Neural Computation

Wave recurrent neural networks (wRNNs) are biologically inspired recurrent architectures that use traveling-wave dynamics to support sequence learning and memory. However, their input-to-hidden pathway remains relatively simple compared with biological neurons, where dendrites perform nonlinear input integration. In this study, we introduce the Dendritic Wave Recurrent Neural Network (DWRNN), which augments the input pathway of the wRNN with nonlinear basal dendritic branches while preserving the original recurrent wave dynamics. We evaluate DW-RNN on a simple copy task, sequential MNIST (sMNIST), permuted sequential MNIST (psMNIST), and noisy sequential CIFAR-10 (nsCIFAR-10). On the copy task, DW-RNN shows learning behavior comparable to the standard wRNN, suggesting that dendritic input integration does not disrupt the recurrent wave-based memory mechanism. On the three sequential image-classification benchmarks, DW-RNN outperforms the standard wRNN, improving accuracy from 97.27 {+/-} 0.15% to 97.82 {+/-} 0.12% on sMNIST, from 96.74 {+/-} 0.17% to 96.92 {+/-} 0.10% on psMNIST, and from 54.30 {+/-} 0.79% to 55.65 {+/-} 0.55% on nsCIFAR-10. In addition to improving mean accuracy, DW-RNN exhibits lower across-seed variability on all three classification benchmarks, suggesting that dendritic input integration may improve the stability of wRNN training. Hidden-activity visualizations further show that DW-RNN preserves the characteristic traveling-wave patterns of the original wRNN. These results suggest that dendritic computation and traveling-wave recurrent dynamics provide complementary mechanisms for biologically inspired sequence learning.

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation that has demonstrated competitive performance across a range of machine learning tasks. Recent work has extended EP to spiking neural networks (SNNs), leveraging leaky integrate-and-fire (LIF) neurons and spike-based plasticity rules to improve biological realism while maintaining strong performance. In this work, we propose an EP-based SNN framework that combines LIF neural dynamics with a predictive learning rule, replacing conventional spike-timing-dependent plasticity (STDP) with a learning rule more directly aligned with predictive coding principles. We evaluate the proposed model on multiple image classification benchmarks, including MNIST, KMNIST, and Fashion-MNIST, and compare its performance with a BP-trained LIF SNN baseline. Our results show that the proposed EP-based LIF model (EP+LIF) achieves competitive accuracy across datasets, with performance approaching that of the BP-trained counterpart (BP+LIF) while relying on a biologically motivated local learning rule. In addition, analysis of hidden-layer spiking activity reveals that EP+LIF produces more persistent hidden-state activity, whereas BP+LIF yields sparser spiking representations. These results demonstrate that predictive learning can support effective EP-based training in LIF spiking networks, while also highlighting differences in activity patterns that motivate future work on activity regulation and sparse spiking dynamics.

The learning dynamics of biological brains and artificial neural networks are of interest to both neuroscience and machine learning. A key difference between them is that neural networks are often trained from a randomly initialized state whereas each brain is the product of generations of evolutionary optimization, yielding innate structures that enable few-shot learning and inbuilt reflexes. Artificial neural networks, by contrast, require non-ethological quantities of training data to attain comparable performance. To investigate the effect of evolutionary optimization on the learning dynamics of neural networks, we combined algorithms simulating natural selection and online learning to produce a method for evolutionarily conditioning artificial neural networks, and applied it to both reinforcement and supervised learning contexts. We found the evolutionary conditioning algorithm, by itself, performs comparably to an unoptimized baseline. However, evolutionarily conditioned networks show signs of unique and latent learning dynamics, and can be rapidly fine-tuned to optimal performance. These results suggest evolution constitutes an inductive bias that tunes neural systems to enable rapid learning.

