Understanding the computation of time using neural network models

Orthogonality of sensory and contextual categorical dynamics embedded in a continuum of responses from the second somatosensory cortex

How does the brain simultaneously process signals that bring complementary information, like raw sensory signals and their transformed counterparts, without any disruptive interference? Contemporary research underscores the brain's adeptness in using decorrelated responses to reduce such interference. Both neurophysiological findings and artificial neural networks support the notion of orthogonal representation for signal differentiation and parallel processing. Yet, where, and how raw sensory signals are transformed into more abstract representations remains unclear. Using a temporal pattern discrimination task in trained monkeys, we revealed that the second somatosensory cortex (S2) efficiently segregates faithful and transformed neural responses into orthogonal subspaces. Importantly, S2 population encoding for transformed signals, but not for faithful ones, disappeared during a nondemanding version of this task, which suggests that signal transformation and their decoding from downstream areas are only active on-demand. A mechanistic computation model points to gain modulation as a possible biological mechanism for the observed context-dependent computation. Furthermore, individual neural activities that underlie the orthogonal population representations exhibited a continuum of responses, with no well-determined clusters. These findings advocate that the brain, while employing a continuum of heterogeneous neural responses, splits population signals into orthogonal subspaces in a context-dependent fashion to enhance robustness, performance, and improve coding efficiency.

Memorability shapes perceived time (and vice versa)

Visual stimuli are known to vary in their perceived duration. Some visual stimuli are also known to linger for longer in memory. Yet, whether these two features of visual processing are linked is unknown. Despite early assumptions that time is an extracted or higher-order feature of perception, more recent work over the past two decades has demonstrated that timing may be instantiated within sensory modality circuits. A primary location for many of these studies is the visual system, where duration-sensitive responses have been demonstrated. Furthermore, visual stimulus features have been observed to shift perceived duration. These findings suggest that visual circuits mediate or construct perceived time. Here we present evidence across a series of experiments that perceived time is affected by the image properties of scene size, clutter and memorability. More specifically, we observe that scene size and memorability dilate time, whereas clutter contracts it. Furthermore, the durations of more memorable images are also perceived more precisely. Conversely, the longer the perceived duration of an image, the more memorable it is. To explain these findings, we applied a recurrent convolutional neural network model of the ventral visual system, in which images are progressively processed over time. We find that more memorable images are processed faster, and that this increase in processing speed predicts both the lengthening and the increased precision of perceived durations. These findings provide evidence for a link between image features, time perception and memory that can be further explored with models of visual processing.

Probing latent brain dynamics in Alzheimer's disease via recurrent neural network

The impairment of cognitive function in Alzheimer's disease (AD) is clearly correlated to abnormal changes in cortical rhythm. However, the mechanisms underlying this correlation are still poorly understood. Here, we investigate how network structure and dynamical characteristics alter their abnormal changes in cortical rhythm. To that end, biological data of AD and normal participates are collected. By extracting the energy characteristics of different sub-bands in EEG signals, we find that the rhythm of AD patients is special particularly in theta and alpha bands. The cortical rhythm of normal state is mainly at alpha band, while that of AD state shift to the theta band. Furthermore, recurrent neural network (RNN) is trained to explore the rhythm formation and transformation between two neural states from the perspective view of neurocomputation. It is found that the neural coupling strength decreases significantly under AD state when compared with normal state, which weakens the ability of information transmission in AD state. Besides, the low-dimensional properties of RNN are obtained. By analyzing the relationship between the cortical rhythm transition and the low-dimensional trajectory, it is concluded that the low-dimensional trajectory update is slower and the communication cost is higher in AD state, which explains the abnormal synchronization of AD brain network. Our work reveals the causes for the formation of abnormal brain synchronous functional network status, which may expand our understanding of the mechanism of cognitive impairment in AD and provide an EEG biomarker for early AD.

