Bayesian Computation through Cortical Latent Dynamics

The effects of the post-delay epochs on working memory error reduction

Accurate retrieval of the maintained information is crucial for working memory. This process primarily occurs during post-delay epochs, when subjects receive cues and generate responses. However, the computational and neural mechanisms that underlie these post-delay epochs to support robust memory remain poorly understood. To address this, we trained recurrent neural networks (RNNs) on a color delayed-response task, where certain colors (referred to as common colors) were more frequently presented for memorization. We found that the trained RNNs reduced memory errors for common colors by decoding a broader range of neural states into these colors through the post-delay epochs. This decoding process was driven by convergent neural dynamics and a non-dynamic, biased readout process during the post-delay epochs. Our findings highlight the importance of post-delay epochs in working memory and suggest that neural systems adapt to environmental statistics by using multiple mechanisms across task epochs.

A mechanism linking dopamine's roles in reinforcement, movement and motivation

Dopamine neurons (DANs) play seemingly distinct roles in reinforcement, 1-3 motivation, 4,5 and movement, 6,7 and DA-modulating therapies relieve symptoms across a puzzling spectrum of neurologic and psychiatric symptoms. 8 Yet, the mechanistic relationship among these roles is unknown. Here, we show DA's tripartite roles are causally linked by a process in which phasic striatal DA rapidly and persistently recalibrates the propensity to move, a measure of vigor. Using a self-timed movement task, we found that single exposures to reward-related DA transients (both endogenous and exogenously-induced) exerted one-shot updates to movement timing-but in a surprising fashion. Rather than reinforce specific movement times, DA transients quantitatively changed movement timing on the next trial, with larger transients leading to earlier movements (and smaller to later), consistent with a stochastic search process that calibrates the frequency of movement. Both abrupt and gradual changes in external and internal contingencies-such as timing criterion, reward content, and satiety state-caused changes to the amplitude of DA transients that causally altered movement timing. The rapidity and bidirectionality of the one-shot effects are difficult to reconcile with gradual synaptic plasticity, and instead point to more flexible cellular mechanisms, such as DA-dependent modulation of neuronal excitability. Our findings shed light on how natural reinforcement, as well as DA-related disorders such as Parkinson's disease, could affect behavioral vigor.

Expectation-driven sensory adaptations support enhanced acuity during categorical perception

Expectations can influence perception in seemingly contradictory ways, either by directing attention to expected stimuli and enhancing perceptual acuity or by stabilizing perception and diminishing acuity within expected stimulus categories. The neural mechanisms supporting these dual roles of expectation are not well understood. Here, we trained European starlings to classify ambiguous song syllables in both expected and unexpected acoustic contexts. We show that birds employ probabilistic, Bayesian integration to classify syllables, leveraging their expectations to stabilize their perceptual behavior. However, auditory sensory neural populations do not reflect this integration. Instead, expectation enhances the acuity of auditory sensory neurons in high-probability regions of the stimulus space. This modulation diverges from patterns typically observed in motor areas, where Bayesian integration of sensory inputs and expectations predominates. Our results suggest that peripheral sensory systems use expectation to improve sensory representations and maintain high-fidelity representations of the world, allowing downstream circuits to flexibly integrate this information with expectations to drive behavior.

Bayesian inference by visuomotor neurons in the prefrontal cortex

Perceptual judgments of the environment emerge from the concerted activity of neural populations in decision-making areas downstream of the sensory cortex. When the sensory input is ambiguous, perceptual judgments can be biased by prior expectations shaped by environmental regularities. These effects are examples of Bayesian inference, a reasoning method in which prior knowledge is leveraged to optimize uncertain decisions. However, it is not known how decision-making circuits combine sensory signals and prior expectations to form a perceptual decision. Here, we study neural population activity in the prefrontal cortex of macaque monkeys trained to report perceptual judgments of ambiguous visual stimuli under two different stimulus distributions. We isolate the component of the neural population response that represents the formation of the perceptual decision (the decision variable, DV), and find that its dynamical evolution reflects the integration of sensory signals and prior expectations. Prior expectations impact the DV's trajectory both before and during stimulus presentation such that DV trajectories with a smaller dynamic range result in more biased and less sensitive perceptual decisions. We show that these results resemble a specific variant of Bayesian inference known as approximate hierarchical inference. Our findings expand our understanding of the mechanisms by which prefrontal circuits can execute Bayesian inference.

Medium Spiny Neurons Mediate Timing Perception in Coordination with Prefrontal Neurons in Primates

Timing perception is a fundamental cognitive function that allows organisms to navigate their environment effectively, encompassing both prospective and retrospective timing. Despite significant advancements in understanding how the brain processes temporal information, the neural mechanisms underlying these two forms of timing remain largely unexplored. In this study, it aims to bridge this knowledge gap by elucidating the functional roles of various neuronal populations in the striatum and prefrontal cortex (PFC) in shaping subjective experiences of time. Utilizing a large-scale electrode array, it recorded responses from over 3000 neurons in the striatum and PFC of macaque monkeys during timing tasks. The analysis classified neurons into distinct groups and revealed that retrospective and prospective timings are governed by separate neural processes. Specifically, this study demonstrates that medium spiny neurons (MSNs) in the striatum play a crucial role in facilitating these timing processes. Through cell-type-specific manipulation, it identified D2-MSNs as the primary contributors to both forms of timing. Additionally, the findings indicate that effective processing of timing requires coordination between the PFC and the striatum. In summary, this study advances the understanding of the neural foundations of timing perception and highlights its behavioral implications.

Global to local influences on temporal expectation in marmosets and humans

Marmosets are emerging rapidly as experimental models for studying the neural bases of cognition and, importantly, for modeling disorders of human cognition, but many aspects of their mental attributes remain to be characterized. When judging elapsed time, humans implicitly use prior information to predict upcoming events and reduce perceptual and decision-making uncertainty. An influential model of temporal expectation is the hazard rate model, which posits the likelihood of an event occurring in the future, provided it has not occurred already. Here, we report that marmosets trained on a reaction time task acquire the hazard rate model of expectation, consistent with the global task structure. The model emerges progressively with learning but unexpectedly continues to be modified by local contingencies, as demonstrated by a serial effect of trial duration on responses. The combined effects of global and local task structure are well described by a multiple regression model and computationally by Bayesian updating of the hazard function. Parallel experiments in human subjects similarly demonstrate global followed by local influences on reaction times and temporal expectation. Thus, in both marmosets and humans, task history and local structure continuously update task-specific responses, surprisingly at the expense of optimal responses after the competent acquisition of an internal model.