Segregation of speech into syllables is a key step in neural speech processing. It relies on the alignment of neural activity with the rhythmic structure of speech. Two competing hypotheses explain this neural speech tracking, phase-resetting and evoked responses. While phenomenological modelling of these hypotheses has been successful, we still lack understanding of the underlying cortical circuits. To investigate these mechanisms, we evaluate whether a biophysical next-generation neural mass model can reproduce several features of neural speech tracking, using phenomenological models of the competing hypotheses as algorithmic baselines. We investigate the models dynamics with four tests: recreating in-silico an EEG experiment that identified a correlation between tracking strength and phoneme sharpness, computing the Phase Concentration Metric, testing the effect of varying syllabic rates, and evaluating the Inter Event Phase Coherence across phoneme onsets. While all of the models that we study reproduce the sharpness-tuned rhythmic speech tracking, the evoked model requires a pre-processed acoustic edge impulse stimulus. We demonstrate that the neural mass model is performing thresholded phase-resetting triggered by sharp onsets in the continuous speech envelope. This produces cross-frequency nested oscillations that qualitatively match an experimentally-observed dual-peak signature in the Inter Event Phase Coherence. Our results indicate that the biophysical neural mass model provides a mechanistic bridge between generic oscillatory dynamics in cortical populations and the cognitive computations of speech tracking. Indeed, the non-linear dynamics of the neural mass model offer an explanation for how peak-rate event representations in auditory cortex activity arise in response to continuous acoustic input. Significance StatementSyllable segregation is crucial but challenging as natural speech lacks clear boundaries, yet humans perform this computation effortlessly. Speech aligns neural activity to syllabic rhythms, predicting syllable timing, but the underlying cortical mechanisms remain unknown. Relating this macroscopic behaviour to neurobiology is challenging; however, next-generation neural mass models promise to resolve this. We demonstrate that these models reproduce sharpness-tuned tracking and acoustic edge extraction. Dynamical analyses indicate this occurs through thresholded phase-resetting to phoneme onsets, triggering cross-frequency nested oscillations. Our results both advance biophysical understanding of syllable segregation and validate the models capacity for simulating macroscopic neural activity. These models offer a bridge between the neurobiology of the auditory cortex and speech processing dynamics that phenomenological models cannot provide.

Improving long-term memory in artificial neural networks remains an open challenge. To address this, we developed a novel brain-inspired framework for memory prioritization based on the principle of emotional valence. Our framework includes: (i) a valence-weighted cross-entropy loss that scales the learning signal by the valence magnitude, analogous to neuromodulation; (ii) an amygdala-inspired module that learns high-dimensional valence embeddings; and (iii) a hippocampus-inspired module that integrates valence embeddings into the attention mechanism to modulate information retrieval. We demonstrated the generalization of our framework across spatial, episodic, and language-based memory tasks, consistently improving memory prioritization and long-term retention of high-salience information. In addition to improving long-term memory, we also showed that our framework can help mitigate the "lost-in-the-middle" problem in language modeling. More generally, this research provides further evidence of the potential of brain-inspired algorithms to advance the field of machine learning.

The retina must encode visual information in a way that supports fast, predictive behavior despite significant processing delays. How this encoding adapts in an ever-changing world, when the temporal statistics of visual input shift, remains an open question. Here we record from populations of retinal ganglion cells in the axolotl as they respond to a stochastic moving bar stimulus across five different temporal correlation scales. Using the information bottleneck (IB) framework, and treating the prediction horizon as a free parameter inferred from the data, we ask what timescale of future motion the retina is optimized to predict under each stimulus condition. We find that the retina adapts its predictive encoding to the changing stimulus statistics: as the time constant of the stimulus dynamics increases, the inferred prediction horizon lengthens. The population shifts toward encoding more velocity information, and motion anticipation grows, all the while maintaining near-optimal prediction efficiency. Population surprise, quantified through a Boltzmann machine model of the retinal response distribution, tracks stimulus surprise under the inferred optimal compression. This connects the retinas reversal response to efficient predictive encoding. These results show that retinal population codes flexibly adjust their predictive timescale to the temporal structure of their inputs. More broadly, they demonstrate that the IB framework can be used to discover, not just test for, computational objectives in sensory populations.

