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.

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.

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.

Recurrent neural networks (RNNs) trained with backpropagation through time (BPTT) use gradients and global error signals to solve tasks, while evolutionary algorithms (EAs) offer an alternative solution through gradient-free optimization. Both classes of methods can solve the same tasks by modifying network weights, but it remains unclear how the choice of training paradigm biases the final connectivity structure and resulting dynamics. When drawing conclusions from task-trained RNNs, especially as proxies for neurobiological computation, it is important to consider whether the resulting network structure is due to the training method itself. Here, we compare four training paradigms--BPTT, evolution strategies (ES), genetic algorithms (GA), and GA combined with Ojas Hebbian plasticity rule (GA+Oja) -- across RNNs of 32, 64, and 128 neurons. These training paradigms were applied to two contrasting tasks that are exemplary of tasks which animals perform: a discrete working memory task and a continuous sensorimotor integration task. For both tasks, we analyzed how each training algorithm modified the network through four measurements: weight change allocations across input (Win), recurrent (Wrec), and output (Wout) layers, the effective rank of the recurrent weight matrix, the dimensionality of hidden-state dynamics, and task accuracy. BPTT achieved near-perfect accuracy across all task conditions, progressively allocated more weight changes to Wout as the working memory tasks difficulty increased, and confined hidden-state activity to a lower-dimensional subspace than any evolutionary method. Evolutionary methods maintained higher recurrent effective rank, higher activity dimensionality, and no comparable difficulty-dependent reallocation toward the readout, all while maintaining comparable task accuracy as BPTT. These findings show how gradient-based and gradient-free algorithms discover distinct structural and dynamical solutions to the same computational problems, especially in tasks involving working memory, with important implications for analyzing task-trained RNNs as models of biological neural computation. Biological neural circuits, which are shaped by evolution and local plasticity rather than gradient descent, may operate in higher-dimensional regimes than gradient-trained RNN models predict.

The ability to extract and exploit temporal structure across diverse tasks is central to human cognition. Neuroscientists have typically relied on recurrent neural networks (RNNs) trained with backpropagation through time (BPTT) when modelling neural and behavioural processes such as decision-making and motor control. However, this algorithm has limited biological plausibility, hence the computational principles underlying efficient learning of temporal dependencies remain unresolved. Here, we investigate temporal predictive coding (tPC), a recently proposed framework that extends predictive coding to the temporal domain while preserving local Hebbian update rules. We analyse and extend tPC to establish its relationship with several influential computational models of learning in RNNs, including BPTT, reservoir computing, and eligibility propagation (e-prop). We first demonstrate a functional equivalence between tPC and tBPTT1, a variant of BPTT in which gradients are propagated only one time step into the past. We then show that tPC can leverage reservoir dynamics to encode short-range temporal context, and simultaneously sculpt neural trajectories in state space to support downstream readout. We further demonstrate that hierarchical recurrent dynamics can facilitate learning of more complex temporal dependencies, while additionally conferring robustness to strong distractors. Finally, we show that tPC networks can be augmented with biologically inspired eligibility traces to solve temporally extended context-dependent tasks. Together, these results reveal that relatively simple recurrent networks governed by local plasticity can support temporal learning in more complex settings than previously appreciated.

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.

Oscillations and oscillatory synchronization are pervasive in motor circuits, where their role in rhythm generation and entrainment is well established but their role in feedback control of movement remains unclear. Here I show analytically that two oscillators of any type, coupled through a delayed interaction that is an odd function of their phase difference, necessarily implement a proportional-derivative (PD) control law in the near-synchrony limit. The proportional gain follows from the slope of the coupling function and the derivative gain is set by the coupling delay, so that PD control emerges with no additional machinery. Simulations confirm that such oscillators reproduce ideal PD step responses near synchrony and that control quality degrades systematically away from it. This establishes a direct, model-independent bridge between oscillatory synchronization and feedback control, and suggests concrete experimental signatures for candidate systems.

