Neural Networks

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.

Whole-brain connectomes are increasingly used as wiring diagrams for spiking simulations and as structural priors for artificial networks, usually after an ad hoc synapse-count threshold whose effect on validated function has never been measured. We define function-preserving sparsification - removing edges under a fixed budget while preserving validated behaviour and population responses - and study it in the leaky integrate-and-fire whole-brain model of Shiu et al. (2024). Six operators - weak-synapse pruning, uniform and weight-proportional random removal, degree-preserving rewiring, weight shuffling and a task-aware criterion - were compared at identical edge budgets across three validated circuits (sugar-evoked proboscis extension, its bitter suppression, grooming pathway specificity), silent and spontaneously active network states, and multiple seeds. Weak-synapse pruning preserves 79% of feeding output with 6% of edges, with a cliff at k* of approximately 9 synapses, whereas random, degree-preserving and weight-shuffled controls at the same budget abolish output, and weight-proportional random sampling survives only while it retains the strong-edge set: function resides in the conjunction of wiring placement and strength, not in degree statistics or synaptic mass. The cliff is task-dependent - grooming specificity collapses below k = 2 through disinhibition. In the active state failure changes character: output over-excites instead of vanishing, and bitter suppression is lost progressively from k = 5 and reverses at k = 31. A task-aware criterion preserves its training stimulus at 0.4% of edges but loses held-out inhibition first. These results provide a first benchmark for connectome sparsification and show that what must be kept depends on task and network state.

Neural sequences, characterized by neurons or groups of neurons that fire one after the other, have been observed in multiple brain regions, across species, and are known to underlie a diversity of brain functions. To flexibly support behaviour and cognition, neural sequences exhibit much variability in properties like their temporal width, baseline, and peak firing rate. Despite this variability and the central role that sequences play in supporting brain function, a framework that explains how flexible sequences are generated and dynamically maintained within a circuit is still missing. Here we go beyond traditional approaches that investigate a one-to-one relationship between network connectivity and specific sequential dynamics. Instead, we train recurrent neural network models to generate a repertoire of sequential dynamics and characterize the obtained connectivity matrices. We found that different connectivity matrices can generate the same neural sequence, yet all connectivity matrices that generate a specific sequence share a common connectivity profile, defined here as the average weight between pairs of neurons as a function of their distance in the sequence ordering. It is the connectivity profile, as opposed to the connectivity matrix, that serves as a fingerprint of the sequential dynamics and shapes the network response to perturbations of the neural activity. Our model predictions were consistent with results obtained from experimental data recorded across brain regions and across species. Finally, we demonstrated that neural sequences can facilitate and constrain the formation of a large repertoire of sequences in downstream brain regions, with the potential of acting as scaffolds for a wide range of computations. Altogether, our results explain how network connectivity can generate a diversity of neural sequences across circuits and how those sequences can be flexibly adapted. Our framework reveals sequences as a common algorithm to support brain function across brain regions and species.

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.

Flexibly recombining computational modules is essential for biological and artificial neural networks to rapidly adapt to changing environments. This requires modules to be shared across tasks rather than rigidly segregated, yet what determines this organization remains unknown. Previous work suggests that weight initialization shapes whether networks learn task-specific or generic representations, but it is unclear whether this extends to recurrent networks and, more importantly, to network connectivity. Here, we systematically vary the initial weight variance of recurrent neural networks and study them using a framework that allows us to identify the functionally relevant connectivity subspaces for each computational module. We find that networks with low initial weight variance converge to solutions in which different subtasks rely on largely overlapping weight subspaces, whereas high-variance networks implement subtasks in higher-dimensional, more segregated weight subspaces. Our results also provide mechanistic insights with implications for interpreting biological neural circuits and for designing efficient recurrent architectures.

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.

Neural recordings are usually analyzed by comparing neural spiketrains or comparing time bins (population vectors). If multiple variables drive the neural activity these comparisons will be affected by all of them. Our aim is to disentangle these different latent variables or covariates that drive neural activity and reveal their structure and geometry. The central idea of the paper is that a matrix is disentangled when its rows and columns are local on each other, a condition we call bidirectional locality. In such a matrix, rows and columns encode the same geometry and they respond to only one localized part of it. This suggests finding bidirectional local matrices in a given data matrix, from which we can recover the geometry of the covariates driving it in a straightforward way. We present two ways of doing just this. The first method, coherent projections, works by finding non-negative projections of the neural data matrix (neurons by time bins) that are bidirectionally local. The second method, clumps, works by finding dense submatrices of the neural data matrix, that each identify a local region of one covariate. We apply these methods to two neural datasets, showing that they can separate grid cell modules and reveal a movement-driven low-dimensional structure in the motor cortex.