Stabilizing synaptic plasticity together with the neurons activity has remained a central challenge in theoretical neuroscience since the introduction of Hebbian learning principles. Classical Hebbian learning rules typically lead to unbounded synaptic growth, motivating the development of stabilization mechanisms such as normalization methods, BCM-type learning, synaptic scaling and others. While these approaches can prevent divergence, they can also exhibit different limitations e.g. resulting in too-sparse synaptic configurations or leading to poor scalability with increasing network size. A recently introduced meta-plasticity mechanism, termed annealed linear learning (ALL), dynamically reduces the learning rate as neuronal output increases, thereby preserving stable and interpretable fixed-point behavior of the output. However, the original formulation leads to an irreversible decay of the learning rate, preventing adaptation to changing environmental conditions. To address this, in the present study, we balance learning rate reduction at large outputs with recovery at small outputs and in addition introduce forgetting that gradually reduces synaptic weights. These extensions allow the system to discard outdated representations and adapt to novel input conditions. Analytical investigations demonstrate that the favorable output fixed-point properties of the original ALL framework are preserved under the extended rule. Furthermore, simulations with an artificial agent show that the proposed mechanism enables robust and fast re-learning and adaptation in changing environments.

Dopaminergic signalling is central to value learning and decision making. It has been observed that multiple pathways with different patterns of connectivity project to midbrain dopaminergic neurons, some involving direct excitatory projections while others involve disinhibition. However, the respective contributions of these patterns to dopamine control, and their computational and functional advantages remain unclear. In the current work we simulate and evaluate two fully spiking neural models of dopaminergic control, based either solely on disinhibition, or solely on direct inhibitory and excitatory projections. We compare these models in terms of their engineering properties, their resulting spiking profiles, and their ability to successfully acquire representations of expected value in a 3-armed bandit task. We find that both models are able to operate at an asynchronous-irregular firing regime, but that the firing profile of the direct integration model is less resilient to disruption and more sensitive to incoming signals. In addition, the disinhibition model performs better in the learning task. We conclude that while the direct model is more parsimonious, disinhibition-based control remains advantageous in the operational context. Our results have implications for the study of decision-making brain circuits as well as for the design of brain-inspired systems.

Robotic motor control built on liquid neural networks and related continuous-time models, such as LTC and CfC, is typically trained offline via backpropagation through time and lacks an explicit mechanism for recalibrating online as plant dynamics change. We ask whether a frozen CfC core, whose liquid state spans a fixed continuous-time basis, can support cerebellar-style online adaptation by adapting only its linear readout with a climbing-fiber-like error signal. In a planar two-link reaching simulation with a velocity-dependent curl force field, we adapt the readout online with a feedback-error-learning (FEL) signal under a least-mean-squares (LMS) rule, leaving the core untouched. The frozen-core readout-only controller re-straightens curl-perturbed reaches and, upon field removal, produces a mirror-image after-effect, a behavioral signature consistent with internal-model learning, which a feedback-only controller does not produce. The result generalizes from a dense CfC to a sparse Neural-Circuit-Policy (NCP) wiring when the recurrent state, rather than the projected motor output, is used as the readout basis; it is robust to force-field strength and direction; and a recursive-least-squares variant adapts faster but de-adapts slowly because its covariance collapses, a rigidity that a covariance-reset safe-forgetting rule removes. Within the explored two-link planar simulation range, we did not find a readout-only failure case that required adapting the frozen core in the tested conditions. In this simulation study, adapting only the readout therefore provides a biologically inspired, low-cost online error-adaptation layer for offline-trained continuous-time controllers.

The awake brain is known to display asynchronous (AS) states during periods of attention and arousal, but the responsiveness properties of such states remain unclear. Here, we investigate this question using computational models of spiking networks of excitatory and inhibitory neurons, mimicking recurrently-connected networks in layer 2/3 of the cerebral cortex. The networks can generate a continuum of AS states, but with different responsiveness characteristics. By using a mean-field model to infer the dynamic properties of the system, we find that there are two families of AS states, which we call "underdamped" (UD) and "overdamped" (OD). Responsiveness is maximised at the transition between OD and UD states, which identifies a "working point" that may present advantageous computational properties.

