched budgets were stable or nearly stable, intermediate budgets were mixed, and BI = 7980 failed in all tested runs. These results show that inhibitory plasticity in competitive STDP networks is not governed by a local homeostatic update alone. Stable plastic competition depends jointly on the operating regime and on an inhibitory budget that fixes the total strength of competition while allowing local inhibitory weights to adapt. Mechanistically, budget matching separates local redistribution of inhibitory weights from changes in total inhibitory drive, preventing plasticity from shifting the network away from a stable competitive state. This identifies inhibitory budget matching as a practical design principle for replacing fixed inhibition with plastic, homeostatically regulated competition in STDP-based spiking networks.

Mean-field models are extensively used in large-scale brain simulations because they provide a wieldy description of population dynamics while preserving key features of neural activity. Despite their widespread adoption, no common and reproducible methodology currently exists to systematically derive and validate mean-field models starting from biologically grounded single neuron dynamics. As a result, implementations are often ad hoc, difficult to reproduce and rarely reusable. Here we introduce BRIDGE, a modular, open-source Python pipeline that enables the bottom-up reconstruction, analysis, validation, and simulation of mean-field models from single neurons. The framework integrates single neurons modelling, network simulations, extraction of population statistics, parameters analysis, quantitative comparisons between spiking neural networks and corresponding mean-field representations, and simulation of network of mean-fields. Its flexible architecture allows users to incorporate different neuron models and to generate region-specific or state-dependent mean-field formulations. BRIDGE provides a reproducible foundation for developing biologically informed mean-field models suitable for large-scale and whole-brain simulations, supporting the transition from generic homogeneous population models toward region-specific ones. Graphical abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=91 SRC="FIGDIR/small/742067v1_ufig1.gif" ALT="Figure 1"> View larger version (28K): org.highwire.dtl.DTLVardef@1124404org.highwire.dtl.DTLVardef@2f8b2aorg.highwire.dtl.DTLVardef@1598f37org.highwire.dtl.DTLVardef@c9814b_HPS_FORMAT_FIGEXP M_FIG C_FIG

Decision formation is commonly described as the accumulation of noisy evidence in a low-dimensional decision variable, but it remains unclear how this latent computation is implemented by heterogeneous neural responses. Here, we propose that ramping and sequentially firing neurons form complementary population codes for the same decision variable. Inspired by Laplace-domain neural representations of time, exponential receptive fields in a ramping population give rise to a translatable edge-like activity profile; localized receptive fields in a sequential population give rise to an aligned bump-like profile. We construct a continuous attractor neural network that dynamically maintains these complementary representations while implementing evidence accumulation along a shared latent manifold. At the behavioral level, simulations show that the circuit closely reproduces the single-trial trajectories, choice probabilities, and reaction-time statistics of a standard diffusion decision model while generating heterogeneous ramping and sequential neural responses. Our framework connects latent behavioral dynamics, population geometry, and recurrent circuit mechanisms. More broadly, it provides a circuit-level realization of computation in the Laplace domain that may support the representation and updating of continuous cognitive variables across decision making, timing, memory, and spatial cognition.

Locusts possess a collision-sensitive pathway in their visual system culminating in a neuron, the lobula giant movement detector (LGMD), which preferentially responds to looming stimuli. The LGMD is also notable for its reduced or absent response to other stimuli, such as translating objects, wide-field motion, and incoherent images of looming objects. While experimental and modelling work have both shed light on the various mechanisms underpinning these properties, broad examinations of how these mechanisms interact with each other and with diverse stimulus types have been limited. To address this, we developed a model incorporating mechanisms from recent literature, and subjected to an array of looming stimuli with varying size-to-speed ratio, polarity (OFF and ON), and coherence; wide-field background motion, translating stimuli, and trajectory changes were also examined. The model showed quantitative and qualitative fidelity to biological data in its replication of a wide variety of stimulus responses, with its preference for incoherent visual stimuli being a notable exception. Based on investigations with various inhibition types removed, it was shown that lateral inhibition predominantly suppressed wide-field motion responses. Global inhibition both normalized growing excitation over the course of looming, and improved recognition of looming stimuli against moving backgrounds. Feedforward inhibition was found to have diverse roles, including shaping peak response time and its variability, and improving coherence selectivity. The success of the model in replicating multiple stimuli also showed the plausibility of several underlying assumptions, including sharing of input between the LGMD and multiple other neuron types.

Parkinson's disease (PD) gait is characterized by reduced walking speed, short shuffling steps, increased double stance time, and increased step time variability. The most debilitating symptom in PD is freezing of gait (FOG), a context-dependent locomotion arrest, mostly occurring while encountering turns, obstacles, and narrow pathways. FOG is more pronounced during turning, a complex task that challenges motor planning and execution. Here, we simulate this phenomenon using a computational model inspired by the cortico-basal ganglia circuitry, based on reinforcement learning (RL) principles. In the model, the agent was trained to learn a value profile while navigating a path that involved turning. To simulate PD conditions, we clamped the temporal difference (TD) error, typically associated with dopaminergic signaling. Our model results show that compared to healthy controls (HC), PD non-freezers and PD freezers exhibit a reduction in turning velocity and step length, alongside an attenuated compensatory step-width widening at the sharpest turn, more pronounced in PD freezers, who additionally show increased step time variability. These kinematic impairments worsen during tighter turns. Ultimately, this model implicates FOG as a problem of impaired estimation of value over space and could potentially represent a generalized deficit in gait impairments in PD.