Journal of Computational Neuroscience

Visual signals from the two eyes merge gradually as they pass through the primary visual cortex (V1). Here we use a computational model of Macaque V1 to study the first stage of this integration along the magnocellular pathway, in layer 4C, aiming to infer neuroanatomical origins of binocular response. It is known that neurons in layer 4C are predominantly monocular, though some do exhibit varying degrees of binocularity. We find (1) the emergence of narrow binocular strips along borders of ocular dominance columns (ODC), a finding that aligns with experiments; (2) most consistent with data is when 10 - 30% of interactions near ODC boundaries are cross-columnar; and (3) feedback from layer 6 is largely monocular. These results were obtained through systematic hypothesis testing using a multiscale model that is orders of magnitude faster than its biologically-detailed predecessors. We propose that multiscale modeling can be an effective tool for bridging anatomy and function.

Fixational eye movements (FEMs) comprise the involuntary small scale eye motion conducted during fixation on a stationary stimulus. As a consequence, the visual information can be spread across multiple photoreceptors reducing the local signal-to-noise ratio. Yet, the signals transmitted by individual photoreceptors adapt to constant stimulation so that an entirely still scene would eventually fade from view. Because FEMs convert a stationary stimulus in the world to a temporally varying one on the retina, they can act to prevent this stimulus fading. Thus, FEMs can be understood as a sampling protocol than needs to be adjusted to the underlying processing circuitry. We analyse the impact of FEMs on the rate of information acquisition at the level of the retina for two common tasks of the human eye that typically go hand in hand: detection and localization. Here, we build a simple analytical model of visual perception, i.e. we subject a continuous receptor array to a stimulus moving across the retina as a consequence of FEMs with receptor excitations depending on past stimulation through a linear response function. Using Bayesian inference we quantify both the probability of detection and the accuracy of localization as a function of parameters controlling eye movements and stimulus. We find that localization of a stimulus is equivalent to the detection of the stimulus gradient. This allows us to discern optimal properties of eye movements for the respective tasks and provides a link between two typical psychophysical observables: detection thresholds and Vernier acuity. Our analysis suggests that typical human FEMs tend to facilitate localization at the expense of detection. Simply put, if you can see a stimulus you also know where it is. Finally, we propose a variety of experimental protocols to investigate the interplay between FEMs, detection, and localization with the potential of inferring intrinsic properties of an individuals visual system.

Ampullary electroreceptors are widespread across aquatic vertebrates. The purpose of sensing exogeneous electric fields is conserved across species but the implementations differ and the encoding mechanisms remain incompletely understood. We compared baseline and stimulus-driven response properties of ampullary electroreceptor afferents in the weakly electric fish Apteronotus leptorhynchus and Eigenmannia virescens. We find that their activity is well captured by an extended leaky integrate-and-fire model that generalizes across both species. The model shares similarities to a previous model of the tuberous electroreceptor afferents but further incorporates a low-pass pre-filtering and additional noise sources to reproduce the observed spectral response characteristics. The low-pass is essential to shape stimulus encoding in the high-frequency range. Accurate prediction of low-frequency stimulus encoding further requires two distinct noise sources: stimulus-independent white current noise and activity-dependent noise in the adaptation current, which is shaped by the adaptation time constant to yield effective pink noise dynamics. Using simulation-based inference, we trained a neural network to map model parameters to neuronal response features. This approach enables the generation of heterogeneous, biologically plausible model populations that may serve as a realistic input layer for studying neuronal processing on the next level. With this, we provide a unified and mechanistic model of ampullary electroreceptor encoding in these species and possibly beyond.

Substantial progress in glial electrophysiology has revealed that astrocytes, which account for half of the cells in the human brain, exhibit membrane potentials that often reflect changes in the extracellular environment. Such responses are mediated by a variety of biochemicals, including potassium and neurotransmitters. Recent advances in voltage imaging have provided new insights into voltage activity in astrocyte peripheries, revealing highly localized depolarization that depends on local presynaptic activity. However, the electrophysiological properties of these isolated peripherals have not been explored due to limitations of spatial and temporal resolution. In this study, we aimed to explore differences in the electrophysiological response between whole-cell stimulation and isolated stimuli at different locations in the cell. Therefore, we constructed an empirical conductance-based NEURON model using a realistic morphology to simultaneously capture both astrocyte processes and soma electrophysiological dynamics. Our results predict a breakdown of the Nernstian behavior of astrocytes when potassium stimuli are localized. Instead, local responses are governed by their conductance ratios. Furthermore, we observe strong capabilities for isolating neurotransmitter responses to specific synaptic inputs, with minimal effect on the astrocyte soma. Our study highlights asymmetrical responses of astrocytic electrophysiology that depend on the spatial scale of stimulation.

