Neural Computation

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.

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.

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.

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.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

Neuroscientific learning theories propose that the brain acquires knowledge by constructing internal world models. Supervised learning, the dominant approach in deep neural networks (DNN), relies on external category labels, making it difficult to reconcile with biological learning. There is an increasing trend towards more biologically valid approaches, such as predictive (minimize future surprise) or contrastive (minimize response to expected, maximize to unexpected inputs) objectives, but these approaches typically rely on pretrained DNN models that vary widely in architecture, size, and hyperparameters, making direct comparisons difficult. Here, we isolate the effect of learning by comparing small, identical networks trained with predictive, contrastive, and supervised learning objectives, as well as local (layer-restricted) vs. global (full backpropagation) learning. We show that brain representations after statistical learning are better modeled by a predictive local target than a supervised or contrastive target, and that during learning, the brain attenuates category-specific representations while retaining predictive ones. We additionally show that predictive objectives explain brain variance that standard supervised DNNs do not, and that this variance is tied to predictive rather than stimulus or mismatch processing. These findings demonstrate a controlled approach for testing the algorithmic basis of learning and identify prediction as a core learning mechanism.

In visuomotor sequential tasks, chaining actions smoothly requires tight coordination between sensory and motor systems to deal with competing demands, such as reducing uncertainty about future opportunities for action while controlling ongoing ones. In a football-based decision-making task, experts and novices used different strategies to overcome these competing demands, demonstrating a proactive and a sequential visuomotor strategy, respectively. We propose a computational explanation of expertise-related difference in policy selection, grounded in the active inference framework. We simulated the selection of sequence of actions using a partially observable Markov decision process (POMDP) model, and we manipulated three parameters: the reward structure, the prior beliefs about state transition, and the sensory precision. Simulations showed that selection of the proactive strategy relied on strong prior beliefs, high sensory precision and high valuation of fast passing. Conversely, the sequential policy was selected when rapid performance was not highly valued, or under noisy prior beliefs, or lower level of sensory precision. Decreasing sensory precision and adding noise in prior beliefs also decreased decision accuracy. These results suggest that policy selection leading to novice or expert visuomotor strategy reflects differences in the underlying generative model, particularly in how agents value different aspects of the task.

Microstate analysis studies dynamic brain activity through a discrete representation of electroencephalographic (EEG) signals and their topography. While the body of literature describing findings in diverse experimental and clinical settings is growing rapidly, the effects of several core components of the microstate algorithm are still insufficiently understood. This study systematically investigates how two common temporal smoothing algorithms, parametric smoothing and GFP peak interpolation, influence a wide range of microstate sequence parameters, and how they shape the integrated picture of brain dynamics inferred from these metrics. We study eyes-closed resting-state EEG recordings from N=201 healthy subjects from a public EEG database. For the elementary temporal metrics, we find that widening smoothing windows markedly increase microstate duration, reduce occurrence rates, but leave coverage mostly unaffected. In terms of simple syntax properties, smoothing windows above 30 ms yield an inconsistent picture with a memoryless, first-order Markov structure at short time scales, but a positive Hurst phenomenon suggestive of long-range correlations at long time scales. Evidence of asymmetry and non-equilibrium dynamics are suppressed by smoothing. At intermediate time scales, microstate periodicity was only observed up to a window size of 28 ms. Smoothing had a strong impact on the complexity metrics entropy rate and excess entropy, decreasing the former and increasing the latter. For most metrics, the effects of GFP peak interpolation were comparable to those of smoothing windows in the range between 28 ms and 44 ms. In conclusion, elementary and higher-order microstate parameters must be interpreted in the context of preprocessing, as many parameters change continuously with smoothing intensity. This limits the comparability of microstate parameters obtained with different preprocessing settings. Strong smoothing with a window size above 30 ms or GFP peak interpolation yields a fundamentally different picture of resting state brain dynamics, i.e. that of a memoryless, aperiodic, time-reversible first-order Markov chain. Since insights from other neurophysiological modalities suggest that time series memory and time-irreversibility are markers of normal brain activity, our recommendation is to avoid intense smoothing to minimize alterations of the initial sequences.

Humans efficiently learn the temporal structure of speech, yet the underlying cognitive mechanisms remain unclear. Recent research in visuospatial sequential memory has proposed the successor representation (SR), important in reinforcement learning, which encodes multi-step transitional relationships. To test whether SR also supports the structural learning of rapidly changing speech syllable sequences, we adapted a pyramid-structured sequential learning paradigm using syllable streams presented at a natural speech rate (~ 4 Hz). Participants exhibited robust structural learning, evidenced by asymmetric memory performance modulated by adjacent transitional probabilities. Notably, the SR model captured recognition performance for non-adjacent syllable pairs. Moreover, SR-based learning effects generalized across all syllable sequences, regardless of adjacency. Furthermore, the effectiveness of SR learning was associated with cognitive flexibility and working memory capacity. Together, these findings suggest that humans rely on effortful SR-like mechanisms for the structural learning of syllable sequences, highlighting a modality-general computational principle for sequential learning across various temporal modulation scales.