Complex systems such as brains and other interacting biological and physical processes are difficult to represent because they evolve across many variables, scales, and nonlinear interactions. To capture these multivariate, multiscale interactions we have developed Generative Manifold Networks (GMNs) a machine learning framework consisting of a network of linked dynamical systems. The network is discovered by an interaction function which can focus on causality, shared information, nonlinearity or other metric. Network nodes are low-dimensional data-driven state-space manifolds with generator functions accommodating multiscale dynamics. In contrast to many machine learning approaches GMNs have no latent or randomly initialized variables providing transparent explainability. GMNs generate short term dynamics of chaos on par with echo state networks while outperforming them in long term generation of chaos and neural dynamics, but with a markedly reduced number of dimensions and without sensitive dependence on reservoir parameters or random states. As a result of their holistic, multiscale representation GMNs can learn the complete dynamics of a complex system. We further show that GMNs are universal approximators. GMNs are demonstrated on chaotic dynamics, neural and behavioral recordings of the fruit fly and domestic rat with comparisons to echo state networks and crossformer - a time series transformer. SignificanceA major challenge in machine learning is to model complex systems accurately without losing interpretability. Many methods that succeed in prediction rely on latent variables obscuring mechanistic insight and complicating experimental testing. Generative manifold networks (GMN) construct a network of low-dimensional functional manifolds directly from observed variables with no latent or randomly initialized variables: the model remains transparent and experimentally testable. We prove that GMN are universal approximators showing that high representational power can be achieved without sacrificing explainability. GMN therefore provides a general framework for prediction and simulation in neuroscience and complex systems where unraveling the links between variables in an experimentally testable manner is as important as forecasting their behavior.

Categorisation is often treated as a form of compression: a high-dimensional stimulus space is reduced to a smaller set of behaviourally or cognitively useful classes. However, compression alone does not determine whether a category map is useful. The present manuscript develops an information-theoretic framework for evaluating categorisation in terms of both category complexity and target-relevant information preservation. Across a set of synthetic demonstrations, alternative category maps over the same stimulus space are shown to preserve different target variables, including identity, action, nuisance, and hierarchical category structure. The framework is then extended to learned visual representations by analysing layer-derived category maps from a pretrained ResNet-50 network applied to CIFAR-10 images. Two scenarios are compared: a clean-only object run and a pooled nuisance run containing clean, blurred, pixelated, and noise-perturbed images. The results show that category maps can have substantial entropy while preserving information about a variable that is not aligned with the specified target, and that the value of a categorisation depends on the target variable to be preserved. The manuscript argues that categorisation should therefore be evaluated not only by compression or separability, but by the information retained about a specified cognitive, behavioural, or computational target.

In many brain regions, the stimulus tuning of neurons is stable on a timescale of hours but not on a timescale of weeks, a phenomenon often called representational drift. This would seem to imply that these brain regions cannot be used for stable recognition of sensory stimuli or the retrieval of associative memories learned several weeks prior. However, decoding approaches have demonstrated that in some cases, stable decoding of drifting representations is possible. In principle, adaptive decoding provides a plausible resolution to the paradox of how the brain operates with drifting representations, but we lack a deep understanding of what the requirements are for stable decoding to be possible. Here, we offer a general mathematical framework that explains when and why stable decoding from a drifting representation can be achieved. First, we demonstrate that both feedforward and recurrent networks preserve the geometry of their inputs when the network is sufficiently large, meaning that representational drift must also preserve geometry in these networks. Second, we demonstrate that drifting representations that have stable geometry are decodable with adaptive decoders. Therefore, not only the existence of preserved geometry in the presence of representational drift but also the ability to decode from drifting representations simply requires the population of neurons exhibiting representational drift to be large. This theoretical framework not only suggests that preserved geometry should be a general feature of drifting representations, it also explains the conditions under which empirical efforts to measure stable geometry will be successful.