Effect in the spectra of eigenvalues and dynamics of RNNs trained with excitatory-inhibitory constraint

In order to comprehend and enhance models that describes various brain regions it is important to study the dynamics of trained recurrent neural networks. Including Dale's law in such models usually presents several challenges. However, this is an important aspect that allows computational models to better capture the characteristics of the brain. Here we present a framework to train networks using such constraint. Then we have used it to train them in simple decision making tasks. We characterized the eigenvalue distributions of the recurrent weight matrices of such networks. Interestingly, we discovered that the non-dominant eigenvalues of the recurrent weight matrix are distributed in a circle with a radius less than 1 for those whose initial condition before training was random normal and in a ring for those whose initial condition was random orthogonal. In both cases, the radius does not depend on the fraction of excitatory and inhibitory units nor the size of the network. Diminution of the radius, compared to networks trained without the constraint, has implications on the activity and dynamics that we discussed here.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-023-09956-w.

Understanding the role of pathways in a deep neural network

Deep neural networks have demonstrated superior performance in artificial intelligence applications, but the opaqueness of their inner working mechanism is one major drawback in their application. The prevailing unit-based interpretation is a statistical observation of stimulus-response data, which fails to show a detailed internal process of inherent mechanisms of neural networks. In this work, we analyze a convolutional neural network (CNN) trained in the classification task and present an algorithm to extract the diffusion pathways of individual pixels to identify the locations of pixels in an input image associated with object classes. The pathways allow us to test the causal components which are important for classification and the pathway-based representations are clearly distinguishable between categories. We find that the few largest pathways of an individual pixel from an image tend to cross the feature maps in each layer that is important for classification. And the large pathways of images of the same category are more consistent in their trends than those of different categories. We also apply the pathways to understanding adversarial attacks, object completion, and movement perception. Further, the total number of pathways on feature maps in all layers can clearly discriminate the original, deformed, and target samples.

Exploring Flip Flop memories and beyond: training Recurrent Neural Networks with key insights

Training neural networks to perform different tasks is relevant across various disciplines. In particular, Recurrent Neural Networks (RNNs) are of great interest in Computational Neuroscience. Open-source frameworks dedicated to Machine Learning, such as Tensorflow and Keras have produced significant changes in the development of technologies that we currently use. This work contributes by comprehensively investigating and describing the application of RNNs for temporal processing through a study of a 3-bit Flip Flop memory implementation. We delve into the entire modeling process, encompassing equations, task parametrization, and software development. The obtained networks are meticulously analyzed to elucidate dynamics, aided by an array of visualization and analysis tools. Moreover, the provided code is versatile enough to facilitate the modeling of diverse tasks and systems. Furthermore, we present how memory states can be efficiently stored in the vertices of a cube in the dimensionally reduced space, supplementing previous results with a distinct approach.

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.

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.

Neurocomputational Models of Interval Timing: Seeing the Forest for the Trees

Extracting temporal regularities and relations from experience/observation is critical for organisms' adaptiveness (communication, foraging, predation, prediction) in their ecological niches. Therefore, it is not surprising that the internal clock that enables the perception of seconds-to-minutes-long intervals (interval timing) is evolutionarily well-preserved across many species of animals. This comparative claim is primarily supported by the fact that the timing behavior of many vertebrates exhibits common statistical signatures (e.g., on-average accuracy, scalar variability, positive skew). These ubiquitous statistical features of timing behaviors serve as empirical benchmarks for modelers in their efforts to unravel the processing dynamics of the internal clock (namely answering how internal clock "ticks"). In this chapter, we introduce prominent (neuro)computational approaches to modeling interval timing at a level that can be understood by general audience. These models include Treisman's pacemaker accumulator model, the information processing variant of scalar expectancy theory, the striatal beat frequency model, behavioral expectancy theory, the learning to time model, the time-adaptive opponent Poisson drift-diffusion model, time cell models, and neural trajectory models. Crucially, we discuss these models within an overarching conceptual framework that categorizes different models as threshold vs. clock-adaptive models and as dedicated clock/ramping vs. emergent time/population code models.

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.

