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.

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.

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.

Despite extensive study of cellular mechanisms underlying long-term potentiation, no single specific protein or gene has been identified which encodes an individual unit of information, or memory bit. Indeed, the brain engram remains a knowledge gap. The theory of exclusion led us to cancel one-by-one several unrealistic biological options, suggesting that the explanation resides somewhere else. Superposition of up to concentric 300 myelin layers, spiraled, and highly compacted wrapping a single axon and each wrap could host hundreds to thousands of niches, as memory cells, collectively consisting of a massive array of cells. The disjointed 3D spatial superposition allows storage of charges, nodes not facing from a layer to next. The thickness of a single myelin layer ranges from 7.0 to 20 nm. The dimension scale is approximately the exact dimensions of the charge trap, the tunnel and dielectric also equipping current AI microchips. Stored charges are positive ions, with similar effect whether charges are negative or positive charges creating an electromagnetic field. To write data, following an action potential, this voltage applies to the control gates of the myelin layers producing an ionic charge injection. This causes charges to gain energy and tunnel through the myelin layer across Ranvier nodes, via quantum tunneling, and deep into the concentric myelin multilayers. This is creating an insulated trapping of K+ ions isolated from the system. In a long white matter tract bundle, the near-perfect isolation of millions of axons within compressed myelin wrap-ion channel K+/Na+ systems provides quantum coherence and precision of asynchronous firing property. The injected ionic charges (K+) become physically stuck in traps within the myelin layers. The K+ ions may not move freely, completely trapped after AP ceases. Mirroring a single-bit, single-level-cell, a trapped ionic charge (ions K+) may represent a 1, while an empty cell (absence of K+) represents a 0. The trial-and-error process, with a Bayesian inference which may have also been the core evolution of the learning human brain. Based on selected mathematical equations, we analyzed the general scheme on how deep learning may be embedded in the brain

Abnormal states such as erroneous behaviors are generally difficult to represent from neural data. However, such states are also known to have specific spatiotemporal features, indicating a feasibility of developing a method to focus on them. If a method can highlight these spatiotemporal features, it may effectively represent such abnormal states, helping evaluate abnormal brain functions. In the present study, we proposed the hierarchy of supported modules (HSM) to highlight spatiotemporal features that can represent abnormal states. HSM spatiotemporally transforms multidimensional neural time-series based on their spatiotemporal context. We evaluated HSM through decoding and similarity analyses using multiple publicly available datasets. In the HSM results, decoding accuracies were higher for erroneous behaviors than for normal behaviors, and similarities were lower between erroneous behaviors and normal behaviors than between normal behaviors, demonstrating the ability of HSM to capture the spatiotemporal features of erroneous behaviors. Surprisingly, many parts of these results were also present even before HSM learning, showing the virtue of HSM as a simple-to-use method. The proposed HSM method may help elucidate the mechanisms underlying erroneous behaviors.

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.

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.

Neural systems exhibit multiple firing states that reflect an organism's internal state and modulate the relationship between external environmental stimuli and behavior. Several studies have inferred these latent states by supplementing the traditional hidden Markov Model (HMM) with generalized linear models (GLMs) with non-Poisson behavioral observations. However, understanding the relationship between internal brain states and behavior also requires modeling the neural activity. Nonetheless, fitting multi-neuron GLM-HMMs is non-trivial due to high sparsity, collinearity, and low trial counts in neuronal datasets. Therefore, we built a robust multi-neuron GLM-HMM framework that uncovers latent states from population activity while incorporating the influence of time-stamped task variables and spike histories. To obtain reliable model parameters, we employ a modified expectation-maximization procedure. Specifically, we show that incorporating neuron-adaptive penalization in the maximization step overcomes the covariate co-linearity issues typical of time-stamped events and sparse spiking, yielding stable estimates of Poisson GLM coefficients. Furthermore, we incorporate a trust-region algorithm to ensure stable M-step convergence in the presence of ill-conditioned Hessians that can lead to unstable Newton-Raphson updates. We further demonstrate the utility of leave-one-out cross-validation analysis for evaluating model performance on datasets with low trial counts and without breaking their temporal structure. We evaluate our framework on three electrophysiological datasets from primates and rodents as they perform a decision-making task, demonstrate stable model convergence, and discuss the behavioral relevance of the inferred states.

Neural decoding can be viewed as a representation learning problem in which neural activity is mapped into an intermediate representation before downstream reconstruction. The choice of intermediate representation influences both performance and learning difficulty. Here we developed a novel framework for studying how intermediate representation choice influences downstream learning and reconstruction. As a proof-of-concept, we instantiated our framework using diffusion latent representations extracted from different diffusion timesteps for neural speech decoding. Component-wise evaluation showed that reconstruction performance differed substantially across diffusion timesteps, with teacher-forced Word Error Rates of 44.7%, 7.5%, and 3.5% for different latent models. These results demonstrate that diffusion latent representations can serve as effective intermediate representations for learning from neural activity, but that their effectiveness depends strongly on the selected diffusion timestep. More broadly, our framework provides a basis for systematically studying how intermediate representation choice influences downstream learning and reconstruction.