A clinician guiding a stroke patient through a 45-minute rehabilitation session, a coach planning a training day, a teacher choosing the order of practice problems, they all face the same question: "given everything practiced so far, what should the next trial be?" The motor-learning literature offers two coarse answers, blocked and interleaved ("random") practice, with a well-known dissociation, blocked practice gives faster acquisition but worse retention, while interleaved practice gives the opposite. We argue that this dissociation is not a fixed property of practice schedules but a shadow of a richer structure. In particular, for a learner whose memory has a fast shared component and slower context-specific components, the best schedule should be a function of the learners current internal state and the time remaining before the retention probe. We make this precise in a minimal two-context fast-slow learner model whose optimal schedules can be computed exactly for short sessions and approximated by a structured beam-search upper bound for longer ones. The optimal schedule is not blocked, not interleaved, and not a single rule; it is a family of schedules determined by how much retention is weighted relative to acquisition. The family has three regimes (alternating, mixed, blocked-with-late-correction) and for long sessions, the optimal schedule has an interpretable structure -- exploit one context, repair the neglected one, then interleave to lock in retention. We then investigate whether a reinforcement-learning teacher, observing only the learners actions and errors without access to their internal memory states, can learn these optimal policies from interaction alone. Comparing these learned policies against the exact optima, we show that a model-free agent (PPO) recovers the short-horizon schedules and the long-horizon block-repair-interleave motif in the intermediate regime, but the benchmark also exposes a sharp failure in the acquisition-dominated regime, where PPO collapses to pure blocking and misses a sparse terminal correction. A warm-start diagnostic shows this failure is a genuine metastability of policy gradients rather than a tuning artifact, with blocked-plus-switch and pure-blocked acting as competing attractors that PPO cannot stabilize between. A hyperparameter sweep over observation history reveals that the agent requires very little behavioral context to plan optimally, demonstrating that partial observability is not a major barrier to finding optimal practice schedules. Finally, we discuss the implications of our framework for motor adaptation and contextual interference, offering practical insights on how instructors can design finite practice sessions to favor long-term retention.

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

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.

How much machinery does a network need to memorize and recall discrete sequences when constrained to a biologically plausible substrate? We address this question using 50 short monophonic melodies in 4/4, used only as a controlled sequence-memory benchmark. Each beat is encoded with two clean one-hot populations - a 12-way pitch code and a separate 2-way {onset, sustain} code - and the decoder emits the same 14-dimensional code, so the autoregressive loop closes in a single neural format. The model obeys Dales law: latent units are excitatory or inhibitory, synaptic weights are non-negative, the decoder is implemented as explicit multi-contact bundles, and the encoder is a frozen sparse random projection wired at cortical ([~]10%) density. On this substrate, a local ENGRAMMER signed-XOR read-out rule combined with a sparse k-winner-take-all code stores the training corpus exactly. With a modest latent expansion (L = 512), the model reaches 100% teacher-forced and autoregressive pitch accuracy, recognizes all training melodies, and separates all held-out melodies as novel with zero overlap. Ablations show that the signed error, sparse code, explicit E/I routing, and multi-contact synapses are the main load-bearing ingredients, whereas learning the encoder is strongly detrimental and dense input wiring does not help. Capacity sweeps show that Dales law mainly increases the capacity required for stable autoregressive recall: teacher-forced storage saturates between L = 128 and L = 256, while free-running recall becomes perfect by L = 512. A matched random corpus reaches the same final fidelity and is recalled at least as well at every capacity, indicating that musical structure does not improve recall on this benchmark and that final fidelity is set by capacity rather than by structure. The result is a Dale-compliant, gradient-free sparse associative memory rather than a general sequence learner.

