Neural Computation

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.

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.

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

Microstate analysis starts with clustering and the meta-criterion is a heuristic to find an optimum cluster number. We address the following questions: (i) what number is found for non-cluster-forming dynamical systems, (ii) do centroids fall in random attractor regions, (iii) do EEG topographies form clusters or a single connected structure in sensor space? We find that (i) the meta-criterion suggests spurious optimal cluster numbers (4-8) with high confidence on different attractor geometries, (ii) cluster centroids reliably fall in the same attractor regions, (iii) topological analysis of dynamical systems and resting-state EEG suggests that all form a single connected structure in their respective phase space, not clusters. We conclude that the meta-criterion should be used with caution and its results should not be taken as representing a ground truth. Cluster numbers deviating from the meta-criterion should not be discarded. A more far-reaching implication is that evidence for the existence of clusters in resting-state EEG data is still lacking. Microstate clustering may correspond to the partitioning of a single connected structure.

Extensive studies suggest the brain performs Bayesian inference to infer the latent world states. It is a fundamental neuroscience question that how canonical recurrent neural circuits in the brain implement Bayesian inference. Many existing theoretical studies focused on how the recurrent circuits compute the posterior, while largely overlooking how the circuits compute the model evidence (normalization constant in Bayes' theorem), a key quantity that measures how well a model explains the observed data.Thus, it remains largely unknown about how the recurrent circuits compute the model evidence. The present study performs rigorous theoretical analyses of the continuous attractor networks, a canonical recurrent circuit model, and reveals that the nonlinear circuit dynamics can simultaneously compute the posterior and model evidence in first two dominant subspaces within the circuit dynamics. Specifically, the circuit dynamics in the stimulus feature subspace implements the Langevin posterior sampling, and the circuit dynamics in the subspace of total neuronal activity computes the model evidence in a way analogous to the evidence lower bound in stochastic variational inference. We further extend the circuit model to compute the model evidence of multiple inputs, and simulations validate the computation in the network. Our work for the first time reveals the concurrent model evidence and posterior sampling in subspaces in continuous attractor networks, significantly deepen our understanding of the computational algorithms adopted by the neural circuits.

Echo state networks (ESNs) are efficient, neuro-inspired computational frameworks well suited to time-series data. However, ESN decision confidence is typically quantified in limited ways. We propose an explicit decision-confidence readout neuron, trained from decision readout outputs, to continuously monitor confidence as decisions form. In a simulated decision task, confidence activity increased with stimulus strength, linking greater discriminability to higher confidence. We then evaluated the model on EEG-based motor imagery classification, showing that confidence activity increased with decision accuracy and discriminated correct from error decisions, particularly in higher-performing participants, reflecting human-like metacognition. Overall, this approach enables continual monitoring of decision confidence, supporting more trustworthy ESN decisions, particularly in biomedical applications.

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.

Emerging research on desynchronization reveals strong relations to memory formation and recollection with much of the evidence originating from studies of the hippocampus, a brain region central to memory processing. However, growing evidence emphasizing the role of desynchronization is accompanied by challenges, most notably the synchronization/desynchronization conundrum. The conundrum arises from an apparent contradiction between learning and Shannon's information theory: spike-timing-dependent plasticity (STDP) acquires information via synchronized populational activity whereas information theory suggests that information channel is encoded through higher variability. Both frameworks are well-founded. Learning is widely accepted as the mathematical abstraction of STDP while Shannon's information theory showcases its power ubiquitously across fields from communication systems to neuroscience. Here, we propose that learning and Shannon's information theory are not necessarily opposing principles. Rather, learning plays a critical role in the process of synchronization and desynchronization. To justify our claim, we conduct computational simulations based on a Hodgkin-Huxley neuronal model coupled with NMDA, AMPA, and GABA synapses with inputs of biologically realistic spiking data. Our results show that enabling STDP significantly influences synchronization and desynchronization dynamics. Specifically, we find that STDP and desynchronization form a regulatory loop, in which STDP regulates the level of synchrony, and synchrony regulates subsequent learning strength. Further study reveals STDP is capable of switching neurons from synchronization to desynchronization. This framework mitigates the synchronization/desynchronization conundrum by clarifying the relationship between desynchronization and learning, and offers a new perspective on how synchrony contributes to memory formation and recollection.

Predictive coding is a powerful normative framework for understanding cortical computation, but it is still an open question how biologically plausible networks with local plasticity support predictive inference and representation learning. In this work we show that a recurrent excitatory-inhibitory circuit with purely local plasticity can perform predictive inference without explicit error representations. We establish a direct analytic link that shows that learning in these circuits requires the weights to remain on a consistency manifold where recurrent inhibition matches the inhibition required by the predictive coding objective. Using a closed-form derivation of the consistency condition, we derive a plasticity rule that maintains it exactly under a Gaussian prior. Under a non-Gaussian prior, we find the rule supports learning sparse, factorized features, such as edge detectors from natural images. We show empirically that a BCM-like rule with an activity-dependent threshold approximates this well, while other Hebbian-like rules tend to learn less accurate solutions because they keep the weights too far from this manifold. With recurrent excitation the networks acquire spatiotemporal features like direction selectivity, and the ability to complete partially observed sequences. Time-continuous learning then leads to the development of low-dimensional attractor-like structures and noise-driven replay. Overall, these results link predictive coding to local circuit plasticity, show it does not require an explicit prediction error representation, and suggest a normative role for BCM-like plasticity in excitatory synapses.

