A unifying perspective on neural manifolds and circuits for cognition

Relating sex-bias in human cortical and hippocampal microstructure to sex hormones

Determining sex-bias in brain structure is of great societal interest to improve diagnostics and treatment of brain-related disorders. So far, studies on sex-bias in brain structure predominantly focus on macro-scale measures, and often ignore factors determining this bias. Here we study sex-bias in cortical and hippocampal microstructure in relation to sex hormones. Investigating quantitative intracortical profiling in-vivo using the T1w/T2w ratio in 1093 healthy females and males of the cross-sectional Human Connectome Project young adult sample, we find that regional cortical and hippocampal microstructure differs between males and females and that the effect size of this sex-bias varies depending on self-reported hormonal status in females. Microstructural sex-bias and expression of sex hormone genes, based on an independent post-mortem sample, are spatially coupled. Lastly, sex-bias is most pronounced in paralimbic areas, with low laminar complexity, which are predicted to be most plastic based on their cytoarchitectural properties. Albeit correlative, our study underscores the importance of incorporating sex hormone variables into the investigation of brain structure and plasticity.

Focal seizures induce spatiotemporally organized spiking activity in the human cortex

Epileptic seizures are debilitating because of the clinical symptoms they produce. These symptoms, in turn, may stem directly from disruptions in neural coding. Recent evidence has suggested that the specific temporal order, or sequence, of spiking across a population of cortical neurons may encode information. Here, we investigate how seizures disrupt neuronal spiking sequences in the human brain by recording multi-unit activity from the cerebral cortex in five male participants undergoing monitoring for seizures. We find that pathological discharges during seizures are associated with bursts of spiking activity across a population of cortical neurons. These bursts are organized into highly consistent and stereotyped temporal sequences. As the seizure evolves, spiking sequences diverge from the sequences observed at baseline and become more spatially organized. The direction of this spatial organization matches the direction of the ictal discharges, which spread over the cortex as traveling waves. Our data therefore suggest that seizures can entrain cortical spiking sequences by changing the spatial organization of neuronal firing, providing a possible mechanism by which seizures create symptoms.

Flexible gating between subspaces in a neural network model of internally guided task switching

Behavioral flexibility relies on the brain's ability to switch rapidly between multiple tasks, even when the task rule is not explicitly cued but must be inferred through trial and error. The underlying neural circuit mechanism remains poorly understood. We investigated recurrent neural networks (RNNs) trained to perform an analog of the classic Wisconsin Card Sorting Test. The networks consist of two modules responsible for rule representation and sensorimotor mapping, respectively, where each module is comprised of a circuit with excitatory neurons and three major types of inhibitory neurons. We found that rule representation by self-sustained persistent activity across trials, error monitoring and gated sensorimotor mapping emerged from training. Systematic dissection of trained RNNs revealed a detailed circuit mechanism that is consistent across networks trained with different hyperparameters. The networks' dynamical trajectories for different rules resided in separate subspaces of population activity; the subspaces collapsed and performance was reduced to chance level when dendrite-targeting somatostatin-expressing interneurons were silenced, illustrating how a phenomenological description of representational subspaces is explained by a specific circuit mechanism.

Ghost Channels and Ghost Cycles Guiding Long Transients in Dynamical Systems

Dynamical descriptions and modeling of natural systems have generally focused on fixed points, with saddles and saddle-based phase-space objects such as heteroclinic channels or cycles being central concepts behind the emergence of quasistable long transients. Reliable and robust transient dynamics observed for real, inherently noisy systems is, however, not met by saddle-based dynamics, as demonstrated here. Generalizing the notion of ghost states, we provide a complementary framework that does not rely on the precise knowledge or existence of (un)stable fixed points, but rather on slow directed flows organized by ghost sets in ghost channels and ghost cycles. Moreover, we show that the appearance of these novel objects is an emergent property of a broad class of models typically used for description of natural systems.

Sustained behaviour: Encoding of cumulative experience in the anterior cingulate

Time is a ubiquitous dimension of behaviour. A new study demonstrates that low-dimensional temporal drift in rodent anterior cingulate ensembles encodes cumulative experience. These data provide fresh insight into how neurons encode extended periods of time to guide high-level behaviours.