Cognition of Time and Thinking Beyond

A common research protocol in cognitive neuroscience is to train subjects to perform deliberately designed experiments while recording brain activity, with the aim of understanding the brain mechanisms underlying cognition. However, how the results of this protocol of research can be applied in technology is seldom discussed. Here, I review the studies on time processing of the brain as examples of this research protocol, as well as two main application areas of neuroscience (neuroengineering and brain-inspired artificial intelligence). Time processing is a fundamental dimension of cognition, and time is also an indispensable dimension of any real-world signal to be processed in technology. Therefore, one may expect that the studies of time processing in cognition profoundly influence brain-related technology. Surprisingly, I found that the results from cognitive studies on timing processing are hardly helpful in solving practical problems. This awkward situation may be due to the lack of generalizability of the results of cognitive studies, which are under well-controlled laboratory conditions, to real-life situations. This lack of generalizability may be rooted in the fundamental unknowability of the world (including cognition). Overall, this paper questions and criticizes the usefulness and prospect of the abovementioned research protocol of cognitive neuroscience. I then give three suggestions for future research. First, to improve the generalizability of research, it is better to study brain activity under real-life conditions instead of in well-controlled laboratory experiments. Second, to overcome the unknowability of the world, we can engineer an easily accessible surrogate of the object under investigation, so that we can predict the behavior of the object under investigation by experimenting on the surrogate. Third, the paper calls for technology-oriented research, with the aim of technology creation instead of knowledge discovery.

Cortico-spinal modularity in the parieto-frontal system: A new perspective on action control

Classical neurophysiology suggests that the motor cortex (MI) has a unique role in action control. In contrast, this review presents evidence for multiple parieto-frontal spinal command modules that can bypass MI. Five observations support this modular perspective: (i) the statistics of cortical connectivity demonstrate functionally-related clusters of cortical areas, defining functional modules in the premotor, cingulate, and parietal cortices; (ii) different corticospinal pathways originate from the above areas, each with a distinct range of conduction velocities; (iii) the activation time of each module varies depending on task, and different modules can be activated simultaneously; (iv) a modular architecture with direct motor output is faster and less metabolically expensive than an architecture that relies on MI, given the slow connections between MI and other cortical areas; (v) lesions of the areas composing parieto-frontal modules have different effects from lesions of MI. Here we provide examples of six cortico-spinal modules and functions they subserve: module 1) arm reaching, tool use and object construction; module 2) spatial navigation and locomotion; module 3) grasping and observation of hand and mouth actions; module 4) action initiation, motor sequences, time encoding; module 5) conditional motor association and learning, action plan switching and action inhibition; module 6) planning defensive actions. These modules can serve as a library of tools to be recombined when faced with novel tasks, and MI might serve as a recombinatory hub. In conclusion, the availability of locally-stored information and multiple outflow paths supports the physiological plausibility of the proposed modular perspective.

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.

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.

Memory rescue and learning in synaptic impaired neuronal circuits

Neuronal impairment is a characteristic of Alzheimer's disease (AD), but its effect on neural activity dynamics underlying memory deficits is unclear. Here, we studied the effects of synaptic impairment on neural activities associated with memory recall, memory rescue, and learning a new memory, in an integrate-and-fire neuronal network. Our results showed that reducing connectivity decreases the neuronal synchronization of memory neurons and impairs memory recall performance. Although, slow-gamma stimulation rescued memory recall and slow-gamma oscillations, the rescue caused a side effect of activating mixed memories. During the learning of a new memory, reducing connectivity caused impairment in storing the new memory, but did not affect previously stored memories. We also explored the effects of other types of impairments including neuronal loss and excitation-inhibition imbalance and the rescue by general increase of excitability. Our results reveal potential computational mechanisms underlying the memory deficits caused by impairment in AD.