Some blind individuals use echolocation, a skill that allows them to better navigate their environment using echoes from self-generated mouth clicks reflected off surrounding surfaces. Echolocation involves a complex interplay of sensory accumulation, information processing, dynamic prediction, motor planning and execution in real-time. Computational modeling offers a valuable approach to understanding the cognitive and neural mechanisms underlying echolocation performance, in particular the temporal dynamics of the process. We present a computational model of human echolocation behavior based on a Kalman filter, where we treat the echolocator as an active sensor that maintains an internal belief about the target's location and continuously refines it via echo feedback. The model, based on observations of echolocation in blind human experts, simulates the use of mouth clicks and returning echoes to localize and orient toward a target under varying conditions. In the experiment, the target is placed at a random azimuth in the frontal plane. An echolocator aims a series of mouth clicks in various directions and infers the target azimuth using acoustic information received from the click echoes. The system integrates three major components: (1) a simulation of echoacoustic interaural time differences (ITD) to estimate the relative head-target angle; (2) a Kalman filter that processes these ITDs to iteratively update probabilistic beliefs about target location and associated uncertainty; and (3) a motor control system that modulates head movements with the current belief state. The Kalman filter serves as a representation of the internal state of the observer, where its beliefs drive the direction of head rotation, and its uncertainty estimates drive head velocity adjustments. Model performance demonstrates that simple predictive computational approaches can reproduce key aspects of echo-guided sensorimotor learning, providing a framework that may be leveraged to develop biologically plausible models, advance understanding of best practices, and potentially improve intervention strategies.

Deep brain stimulation has demonstrated its therapeutic potential in modulating pathological oscillations associated with Parkinsons disease and epilepsy. However, its efficacy in treating disrupted theta-gamma phase-amplitude coupling seen in memory-related disorders, such as Alzheimers disease, remains poorly understood. While recent studies have targeted the entorhinal-hippocampal circuit, results remain inconsistent. This discrepancy stems from a lack of mechanistic understanding regarding how stimulation protocols affect this circuit. In this work, we present a reduced multicompartment model of the hippocampal CA1 area that reproduces theta-nested gamma oscillations characteristic of healthy neural activity during memory performance. The model comprises pyramidal, basket and OLM cells with simplified morphologies. We also incorporated CA3-to-CA1 axonal projections, providing a foundational framework for studying how stimulation-induced recruitment of afferent pathways modulates CA1 dynamics. By balancing computational efficiency with anatomical accuracy, our model enables systematic investigation of the effects of electrode placement and orientation, as well as stimulation amplitude and frequency on CA1 neural activity. We demonstrate that the excitatory response in CA1 is primarily driven by the recruitment of Schaffer collateral projections. Overall, this work provides a computationally efficient template for exploring diverse stimulation configurations and could be expanded for developing neuromodulatory strategies to restore physiological network dynamics. Author summaryDeep brain stimulation has shown success in treating Parkinsons disease by suppressing abnormal neural activity responsible for movement disorders. However, when applied to memory-related pathologies, such as Alzheimers disease, the therapeutic outcomes remain unpredictable, ranging from cognitive improvement to impairment. This discrepancy highlights a critical gap in our understanding of how stimulation protocols interact with neural dynamics of the targeted circuits. To address this, we developed a computationally efficient model of the hippocampus, which is involved in memory processes, in order to understand how deep brain stimulation might influence its activity. Our model maintains enough biological accuracy to capture essential memory-related neural activity while remaining lightweight enough for rapid execution and systematic exploration of different protocols. This computational efficiency allowed us to conduct systematic investigations of several stimulation configurations to study their effects on hippocampal dynamics. Overall, this model could provide a useful and computationally cost-efficient tool for exploring the mechanisms of deep brain stimulation and help optimize stimulation protocols aimed at alleviating memory disorders.