Every brain must adapt to an unpredictable world, yet individuals differ in how readily they learn. Theoretical work suggests that learning is fastest when a system, whether biological or synthetic, is initialized in a state close to instability - i.e., near criticality - because critical dynamics are imbued with a diverse repertoire of patterns and multi-scale correlations. Here, we empirically estimate distance to criticality in the brain and show that it predicts the rate of adaptability underlying learning, neuronal tuning, and general intelligence. In mouse motor cortex, proximity to criticality forecasts learning rate of two future complex tasks: prey capture hunt and ladder crossing. In contrast, distance to criticality predicted neither an animal's naive ability nor its asymptotic skill - isolating the rate of learning itself. In visual cortex of young ferrets, proximity to criticality predicts how strongly experience reshapes neural tuning. In human frontal cortex, it correlates with general cognitive ability. A minimal recurrent network model reproduced these results and offers a mechanism: proximity to criticality defines the timescale over which a system can learn from its past experiences, directly setting the rate of learning. A single dynamical property can account for the capacity to learn, from artificial networks to the mammalian brain.

Substantial progress has been made in recent years on understanding how the human brain parses and processes natural speech. Much of this progress has been based on modeling how brain activity relates to the different acoustic and linguistic features of speech. By fitting and testing models based on those features, one can test hypotheses about the kinds of computations and representations the brain uses to convert speech sounds into understanding. While much of this work has focused on modeling BOLD activity using functional neuroimaging or intracranially recorded electrophysiological signals, the approach has also proven useful with MEG and EEG. Indeed, noninvasive EEG has certain advantages for studying speech processing in terms of translational research and application. Research over the last decade or so has shown that EEG can be successfully modeled based on numerous acoustic, linguistic, and paralinguistic speech features. However, an important unanswered question hangs over all of this work: namely, what constitutes a good model of EEG responses to natural speech? Or, to put it another way, how much variance in EEG recorded during natural speech listening is explainable as having derived from that speech input? The present study aims to tackle this issue. We do so under the assumption that the best model for a person's EEG response to natural speech is a set of EEG responses from other people listening to the same speech. Using this assumption, we construct inter-subject models using EEG from 19 healthy adult native speakers of English who all listened to the same audiobook. The model for each subject involves predicting their EEG data using (dimensionality-reduced) EEG from different numbers of other subjects and then extrapolating to estimate the total explainable variance in the target individual's response to speech. Following this, we show that linear models (temporal response functions) based on several commonly used acoustic and linguistic speech features can predict most - but importantly not all - of the estimated total explainable variance in EEG responses across subjects.

Background / Introduction: Biologically inspired spiking neural networks can model adaptive behavior, but learning multiple goals is difficult because synaptic updates for different targets can interfere. We tested whether multi-timescale plasticity and context-specific credit assignment could improve continual multi-goal learning in a spiking navigation system inspired by entorhinal-hippocampal circuitry. Methods: We developed a closed-loop spiking model containing grid-like, place-like, target-related, association, and motor-output populations. An agent navigated in a two-dimensional environment with randomized starting locations and learned through reward-modulated spike-timing dependent plasticity (STDP/RL) and a novel evidence-gated plasticity (EGP) framework. EGP accumulates candidate synaptic modifications, evaluates them using reward evidence, and consolidates only changes that improve performance. A target-context variant maintained separate proposal stores and reward evaluation for each target. Results: STDP/RL learned and retained a single-target navigation policy, but multi-target training produced substantial interference, including attraction to incorrect targets after learning. Across 10 connectivity seeds, target-context EGP achieved higher late-stage reward than global EGP, improved weakest-target performance, and increased the fraction of targets achieving positive reward. In a longer continual-learning simulation, reward increased for all targets, TEST-phase performance increasingly exceeded TRAIN-phase performance, and proposal magnitudes grew over learning. Dwell-time confusion analyses showed that target-context EGP reduced wrong-target attraction and improved target selectivity relative to multi-target STDP/RL. Conclusions: These results demonstrate that spiking navigation circuits can learn goal-directed behavior using local plasticity, but robust multi-goal learning benefits from context-specific evidence-based consolidation. Target-context EGP provides a biologically motivated mechanism for reducing interference during continual reinforcement learning in spiking neural networks.