The power spectrum of electrophysiological signals exhibits both narrowband peaks and a broadband 1/f-like slope. The two are routinely treated as separable components: a "periodic" foreground and an "aperiodic" background; and each has been related to behaviour, cognition, and clinical status. This paper argues, and illustrates with simulations and case studies, that the boundary between the two is less sharp than the standard decomposition assumes: non-stationary amplitude modulation of an oscillation can inflate the apparent spectral trend (whereas clean periodic modulation does not, its sidebands being absorbed into the peak), and a broadband process viewed through any narrow band produces an envelope that mimics amplitude modulation. The two phenomena are mirror images of the same underlying property, that the temporal envelope and the spectral slope are coupled. I show what this means in practice with a set of illustrative scenarios and three case studies (a simulated alpha lateralisation paradigm, an auditory oddball ERP, and simultaneous scalp EEG and ECoG under rest and propofol sedation). I argue that the question "is the observed change a change in the aperiodic component" cannot in general be answered from time-series analysis alone, and that the temporal envelope of detected oscillations carries information that the static power spectrum loses. I ultimately argue that the conventional periodic/aperiodic partition of neural power spectra conflates a more fundamental distinction: between processes whose amplitude is stationary over the analysis window and processes whose amplitude changes. Transferring the dichotomy from the spectral domain to the time domain, from periodic/aperiodic to static/dynamic, reveals structure that the power spectrum alone cannot recover.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

Online identification of nonlinear dynamical systems faces two challenges. Noisy, partial observations make the latent state difficult to estimate. Local attractors can also keep passive trajectories in regions that reveal little about the unknown dynamics. Both challenges commonly arise in closed-loop neural experiments where stimulation must be chosen from noisy spike counts, while neural activity may remain near a stable state unless stimulation drives it elsewhere. We address this problem by actively selecting inputs to collect informative observations during the experiment. We introduce PALDI (Planning-based Active Latent Dynamics Identification), which combines extended-Kalman state prediction, single-step Laplace state updates, blockwise Gaussian parameter updates, and finite-horizon planning. Its parameter expected-information-gain surrogate combines dynamics sensitivity with state Fisher information and discounts apparent parameter information when latent states are uncertain. We compare PALDI with nonadaptive inputs, a myopic policy, and two active baselines: the one-step D-optimal method FLEX and receding-horizon curiosity with uncertainty sampling. On a bistable Wilson-Cowan model of excitatory and inhibitory populations, PALDI approaches the true-model reference and remains strongest as the observation signal-to-noise ratio decreases or the readout geometry becomes biased. We then test identification in a spiking decision network where we use a reduced dynamics and observation model to approximate the data-generating process. PALDI reaches a median held-out prediction R2 of 0.90, close to a fitted reference, and its model gives the highest change-of-mind success among identification policies. Information-guided finite-horizon planning is a practical strategy for identifying neural circuit dynamics with closed-loop stimulation.

The brain frequently updates or controls its internal representations of sensory or motor variables over time. An example is transsaccadic updating of stimuli's retinotopic positions: When the eye moves in one direction, the positions are updated continuously in the opposite direction, and the process is controlled by the corollary discharge (CD) of the saccade motor command. We previously trained neural networks to perform such updating using the desired time courses of stimuli's positions at every time step. However, this may not be biologically plausible because, before a system learns to perform the task, it may not have access to complete time courses and the actual visual inputs are delayed and thus incorrect. Here we show that by adding the continuity equation to the loss, we can train neural networks with only stimuli's pre- and post-saccadic retinotopic positions (without specifying the intermediate transitions), and with heavily down-sampled time courses. Moreover, both the connectivity patterns and the CD control signal can be learned simultaneously. Since the continuity equation can be applied to waves of neural population activities that are distributed representations of variables, our work also suggests an advantage of distributed representations which are ubiquitous in the brain.

Real-world acoustic inputs contain rich sensory information that we parse into discrete auditory objects and categories. Although deep neural networks (DNNs) are increasingly used to model auditory perception, the field lacks rigorous behavioral benchmarks, particularly for auditory event categorization. Here, we developed a 25-way categorization paradigm for broad classes of natural sounds to test whether categorical invariances of DNNs align with those of human observers. We first confirmed that humans could reliably categorize the natural sounds, demonstrating that our paradigm is well-suited for testing invariances in auditory categories. To probe model invariances, we evaluated human recognition of model metamers (synthetic stimuli matched to the models internal activations for each natural stimulus) for a wide range of architectures trained on speech or auditory event recognition. Evaluating widely-used public models, we found that human recognition of auditory event model metamers was generally influenced by the training task and data distribution; speech models trained on standard, curated datasets produced less recognizable metamers than auditory event recognition models. We additionally analyzed a controlled set of models to directly investigate the influence of training task and adversarial training, revealing that improved metamer recognition induced by adversarial training is task-dependent. However, even in the best-performing models, we observed a sharp decline in human recognition at the final classification layer compared to the penultimate representation layer. Overall, our results suggest that while invariances in modern architectures better align with human observers for auditory event categorization, there is still a large discrepancy between the categorical invariances of auditory neural networks and the invariances of human observers. Code and models are available at https://github.com/Feather-Lab/env-sound-metamers