Representations of the same physical stimulus vary between individuals. Characterizing individual differences has practical implications, but is challenging because these representations are not directly observable. Given a model of how representations vary within a population, we propose a Bayesian adaptive procedure for estimating an individual observer's representation from a series of targeted perceptual discrimination judgments. A key component of our approach is using Fisher information to identify stimulus distortions that efficiently differentiate observers in the population. As a proof of concept, we focus on individual differences in color perception and simulate observers with cone fundamentals drawn from an individual colorimetric observer model. We demonstrate that our approach can recover key aspects of a sampled observer's cone fundamentals using simulated three-alternative forced-choice oddity judgments with approximately 500 trials, corresponding to an experimental duration of approximately one hour. Our Bayesian adaptive framework provides a promising and generalizable approach to efficiently link behavioral measurements to individual differences in sensory representations.

Diffuse gliomas are deadly because the individual tumor cells invade - they travel far from the imageable mass, so it is impossible to remove the tumor completely. On the cellular level, glioma cells seem to be in either a "go" state (in which they do not divide) or a "grow" state (in which they do not migrate). We investigate what this tiny choice has to say about the large-scale speed of the invasion front and whether the implication is sufficiently strong to rule out the classical description of the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) type, in which a single phenotype migrates and proliferates. We derive a two-phenotype reaction-diffusion model with density-dependent switching, and we prove the cooperative (quasi-monotone) structure and the associated comparison principle and study travelling-wave solutions of the model. A leading-edge linearization gives minimal front speed as minimizer of an explicit dispersion relation, and direct simulation verifies the predicted speed. In the experimentally relevant fast switching limit, we find a closed-form expression for the speed, that is, we obtain an effective Fisher-KPP equation with rescaled diffusivity and growth rate, with the fractions of the phenotypes. The "go-or-grow" (GoG) front can move at a maximum speed of half the Fisher speed for the same single-cell motility $D$ and proliferation rate $r$, which occurs only when the cells divide their time equally between the two phenotypes. This bound is directly testable: measurement of the front speed, plus independent determination of $D$ and $r$, discriminates the two hypotheses, and in the GoG case, yields recovery of the phenotype balance. We then extend the result to anisotropic (DTI-informed) invasion along white-matter tracts and discuss implications for understanding clinical measurements of growth rate.

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.

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.

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.

Although muscle spindle sensory signals have been extensively studied, little is known about how and why muscle spindle firing is modulated by the central nervous system during movement. Specialized motor neurons to the muscle spindle, i.e. gamma motor neurons, can profoundly alter spindle firing during behavior, but technological limitations hinder our ability to record gamma motor and muscle spindle sensory signals during most behaviors. We used a biophysical model of a muscle spindle within a muscle-tendon unit to simulate how gamma drive may modulate muscle spindle Ia firing during locomotion. Based on a few available recordings from decerebrate animals, we demonstrate that our model, tuned to passive stretch conditions, can reproduce profound changes in muscle spindle firing in response to identical joint motions in locomotor vs. relaxed stretch conditions. Our model can discover phasic patterns of two types of gamma motor neuron drive based on recorded muscle spindle Ia firing and joint motion. By simulating perturbations, we conclude that: 1) sinusoidal activation of static gamma motor neurons during locomotion, encoding intended movement, modulates muscle spindle signals such that they act as sensorimotor feedback signals based on errors from the intended muscle fascicle length; 2) phasic on/off activation of dynamic gamma motor neurons during locomotion acts as an event detector, heightening muscle spindle Ia responses to discrete perturbations. As such, their muscle-within-muscle structure allows the muscle spindle to act as a highly tunable physical internal model of muscle state to guide movement. Our model supports proposed but as-yet-untested theories of muscle spindle function and offers a framework for extending the testing of muscle spindle function to active, behavioral conditions.

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.