How does the brain generate sequences of discrete elements, such as actions or words, that follow an abstract rule (a grammar)? Motivated by an experiment in which monkeys learned to draw multi-object images according to grammatical rules, we trained a recurrent neural network to generate sequences Am Bn: producing shape A m times, then B n times, or vice versa. Our findings are threefold. First, the network plans the sequence by moving to an initial state encoding m and n along orthogonal directions for upcoming execution. Second, the network repeats each shape by progressing along a shape-specific manifold. Third, transitions from Am to Bn follow parallel trajectories between manifolds across values of n, thus preserving n. Each of these is an experimentally testable prediction. The network generalizes to longer novel sequences by starting further along the same orthogonal directions. These results reveal a neural circuit implementation of a symbolic algorithm for generating rule-based action sequences.

Perception has been proposed to involve an inferential process that combines noisy sensory evidence with prior expectations to estimate the latent states of the environment. Exact Bayesian inference is intractable in the continuous, high-dimensional state spaces of the natural world. Variational schemes address this by restricting the form of the posterior, whereas sampling schemes represent the posterior with a finite set of samples. In both cases the approximation concerns the posterior rather than the state space over which it is defined. Here we place the approximation elsewhere. Rather than restricting the form of the posterior, we restrict the state space, modeling environmental states as discrete and thereby making Bayesian filtering exact. Beliefs are then unconstrained in shape and what has to be learned can be reduced to a transition matrix updated online by a local rule. The cost is that the states, rather than the distribution, must be specified in advance. The Simultaneous Learning and Inference Model (SLIM) combines this exact filtering with a gated Hebbian rule that learns transitions from inferred rather than observed states. In simulations SLIM recovers environmental dynamics under sensory noise and adapts when those dynamics change, with error growing only once the sensor becomes uninformative. A hierarchical instantiation reproduces local and global prediction error effects. Applied to two auditory decision-making experiments under noise, SLIM reproduces behavioral signatures of expectation and supplies trial-level measures of expectation and surprise. Exact inference over a small discrete state space with a single local Hebbian rule is therefore sufficient to account for these phenomena, without an explicit optimization objective and without a parametric approximation to the posterior.

The Hierarchical Gaussian Filter (HGF) is a hierarchical Bayesian model of learning under uncertainty and volatility, with a widely used MATLAB implementation. We present HGFX 1.0.0, a Python/JAX toolbox whose primary objective is validated behavioral and numerical compatibility with a frozen HGF Toolbox 8.2.0 reference, while removing MATLAB as a user-runtime dependency. Reimplementation is treated as a validation problem rather than source translation: configuration semantics, parameter transforms, forward trajectories, observation likelihoods, objectives, fitting and statistical surfaces, simulation workflows, official demo behavior, model selection, and backend agreement are compared against the pinned oracle under predeclared tolerances. Two official MATLAB demo workflows reproduce the reference at frozen trajectory tolerances, including a regime in which classic HGF encounters negative posterior precision while eHGF completes successfully. In paired model-selection validation, all 36 BIC winners agree between MATLAB and HGFX. Physical NVIDIA GPU applicability was confirmed on two Tesla T4 devices, with a maximum CPU-versus-GPU final-objective difference of 1.42e-14 against a frozen 1e-7 criterion. Historical parameter recovery results that did not meet predeclared criteria, together with exact MATLAB/HGFX limitation matches, are preserved and are not reclassified as scientific success. A prospectively gated comparison with pyhgf 0.3.2 shows binary64-scale agreement on mapped perceptual trajectories in one authorized three-level binary-HGF cell, while participant-response negative log-likelihood is retained as not directly comparable. HGFX therefore provides a MATLAB-independent Python implementation with an explicit evidence model that separates direct parity, matched reference limitations, backend applicability, and future performance claims.

When asked to discriminate between two stimuli that differ along some dimension, such as intensity, frequency, or orientation, humans exhibit a smallest stimulus difference, or threshold, below which discrimination becomes impossible. These limits on perceptual sensitivity have traditionally been explained by internal noise. Contemporary theories instead link perceptual sensitivity to efficient coding of the natural environment but have not been comprehensively tested. Here, we measured the psychoacoustic sensitivity of a computational model optimized for everyday sound localization and recognition tasks. We used linear classifiers operating on the model's learned representations to estimate 1632 thresholds spanning the perceptual dimensions of sound. These model-derived thresholds closely matched thresholds measured behaviorally in humans on the same test battery. The results show that many classical psychophysical phenomena emerge from representations optimized for natural behavior and suggest that discrimination thresholds are determined by linear separability in these optimized representations, rather than intrinsic neural noise.