Adult-neurogenesis allows for representational stability and flexibility in early olfactory system

In the early olfactory system, adult-neurogenesis, a process of neuronal replacement results in the continuous reorganization of synaptic connections and network architecture throughout the animal's life. This poses a critical challenge: How does the olfactory system maintain stable representations of odors and therefore allow for stable sensory perceptions amidst this ongoing circuit instability? Utilizing a detailed spiking network model of early olfactory circuits, we uncovered dual roles for adult-neurogenesis: one that both supports representational stability to faithfully encode odor information and also one that facilitates plasticity to allow for learning and adaptation. In the main olfactory bulb, adult-neurogenesis affects neural codes in individual mitral and tufted cells but preserves odor representations at the neuronal population level. By contrast, in the olfactory piriform cortex, both individual cell responses and overall population dynamics undergo progressive changes due to adult-neurogenesis. This leads to representational drift, a gradual alteration in sensory perception. Both processes are dynamic and depend on experience such that repeated exposure to specific odors reduces the drift due to adult-neurogenesis; thus, when the odor environment is stable over the course of adult-neurogenesis, it is neurogenesis that actually allows the representations to remain stable in piriform cortex; when those olfactory environments change, adult-neurogenesis allows the cortical representations to track environmental change. Whereas perceptual stability and plasticity due to learning are often thought of as two distinct, often contradictory processing in neuronal coding, we find that adult-neurogenesis serves as a shared mechanism for both. In this regard, the quixotic presence of adult-neurogenesis in the mammalian olfactory bulb that has been the focus of considerable debate in chemosensory neuroscience may be the mechanistic underpinning behind an array of complex computations.

Flexible gating between subspaces in a neural network model of internally guided task switching

Behavioral flexibility relies on the brain's ability to switch rapidly between multiple tasks, even when the task rule is not explicitly cued but must be inferred through trial and error. The underlying neural circuit mechanism remains poorly understood. We investigated recurrent neural networks (RNNs) trained to perform an analog of the classic Wisconsin Card Sorting Test. The networks consist of two modules responsible for rule representation and sensorimotor mapping, respectively, where each module is comprised of a circuit with excitatory neurons and three major types of inhibitory neurons. We found that rule representation by self-sustained persistent activity across trials, error monitoring and gated sensorimotor mapping emerged from training. Systematic dissection of trained RNNs revealed a detailed circuit mechanism that is consistent across networks trained with different hyperparameters. The networks' dynamical trajectories for different rules resided in separate subspaces of population activity; the subspaces collapsed and performance was reduced to chance level when dendrite-targeting somatostatin-expressing interneurons were silenced, illustrating how a phenomenological description of representational subspaces is explained by a specific circuit mechanism.

Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons

Brain-computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex.

Abstract deliberation by visuomotor neurons in prefrontal cortex

During visually guided behavior, the prefrontal cortex plays a pivotal role in mapping sensory inputs onto appropriate motor plans. When the sensory input is ambiguous, this involves deliberation. It is not known whether the deliberation is implemented as a competition between possible stimulus interpretations or between possible motor plans. Here we study neural population activity in the prefrontal cortex of macaque monkeys trained to flexibly report perceptual judgments of ambiguous visual stimuli. We find that the population activity initially represents the formation of a perceptual choice before transitioning into the representation of the motor plan. Stimulus strength and prior expectations both bear on the formation of the perceptual choice, but not on the formation of the action plan. These results suggest that prefrontal circuits involved in action selection are also used for the deliberation of abstract propositions divorced from a specific motor plan, thus providing a crucial mechanism for abstract reasoning.