Neural representation of action symbols in primate frontal cortex

At the core of intelligence is proficiency in solving new problems, including those that differ dramatically from problems seen before. Problem-solving, in turn, depends on goal-directed generation of novel thoughts and behaviors1, which has been proposed to rely on internal representations of discrete units, or symbols, and processes that can recombine them into a large set of possible composite representations1-11. Although this view has been influential in formulating cognitive-level explanations of behavior, definitive evidence for a neuronal substrate of symbols has remained elusive. Here, we identify a neural population encoding action symbols-internal, recombinable representations of discrete units of motor behavior-localized to a specific area of frontal cortex. In macaque monkeys performing a drawing-like task designed to assess recombination of learned action symbols into novel sequences, we found behavioral evidence for three critical features that indicate actions have an underlying symbolic representation: (i) invariance over low-level motor parameters; (ii) categorical structure, reflecting discrete classes of action; and (iii) recombination into novel sequences. In simultaneous neural recordings across motor, premotor, and prefrontal cortex, we found that planning-related population activity in ventral premotor cortex encodes actions in a manner that, like behavior, reflects motor invariance, categorical structure, and recombination, three properties indicating a symbolic representation. Activity in no other recorded area exhibited this combination of properties. These findings reveal a neural representation of action symbols localized to PMv, and therefore identify a putative neural substrate for symbolic cognitive operations.

Individual variability of neural computations underlying flexible decisions

The ability to flexibly switch our responses to external stimuli according to contextual information is critical for successful interactions with a complex world. Context-dependent computations are necessary across many domains1-3, yet their neural implementations remain poorly understood. Here we developed a novel behavioural task in rats to study context-dependent selection and accumulation of evidence for decision-making4-6. Under assumptions supported by both monkey and rat data, we first show mathematically that this computation can be supported by three dynamical solutions and that all networks performing the task implement a combination of these solutions. These solutions can be identified and tested directly with experimental data. We further show that existing electrophysiological and modelling data are compatible with the full variety of possible combinations of these solutions, suggesting that different individuals could use different combinations. To study variability across individual subjects, we developed automated, high-throughput methods to train rats on our task and trained many subjects using these methods. Consistent with theoretical predictions, neural and behavioural analyses revealed substantial heterogeneity across rats, despite uniformly good task performance. Our theory further predicts a specific link between behavioural and neural signatures, which was robustly supported in the data. In summary, our results provide an experimentally supported theoretical framework to analyse individual variability in biological and artificial systems that perform flexible decision-making tasks, open the door to cellular-resolution studies of individual variability in higher cognition, and provide insights into neural mechanisms of context-dependent computation more generally.

An emerging view of neural geometry in motor cortex supports high-performance decoding

Decoders for brain-computer interfaces (BCIs) assume constraints on neural activity, chosen to reflect scientific beliefs while yielding tractable computations. Recent scientific advances suggest that the true constraints on neural activity, especially its geometry, may be quite different from those assumed by most decoders. We designed a decoder, MINT, to embrace statistical constraints that are potentially more appropriate. If those constraints are accurate, MINT should outperform standard methods that explicitly make different assumptions. Additionally, MINT should be competitive with expressive machine learning methods that can implicitly learn constraints from data. MINT performed well across tasks, suggesting its assumptions are well-matched to the data. MINT outperformed other interpretable methods in every comparison we made. MINT outperformed expressive machine learning methods in 37 of 42 comparisons. MINT's computations are simple, scale favorably with increasing neuron counts, and yield interpretable quantities such as data likelihoods. MINT's performance and simplicity suggest it may be a strong candidate for many BCI applications.

Effects of noise and metabolic cost on cortical task representations

Cognitive flexibility requires both the encoding of task-relevant and the ignoring of task-irrelevant stimuli. While the neural coding of task-relevant stimuli is increasingly well understood, the mechanisms for ignoring task-irrelevant stimuli remain poorly understood. Here, we study how task performance and biological constraints jointly determine the coding of relevant and irrelevant stimuli in neural circuits. Using mathematical analyses and task-optimized recurrent neural networks, we show that neural circuits can exhibit a range of representational geometries depending on the strength of neural noise and metabolic cost. By comparing these results with recordings from primate prefrontal cortex (PFC) over the course of learning, we show that neural activity in PFC changes in line with a minimal representational strategy. Specifically, our analyses reveal that the suppression of dynamically irrelevant stimuli is achieved by activity-silent, sub-threshold dynamics. Our results provide a normative explanation as to why PFC implements an adaptive, minimal representational strategy.

Linking neural population formatting to function

Animals capable of complex behaviors tend to have more distinct brain areas than simpler organisms, and artificial networks that perform many tasks tend to self-organize into modules (1-3). This suggests that different brain areas serve distinct functions supporting complex behavior. However, a common observation is that essentially anything that an animal senses, knows, or does can be decoded from neural activity in any brain area (4-6). If everything is everywhere, why have distinct areas? Here we show that the function of a brain area is more related to how different types of information are combined (formatted) in neural representations than merely whether that information is present. We compared two brain areas: the middle temporal area (MT), which is important for visual motion perception (7, 8), and the dorsolateral prefrontal cortex (dlPFC), which is linked to decision-making and reward expectation (9, 10)). When monkeys based decisions on a combination of motion and reward information, both types of information were present in both areas. However, they were formatted differently: in MT, they were encoded separably, while in dlPFC, they were represented jointly in ways that reflected the monkeys' decision-making. A recurrent neural network (RNN) model that mirrored the information formatting in MT and dlPFC predicted that manipulating activity in these areas would differently affect decision-making. Consistent with model predictions, electrically stimulating MT biased choices midway between the visual motion stimulus and the preferred direction of the stimulated units (11), while stimulating dlPFC produced 'winner-take-all' decisions that sometimes reflected the visual motion stimulus and sometimes reflected the preference of the stimulated units, but never in between. These results are consistent with the tantalizing possibility that a modular structure enables complex behavior by flexibly reformatting information to accomplish behavioral goals.

Dynamic tracking of objects in the macaque dorsomedial frontal cortex

A central tenet of cognitive neuroscience is that humans build an internal model of the external world and use mental simulation of the model to perform physical inferences. Decades of human experiments have shown that behaviors in many physical reasoning tasks are consistent with predictions from the mental simulation theory. However, evidence for the defining feature of mental simulation - that neural population dynamics reflect simulations of physical states in the environment - is limited. We test the mental simulation hypothesis by combining a naturalistic ball-interception task, large-scale electrophysiology in non-human primates, and recurrent neural network modeling. We find that neurons in the monkeys' dorsomedial frontal cortex (DMFC) represent task-relevant information about the ball position in a multiplexed fashion. At a population level, the activity pattern in DMFC comprises a low-dimensional neural embedding that tracks the ball both when it is visible and invisible, serving as a neural substrate for mental simulation. A systematic comparison of different classes of task-optimized RNN models with the DMFC data provides further evidence supporting the mental simulation hypothesis. Our findings provide evidence that neural dynamics in the frontal cortex are consistent with internal simulation of external states in the environment.