The auditory system operates under a fundamental computational constraint: at any moment, it has access only to past and present acoustic information. At the same time, it processes sounds across multiple temporal scales, although the computational advantage of this organization remains unclear. Despite both being defining characteristics of biological auditory processing, causal processing and multiscale temporal processing are rarely considered together in computational models. Here, we introduce the Multiscale Convolutional Recurrent Neural Network (MSCRNN) architecture, a brain-inspired model designed to test whether processing sounds across multiple temporal contexts improves recognition under causal constraints. Multiscale processing substantially improved recognition under causal constraints, enabling performance comparable to non-causal architectures after an initial evidence-accumulation period while providing only limited benefit when future acoustic information was available. Analyses of the networks internal representations revealed a progressive transformation from stream-specific acoustic representations to increasingly integrated category-level representations across recurrent processing stages. Together, these findings provide a computational rationale for why biological auditory systems may benefit from multiscale temporal processing under causal constraints and establish the MSCRNN as an interpretable framework for generating and testing hypotheses about the temporal dynamics of auditory processing using electrophysiological and neuroimaging data.

Researchers in artificial intelligence increasingly intervene on language models to study how their functions are organized, silencing weights and attention components in ways reminiscent of the brain lesions long used to map language in post-stroke aphasia. Under this program of mechanistic interpretability, a common move is to ablate an attention head and read the resulting drop in a behavior as evidence that the head implements it. How much that move can establish about where a behavior is computed remains unclear, because a head whose removal disrupts a behavior is necessary for it but need not be the site where it is computed. We examined this question for the picture naming task, taking the loss of naming (anomia) that defines aphasia as the behavior of interest. Across six vision-language models, spanning three language backbones and a range of parameter scales, we ablated each attention head in turn during single-word picture naming and measured accuracy before and after. The degree of localization varied widely across models. In LLaVA-1.6-Vicuna-13B, a single early head (layer 0, head 20) was necessary: removing it alone reduced naming accuracy from 0.99 to 0.006. The same head was not sufficient, because retaining it while ablating the other 1{,}599 heads also produced 0\% accuracy. Two Mistral-backbone models (LLaVA-Mistral-7B and Idefics2-8B) had no critical head. An early-layer dependence was present in every model but varied in strength, whereas dependence on any single head ranged from dominant to absent. Within Qwen2.5-VL, a dominant head was present in the 7B model but not the 3B model, indicating that this concentration emerged with scale rather than being fixed across a model family, and it was not explained by attention type. These results show that ablating the head whose removal disrupts naming does not establish that the head computes the behavior, that the result generalizes across models, or that the behavior localizes to a head at all.

Nonlinear neural networks develop structured internal representations, yet how their geometry is determined by the tasks being learned remains poorly understood. Here, we develop an analytical framework for piecewise-linear feedforward and recurrent networks that links learning, activation-region structure, and neural selectivity. We show that, at any stationary point of gradient-aligned learning, a nonlinear network decomposes into local linear regressions over its activation regions. Deviations from the corresponding least-squares solutions are jointly constrained by network weights shared across regions and vanish in the low-error regime, yielding an approximate piecewise least-squares decomposition of the task. This structure admits a decision-tree interpretation, which we recover numerically by fitting trees to predict network activation patterns from the input. We further derive how the regions in which neurons are active determine the task statistics they capture, thereby organizing neural selectivity into distinct subpopulations. The resulting predictions closely match the selectivity geometry observed in simulated networks and two empirical neural datasets. Finally, we show that neural baseline regulates activation pattern diversity, placing networks along a continuum between coarse, generalizing representations and fine-grained, expressive representations. Together, these results establish activation regions as a unifying framework for describing how nonlinear networks decompose task structure into local computations and how those computations can be revealed through neural activity.

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.

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or bifurcations, the approach focuses on the geometry of membrane potential trajectories. The changes in concavity during the upstroke of an action potential can be directly obtained from a time series of voltages. The concavity criterion is then extended to models based on autonomous dynamical systems where the changes in concavity can be obtained analytically from a curve of inflection points in phase space. The inflection point manifold defines a region required for excitability: all the orbits that cross it contain action potentials, and all the trajectories that contain action potentials are in it. This analytical principle can then be used to define excitability in a dynamical system, and also a measure of excitability that enables quantification and comparisons of excitability across dynamical system. The measure provides a way to compare the excitabilities of systems that model neurons with different electrophysiological phenotypes and consider different stimulus conditions. The traditionally vague physiological concept of electrical excitability is transformed into a rigorous analytical description by considering the time-dependent curvature of the membrane potential. The criterion is robust across smooth, single compartment models of electrical excitability and can be can be extended to single compartment models in higher dimensions, and multicompartment models as well.