Intrinsic Dynamics and Neural Implementation of a Hypothalamic Line Attractor Encoding an Internal Behavioral State

Line attractors are emergent population dynamics hypothesized to encode continuous variables such as head direction and internal states. In mammals, direct evidence of neural implementation of a line attractor has been hindered by the challenge of targeting perturbations to specific neurons within contributing ensembles. Estrogen receptor type 1 (Esr1)-expressing neurons in the ventrolateral subdivision of the ventromedial hypothalamus (VMHvl) show line attractor dynamics in male mice during fighting. We hypothesized that these dynamics may encode continuous variation in the intensity of an internal aggressive state. Here, we report that these neurons also show line attractor dynamics in head-fixed mice observing aggression. We exploit this finding to identify and perturb line attractor-contributing neurons using 2-photon calcium imaging and holographic optogenetic perturbations. On-manifold perturbations demonstrate that integration and persistent activity are intrinsic properties of these neurons which drive the system along the line attractor, while transient off-manifold perturbations reveal rapid relaxation back into the attractor. Furthermore, stimulation and imaging reveal selective functional connectivity among attractor-contributing neurons. Intriguingly, individual differences among mice in line attractor stability were correlated with the degree of functional connectivity among contributing neurons. Mechanistic modelling indicates that dense subnetwork connectivity and slow neurotransmission are required to explain our empirical findings. Our work bridges circuit and manifold paradigms, shedding light on the intrinsic and operational dynamics of a behaviorally relevant mammalian line attractor.

Nonlinear manifolds underlie neural population activity during behaviour

There is rich variety in the activity of single neurons recorded during behaviour. Yet, these diverse single neuron responses can be well described by relatively few patterns of neural co-modulation. The study of such low-dimensional structure of neural population activity has provided important insights into how the brain generates behaviour. Virtually all of these studies have used linear dimensionality reduction techniques to estimate these population-wide co-modulation patterns, constraining them to a flat "neural manifold". Here, we hypothesised that since neurons have nonlinear responses and make thousands of distributed and recurrent connections that likely amplify such nonlinearities, neural manifolds should be intrinsically nonlinear. Combining neural population recordings from monkey, mouse, and human motor cortex, and mouse striatum, we show that: 1) neural manifolds are intrinsically nonlinear; 2) their nonlinearity becomes more evident during complex tasks that require more varied activity patterns; and 3) manifold nonlinearity varies across architecturally distinct brain regions. Simulations using recurrent neural network models confirmed the proposed relationship between circuit connectivity and manifold nonlinearity, including the differences across architecturally distinct regions. Thus, neural manifolds underlying the generation of behaviour are inherently nonlinear, and properly accounting for such nonlinearities will be critical as neuroscientists move towards studying numerous brain regions involved in increasingly complex and naturalistic behaviours.

Stereotyped goal-directed manifold dynamics in the insular cortex

The insular cortex is involved in diverse processes, including bodily homeostasis, emotions, and cognition. However, we lack a comprehensive understanding of how it processes information at the level of neuronal populations. We leveraged recent advances in unsupervised machine learning to study insular cortex population activity patterns (i.e., neuronal manifold) in mice performing goal-directed behaviors. We find that the insular cortex activity manifold is remarkably consistent across different animals and under different motivational states. Activity dynamics within the neuronal manifold are highly stereotyped during rewarded trials, enabling robust prediction of single-trial outcomes across different mice and across various natural and artificial motivational states. Comparing goal-directed behavior with self-paced free consumption, we find that the stereotyped activity patterns reflect task-dependent goal-directed reward anticipation, and not licking, taste, or positive valence. These findings reveal a core computation in insular cortex that could explain its involvement in pathologies involving aberrant motivations.

Approximating Nonlinear Functions With Latent Boundaries in Low-Rank Excitatory-Inhibitory Spiking Networks

Deep feedforward and recurrent neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.

Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

Distinct manifold encoding of navigational information in the subiculum and hippocampus

The subiculum (SUB) plays a crucial role in spatial navigation and encodes navigational information differently from the hippocampal CA1 area. However, the representation of subicular population activity remains unknown. Here, we investigated the neuronal population activity recorded extracellularly from the CA1 and SUB of rats performing T-maze and open-field tasks. The trajectory of population activity in both areas was confined to low-dimensional neural manifolds homoeomorphic to external space. The manifolds conveyed position, speed, and future path information with higher decoding accuracy in the SUB than in the CA1. The manifolds exhibited common geometry across rats and regions for the CA1 and SUB and between tasks in the SUB. During post-task ripples in slow-wave sleep, population activity represented reward locations/events more frequently in the SUB than in CA1. Thus, the CA1 and SUB encode information distinctly into the neural manifolds that underlie navigational information processing during wakefulness and sleep.