Rastermap: a discovery method for neural population recordings

Neurophysiology has long progressed through exploratory experiments and chance discoveries. Anecdotes abound of researchers listening to spikes in real time and noticing patterns of activity related to ongoing stimuli or behaviors. With the advent of large-scale recordings, such close observation of data has become difficult. To find patterns in large-scale neural data, we developed 'Rastermap', a visualization method that displays neurons as a raster plot after sorting them along a one-dimensional axis based on their activity patterns. We benchmarked Rastermap on realistic simulations and then used it to explore recordings of tens of thousands of neurons from mouse cortex during spontaneous, stimulus-evoked and task-evoked epochs. We also applied Rastermap to whole-brain zebrafish recordings; to wide-field imaging data; to electrophysiological recordings in rat hippocampus, monkey frontal cortex and various cortical and subcortical regions in mice; and to artificial neural networks. Finally, we illustrate high-dimensional scenarios where Rastermap and similar algorithms cannot be used effectively.

Representation of a perceptual bias in the prefrontal cortex

Perception is influenced by sensory stimulation, prior knowledge, and contextual cues, which collectively contribute to the emergence of perceptual biases. However, the precise neural mechanisms underlying these biases remain poorly understood. This study aims to address this gap by analyzing neural recordings from the prefrontal cortex (PFC) of monkeys performing a vibrotactile frequency discrimination task. Our findings provide empirical evidence supporting the hypothesis that perceptual biases can be reflected in the neural activity of the PFC. We found that the state-space trajectories of PFC neuronal activity encoded a warped representation of the first frequency presented during the task. Remarkably, this distorted representation of the frequency aligned with the predictions of its Bayesian estimator. The identification of these neural correlates expands our understanding of the neural basis of perceptual biases and highlights the involvement of the PFC in shaping perceptual experiences. Similar analyses could be employed in other delayed comparison tasks and in various brain regions to explore where and how neural activity reflects perceptual biases during different stages of the trial.

Decoding contextual influences on auditory perception from primary auditory cortex

Perception can be highly dependent on stimulus context, but whether and how sensory areas encode the context remains uncertain. We used an ambiguous auditory stimulus - a tritone pair - to investigate the neural activity associated with a preceding contextual stimulus that strongly influenced the tritone pair's perception: either as an ascending or a descending step in pitch. We recorded single-unit responses from a population of auditory cortical cells in awake ferrets listening to the tritone pairs preceded by the contextual stimulus. We find that the responses adapt locally to the contextual stimulus, consistent with human MEG recordings from the auditory cortex under the same conditions. Decoding the population responses demonstrates that cells responding to pitch-changes are able to predict well the context-sensitive percept of the tritone pairs. Conversely, decoding the individual pitch representations and taking their distance in the circular Shepard tone space predicts the opposite of the percept. The various percepts can be readily captured and explained by a neural model of cortical activity based on populations of adapting, pitch and pitch-direction cells, aligned with the neurophysiological responses. Together, these decoding and model results suggest that contextual influences on perception may well be already encoded at the level of the primary sensory cortices, reflecting basic neural response properties commonly found in these areas.

Common neural mechanisms supporting time judgements in humans and monkeys

There has been an increasing interest in identifying the biological underpinnings of human time perception, for which purpose research in non-human primates (NHP) is common. Although previous work, based on behaviour, suggests that similar mechanisms support time perception across species, the neural correlates of time estimation in humans and NHP have not been directly compared. In this study, we assess whether brain evoked responses during a time categorization task are similar across species. Specifically, we assess putative differences in post-interval evoked potentials as a function of perceived duration in human EEG (N = 24) and local field potential (LFP) and spike recordings in pre-supplementary motor area (pre-SMA) of one monkey. Event-related potentials (ERPs) differed significantly after the presentation of the temporal interval between "short" and "long" perceived durations in both species, even when the objective duration of the stimuli was the same. Interestingly, the polarity of the reported ERPs was reversed for incorrect trials (i.e., the ERP of a "long" stimulus looked like the ERP of a "short" stimulus when a time categorization error was made). Hence, our results show that post-interval potentials reflect the perceived (rather than the objective) duration of the presented time interval in both NHP and humans. In addition, firing rates in monkey's pre-SMA also differed significantly between short and long perceived durations and were reversed in incorrect trials. Together, our results show that common neural mechanisms support time categorization in NHP and humans, thereby suggesting that NHP are a good model for investigating human time perception.

Perturbation context in paced finger tapping tunes the error-correction mechanism

Sensorimotor synchronization (SMS) is the mainly specifically human ability to move in sync with a periodic external stimulus, as in keeping pace with music. The most common experimental paradigm to study its largely unknown underlying mechanism is the paced finger-tapping task, where a participant taps to a periodic sequence of brief stimuli. Contrary to reaction time, this task involves temporal prediction because the participant needs to trigger the motor action in advance for the tap and the stimulus to occur simultaneously, then an error-correction mechanism takes past performance as input to adjust the following prediction. In a different, simpler task, it has been shown that exposure to a distribution of individual temporal intervals creates a "temporal context" that can bias the estimation/production of a single target interval. As temporal estimation and production are also involved in SMS, we asked whether a paced finger-tapping task with period perturbations would show any time-related context effect. In this work we show that a perturbation context can indeed be generated by exposure to period perturbations during paced finger tapping, affecting the shape and size of the resynchronization curve. Response asymmetry is also affected, thus evidencing an interplay between context and intrinsic nonlinearities of the correction mechanism. We conclude that perturbation context calibrates the underlying error-correction mechanism in SMS.

Dynamical mechanisms of how an RNN keeps a beat, uncovered with a low-dimensional reduced model

Despite music's omnipresence, the specific neural mechanisms responsible for perceiving and anticipating temporal patterns in music are unknown. To study potential mechanisms for keeping time in rhythmic contexts, we train a biologically constrained RNN, with excitatory (E) and inhibitory (I) units, on seven different stimulus tempos (2-8 Hz) on a synchronization and continuation task, a standard experimental paradigm. Our trained RNN generates a network oscillator that uses an input current (context parameter) to control oscillation frequency and replicates key features of neural dynamics observed in neural recordings of monkeys performing the same task. We develop a reduced three-variable rate model of the RNN and analyze its dynamic properties. By treating our understanding of the mathematical structure for oscillations in the reduced model as predictive, we confirm that the dynamical mechanisms are found also in the RNN. Our neurally plausible reduced model reveals an E-I circuit with two distinct inhibitory sub-populations, of which one is tightly synchronized with the excitatory units.