Neurons in primate visual cortical area V4 display tuning for multiple visual features, including color, shape, texture, and depth. Whether and how these neurons are organized into functional architectures remains largely unknown. Using two-photon calcium imaging in anesthetized macaques, we recorded responses of hundreds of V4 neurons to natural images and used these data to train deep convolutional neural network models (digital twins), obtaining synthetic images (SI) that maximized neuronal responses. Based on their SIs, these neurons clustered into classes that spatially matched the orientation, color, and curvature maps from intrinsic signal imaging. Furthermore, lesion study in digital twins revealed different integration rules for different neuron classes. Thus, digital twins of V4 neurons can be applied as a promising tool to characterize neurons fundamental features, which underlie the functional clustering in this area. HighlightsO_LINeurons in V4 are examined with two-photon calcium imaging and DCNN modeling (digital twins) C_LIO_LISynthetic images derived from neurons digital twins reveal distinct neuron groups C_LIO_LIThese groups match functional types defined by intrinsic signal optical imaging C_LIO_LILesion study in digital twins demonstrates neural mechanisms underlying feature tuning C_LI

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.

Large-scale Neuropixels recordings sample many brain areas, but no single experimental session records every area of interest. NeuroPaint, a transformer-based autoencoder, integrates such recordings by aligning area-specific latent dynamics across sessions and "inpainting" activity in unrecorded areas. Could a linear model, which would be computationally efficient and potentially more interpretable, suffice to achieve this? To address this question, we introduce Linear NeuroPaint, a linear variant of NeuroPaint, and evaluate it on two multi-area Neuropixels datasets. Linear NeuroPaint achieves strong predictive performance on recorded areas, however, it is less accurate than nonlinear models at cross-area inpainting, despite extensive hyperparameter optimization. Moreover, its parameters are not readily interpretable: incomplete cross-session alignment leads parameter-defined neuron clusters to exhibit heterogeneous response profiles. Together, these results show that linear transformations are insufficient for cross-session alignment and cross-area prediction. Nevertheless, Linear NeuroPaint provides a computationally efficient baseline for benchmarking multi-session neural models.

The human visual system integrates both static and dynamic information to support form and shape perception, yet the computational principles underlying the integration of motion for object recognition remain unclear. Artificial neural networks (ANNs) offer a computational framework for developing and testing hypotheses about these principles: if ANNs trained on motion-related tasks develop representations that align with brain activity and support object categorization, this would suggest that the training objectives and architectural constraints of these networks may capture key aspects of motion processing in biological visual systems in general, and motion processing for object recognition, in particular. Here, we investigated this question using "object kinematograms", stimuli in which object form is conveyed solely through motion cues. We measured neural responses of two higher regions of the lateral and the dorsal visual pathways, respectively, with strong sensitivity to dynamic cues from objects: lateral occipitotemporal cortex (LOTbio), and left supramarginal gyrus (SMGlh), as well as primary visual cortex (V1). We compared brain responses to representations extracted from two neural networks: SlowFast, a dual-pathway architecture trained on action recognition that processes slow- and fast-varying visual information with cross-pathway integration, and DorsalNet, a model of the primate dorsal visual pathway trained on embodied self-motion estimation. Representational similarity analysis revealed distinct representational profiles across brain areas, demonstrating functional specialization in motion-based form processing. LOTbio was best characterized by the slow pathway of the SlowFast model, whereas SMGlh showed strong similarity to both models. Critically, we found that representations aligned with brain activity also better supported behavioral function: the full SlowFast model, incorporating both slow and fast pathways, outperformed other models in few-shot categorization of object kinematograms and showed the highest similarity to human perceptual judgments. These findings demonstrate that with appropriate inductive biases, specifically, dual-pathway architectures for multi-scale motion processing and training objectives focused on dynamic visual tasks, ANNs can develop functionally useful representations of motion-defined forms that exhibit better alignment with the visual regions involved in processing dynamic visual signals.

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.