Causation in neuroscience: keeping mechanism meaningful

A fundamental goal of research in neuroscience is to uncover the causal structure of the brain. This focus on causation makes sense, because causal information can provide explanations of brain function and identify reliable targets with which to understand cognitive function and prevent or change neurological conditions and psychiatric disorders. In this research, one of the most frequently used causal concepts is 'mechanism' - this is seen in the literature and language of the field, in grant and funding inquiries that specify what research is supported, and in journal guidelines on which contributions are considered for publication. In these contexts, mechanisms are commonly tied to expressions of the main aims of the field and cited as the 'fundamental', 'foundational' and/or 'basic' unit for understanding the brain. Despite its common usage and perceived importance, mechanism is used in different ways that are rarely distinguished. Given that this concept is defined in different ways throughout the field - and that there is often no clarification of which definition is intended - there remains a marked ambiguity about the fundamental goals, orientation and principles of the field. Here we provide an overview of causation and mechanism from the perspectives of neuroscience and philosophy of science, in order to address these challenges.

If Engrams Are the Answer, What Is the Question?

Engram labelling and manipulation methodologies are now a staple of contemporary neuroscientific practice, giving the impression that the physical basis of engrams has been discovered. Despite enormous progress, engrams have not been clearly identified, and it is unclear what they should look like. There is an epistemic bias in engram neuroscience toward characterizing biological changes while neglecting the development of theory. However, the tools of engram biology are exciting precisely because they are not just an incremental step forward in understanding the mechanisms of plasticity and learning but because they can be leveraged to inform theory on one of the fundamental mysteries in neuroscience-how and in what format the brain stores information. We do not propose such a theory here, as we first require an appreciation for what is lacking. We outline a selection of issues in four sections from theoretical biology and philosophy that engram biology and systems neuroscience generally should engage with in order to construct useful future theoretical frameworks. Specifically, what is it that engrams are supposed to explain? How do the different building blocks of the brain-wide engram come together? What exactly are these component parts? And what information do they carry, if they carry anything at all? Asking these questions is not purely the privilege of philosophy but a key to informing scientific hypotheses that make the most of the experimental tools at our disposal. The risk for not engaging with these issues is high. Without a theory of what engrams are, what they do, and the wider computational processes they fit into, we may never know when they have been found.

From cell types to population dynamics: Making hippocampal manifolds physiologically interpretable

The study of the hippocampal code is gaining momentum. While the physiological approach targets the contribution of individual cells as determined by genetic, biophysical and circuit factors, the field pushes for a population dynamic approach that considers the representation of behavioural variables by a large number of neurons. In this alternative framework, neuronal activity is projected into low-dimensional manifolds. These manifolds can reveal the structure of population representations, but their physiological interpretation is challenging. Here, we review the recent literature and propose that integrating information regarding behavioral traits, local field potential oscillations and cell-type-specificity into neural manifolds offers strategies to make them interpretable at the physiological level.

Circular and unified analysis in network neuroscience

Genuinely new discovery transcends existing knowledge. Despite this, many analyses in systems neuroscience neglect to test new speculative hypotheses against benchmark empirical facts. Some of these analyses inadvertently use circular reasoning to present existing knowledge as new discovery. Here, I discuss that this problem can confound key results and estimate that it has affected more than three thousand studies in network neuroscience over the last decade. I suggest that future studies can reduce this problem by limiting the use of speculative evidence, integrating existing knowledge into benchmark models, and rigorously testing proposed discoveries against these models. I conclude with a summary of practical challenges and recommendations.