Bayesian inference by visuomotor neurons in prefrontal cortex

Perceptual judgements of the environment emerge from the concerted activity of neural populations in decision-making areas downstream of sensory cortex [1, 2, 3]. When the sensory input is ambiguous, perceptual judgements can be biased by prior expectations shaped by environmental regularities [4, 5, 6, 7, 8, 9,10,11]. These effects are examples of Bayesian inference, a reasoning method in which prior knowledge is leveraged to optimize uncertain decisions [12, 13]. However, it is not known how decision-making circuits combine sensory signals and prior expectations to form a perceptual decision. Here, we study neural population activity in the prefrontal cortex of macaque monkeys trained to report perceptual judgments of ambiguous visual stimuli under two different stimulus distributions. We analyze the component of the neural population response that represents the formation of the perceptual decision (the decision variable, DV), and find that its dynamical evolution reflects the integration of sensory signals and prior expectations. Prior expectations impact the DV's trajectory both before and during stimulus presentation such that DV trajectories with a smaller dynamic range result in more biased and less sensitive perceptual decisions. These results reveal a mechanism by which prefrontal circuits can execute Bayesian inference.

A computational mechanism of cue-stimulus integration for pain in the brain

The brain integrates information from pain-predictive cues and noxious inputs to construct the pain experience. Although previous studies have identified neural encodings of individual pain components, how they are integrated remains elusive. Here, using a cue-induced pain task, we examined temporal functional magnetic resonance imaging activities within the state space, where axes represent individual voxel activities. By analyzing the features of these activities at the large-scale network level, we demonstrated that overall brain networks preserve both cue and stimulus information in their respective subspaces within the state space. However, only higher-order brain networks, including limbic and default mode networks, could reconstruct the pattern of participants' reported pain by linear summation of subspace activities, providing evidence for the integration of cue and stimulus information. These results suggest a hierarchical organization of the brain for processing pain components and elucidate the mechanism for their integration underlying our pain perception.

Propofol anesthesia destabilizes neural dynamics across cortex

Every day, hundreds of thousands of people undergo general anesthesia. One hypothesis is that anesthesia disrupts dynamic stability-the ability of the brain to balance excitability with the need to be stable and controllable. To test this hypothesis, we developed a method for quantifying changes in population-level dynamic stability in complex systems: delayed linear analysis for stability estimation (DeLASE). Propofol was used to transition animals between the awake state and anesthetized unconsciousness. DeLASE was applied to macaque cortex local field potentials (LFPs). We found that neural dynamics were more unstable in unconsciousness compared with the awake state. Cortical trajectories mirrored predictions from destabilized linear systems. We mimicked the effect of propofol in simulated neural networks by increasing inhibitory tone. This in turn destabilized the networks, as observed in the neural data. Our results suggest that anesthesia disrupts dynamical stability that is required for consciousness.

Reach-dependent reorientation of rotational dynamics in motor cortex

During reaching, neurons in motor cortex exhibit complex, time-varying activity patterns. Though single-neuron activity correlates with movement parameters, movement correlations explain neural activity only partially. Neural responses also reflect population-level dynamics thought to generate outputs. These dynamics have previously been described as "rotational," such that activity orbits in neural state space. Here, we reanalyze reaching datasets from male Rhesus macaques and find two essential features that cannot be accounted for with standard dynamics models. First, the planes in which rotations occur differ for different reaches. Second, this variation in planes reflects the overall location of activity in neural state space. Our "location-dependent rotations" model fits nearly all motor cortex activity during reaching, and high-quality decoding of reach kinematics reveals a quasilinear relationship with spiking. Varying rotational planes allows motor cortex to produce richer outputs than possible under previous models. Finally, our model links representational and dynamical ideas: representation is present in the state space location, which dynamics then convert into time-varying command signals.

Irrational choices via a curvilinear representational geometry for value

We make decisions by comparing values, but it is not yet clear how value is represented in the brain. Many models assume, if only implicitly, that the representational geometry of value is linear. However, in part due to a historical focus on noisy single neurons, rather than neuronal populations, this hypothesis has not been rigorously tested. Here, we examine the representational geometry of value in the ventromedial prefrontal cortex (vmPFC), a part of the brain linked to economic decision-making, in two male rhesus macaques. We find that values are encoded along a curved manifold in vmPFC. This curvilinear geometry predicts a specific pattern of irrational decision-making: that decision-makers will make worse choices when an irrelevant, decoy option is worse in value, compared to when it is better. We observe this type of irrational choices in behavior. Together, these results not only suggest that the representational geometry of value is nonlinear, but that this nonlinearity could impose bounds on rational decision-making.

Flexible neural population dynamics govern the speed and stability of sensory encoding in mouse visual cortex

Time courses of neural responses underlie real-time sensory processing and perception. How these temporal dynamics change may be fundamental to how sensory systems adapt to different perceptual demands. By simultaneously recording from hundreds of neurons in mouse primary visual cortex, we examined neural population responses to visual stimuli at sub-second timescales, during different behavioural states. We discovered that during active behavioural states characterised by locomotion, single-neurons shift from transient to sustained response modes, facilitating rapid emergence of visual stimulus tuning. Differences in single-neuron response dynamics were associated with changes in temporal dynamics of neural correlations, including faster stabilisation of stimulus-evoked changes in the structure of correlations during locomotion. Using Factor Analysis, we examined temporal dynamics of latent population responses and discovered that trajectories of population activity make more direct transitions between baseline and stimulus-encoding neural states during locomotion. This could be partly explained by dampening of oscillatory dynamics present during stationary behavioural states. Functionally, changes in temporal response dynamics collectively enabled faster, more stable and more efficient encoding of new visual information during locomotion. These findings reveal a principle of how sensory systems adapt to perceptual demands, where flexible neural population dynamics govern the speed and stability of sensory encoding.

Emergent perceptual biases from state-space geometry in trained spiking recurrent neural networks

A stimulus held in working memory is perceived as contracted toward the average stimulus. This contraction bias has been extensively studied in psychophysics, but little is known about its origin from neural activity. By training recurrent networks of spiking neurons to discriminate temporal intervals, we explored the causes of this bias and how behavior relates to population firing activity. We found that the trained networks exhibited animal-like behavior. Various geometric features of neural trajectories in state space encoded warped representations of the durations of the first interval modulated by sensory history. Formulating a normative model, we showed that these representations conveyed a Bayesian estimate of the interval durations, thus relating activity and behavior. Importantly, our findings demonstrate that Bayesian computations already occur during the sensory phase of the first stimulus and persist throughout its maintenance in working memory, until the time of stimulus comparison.