We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su(3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

Although neural activity often evolves along low-dimensional manifolds, such descriptions do not explain the dynamical mechanisms that generate, constrain, and stabilize computation. Identifying these mechanisms is essential for predicting responses to perturbations, understanding generalization to untrained signals, and explaining how similar computations arise from distinct circuit implementations. Here we use recurrent neural networks trained on an interval timing task as a model system to uncover the dynamical mechanisms of neural computation. We show that, despite converging to highly diverse attractor architectures, trained networks share a conserved transient dynamics. During learning, networks self-organize near dynamical bifurcations, forming structured ghost sets of slow points characterized by graded spectra of near-zero eigenvalues. These slow sets form a dynamical scaffold that constrains trajectory evolution. Inputs transiently reconfigure the vector field and reposition activity within this scaffold, while the underlying slow set governs subsequent dynamics. As a result, temporal computation is implemented through structured transient evolution rather than convergence to fixed points or persistent activity states. The extent of the slow sets predicts generalization to unseen temporal intervals, and networks lacking such organization fail to extrapolate reliably. To test sufficiency, we construct a minimal dynamical system endowed with analogous slow set geometry that reproduces interval timing without learning, providing a benchmark for identifying the essential dynamical ingredients of temporal computation. Together, these results identify structured slow transients as a candidate dynamical mechanism for temporal computation, provide a mechanistic interpretation of slow low-dimensional manifolds as emergent consequences of underlying state-space structure, and suggest that computational capacity in near-critical systems arises from the organization of transient flow rather than attractor states alone.

Many neural recordings have revealed low-dimensional sets of behaviorally relevant variables encoded within large-scale neural activity patterns. However, dimensionality reduction analyses alone cannot yield causal explanations for how networks stably implement computations that are resilient to the substantial variability of single neuron dynamics. Further, existing methods for dimensionality reduction often rely on simplifying assumptions about network structure that limit their applicability and explanatory power. To provide a theoretical framework describing the dynamics of low-dimensional computation in high-dimensional neural networks, here we introduce the concept of latent processing units (LPUs), which are architecture-agnostic computational elements operating within biological neural circuitry. Six theorems governing coding and computation by LPUs collectively provide explanations for a range of common biological findings: low-dimensional sets of coding variables can generate high-dimensional neural dynamics; many neurons have activity patterns that represent behaviorally relevant variables but exert little influence on downstream circuits; linear readouts of neural population activity commonly permit near-optimal decoding; the drift of neural representations is often substantial even while network computations remain intact. Overall, our treatment of LPUs, as enacted in network dynamics, unifies the geometric and dynamical views of neural computation under a joint framework and provides systems neuroscience with a causal account of how the brain executes reliable computations.

Flexible cognition utilizes reusable components to enable rapid adaptation of behavior to different contexts or tasks. Analysis of artificial neural networks trained on multiple tasks suggested that this compositionality is supported by dynamical structures which are shared and re-used across tasks. However, the nature of these shared components, and how they can be used in a task-dependent manner, remained unclear. Here, we develop a theory of interpretable compositional computation based on shared dynamical structures in the low-dimensional latent space of low-rank recurrent neural networks. We show that these shared latent components are not immediately visible in the neural activity, and are thus compatible with task-dependent activity. We identify hallmarks of shared latent components both in the connectivity statistics and the neural representations. These hallmarks yield testable predictions for the networks response to specific perturbation experiments. Finally, we identify distinct loci where task-dependence can enter the computation, allowing us to characterize qualitatively different solutions to compositional tasks. In summary, our theory provides a mechanistic understanding and testable hallmarks of compositional computation via shared components in low-rank networks.

Humans exhibit structured patterns of memory recall, including a tendency to recall more recent information and to recall events in the same order they were experienced. Classic computational models explain these patterns by positing that memories incorporate the ongoing ''temporal context'', formed by smoothly integrating the stimulus history. However, it is unclear whether a single mechanism can account for the full repertoire of human memory strategies, as the optimal approach may be task-dependent. For example, human memory experts widely apply the ''memory palace'' strategy, which is empirically better but not captured by temporal context models. Here we show that neural networks optimized for free recall develop diverse retrieval strategies, with only some of them resembling temporal context models.The best-performing models discovered a stimulus-invariant index code that emphasizes the studied position of each list item, instead of its temporal context. This creates a stable scaffold for forward recall akin to the memory palace technique. This index code was more likely to emerge when networks were i) encouraged to recall all studied items rather than prioritizing a few items, and ii) prevented from relying on recency, resonating with human data. Our findings demonstrate that human-like recall patterns can arise from multiple distinct computational mechanisms, and that sequential retrieval using item index is an optimal strategy that explains expert-level recall performance.

Inverse reinforcement learning can recover reward functions from observed behavior, but interpreting those rewards remains a fundamental challenge for understanding intelligent behavior and decision-making. To address this challenge, we introduce a novel framework for reward interpretation that combines reward-function analysis, latent mode assignments, and short-history behavioral analysis to infer latent motivations and behavioral dynamics. As a proof-of-concept, we instantiated the framework using switching inverse reinforcement learning on a large-scale dataset of multi-agent social interactions. Our framework interpreted the learned latent modes as cautious and volatile motivational profiles, demonstrating that recovered reward functions can reveal distinct patterns of behavioral dynamics. More broadly, these findings suggest that the proposed framework provides a promising approach for reverse-engineering and interpreting latent rewards underlying intelligent behavior and decision-making.