The enigmatic HCN channels: A cellular neurophysiology perspective

What physiological role does a slow hyperpolarization-activated ion channel with mixed cation selectivity play in the fast world of neuronal action potentials that are driven by depolarization? That puzzling question has piqued the curiosity of physiology enthusiasts about the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are widely expressed across the body and especially in neurons. In this review, we emphasize the need to assess HCN channels from the perspective of how they respond to time-varying signals, while also accounting for their interactions with other co-expressing channels and receptors. First, we illustrate how the unique structural and functional characteristics of HCN channels allow them to mediate a slow negative feedback loop in the neurons that they express in. We present the several physiological implications of this negative feedback loop to neuronal response characteristics including neuronal gain, voltage sag and rebound, temporal summation, membrane potential resonance, inductive phase lead, spike triggered average, and coincidence detection. Next, we argue that the overall impact of HCN channels on neuronal physiology critically relies on their interactions with other co-expressing channels and receptors. Interactions with other channels allow HCN channels to mediate intrinsic oscillations, earning them the "pacemaker channel" moniker, and to regulate spike frequency adaptation, plateau potentials, neurotransmitter release from presynaptic terminals, and spike initiation at the axonal initial segment. We also explore the impact of spatially non-homogeneous subcellular distributions of HCN channels in different neuronal subtypes and their interactions with other channels and receptors. Finally, we discuss how plasticity in HCN channels is widely prevalent and can mediate different encoding, homeostatic, and neuroprotective functions in a neuron. In summary, we argue that HCN channels form an important class of channels that mediate a diversity of neuronal functions owing to their unique gating kinetics that made them a puzzle in the first place.

Neuropeptide Signaling is Required to Implement a Line Attractor Encoding a Persistent Internal Behavioral State

Internal states drive survival behaviors, but their neural implementation is not well understood. Recently we identified a line attractor in the ventromedial hypothalamus (VMH) that represents an internal state of aggressiveness. Line attractors can be implemented by recurrent connectivity and/or neuromodulatory signaling, but evidence for the latter is scant. Here we show that neuropeptidergic signaling is necessary for line attractor dynamics in this system, using a novel approach that integrates cell type-specific, anatomically restricted CRISPR/Cas9-based gene editing with microendoscopic calcium imaging. Co-disruption of receptors for oxytocin and vasopressin in adult VMH Esr1 + neurons that control aggression suppressed attack, reduced persistent neural activity and eliminated line attractor dynamics, while only modestly impacting neural activity and sex- or behavior-tuning. These data identify a requisite role for neuropeptidergic signaling in implementing a behaviorally relevant line attractor. Our approach should facilitate mechanistic studies in neuroscience that bridge different levels of biological function and abstraction.

Cortical network and projection neuron types that articulate serial order in a skilled motor behavior

Skilled motor behaviors require orderly coordination of multiple constituent movements with sensory cues towards achieving a goal, but the underlying brain circuit mechanisms remain unclear. Here we show that target-guided reach-grasp-to-drink (RGD) in mice involves the ordering and coordination of a set of forelimb and oral actions. Cortex-wide activity imaging of multiple glutamatergic projection neuron (PN) types uncovered a network, involving the secondary motor cortex (MOs), forelimb primary motor and somatosensory cortex, that tracked RGD movements. Photo-inhibition highlighted MOs in coordinating RGD movements. Within the MOs, population neural trajectories tracked RGD progression and single neuron activities integrated across constituent movements. Notably, MOs intratelencephalic, pyramidal tract, and corticothalamic PN activities correlated with action coordination, showed distinct neural dynamics trajectories, and differentially contributed to movement coordination. Our results delineate a cortical network and key areas, PN types, and neural dynamics therein that articulate the serial order and coordination of a skilled behavior.

A Critical Perspective on Neural Mechanisms in Cognitive Neuroscience: Towards Unification

A central pursuit of cognitive neuroscience is to find neural mechanisms of cognition, with research programs favoring different strategies to look for them. But what is a neural mechanism, and how do we know we have captured them? Here I answer these questions through a framework that integrates Marr's levels with philosophical work on mechanism. From this, the following goal emerges: What needs to be explained are the computations of cognition, with explanation itself given by mechanism-composed of algorithms and parts of the brain that realize them. This reveals a delineation within cognitive neuroscience research. In the premechanism stage, the computations of cognition are linked to phenomena in the brain, narrowing down where and when mechanisms are situated in space and time. In the mechanism stage, it is established how computation emerges from organized interactions between parts-filling the premechanistic mold. I explain why a shift toward mechanistic modeling helps us meet our aims while outlining a road map for doing so. Finally, I argue that the explanatory scope of neural mechanisms can be approximated by effect sizes collected across studies, not just conceptual analysis. Together, these points synthesize a mechanistic agenda that allows subfields to connect at the level of theory.