Decoding contextual influences on auditory perception from primary auditory cortex

Perception can be highly dependent on stimulus context, but whether and how sensory areas encode the context remains uncertain. We used an ambiguous auditory stimulus - a tritone pair - to investigate the neural activity associated with a preceding contextual stimulus that strongly influenced the tritone pair's perception: either as an ascending or a descending step in pitch. We recorded single-unit responses from a population of auditory cortical cells in awake ferrets listening to the tritone pairs preceded by the contextual stimulus. We find that the responses adapt locally to the contextual stimulus, consistent with human MEG recordings from the auditory cortex under the same conditions. Decoding the population responses demonstrates that cells responding to pitch-class-changes are able to predict well the context-sensitive percept of the tritone pairs. Conversely, decoding the individual pitch-class representations and taking their distance in the circular Shepard tone space predicts the opposite of the percept. The various percepts can be readily captured and explained by a neural model of cortical activity based on populations of adapting, pitch-class and pitch-class-direction cells, aligned with the neurophysiological responses. Together, these decoding and model results suggest that contextual influences on perception may well be already encoded at the level of the primary sensory cortices, reflecting basic neural response properties commonly found in these areas.

Computational role of structure in neural activity and connectivity

One major challenge of neuroscience is identifying structure in seemingly disorganized neural activity. Different types of structure have different computational implications that can help neuroscientists understand the functional role of a particular brain area. Here, we outline a unified approach to characterize structure by inspecting the representational geometry and the modularity properties of the recorded activity and show that a similar approach can also reveal structure in connectivity. We start by setting up a general framework for determining geometry and modularity in activity and connectivity and relating these properties with computations performed by the network. We then use this framework to review the types of structure found in recent studies of model networks performing three classes of computations.

Desiderata for Normative Models of Synaptic Plasticity

Normative models of synaptic plasticity use computational rationales to arrive at predictions of behavioral and network-level adaptive phenomena. In recent years, there has been an explosion of theoretical work in this realm, but experimental confirmation remains limited. In this review, we organize work on normative plasticity models in terms of a set of desiderata that, when satisfied, are designed to ensure that a given model demonstrates a clear link between plasticity and adaptive behavior, is consistent with known biological evidence about neural plasticity and yields specific testable predictions. As a prototype, we include a detailed analysis of the REINFORCE algorithm. We also discuss how new models have begun to improve on the identified criteria and suggest avenues for further development. Overall, we provide a conceptual guide to help develop neural learning theories that are precise, powerful, and experimentally testable.

Single trial Bayesian inference by population vector readout in the barn owl's sound localization system

Bayesian models have proven effective in characterizing perception, behavior, and neural encoding across diverse species and systems. The neural implementation of Bayesian inference in the barn owl's sound localization system and behavior has been previously explained by a non-uniform population code model. This model specifies the neural population activity pattern required for a population vector readout to match the optimal Bayesian estimate. While prior analyses focused on trial-averaged comparisons of model predictions with behavior and single-neuron responses, it remains unknown whether this model can accurately approximate Bayesian inference on single trials under varying sensory reliability, a fundamental condition for natural perception and behavior. In this study, we utilized mathematical analysis and simulations to demonstrate that decoding a non-uniform population code via a population vector readout approximates the Bayesian estimate on single trials for varying sensory reliabilities. Our findings provide additional support for the non-uniform population code model as a viable explanation for the barn owl's sound localization pathway and behavior.

Biases in hand perception are driven by somatosensory computations, not a distorted hand model

To sense and interact with objects in the environment, we effortlessly configure our fingertips at desired locations. It is therefore reasonable to assume that the underlying control mechanisms rely on accurate knowledge about the structure and spatial dimensions of our hand and fingers. This intuition, however, is challenged by years of research showing drastic biases in the perception of finger geometry.1,2,3,4,5 This perceptual bias has been taken as evidence that the brain's internal representation of the body's geometry is distorted,6 leading to an apparent paradox regarding the skillfulness of our actions.7 Here, we propose an alternative explanation of the biases in hand perception-they are the result of the Bayesian integration of noisy, but unbiased, somatosensory signals about finger geometry and posture. To address this hypothesis, we combined Bayesian reverse engineering with behavioral experimentation on joint and fingertip localization of the index finger. We modeled the Bayesian integration either in sensory or in space-based coordinates, showing that the latter model variant led to biases in finger perception despite accurate representation of finger length. Behavioral measures of joint and fingertip localization responses showed similar biases, which were well fitted by the space-based, but not the sensory-based, model variant. The space-based model variant also outperformed a distorted hand model with built-in geometric biases. In total, our results suggest that perceptual distortions of finger geometry do not reflect a distorted hand model but originate from near-optimal Bayesian inference on somatosensory signals.

Body-part specificity for learning of multiple prior distributions in human coincidence timing

During timing tasks, the brain learns the statistical distribution of target intervals and integrates this prior knowledge with sensory inputs to optimise task performance. Daily events can have different temporal statistics (e.g., fastball/slowball in baseball batting), making it important to learn and retain multiple priors. However, the rules governing this process are not yet understood. Here, we demonstrate that the learning of multiple prior distributions in a coincidence timing task is characterised by body-part specificity. In our experiments, two prior distributions (short and long intervals) were imposed on participants. When using only one body part for timing responses, regardless of the priors, participants learned a single prior by generalising over the two distributions. However, when the two priors were assigned to different body parts, participants concurrently learned the two independent priors. Moreover, body-part specific prior acquisition was faster when the priors were assigned to anatomically distant body parts (e.g., hand/foot) than when they were assigned to close body parts (e.g., index/middle fingers). This suggests that the body-part specific learning of priors is organised according to somatotopy.

Chaotic neural dynamics facilitate probabilistic computations through sampling

Cortical neurons exhibit highly variable responses over trials and time. Theoretical works posit that this variability arises potentially from chaotic network dynamics of recurrently connected neurons. Here, we demonstrate that chaotic neural dynamics, formed through synaptic learning, allow networks to perform sensory cue integration in a sampling-based implementation. We show that the emergent chaotic dynamics provide neural substrates for generating samples not only of a static variable but also of a dynamical trajectory, where generic recurrent networks acquire these abilities with a biologically plausible learning rule through trial and error. Furthermore, the networks generalize their experience in the stimulus-evoked samples to the inference without partial or all sensory information, which suggests a computational role of spontaneous activity as a representation of the priors as well as a tractable biological computation for marginal distributions. These findings suggest that chaotic neural dynamics may serve for the brain function as a Bayesian generative model.