Natural physical environments constantly fluctuate across multiple timescales, often following a scale-free (1/f ) pattern where = 0.5 governs the fractional adaptation dynamics (Drew and Abbott 2006, Lundstrom et al. 2008). Here, we demonstrate how a multi-timescale sensory model successfully tracks these long-term trends to maintain stable encoding. Using an event-based Generalized Leaky Integrate-and-Fire (GLIF) paradigm, we found that a fast-adapting, single-exponential model with a short time constant{tau} [≤] 31.6 ms quickly crashes into complete refractory saturation when faced with large, low-frequency environmental shifts. In contrast, introducing a deep fractional memory tail of 1000.0 ms acts as an automated, high-pass balancing mechanism that continuously tracks and subtracts slow environmental variance. This predictive balancing prevents sensory collapse, anchors the mean firing rate to a steady homeostatic baseline, and maximizes coding efficiency for rapid, localized signals. Our results show that while a simple single-pole exponential model fails to retain history, a parallel bank of physiological relaxation processes converging on a target fractional profile t-0.5 provides the necessary historical memory to safely navigate natural stimulus fluctuations. Comfortingly, even a simplified three-pole approximation captures the bulk of this homeostatic benefit, making efficient fractional adaptation biologically viable at the sensory periphery without requiring infinite historical storage.

Cortical populations exhibit a wide range of tuning properties, raising the question of whether such variability is a feature or a bug of cortical function. Prior work has shown that tuning diversity can improve population codes by mitigating the effects of correlated noise and increasing the discrimination and identification capacity of geometric representations. Motivated by these findings, we study a model in which a heterogeneous family of tuning curves, coding for a circular variable, is replicated at equally spaced preferred angles. We show that this heterogeneous population achieves better discrimination and detection than an equally sized homogeneous population constructed from shifted copies of the family's mean tuning curve, while using the same spike budget. Thus, homogeneous tuning is unstable under perturbations that preserve the mean tuning curve, because such perturbations leave metabolic cost unchanged while improving coding performance. We propose that such instability creates evolutionary pressure toward heterogeneity of tuning, making its prevalence a consequence of a process that optimizes coding performance under metabolic constraints.

Understanding how network connectivity shapes neural representations is central to systems neuroscience. While dimensionality reduction methods uncover low-dimensional manifold structure in population recordings, a rigorous framework connecting manifold geometry to network mechanisms and information encoding remains lacking. We develop a differential geometric approach for analyzing neural manifolds in rate-based recurrent networks receiving tuned feedforward inputs. We derive expressions for the pullback metric of neural manifolds, showing how input tuning curves, feedforward and recurrent synaptic connectivity shape manifold geometry. Critically, we establish that the Fisher information matrix at steady states also has the structure of a pullback metric, directly linking intrinsic manifold geometry to stimulus discriminability and information encoding. For noise with slow temporal correlations propagated through the network, we show that recurrent effects on information geometry cancel: Fisher information depends only on the feedforward connectivity. Thus, feedforward connectivity critically determines representational geometry. As an example, we demonstrate that the representation of space by a module of hexagonal grid cells is approximately isometric for random distribution of grid phases. Moreover, a linear feedforward transformation can map spatially random input tuning curves into a population of hexagonal grid cells, forming a toroidal manifold. Thus, feedforward connectivity alone can generate structured spatial representations without requiring carefully tuned recurrent connectivity or continuous attractor dynamics. Recurrent connectivity, however, is shown to improve stimulus encoding under fast noise, thereby implementing a selective noise reduction.

Brain dynamics can be described in three different convenient mathematical languages, namely connectome harmonics, turbulence and complex harmonics (CHARM). Here we demonstrate that these theoretical frameworks can be rigorously unified, under the functional calculus, as one self-adjoint operator and its single spectral measure. The connectome Laplacian carries that measure; the harmonics are its spectral projections, the turbulence smoothing kernel is its resolvent, and the CHARM form is its unitary propagator. The bridge that makes this exact is a textbook fact: The exponential distance rule, which is the empirical kernel of the turbulence model, is the Greens function of a screened Laplacian, so the local order parameter is the phase field passed through the resolvent of the same operator whose eigenfunctions are the harmonics. A single shared control parameter, the spectral gap, simultaneously yields the cortical hierarchy, the turbulent information cascade and the structured interference the CHARM form measures. This unification makes a strong predictive claim. If the harmonic projections, the turbulence resolvent and the CHARM propagator really are three functions of one operator, then any structural perturbation that re-tunes the operator must move all three signatures in unison and must do so with a single coupling. We test this prediction with a pharmacological perturbation by lysergic acid diethylamide (LSD), which is known to change the emotional state, by empirically perturbing the operator with a 5-HT2A receptor density map and asking whether one scalar coupling can simultaneously predict the multi-scale turbulence shift observed, through the resolvent, and the macroscale harmonic energy redistribution, through first-order Rayleigh-Schrodinger perturbation theory. We found that the two independent functional domains respond in unison to one structural perturbation of one operator. The identity is exact as operator calculus and its purchase on the brain depends on a single load-bearing seam, the degree heterogeneity of the connectome, which we make explicit. We propose that this single-operator structure is the necessary mathematical scaffolding of our Entangled Loop theory.