Large-scale prediction of stream water quality using an interpretable deep learning approach

Deep learning methods, which have strong capabilities for mapping highly nonlinear relationships with acceptable calculation speed, have been increasingly applied for water quality prediction in recent studies. However, it is argued that the practicality of deep learning methods is limited due to the lack of physical mechanics to explain the prediction results of water quality changes. A knowledge gap exists in rationalizing the deep learning results for water quality predictions. To address this gap, an interpretable deep learning framework was established to predict the spatiotemporal variations of water quality parameters in a large spatial region. Mereological, land-use, and socioeconomic variables were adopted to predict the daily variations of stream water quality parameters across 138 sub-catchments in a total of over 575,250 km² in southern China. The coefficients of determination of chemical oxygen demand (COD), total phosphorus (TP), and total nitrogen (TN) predictions were over 0.80, suggesting a satisfactory prediction performance. The model performance in terms of prediction accuracy could be improved by involving land-use and socioeconomic predictors in addition to hydrological variables. The SHapley Additive exPlanations method used in this study was demonstrated to be effective for interpreting the prediction results by identifying the significant variables and reasoning their influencing directions on the variation of each water quality parameter. The air temperature, proportion of forest area, grain production, population density, and proportion of urban area in each sub-catchment as well as the accumulated rainfall within the previous 3 days were identified as the most significant variables affecting the variations of dissolved oxygen, COD, ammoniacal nitrogen(NH₃-N), TN, TP, and turbidity in the stream water in the case area, respectively.

Parametric control of flexible timing through low-dimensional neural manifolds

Biological brains possess an unparalleled ability to adapt behavioral responses to changing stimuli and environments. How neural processes enable this capacity is a fundamental open question. Previous works have identified two candidate mechanisms: a low-dimensional organization of neural activity and a modulation by contextual inputs. We hypothesized that combining the two might facilitate generalization and adaptation in complex tasks. We tested this hypothesis in flexible timing tasks where dynamics play a key role. Examining trained recurrent neural networks, we found that confining the dynamics to a low-dimensional subspace allowed tonic inputs to parametrically control the overall input-output transform, enabling generalization to novel inputs and adaptation to changing conditions. Reverse-engineering and theoretical analyses demonstrated that this parametric control relies on a mechanism where tonic inputs modulate the dynamics along non-linear manifolds while preserving their geometry. Comparisons with data from behaving monkeys confirmed the behavioral and neural signatures of this mechanism.

Different eigenvalue distributions encode the same temporal tasks in recurrent neural networks

Different brain areas, such as the cortex and, more specifically, the prefrontal cortex, show great recurrence in their connections, even in early sensory areas. Several approaches and methods based on trained networks have been proposed to model and describe these regions. It is essential to understand the dynamics behind the models because they are used to build different hypotheses about the functioning of brain areas and to explain experimental results. The main contribution here is the description of the dynamics through the classification and interpretation carried out with a set of numerical simulations. This study sheds light on the multiplicity of solutions obtained for the same tasks and shows the link between the spectra of linearized trained networks and the dynamics of the counterparts. The patterns in the distribution of the eigenvalues of the recurrent weight matrix were studied and properly related to the dynamics in each task.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09802-5.

The neural bases for timing of durations

Durations are defined by a beginning and an end, and a major distinction is drawn between durations that start in the present and end in the future ('prospective timing') and durations that start in the past and end either in the past or the present ('retrospective timing'). Different psychological processes are thought to be engaged in each of these cases. The former is thought to engage a clock-like mechanism that accurately tracks the continuing passage of time, whereas the latter is thought to engage a reconstructive process that utilizes both temporal and non-temporal information from the memory of past events. We propose that, from a biological perspective, these two forms of duration 'estimation' are supported by computational processes that are both reliant on population state dynamics but are nevertheless distinct. Prospective timing is effectively carried out in a single step where the ongoing dynamics of population activity directly serve as the computation of duration, whereas retrospective timing is carried out in two steps: the initial generation of population state dynamics through the process of event segmentation and the subsequent computation of duration utilizing the memory of those dynamics.