Common neural mechanisms supporting time judgements in humans and monkeys

There has been an increasing interest in identifying the biological underpinnings of human time perception, for which purpose research in non-human primates (NHP) is common. Although previous work, based on behaviour, suggests that similar mechanisms support time perception across species, the neural correlates of time estimation in humans and NHP have not been directly compared. In this study, we assess whether brain evoked responses during a time categorization task are similar across species. Specifically, we assess putative differences in post-interval evoked potentials as a function of perceived duration in human EEG (N = 24) and local field potential (LFP) and spike recordings in pre-supplementary motor area (pre-SMA) of one monkey. Event-related potentials (ERPs) differed significantly after the presentation of the temporal interval between "short" and "long" perceived durations in both species, even when the objective duration of the stimuli was the same. Interestingly, the polarity of the reported ERPs was reversed for incorrect trials (i.e., the ERP of a "long" stimulus looked like the ERP of a "short" stimulus when a time categorization error was made). Hence, our results show that post-interval potentials reflect the perceived (rather than the objective) duration of the presented time interval in both NHP and humans. In addition, firing rates in monkey's pre-SMA also differed significantly between short and long perceived durations and were reversed in incorrect trials. Together, our results show that common neural mechanisms support time categorization in NHP and humans, thereby suggesting that NHP are a good model for investigating human time perception.

Separating cognitive and motor processes in the behaving mouse

The cognitive processes supporting complex animal behavior are closely associated with ubiquitous movements responsible for our posture, facial expressions, ability to actively sample our sensory environments, and other critical processes. These movements are strongly related to neural activity across much of the brain and are often highly correlated with ongoing cognitive processes, making it challenging to dissociate the neural dynamics that support cognitive processes from those supporting related movements. In such cases, a critical issue is whether cognitive processes are separable from related movements, or if they are driven by common neural mechanisms. Here, we demonstrate how the separability of cognitive and motor processes can be assessed, and, when separable, how the neural dynamics associated with each component can be isolated. We establish a novel two-context behavioral task in mice that involves multiple cognitive processes and show that commonly observed dynamics taken to support cognitive processes are strongly contaminated by movements. When cognitive and motor components are isolated using a novel approach for subspace decomposition, we find that they exhibit distinct dynamical trajectories. Further, properly accounting for movement revealed that largely separate populations of cells encode cognitive and motor variables, in contrast to the 'mixed selectivity' often reported. Accurately isolating the dynamics associated with particular cognitive and motor processes will be essential for developing conceptual and computational models of neural circuit function and evaluating the function of the cell types of which neural circuits are composed.

Tracking subjects' strategies in behavioural choice experiments at trial resolution

Investigating how, when, and what subjects learn during decision-making tasks requires tracking their choice strategies on a trial-by-trial basis. Here, we present a simple but effective probabilistic approach to tracking choice strategies at trial resolution using Bayesian evidence accumulation. We show this approach identifies both successful learning and the exploratory strategies used in decision tasks performed by humans, non-human primates, rats, and synthetic agents. Both when subjects learn and when rules change the exploratory strategies of win-stay and lose-shift, often considered complementary, are consistently used independently. Indeed, we find the use of lose-shift is strong evidence that subjects have latently learnt the salient features of a new rewarded rule. Our approach can be extended to any discrete choice strategy, and its low computational cost is ideally suited for real-time analysis and closed-loop control.

Neuroimaging Signatures of Metacognitive Improvement in Sensorimotor Timing

Error monitoring is an essential human ability underlying learning and metacognition. In the time domain, humans possess a remarkable ability to learn and adapt to temporal intervals, yet the neural mechanisms underlying this are not clear. Recently, we demonstrated that humans improve sensorimotor time estimates when given the chance to incorporate previous trial feedback ( Bader and Wiener, 2021), suggesting that humans are metacognitively aware of their own timing errors. To test the neural basis of this metacognitive ability, human participants of both sexes underwent fMRI while they performed a visual temporal reproduction task with randomized supra-second intervals (1.5-6 s). Crucially, each trial was repeated following feedback, allowing a "re-do" to learn from the successes or errors in the initial trial. Behaviorally, we replicated our previous finding of improved re-do trial performance despite temporally uninformative (i.e., early or late) feedback. For neuroimaging, we observed a dissociation between estimating and reproducing time intervals. Estimation engaged the default mode network (DMN), including the superior frontal gyri, precuneus, and posterior cingulate, whereas reproduction activated regions associated traditionally with the "timing network" (TN), including the supplementary motor area (SMA), precentral gyrus, and right supramarginal gyrus. Notably, greater and more extensive DMN involvement was observed in re-do trials, whereas for the TN, it was more constrained. Task-based connectivity between these networks demonstrated higher inter-network correlation primarily when estimating initial trials, while re-do trial communication was higher during reproduction. Overall, these results suggest that the DMN and TN jointly mediate subjective self-awareness to improve timing performance.

Pre-supplementary Motor Cortex Mediates Learning Transfer from Perceptual to Motor Timing

When we intensively train a timing skill, such as learning to play the piano, we not only produce brain changes associated with task-specific learning but also improve our performance in other temporal behaviors that depend on these tuned neural resources. Since the neural basis of time learning and generalization is still unknown, we measured the changes in neural activity associated with the transfer of learning from perceptual to motor timing in a large sample of subjects (n = 65; 39 women). We found that intense training in an interval discrimination task increased the acuity of time perception in a group of subjects that also exhibited learning transfer, expressed as a reduction in inter-tap interval variability during an internally driven periodic motor task. In addition, we found subjects with no learning and/or generalization effects. Notably, functional imaging showed an increase in pre-supplementary motor area and caudate-putamen activity between the post- and pre-training sessions of the tapping task. This increase was specific to the subjects that generalized their timing acuity from the perceptual to the motor context. These results emphasize the central role of the cortico-basal ganglia circuit in the generalization of timing abilities between tasks.