The activity of neural populations typically encodes more information about sensory or motor variables than can be captured by point estimates of the variables. We present and compare two approaches to quantifying this additional or ancillary information and its relationship to uncertainty: the mutual information between activity and estimation error, and the Fisher information loss, which can be interpreted in terms of curvature in information geometry. We show that deviations from Gaussianity of estimation errors, including the long tails frequently observed in human behavioural tasks, are an expected corollary of the presence of ancillary information. However, populations with similar distributions of estimation error can differ substantially in their ancillary information content depending on the noise characteristics. For a given population tuning and noise model, our results quantify an upper bound on the information about uncertainty that can be obtained from population activity alone: behaviour demonstrating knowledge in excess of this bound would indicate access to a separate source of information about uncertainty. Finally, we contrast the effects of external noise and decreasing internal signal strength on ancillary information and the Gaussianity of errors. Our work directly relates knowledge about uncertainty to non-Gaussianity in sensory estimates, and establishes a coherent theoretical foundation for investigating the basis of metacognition in neural population activity. Author summaryThe brain processes sensory evidence about the external world via inherently noisy neural activity. As a result, behavioural judgments - such as estimating the direction of a moving object - are fundamentally uncertain. While animals, including humans, routinely use uncertainty to guide decisions under risk, how neural populations represent this uncertainty remains unclear. In this work, we show how the same neural activity used to decode a sensory variable can also provide information about the estimates reliability. We introduce a mathematical framework to quantify this "ancillary information" directly from a neural populations encoding model. We demonstrate that ancillary information predicts non-Gaussianity in estimation errors and sets an upper bound on metacognitive sensitivity (how accurately subjective confidence tracks performance). Crucially, we show that neural populations with distinct noise characteristics can yield near-identical estimation errors while providing very different degrees of uncertainty information. This highlights the importance of evaluating ancillary information, not just error patterns, when comparing competing models of sensory coding.

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

We ask how a forward-model-based predictive state observer should set its sensory prediction-error correction gain during muscle-driven reaching, and whether that gain can be adapted from agent-available signals -- innovation history and per-episode reaching outcome -- rather than from swept oracle labels. We evaluate a residual-MLP forward model in a 34-muscle MyoSuite arm on an IK-reachable below-shoulder task, deployed in closed loop with a stabilized endpoint probe controller that uses non-negative least-squares muscle routing and a virtual target ramp; the controller is a stabilized probe for evaluating state-estimation effects, not a biological motor planner. A swept fixed-gain closed-loop oracle reveals a delay-dependent correction structure: with no sensory delay, intermediate correction gains are best (K = 0.25-0.50), whereas with 18-step delay observation-heavy correction wins (K = 1.0). The forward-model-only K = 0 ablation is not the oracle: it is systematically worse than the best fixed K by 1.9-6.1 cm and shows large NNLS controller residuals caused by long-horizon autoregressive drift; we therefore report K = 0 as a diagnostic. Outcome-trained reliability-adaptive observers improve the delayed regime by 1.9-2.5 cm over default reliability while remaining neutral in no-delay cells, where the oracle is already intermediate. A feature-conditioned {beta} adapter that maps cell-level innovation statistics to per-field gain parameters nearly matches a per-cell trained diagnostic in 5/6 cells, but both remain 1.4-1.8 cm worse than the swept fixed-K oracle at 18-step delay. These results separate the delay-dependent correction structure, the forward-model-only failure mode of K = 0, and the remaining limits of agent-available adaptive correction.

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.

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.