Oscillatory Resonance and Dynamic Manifolds in Cortical Networks with Time Delay and Multiple External Stimuli

Rhythmic oscillation is crucial for information transmission and neural communication among different brain areas. Stochastic resonance (SR) can evoke different patterns of neural oscillation. However, the characteristics of network resonance and underlying dynamical mechanisms are still unclear. In this paper, a biological model of cortical network is established and its dynamical response to external periodic stimulation is investigated. We explore the oscillatory resonance of excitatory and inhibitory populations in cortical network. It is found that the intrinsic parameters of neural populations determine the extent of resonant activity, indicating that the firing rate exhibits coherent oscillation when the frequency of external stimulation is close to intrinsic frequency of neural population. In addition, the nonlinear dynamics of cortical network in oscillatory resonance can be represented by helical manifolds in low-dimensional state space. The geometry of neural manifolds reveals the periodic dynamics and state transition in oscillatory resonance. Moreover, time delay in chemical synapses can induce multiple resonances, which appear intermittently at integer multiples of the period of input signal. The dynamical response of neural population achieves maximal periodically, due to the transition of network states induced by time delay. Furthermore, mean-field theory is applied to analyze theoretical dynamic of cortical networks with time delay and demonstrate the effective transmission of stimulation information via oscillatory resonance in the brain. Consequently, the obtained results contribute to the improvement of neuromodulation for neurological disease from the viewpoint of the neural basis.

Neural Mechanisms of Working Memory Accuracy Revealed by Recurrent Neural Networks

Understanding the neural mechanisms of working memory has been a long-standing Neuroscience goal. Bump attractor models have been used to simulate persistent activity generated in the prefrontal cortex during working memory tasks and to study the relationship between activity and behavior. How realistic the assumptions of these models are has been a matter of debate. Here, we relied on an alternative strategy to gain insights into the computational principles behind the generation of persistent activity and on whether current models capture some universal computational principles. We trained Recurrent Neural Networks (RNNs) to perform spatial working memory tasks and examined what aspects of RNN activity accounted for working memory performance. Furthermore, we compared activity in fully trained networks and immature networks, achieving only imperfect performance. We thus examined the relationship between the trial-to-trial variability of responses simulated by the network and different aspects of unit activity as a way of identifying the critical parameters of memory maintenance. Properties that spontaneously emerged in the artificial network strongly resembled persistent activity of prefrontal neurons. Most importantly, these included drift of network activity during the course of a trial that was causal to the behavior of the network. As a consequence, delay period firing rate and behavior were positively correlated, in strong analogy to experimental results from the prefrontal cortex. These findings reveal that delay period activity is computationally efficient in maintaining working memory, as evidenced by unbiased optimization of parameters in artificial neural networks, oblivious to the properties of prefrontal neurons.

Distributed coding of duration in rodent prefrontal cortex during time reproduction

As we interact with the external world, we judge magnitudes from sensory information. The estimation of magnitudes has been characterized in primates, yet it is largely unexplored in nonprimate species. Here, we use time interval reproduction to study rodent behavior and its neural correlates in the context of magnitude estimation. We show that gerbils display primate-like magnitude estimation characteristics in time reproduction. Most prominently their behavioral responses show a systematic overestimation of small stimuli and an underestimation of large stimuli, often referred to as regression effect. We investigated the underlying neural mechanisms by recording from medial prefrontal cortex and show that the majority of neurons respond either during the measurement or the reproduction of a time interval. Cells that are active during both phases display distinct response patterns. We categorize the neural responses into multiple types and demonstrate that only populations with mixed responses can encode the bias of the regression effect. These results help unveil the organizing neural principles of time reproduction and perhaps magnitude estimation in general.

How movements shape the perception of time

In order to keep up with a changing environment, mobile organisms must be capable of deciding both where and when to move. This precision necessitates a strong sense of time, as otherwise we would fail in many of our movement goals. Yet, despite this intrinsic link, only recently have researchers begun to understand how these two features interact. Primarily, two effects have been observed: movements can bias time estimates, but they can also make them more precise. Here we review this literature and propose that both effects can be explained by a Bayesian cue combination framework, in which movement itself affords the most precise representation of time, which can influence perception in either feedforward or active sensing modes.