Neuronal travelling waves explain rotational dynamics in experimental datasets and modelling

Spatiotemporal properties of neuronal population activity in cortical motor areas have been subjects of experimental and theoretical investigations, generating numerous interpretations regarding mechanisms for preparing and executing limb movements. Two competing models, representational and dynamical, strive to explain the relationship between movement parameters and neuronal activity. A dynamical model uses the jPCA method that holistically characterizes oscillatory activity in neuron populations by maximizing the data rotational dynamics. Different rotational dynamics interpretations revealed by the jPCA approach have been proposed. Yet, the nature of such dynamics remains poorly understood. We comprehensively analyzed several neuronal-population datasets and found rotational dynamics consistently accounted for by a traveling wave pattern. For quantifying rotation strength, we developed a complex-valued measure, the gyration number. Additionally, we identified parameters influencing rotation extent in the data. Our findings suggest that rotational dynamics and traveling waves are typically the same phenomena, so reevaluation of the previous interpretations where they were considered separate entities is needed.

Identifying Interpretable Latent Factors with Sparse Component Analysis

In many neural populations, the computationally relevant signals are posited to be a set of 'latent factors' - signals shared across many individual neurons. Understanding the relationship between neural activity and behavior requires the identification of factors that reflect distinct computational roles. Methods for identifying such factors typically require supervision, which can be suboptimal if one is unsure how (or whether) factors can be grouped into distinct, meaningful sets. Here, we introduce Sparse Component Analysis (SCA), an unsupervised method that identifies interpretable latent factors. SCA seeks factors that are sparse in time and occupy orthogonal dimensions. With these simple constraints, SCA facilitates surprisingly clear parcellations of neural activity across a range of behaviors. We applied SCA to motor cortex activity from reaching and cycling monkeys, single-trial imaging data from C. elegans, and activity from a multitask artificial network. SCA consistently identified sets of factors that were useful in describing network computations.

Distinct neural adaptations to time demand in the striatum and the hippocampus

How do neural codes adjust to track time across a range of resolutions, from milliseconds to multi-seconds, as a function of the temporal frequency at which events occur? To address this question, we studied time-modulated cells in the striatum and the hippocampus, while macaques categorized three nested intervals within the sub-second or the supra-second range (up to 1, 2, 4, or 8 s), thereby modifying the temporal resolution needed to solve the task. Time-modulated cells carried more information for intervals with explicit timing demand, than for any other interval. The striatum, particularly the caudate, supported the most accurate temporal prediction throughout all time ranges. Strikingly, its temporal readout adjusted non-linearly to the time range, suggesting that the striatal resolution shifted from a precise millisecond to a coarse multi-second range as a function of demand. This is in line with monkey's behavioral latencies, which indicated that they tracked time until 2 s but employed a coarse categorization strategy for durations beyond. By contrast, the hippocampus discriminated only the beginning from the end of intervals, regardless of the range. We propose that the hippocampus may provide an overall poor signal marking an event's beginning, whereas the striatum optimizes neural resources to process time throughout an interval adapting to the ongoing timing necessity.

A Second Introduction to the Neurobiology of Interval Timing

Time is a critical variable that organisms must be able to measure in order to survive in a constantly changing environment. Initially, this paper describes the myriad of contexts where time is estimated or predicted and suggests that timing is not a single process and probably depends on a set of different neural mechanisms. Consistent with this hypothesis, the explosion of neurophysiological and imaging studies in the last 10 years suggests that different brain circuits and neural mechanisms are involved in the ability to tell and use time to control behavior across contexts. Then, we develop a conceptual framework that defines time as a family of different phenomena and propose a taxonomy with sensory, perceptual, motor, and sensorimotor timing as the pillars of temporal processing in the range of hundreds of milliseconds.

Diverse Time Encoding Strategies Within the Medial Premotor Areas of the Primate

The measurement of time in the subsecond scale is critical for many sophisticated behaviors, yet its neural underpinnings are largely unknown. Recent neurophysiological experiments from our laboratory have shown that the neural activity in the medial premotor areas (MPC) of macaques can represent different aspects of temporal processing. During single interval categorization, we found that preSMA encodes a subjective category limit by reaching a peak of activity at a time that divides the set of test intervals into short and long. We also observed neural signals associated with the category selected by the subjects and the reward outcomes of the perceptual decision. On the other hand, we have studied the behavioral and neurophysiological basis of rhythmic timing. First, we have shown in different tapping tasks that macaques are able to produce predictively and accurately intervals that are cued by auditory or visual metronomes or when intervals are produced internally without sensory guidance. In addition, we found that the rhythmic timing mechanism in MPC is governed by different layers of neural clocks. Next, the instantaneous activity of single cells shows ramping activity that encodes the elapsed or remaining time for a tapping movement. In addition, we found MPC neurons that build neural sequences, forming dynamic patterns of activation that flexibly cover all the produced interval depending on the tapping tempo. This rhythmic neural clock resets on every interval providing an internal representation of pulse. Furthermore, the MPC cells show mixed selectivity, encoding not only elapsed time, but also the tempo of the tapping and the serial order element in the rhythmic sequence. Hence, MPC can map different task parameters, including the passage of time, using different cell populations. Finally, the projection of the time varying activity of MPC hundreds of cells into a low dimensional state space showed circular neural trajectories whose geometry represented the internal pulse and the tapping tempo. Overall, these findings support the notion that MPC is part of the core timing mechanism for both single interval and rhythmic timing, using neural clocks with different encoding principles, probably to flexibly encode and mix the timing representation with other task parameters.

Heterogeneous encoding of temporal stimuli in the cerebellar cortex

Local feedforward and recurrent connectivity are rife in the frontal areas of the cerebral cortex, which gives rise to rich heterogeneous dynamics observed in such areas. Recently, similar local connectivity motifs have been discovered among Purkinje and molecular layer interneurons of the cerebellar cortex, however, task-related activity in these neurons has often been associated with relatively simple facilitation and suppression dynamics. Here, we show that the rodent cerebellar cortex supports heterogeneity in task-related neuronal activity at a scale similar to the cerebral cortex. We provide a computational model that inculcates recent anatomical insights into local microcircuit motifs to show the putative basis for such heterogeneity. We also use cell-type specific chronic viral lesions to establish the involvement of cerebellar lobules in associative learning behaviors. Functional heterogeneity in neuronal profiles may not merely be the remit of the associative cerebral cortex, similar principles may be at play in subcortical areas, even those with seemingly crystalline and homogenous cytoarchitectures like the cerebellum.