Expectations guide behavior and shape sensory responses in single neurons, but their influence on population-level neural dynamics is unknown. Here, we employ a dynamical systems framework to examine the collective spiking activity of neuronal populations in the auditory forebrain of European starlings, a species of songbird, as they categorize natural song syllables while sensory expectations are manipulated. We show first that sensory-driven neural population spiking activity traces smooth, low-dimensional latent trajectories that closely reflect the identity of sensory signals. Like the stimulus-driven responses of single neurons, the geometry of the population trajectories is also modulated by expectation. In single neurons, expectation sharpens differences between responses to signals in the same category, but at the population-level the effect is opposite: expectation increases the similarity between responses to signals in the same category. To understand how population-level response dynamics can differ from those in single neurons, we develop (and test empirically) a dynamical model that relates spiking activity at these two biological scales. The model leverages response redundancy between neurons, a capacity we term degeneracy-enabled remapping, and enables the observed simultaneous expectation-dependent increases in the separability of single-neuron responses \textit{and} decreases in the separability of population trajectories in the task-potent subspace, i.e., the population activity dimensions tied to behavioral categorization. Examining the relationship between expectation-modulated population trajectories and behavior in detail, we find that single-trial categorization errors are tied to drift in the trajectory toward the opposing task-potent manifold. This suggests that expectations help establish structured, hypothesis-dependent initial conditions that precede the target-driven population response. In support of this, both behavioral accuracy and behavioral reaction time are predicted by the direction of early population motion within the task-potent subspace. We conclude that expectation drives anticipatory organization of population response variability into a structured, behaviorally relevant geometry that pre-positions subsequent population activity on task-potent manifolds to support rapid, accurate, behavioral outcomes.

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.

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.

The relationship between genotypic and phenotypic variation is determined by the complex interaction of genetic and environmental factors. While statistical methods capable of detecting such interactions exist, an axiomatic mathematical framework that seamlessly describes the combined effects of genetic modifications and environmental exposures on a common scale is lacking. In this report, buffering concepts are used to construct a measurement system that enables the geometric representation of both gene-by-gene and gene-by-environment interactions on the extended complex plane (i.e., as projections on the Riemann sphere). In this manner, any such interaction, or combination thereof, can be precisely defined and quantified as the deviation from the neutral value calculated through the applicable complex transformation. When thus conceptualized, the framework's parameterization defines the "state space" of a given measurable phenotype along both the real and imaginary dimensions, thus establishing an unambiguous and broadly applicable method for determining the phenotypic value expected upon combinatorial changes in genetic and/or environmental variables. Remarkably, by applying these methods, it is possible to quantify the effects of any gene-by-environment interaction using the equation, AGxE=Im([z]obs*zexp)/2, where zobs and zexp are complex numbers representing the observed and expected phenotypes of a given genotype expressed in terms of the buffering parameters, and b.

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

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as the parameter dimension grows, a failure usually attributed to dimension itself. We show instead that it is governed by the quality of the summary statistics, with dimension entering only through a separate and milder mechanism, and that the two must act together for the Normal kernel to break. The first ingredient is covariance overinflation: the kernel covariance, estimated from the particle cloud, overshoots the true posterior covariance by a factor set by information loss in the summary statistics. We derive this overscaling factor in closed form for a Gaussian model with sufficient statistics and show that it stays modest at any dimension, shrinking toward its baseline value as the tolerance tightens; the extreme values seen in practice (of order 103) are a signature of insufficient summaries, not of dimension. The second ingredient is perturbation overconcentration: the normalised Normal step size concentrates around one as the dimension grows, so every proposal overshoots by the same factor. Either ingredient alone is harmless; only their combination breaks the Normal kernel. A Cauchy kernel (multivariate t with one degree of freedom) removes the concentration, keeping a positive acceptance rate under arbitrary overscaling at a bounded worst-case cost of 1.87x in expected squared jump distance. In a Metropolis-Hastings framework we derive closed-form acceptance rates for both kernels that illustrate the advantage of the Cauchy kernel in this limit. A series of full ABC-SMC computational experiments on five problems at d = 12, including a hierarchical gene-expression model, show the Cauchy reducing the sliced Wasserstein distance to the reference posterior by factors of up to 50 with the same simulation budget. Since the summary statistics are commonly insufficient for the models that require ABC, overinflation is structural and the Cauchy perturbation kernel is the right default for problems in higher dimensions.

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.