Hippocampal area CA3 is widely believed to serve a core memory function: retrieving distributed patterns of neural activity that were previously stored in the recurrent connections between neurons. However, it remains unknown how the physiological properties of individual neurons contribute to this function. Here, we present a mathematical analysis of a canonical recurrent neural network model of CA3. Our analysis provides three main, experimentally testable predictions for recurrent circuits performing stable memory recall. Two of these predictions, that pyramidal cells should be characterized by elevated intrinsic excitability and by inhibition-dominated recurrent connections, are consistent with previous experimental findings. We thus focused on testing the third prediction: that neuronal activation functions have an exponent slightly above $1$. For this, we performed \textit{in vivo} intracellular recordings of 49 pyramidal neurons from the CA3 area of behaving mice. Fitting a range of parametric models to these voltage traces and performing statistical model comparison revealed an average neural activation exponent slightly above $1$, confirming our theoretical predictions, with substantial heterogeneity across cells, which remains to be accounted for by the theory. An analysis of 133 further cells from two other previous studies provided neural activation exponent estimates highly consistent with those we found in our data. Our results suggest that the properties of hippocampal CA3 area are tuned to support reliable memory recall even at the level of single neurons.

Complex, high-dimensional brain representations are often difficult to understand intuitively. Recent advances in generative neural networks have made it possible to predict the optimal stimulus that maximizes the activity in a specific brain region. Because these stimuli are in image space, they provide an intuitive understanding of the functional properties of that region. Previous work on optimized stimuli has focused on passive perceptual tasks. Yet real-world perception operates in a closed loop with cognition and action, and so passive stimuli are unlikely to be optimal for many brain regions. In a previous study, we used fMRI to record BOLD activity from participants actively navigating through a virtual world. We identified a network of 11 cortical regions that support active navigation and are tuned for complex feature combinations. Here, we used a variational autoencoder to generate video clips predicted to correspond to maximal activity in each region. These preferred visual experiences capture dynamic scenes that incorporate both world events and participant actions. These preferred visual experiences provide intuitive descriptions of the functional properties of each region, and suggest that these regions are more engaged during dynamic than static scenes. These patterns also generate novel, data-driven hypotheses for future study.

Neural encoding of sensory information becomes more efficient when distinct stimuli evoke uncorrelated activity patterns. Spatial frequency (SF) information becomes decorrelated early in visual processing in a manner that involves both temporal differentiation in the dorsal lateral geniculate nucleus (dLGN) and firing rate differentiation in the primary visual cortex (V1). However, the specific functional circuit configurations that enable this synergy are not fully understood. To address this gap, we developed a geniculocortical subunit model to identify functional circuit configurations capable of producing a decorrelated V1 population response. We found that decorrelation could be explained by the combined activity of two complementary circuit configurations with distinct functional organization. The first circuit was characterized by temporally organized, late-onset dLGN inputs coupled to weak and delayed intracortical inhibition, whereas the second was characterized by less temporally constrained, early-onset dLGN inputs coupled to strong and early intracortical inhibition. Eliminating SF selectivity in upstream dLGN subunits did not affect SF decorrelation in the modeled V1 population response, indicating that decorrelation tolerates weak SF selectivity and is primarily driven by temporal organization. Together, these results suggest that biologically plausible circuit configurations are likely to produce SF decorrelation in the cortex through the temporal organization of feedforward inputs and intracortical inhibition.

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.

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.

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.

Recent advances in large-scale electrophysiological recording technologies now allow simultaneous measurement of spike trains from ensembles of neurons. A central challenge in mathematical neuroscience is therefore to identify functional assemblies and their collective organisation directly from this data. The goal of this work is to devise a method to infer the collective organisation of the neurons from their spiking activity. We construct weighted functional networks from neural spike trains using the van Rossum distance to quantify pairwise similarity. The functional network captures similarities in neuron firing patterns and provides a representation of their collective organisation. We hypothesise that similar neuronal assemblies will appear as clustered communities in the network, and employ the Louvain algorithm to detect such assemblies. We validate our approach using synthetic spike train data and simulated data from a stochastic block model of Leaky Integrate and Fire neurons subjected to external Poisson drives, where the ground truth is known. Finally, we apply our approach to large-scale recordings from the Allen Institute Visual Coding: Neuropixels dataset. We find that our methodology works well as long as a sufficient amount of data is available and the temporal structure is strong relative to the noise.