Modulation of prefrontal couplings by prior belief-related responses in ventromedial prefrontal cortex

Humans and other animals can maintain constant payoffs in an uncertain environment by steadily re-evaluating and flexibly adjusting current strategy, which largely depends on the interactions between the prefrontal cortex (PFC) and mediodorsal thalamus (MD). While the ventromedial PFC (vmPFC) represents the level of uncertainty (i.e., prior belief about external states), it remains unclear how the brain recruits the PFC-MD network to re-evaluate decision strategy based on the uncertainty. Here, we leverage non-linear dynamic causal modeling on fMRI data to test how prior belief-dependent activity in vmPFC gates the information flow in the PFC-MD network when individuals switch their decision strategy. We show that the prior belief-related responses in vmPFC had a modulatory influence on the connections from dorsolateral PFC (dlPFC) to both, lateral orbitofrontal (lOFC) and MD. Bayesian parameter averaging revealed that only the connection from the dlPFC to lOFC surpassed the significant threshold, which indicates that the weaker the prior belief, the less was the inhibitory influence of the vmPFC on the strength of effective connections from dlPFC to lOFC. These findings suggest that the vmPFC acts as a gatekeeper for the recruitment of processing resources to re-evaluate the decision strategy in situations of high uncertainty.

Exploring weight initialization, diversity of solutions, and degradation in recurrent neural networks trained for temporal and decision-making tasks

Recurrent Neural Networks (RNNs) are frequently used to model aspects of brain function and structure. In this work, we trained small fully-connected RNNs to perform temporal and flow control tasks with time-varying stimuli. Our results show that different RNNs can solve the same task by converging to different underlying dynamics and also how the performance gracefully degrades as either network size is decreased, interval duration is increased, or connectivity damage is induced. For the considered tasks, we explored how robust the network obtained after training can be according to task parameterization. In the process, we developed a framework that can be useful to parameterize other tasks of interest in computational neuroscience. Our results are useful to quantify different aspects of the models, which are normally used as black boxes and need to be understood in order to model the biological response of cerebral cortex areas.

Reconstructing computational system dynamics from neural data with recurrent neural networks

Computational models in neuroscience usually take the form of systems of differential equations. The behaviour of such systems is the subject of dynamical systems theory. Dynamical systems theory provides a powerful mathematical toolbox for analysing neurobiological processes and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) have become a popular machine learning tool for studying the non-linear dynamics of neural and behavioural processes by emulating an underlying system of differential equations. RNNs have been routinely trained on similar behavioural tasks to those used for animal subjects to generate hypotheses about the underlying computational mechanisms. By contrast, RNNs can also be trained on the measured physiological and behavioural data, thereby directly inheriting their temporal and geometrical properties. In this way they become a formal surrogate for the experimentally probed system that can be further analysed, perturbed and simulated. This powerful approach is called dynamical system reconstruction. In this Perspective, we focus on recent trends in artificial intelligence and machine learning in this exciting and rapidly expanding field, which may be less well known in neuroscience. We discuss formal prerequisites, different model architectures and training approaches for RNN-based dynamical system reconstructions, ways to evaluate and validate model performance, how to interpret trained models in a neuroscience context, and current challenges.

Adaptive oscillators support Bayesian prediction in temporal processing

Humans excel at predictively synchronizing their behavior with external rhythms, as in dance or music performance. The neural processes underlying rhythmic inferences are debated: whether predictive perception relies on high-level generative models or whether it can readily be implemented locally by hard-coded intrinsic oscillators synchronizing to rhythmic input remains unclear and different underlying computational mechanisms have been proposed. Here we explore human perception for tone sequences with some temporal regularity at varying rates, but with considerable variability. Next, using a dynamical systems perspective, we successfully model the participants behavior using an adaptive frequency oscillator which adjusts its spontaneous frequency based on the rate of stimuli. This model better reflects human behavior than a canonical nonlinear oscillator and a predictive ramping model-both widely used for temporal estimation and prediction-and demonstrate that the classical distinction between absolute and relative computational mechanisms can be unified under this framework. In addition, we show that neural oscillators may constitute hard-coded physiological priors-in a Bayesian sense-that reduce temporal uncertainty and facilitate the predictive processing of noisy rhythms. Together, the results show that adaptive oscillators provide an elegant and biologically plausible means to subserve rhythmic inference, reconciling previously incompatible frameworks for temporal inferential processes.

Amodal population clock in the primate medial premotor system for rhythmic tapping

The neural substrate for beat extraction and response entrainment to rhythms is not fully understood. Here we analyze the activity of medial premotor neurons in monkeys performing isochronous tapping guided by brief flashing stimuli or auditory tones. The population dynamics shared the following properties across modalities: the circular dynamics of the neural trajectories form a regenerating loop for every produced interval; the trajectories converge in similar state space at tapping times resetting the clock; and the tempo of the synchronized tapping is encoded in the trajectories by a combination of amplitude modulation and temporal scaling. Notably, the modality induces displacement in the neural trajectories in the auditory and visual subspaces without greatly altering the time-keeping mechanism. These results suggest that the interaction between the medial premotor cortex's amodal internal representation of pulse and a modality-specific external input generates a neural rhythmic clock whose dynamics govern rhythmic tapping execution across senses.

Lost in time: Relocating the perception of duration outside the brain

It is well-accepted in neuroscience that animals process time internally to estimate the duration of intervals lasting between one and several seconds. More than 100 years ago, Henri Bergson nevertheless remarked that, because animals have memory, their inner experience of time is ever-changing, making duration impossible to measure internally and time a source of change. Bergson proposed that quantifying the inner experience of time requires its externalization in movements (observed or self-generated), as their unfolding leaves measurable traces in space. Here, studies across species are reviewed and collectively suggest that, in line with Bergson's ideas, animals spontaneously solve time estimation tasks through a movement-based spatialization of time. Moreover, the well-known scalable anticipatory responses of animals to regularly spaced rewards can be explained by the variable pressure of time on reward-oriented actions. Finally, the brain regions linked with time perception overlap with those implicated in motor control, spatial navigation and motivation. Thus, instead of considering time as static information processed by the brain, it might be fruitful to conceptualize it as a kind of force to which animals are more or less sensitive depending on their internal state and environment.

Common population codes produce extremely nonlinear neural manifolds

Populations of neurons represent sensory, motor, and cognitive variables via patterns of activity distributed across the population. The size of the population used to encode a variable is typically much greater than the dimension of the variable itself, and thus, the corresponding neural population activity occupies lower-dimensional subsets of the full set of possible activity states. Given population activity data with such lower-dimensional structure, a fundamental question asks how close the low-dimensional data lie to a linear subspace. The linearity or nonlinearity of the low-dimensional structure reflects important computational features of the encoding, such as robustness and generalizability. Moreover, identifying such linear structure underlies common data analysis methods such as Principal Component Analysis (PCA). Here, we show that for data drawn from many common population codes the resulting point clouds and manifolds are exceedingly nonlinear, with the dimension of the best-fitting linear subspace growing at least exponentially with the true dimension of the data. Consequently, linear methods like PCA fail dramatically at identifying the true underlying structure, even in the limit of arbitrarily many data points and no noise.