AO_SCPLOWBSTRACTC_SCPLOWThere is a gap between neuroscientific theories of learning and the speed of learning observed in many experiments. Since the Cognitive Revolution of the 1950s, compositionality has played a central role in efforts to bridge this gap. Roughly, a compositional system is one where distinct modules are combined according to a set of rules in order to accomplish complex tasks. Recently, significant progress has been made in understanding the emergence of modules in both biological and artificial neural systems. How, and under what conditions, the rules of module recombination are represented in these systems remains an open question. Here we present a neural model that can leverage these rules to dramatically speed up learning. We first show that when faced with multiple tasks which share subcomponents, models learn a low-dimensional representation that captures how subcomponents are reused across the task set. These low-dimensional spaces encode the structure that governs how modules should be recombined. Restricting learning to these subspaces greatly reduces the amount of experience needed to acquire a novel task, even when learning from reinforcement on single trials. In some cases, we can leverage the geometric regularities of these representations to reduce learning to a form of hypothesis testing over a small set of discrete points. Finally, we use this theory to model both behavioral and neural data from non-human primates performing a compositional task, and show that key features in this data are consistent with a model in which exploration during learning is restricted to these low-dimensional spaces. Overall, this work shows that the advantages of modularity in neural systems can be greatly improved upon when models represent the structure of module reuse. Both these features working in tandem lead to learning on timescales similar to biological intelligences, and hence provide a model for how such fast, adaptable behavior can emerge from systems of neurons.

Transitive inference (TI) is the ability to reason about transitive relationships in an ordered set of items (e.g., if A>B and B>C, then A>C). TI is widely held to depend on a linear representation of the serial (rank) order of those items. By what computational mechanism is such an ordering constructed during learning, and how is it used to make choices that obey transitivity? Here we take a minimalist approach, applying least-squares estimation (LSE) to a serial learning task commonly used to test TI in humans and animals. In this formulation, LSE computes a linear classifier that maps task conditions onto behavioral outcomes. This algorithm makes no explicit assumptions about transitivity or serial order, yet it reproduces key empirical features of TI; namely, the ability to generalize beyond the training set, and a symbolic distance effect (SDE) in performance accuracy. Applying the classifier to individual items produces an internally ordered representation of rank from which both generalization and the SDE naturally emerge. The approach also yields a decision mechanism, in the form of a differencing operation, for selecting the correct item from any pair. These findings reframe TI as a linear classification problem, challenging conventional assumptions about the cognitive mechanisms required for transitive reasoning.

Rhythm is a key building block of human music, speech and numerous other human activities. Understanding the computational substrates of rhythm perception requires models that bridge algorithmic function with biological implementation. We propose a physiologically grounded spiking neural network (SNN) framework to investigate the emergent representation and interpretation of auditory rhythms. Utilizing a recurrent SNN architecture trained on an auditory entrainment task, we characterize the networks latent dynamics through the analysis of firing rates and membrane potential fluctuations. Our results demonstrate that simulated neural populations exhibit phase-locking to the stimulus beat, with endogenous oscillations driven by rhythmic input. We further show that anticipatory dynamics--characterized by pre-stimulus depolarization--emerge naturally from the networks synaptic plasticity and temporal integration properties, rather than from explicitly defined oscillators. By treating network layers as functional analogs of cortical populations, this framework allows for the application of spectral and information-theoretic analyses typical of empirical electrophysiology. More in general, this approach establishes SNNs as robust exploratory tools for uncovering how predictive coding and rhythmic entrainment arise from the inherent constraints of biological neural computation.

Tracking dynamic moving objects in the external world is ethologically important for many organisms. Recent experiments have examined neural dynamics supporting such behaviors by employing visually-guided pursuit in freely moving rodents, yet computational principles underlying this cognitive process are not well understood. To address this, we developed a recurrent neural network model for examining the predictive behaviors and computations that emerge during pursuit. We demonstrate that the model generates internal predictions of the targets future locations, with anticipatory behaviors increasing with exposure to stereotyped trajectories of the target. These internal predictions can be used by the model to pursue a target in a complex environment, and the models emergent strategy is aligned with behavior when tested in rodents. In investigating the computations that underlie the models ability to perform predictive pursuit, we found units sensitive to the position of the target relative to the artificial agent, a representation analogous to egocentric target neurons observed in animals performing pursuit tasks. Ablating these units significantly reduced model performance, establishing a causal role of this functional response type in efficient pursuit. Given the complexity of the task and agent behavior, we hypothesized that RNN models may use high-dimensional neural codes to support predictive pursuit. To test this, we trained models of varying rank and found that anticipatory behavior emerged only when the rank was sufficiently high, despite strong pursuit performance in lower rank models. All RNNs encoded the egocentric location of the target, whereas allocentric self and target locations emerged only in high-dimensional networks. Overall, our results suggest that, unlike commonly studied vision, motor, or memory tasks, predictive pursuit emerges in high-dimensional networks with sufficient resources.