Emergence of prefrontal neuron maturation properties by training recurrent neural networks in cognitive tasks

Working memory and response inhibition are functions that mature relatively late in life, after adolescence, paralleling the maturation of the prefrontal cortex. The link between behavioral and neural maturation is not obvious, however, making it challenging to understand how neural activity underlies the maturation of cognitive function. To gain insights into the nature of observed changes in prefrontal activity between adolescence and adulthood, we investigated the progressive changes in unit activity of recurrent neural networks as they were trained to perform working memory and response inhibition tasks. These included increased delay period activity during working memory tasks and increased activation in antisaccade tasks. These findings reveal universal properties underlying the neuronal computations behind cognitive tasks and explicate the nature of changes that occur as the result of developmental maturation.

•

Properties of RNN networks during training offer insights in prefrontal maturation

•

Fully trained networks exhibit higher levels of activity in working memory tasks

•

Trained networks also exhibit higher activation in antisaccade tasks

•

Partially trained RNNs can generate accurate predictions of immature PFC activity

Stimulus-Driven and Spontaneous Dynamics in Excitatory-Inhibitory Recurrent Neural Networks for Sequence Representation

Recurrent neural networks (RNNs) have been widely used to model sequential neural dynamics ("neural sequences") of cortical circuits in cognitive and motor tasks. Efforts to incorporate biological constraints and Dale's principle will help elucidate the neural representations and mechanisms of underlying circuits. We trained an excitatory-inhibitory RNN to learn neural sequences in a supervised manner and studied the representations and dynamic attractors of the trained network. The trained RNN was robust to trigger the sequence in response to various input signals and interpolated a time-warped input for sequence representation. Interestingly, a learned sequence can repeat periodically when the RNN evolved beyond the duration of a single sequence. The eigenspectrum of the learned recurrent connectivity matrix with growing or damping modes, together with the RNN's nonlinearity, were adequate to generate a limit cycle attractor. We further examined the stability of dynamic attractors while training the RNN to learn two sequences. Together, our results provide a general framework for understanding neural sequence representation in the excitatory-inhibitory RNN.

A geometric framework for understanding dynamic information integration in context-dependent computation

The prefrontal cortex (PFC) plays a prominent role in performing flexible cognitive functions and working memory, yet the underlying computational principle remains poorly understood. Here, we trained a rate-based recurrent neural network (RNN) to explore how the context rules are encoded, maintained across seconds-long mnemonic delay, and subsequently used in a context-dependent decision-making task. The trained networks replicated key experimentally observed features in the PFC of rodent and monkey experiments, such as mixed selectivity, neuronal sequential activity, and rotation dynamics. To uncover the high-dimensional neural dynamical system, we further proposed a geometric framework to quantify and visualize population coding and sensory integration in a temporally defined manner. We employed dynamic epoch-wise principal component analysis (PCA) to define multiple task-specific subspaces and task-related axes, and computed the angles between task-related axes and these subspaces. In low-dimensional neural representations, the trained RNN first encoded the context cues in a cue-specific subspace, and then maintained the cue information with a stable low-activity state persisting during the delay epoch, and further formed line attractors for sensor integration through low-dimensional neural trajectories to guide decision-making. We demonstrated via intensive computer simulations that the geometric manifolds encoding the context information were robust to varying degrees of weight perturbation in both space and time. Overall, our analysis framework provides clear geometric interpretations and quantification of information coding, maintenance, and integration, yielding new insight into the computational mechanisms of context-dependent computation.

A continuum of invariant sensory and behavioral-context perceptual coding in secondary somatosensory cortex

A crucial role of cortical networks is the conversion of sensory inputs into perception. In the cortical somatosensory network, neurons of the primary somatosensory cortex (S1) show invariant sensory responses, while frontal lobe neuronal activity correlates with the animal's perceptual behavior. Here, we report that in the secondary somatosensory cortex (S2), neurons with invariant sensory responses coexist with neurons whose responses correlate with perceptual behavior. Importantly, the vast majority of the neurons fall along a continuum of combined sensory and categorical dynamics. Furthermore, during a non-demanding control task, the sensory responses remain unaltered while the sensory information exhibits an increase. However, perceptual responses and the associated categorical information decrease, implicating a task context-dependent processing mechanism. Conclusively, S2 neurons exhibit intriguing dynamics that are intermediate between those of S1 and frontal lobe. Our results contribute relevant evidence about the role that S2 plays in the conversion of touch into perception.