The dynamics and geometry of choice in premotor cortex

The brain represents sensory variables in the coordinated activity of neural populations, in which tuning curves of single neurons define the geometry of the population code. Whether the same coding principle holds for dynamic cognitive variables remains unknown because internal cognitive processes unfold with a unique time course on single trials observed only in the irregular spiking of heterogeneous neural populations. Here we show the existence of such a population code for the dynamics of choice formation in the primate premotor cortex. We developed an approach to simultaneously infer population dynamics and tuning functions of single neurons to the population state. Applied to spike data recorded during decision-making, our model revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Our results reveal a common geometric principle for neural encoding of sensory and dynamic cognitive variables.

A low dimensional manifold of human exploratory behavior reveals opposing roles for apathy and anxiety

Exploration-exploitation decision-making is a feature of daily life that is altered in a number of neuropsychiatric conditions. Humans display a range of exploration and exploitation behaviors, which can be affected by apathy and anxiety. It remains unknown how factors underlying decision-making generate the spectrum of observed exploration-exploitation behavior and how they relate to states of anxiety and apathy. Here, we report a latent structure underlying sequential exploration and exploitation decisions that explains variation in anxiety and apathy. 1001 participants in a gender-balanced sample completed a three-armed restless bandit task along with psychiatric symptom surveys. Using dimensionality reduction methods, we found that decision sequences reduced to a low-dimensional manifold. The axes of this manifold explained individual differences in the balance between states of exploration and exploitation and the stability of those states, as determined by a statistical mechanics model of decision-making. Position along the balance axis was correlated with opposing symptoms of behavioral apathy and anxiety, while position along the stability axis correlated with the level of emotional apathy. This result resolves a paradox over how these symptoms can be correlated in samples but have opposite effects on behavior. Furthermore, this work provides a basis for using behavioral manifolds to reveal relationships between behavioral dynamics and affective states, with important implications for behavioral measurement approaches to neuropsychiatric conditions.

A Transient High-dimensional Geometry Affords Stable Conjunctive Subspaces for Efficient Action Selection

Flexible action selection requires cognitive control mechanisms capable of mapping the same inputs to diverse output actions depending on goals and contexts. How the brain encodes information to enable this capacity remains one of the longstanding and fundamental problems in cognitive neuroscience. From a neural state-space perspective, solving this problem requires a control representation that can disambiguate similar input neural states, making task-critical dimensions separable depending on the context. Moreover, for action selection to be robust and time-invariant, control representations must be stable in time, thereby enabling efficient readout by downstream processing units. Thus, an ideal control representation should leverage geometry and dynamics that maximize the separability and stability of neural trajectories for task computations. Here, using novel EEG decoding methods, we investigated how the geometry and dynamics of control representations constrain flexible action selection in the human brain. Specifically, we tested the hypothesis that encoding a temporally stable conjunctive subspace that integrates stimulus, response, and context (i.e., rule) information in a high-dimensional geometry achieves the separability and stability needed for context-dependent action selection. Human participants performed a task that requires context-dependent action selection based on pre-instructed rules. Participants were cued to respond immediately at varying intervals following stimulus presentation, which forced responses at different states in neural trajectories. We discovered that in the moments before successful responses, there was a transient expansion of representational dimensionality that separated conjunctive subspaces. Further, we found that the dynamics stabilized in the same time window, and that the timing of entry into this stable and high-dimensional state predicted the quality of response selection on individual trials. These results establish the neural geometry and dynamics the human brain needs for flexible control over behavior.

Toward a computational theory of manifold untangling: from global embedding to local flattening

It has been hypothesized that the ventral stream processing for object recognition is based on a mechanism called cortically local subspace untangling. A mathematical abstraction of object recognition by the visual cortex is how to untangle the manifolds associated with different object categories. Such a manifold untangling problem is closely related to the celebrated kernel trick in metric space. In this paper, we conjecture that there is a more general solution to manifold untangling in the topological space without artificially defining any distance metric. Geometrically, we can either embed a manifold in a higher-dimensional space to promote selectivity or flatten a manifold to promote tolerance. General strategies of both global manifold embedding and local manifold flattening are presented and connected with existing work on the untangling of image, audio, and language data. We also discuss the implications of untangling the manifold into motor control and internal representations.