Deep learning models for electroencephalography (EEG) pathology detection achieve competitive accuracy but offer limited interpretability. In this paper, we introduce concept bottleneck models (CBMs) for EEG pathology detection which use clinical EEG biomarkers computed analytically from the signal as a bottleneck to be used for prediction. Those concepts include band power, spectral ratios, alpha peak frequency and amplitude, hemispheric asymmetry and phase locking values. With the backbone based on shallow convolutional neural network (CNN), we compare a black box baseline with two variants of CBMs. The hybrid variant is a classifier receives a residual projection of the backbone features. The pure variant is a CBM where the classifier receives only the predicted concepts. Models are evaluated on abnormality detection and dementia classification followed by concept prediction quality and leakage analysis. Both CBMs approach the baseline on TUAB (82.7-82.9% vs 83.6%) and are 2-5 percentage points lower on CAUEEG (57.9-60.5% vs 62.7%). The pure CBM exhibits concept fidelity concern where the predicted concepts deviate from their ground truth values. Replacing them with their true values causes severe cost on accuracy by 26 and 22 points on TUAB and CAUEEG. The concept fidelity concern is mitigated by increasing the weight of the concept loss to match the ground truth concepts. the mitigation comes with small accuracy cost on TUAB but a relatively larger cost on CAUEEG. The code of the experiments and full logs are available at https://www.github.com/mhmdrdwn/cbm.

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

The dentate gyrus' principal neuron, the granule cell (GC), plays a key role in pattern separation, transforming similar inputs into dissimilar outputs. We used a new measure based on information theory to evaluate this transformation in an experimentally derived in silico GC model with realistic ion channel distributions across its dendrites. We found that model performance aligned well with current-clamp recordings from mouse brain slices. However, it was also possible to find artificial parameter combinations in the model that functionally outperformed the recorded cells while matching their action potential shapes. Rather than maximising computational power, the biologically realistic GC model balanced energy efficiency against increased functionality in a Pareto optimal way: No possible parameter combination was found to improve one of the objectives without impairing the other. Interestingly, immature GCs adopted a different weighted trade-off with a stronger emphasis on energy efficiency than pattern separation, but they remained Pareto optimal over their putative developmental trajectory. Our results support the idea that evolution favours neurons that can satisfy functional and energetic demands simultaneously.

Mixed-timescale signals are ubiquitous in natural stimuli and real-world applications, yet they remain challenging to process with recurrent neural networks. Reservoir computing offers an efficient framework for temporal processing, but extending its temporal range typically requires tuning neuronal timescales, which can compromise the representation of faster dynamics. Here, we propose an alternative approach in which synaptic plasticity provides an additional, slower timescale for computation. We introduce Hebbian plasticity into recurrent networks and show that its dynamics enable the reservoir to simultaneously process fast and slow components of mixed-timescale inputs: neuronal dynamics encode fast fluctuations, while synaptic dynamics support slower components. Remarkably, the resulting computational benefit extends over more than an order of magnitude beyond the intrinsic timescale of the plasticity. We show that this extended processing range arises from the dependence of the plasticity rule on postsynaptic activity, which effectively injects a filtered memory of past states into the network current. These results identify synaptic plasticity as a mechanism for extending the temporal processing capabilities of recurrent networks without altering neuronal timescales, and also suggest a potential computational role for plastic synapses in the processing of slowly varying stimuli in biological neuronal networks.

Agents are constantly challenged to navigate uncertainty in a world that contains far more information that they can process, improving predictability by exploiting regularities from the environment. This frames the challenge of reducing information intractability as the main problem any artificial or biological agent needs to solve. We argue that this challenge is solved through the systematic use of information bottlenecks--a diverse suite of strategies functioning to compress and selectively filter environmental information so as to build tractable representations of the world. We show that such bottlenecks are adaptive and operate across multiple scales, from the evolution of neural circuits and sensory systems to the actions that organisms use in real-time to select and structure their own sensory inputs. A key aspect of our proposal is that information bottlenecks are not only internal and biological, but can also be externalized through actions in the world. By transforming their environments, agents construct external bottlenecks--material and cultural mechanisms that reduce the cost of inference and transmit regularities that are shared across individuals and even across generations. From this perspective, niche construction, material culture and even social and cultural norms, can be also understood as adaptive informational mechanisms, collective information bottlenecks that alter our worlds in ways that promote predictive success. Agents increasingly solve the intractability problem not only through evolutionary changes in their biology and internal neural mechanisms, but by systematically constructing and exploiting information bottlenecks in the world. Culture itself, we suggest, is just such a bottleneck-constructing mechanism.