The organizational principles of natural neural networks could inspire the new architecture design of artificial neural networks (ANNs). Analysis of single-neuron connectomes of mouse brains revealed distinct profiles of three-node connectivity motifs in various cortical areas and hippocampal formation. A connectome-informed neural network algorithm ("CINA") was developed to incorporate natural connectivity motifs into ANN algorithms represented by recurrent neural network (RNN) and transformer-based large language model (LLM). We found that incorporation of the average profile of cortical motifs improved the RNNs performance in noise-resistant categorization and motor learning benchmark tasks, as compared with RNNs with random connectivity. Notably, incorporating cortex-specific motifs further elevated the RNNs performance in tasks related to the cortical function, and this effect was enhanced by artificially increasing the bias in the motif profile. Similar experimental results were verified on an LLM using Motif-Transformer for natural language question answering and brain-signal decoding tasks. Graph-theoretic analyses showed that incorporating natural motifs drove the emergence of modular and small-world properties in ANNs. Together, we demonstrated not only connectome-inspired optimization of ANN architecture but also functional significance of specific motif profiles in various cortices.

Population analysis methods have become standard for navigating the complexity of neural data. However, these methods often assume a rate code, neglecting information encoded in the precise timing of spikes. Critically, additional information encoded in bursts of action potentials may be missed. Here, we develop a factor analysis method that disentangles the factors associated with bursts and individual spikes. This enables burst codes to be investigated directly from the structure of the data, without requiring external covariates. We demonstrate that analyzing firing rates alone obscures the latent structure and factors underlying bursts. Applying our method to simulated and experimental data, we show that it can infer the correct latent structure and be used to test for the presence of burst coding. By merging the population and burst coding perspectives, we provide a framework for linking changes in bursting to internal variables involved in attention, perception, and learning.

Learning new information in the presence of distracters and changing conditions requires the ability to adapt. In the brain, this adaptive capability has been linked to dynamic interactions between attention and working memory, which enable the selective filtering of irrelevant input while preserving behaviorally relevant information. Specific neural oscillations have been implicated in this process. Here, we introduce a phenomenological data-driven framework for oscillatory network modeling that learns condition-dependent coupling laws directly from neural recordings and enables inference of condition-dependent directed pathways. We apply our approach to magnetoen-cephalography (MEG) data collected while participants performed a working-memory task with and without distracters. Recall dynamics in the non-distracter condition are first modeled using a linear oscillatory network in which each region of interest is represented by two alpha-band harmonic oscillators. We use universal differential equations (UDE), an extension of neural differential equations, to capture distracter-induced changes in coupling laws. Symbolic regression is then used to interpret the modifications identified by UDE as nonlinear functions, and an additional method is proposed to identify the directed pathway from the newly emerging nonlinear terms in the dynamics of brain regions of interest. Despite inter-subject variability, working memory recall data from all four participants examined under distraction showed the emergence of a pathway from the dorsolateral prefrontal cortex (dlPFC) to the primary visual cortex (V1). This finding is consistent with the established role of the dlPFC in cognitive control and suggests that distracter processing recruits a directed interaction from prefrontal to visual regions. More broadly, our results illustrate that combining linear models whose parameters are learned from the data with universal differential equations augmented by interpretability methods enables the identification of condition-dependent coupling laws, their representation as interpretable mathematical functions, and the discovery of candidate directed pathways underlying adaptive changes in oscillatory networks without requiring strong prior assumptions about the underlying mechanisms.