A precise and adaptive neural mechanism for predictive temporal processing in the frontal cortex

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.

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.

Spontaneously emerging internal models of visual sequences combine abstract and event-specific information in the prefrontal cortex

When exposed to sensory sequences, do macaque monkeys spontaneously form abstract internal models that generalize to novel experiences? Here, we show that neuronal populations in macaque ventrolateral prefrontal cortex jointly encode visual sequences by separate codes for the specific pictures presented and for their abstract sequential structure. We recorded prefrontal neurons while macaque monkeys passively viewed visual sequences and sequence mismatches in the local-global paradigm. Even without any overt task or response requirements, prefrontal populations spontaneously form representations of sequence structure, serial order, and image identity within distinct but superimposed neuronal subspaces. Representations of sequence structure rapidly update following single exposure to a mismatch sequence, while distinct populations represent mismatches for sequences of different complexity. Finally, those representations generalize across sequences following the same repetition structure but comprising different images. These results suggest that prefrontal populations spontaneously encode rich internal models of visual sequences reflecting both content-specific and abstract information.

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.

Duration of Untreated Prodromal Psychosis and Cognitive Impairments

Importance

The possible association between the duration of untreated prodromal symptoms (DUPrS) and cognitive functioning in individuals at clinical high risk (CHR) for psychosis remains underexplored.

Objective

To investigate the intricate interplay between DUPrS, cognitive performance, and conversion outcomes, shedding light on the potential role of DUPrS in shaping cognitive trajectories and psychosis risk in individuals at CHR for psychosis.

Design, Setting, and Participants

This cohort study of individuals at CHR for psychosis was conducted at the Shanghai Mental Health Center in China from January 10, 2016, to December 29, 2021. Participants at CHR for psychosis typically exhibit attenuated positive symptoms; they were identified according to the Structured Interview for Prodromal Syndromes, underwent baseline neuropsychological assessments, and were evaluated at a 3-year clinical follow-up. Data were analyzed from August 25, 2021, to May 10, 2023.

Exposure

Duration of untreated prodromal symptoms and cognitive impairments in individuals at CHR for psychosis.

Main Outcomes and Measures

The primary study outcome was conversion to psychosis. The DUPrS was categorized into 3 groups based on percentiles (33rd percentile for short [≤3 months], 34th-66th percentile for median [4-9 months], and 67th-100th percentile for long [≥10 months]). The DUPrS, cognitive variables, and the risk of conversion to psychosis were explored through quantile regression and Cox proportional hazards regression analyses.

Results

This study included 506 individuals (median age, 19 [IQR, 16-21] years; 53.6% [n = 271] women). The mean (SD) DUPrS was 7.8 (6.857) months, and the median (IQR) was 6 (3-11) months. The short and median DUPrS groups displayed poorer cognitive performance than the long DUPrS group in the Brief Visuospatial Memory Test-Revised (BVMT-R) (Kruskal-Wallis χ2 = 8.801; P = .01) and Category Fluency Test (CFT) (Kruskal-Wallis χ2 = 6.670; P = .04). Quantile regression analysis revealed positive correlations between DUPrS rank and BVMT-R scores (<90th percentile of DUPrS rank) and CFT scores (within the 20th-70th percentile range of DUPrS rank). Among the 506 participants, 20.8% (95% CI, 17.4%-24.5%) converted to psychosis within 3 years. Cox proportional hazards regression analysis identified lower educational attainment (hazard ratio [HR], 0.912; 95% CI, 0.834-0.998), pronounced negative symptoms (HR, 1.044; 95% CI, 1.005-1.084), and impaired performance on the Neuropsychological Assessment Battery: Mazes (HR, 0.961; 95% CI, 0.924-0.999) and BVMT-R (HR, 0.949; 95% CI, 0.916-0.984) tests as factors associated with conversion.

Conclusions and Relevance

The finding of this cohort study suggest the intricate interplay between DUPrS, cognitive performance, and conversion risk in individuals at CHR for psychosis. The findings emphasize the importance of considering both DUPrS and cognitive functioning in assessing the trajectory of these individuals.

Temporal Information Processing in the Cerebellum and Basal Ganglia

Temporal information processing in the range of a few hundred milliseconds to seconds involves the cerebellum and basal ganglia. In this chapter, we present recent studies on nonhuman primates. In the studies presented in the first half of the chapter, monkeys were trained to make eye movements when a certain amount of time had elapsed since the onset of the visual cue (time production task). The animals had to report time lapses ranging from several hundred milliseconds to a few seconds based on the color of the fixation point. In this task, the saccade latency varied with the time length to be measured and showed stochastic variability from one trial to the other. Trial-to-trial variability under the same conditions correlated well with pupil diameter and the preparatory activity in the deep cerebellar nuclei and the motor thalamus. Inactivation of these brain regions delayed saccades when asked to report subsecond intervals. These results suggest that the internal state, which changes with each trial, may cause fluctuations in cerebellar neuronal activity, thereby producing variations in self-timing. When measuring different time intervals, the preparatory activity in the cerebellum always begins approximately 500 ms before movements, regardless of the length of the time interval being measured. However, the preparatory activity in the striatum persists throughout the mandatory delay period, which can be up to 2 s, with different rate of increasing activity. Furthermore, in the striatum, the visual response and low-frequency oscillatory activity immediately before time measurement were altered by the length of the intended time interval. These results indicate that the state of the network, including the striatum, changes with the intended timing, which lead to different time courses of preparatory activity. Thus, the basal ganglia appear to be responsible for measuring time in the range of several hundred milliseconds to seconds, whereas the cerebellum is responsible for regulating self-timing variability in the subsecond range. The second half of this chapter presents studies related to periodic timing. During eye movements synchronized with alternating targets at regular intervals, different neurons in the cerebellar nuclei exhibit activity related to movement timing, predicted stimulus timing, and the temporal error of synchronization. Among these, the activity associated with target appearance is particularly enhanced during synchronized movements and may represent an internal model of the temporal structure of stimulus sequence. We also considered neural mechanism underlying the perception of periodic timing in the absence of movement. During perception of rhythm, we predict the timing of the next stimulus and focus our attention on that moment. In the missing oddball paradigm, the subjects had to detect the omission of a regularly repeated stimulus. When employed in humans, the results show that the fastest temporal limit for predicting each stimulus timing is about 0.25 s (4 Hz). In monkeys performing this task, neurons in the cerebellar nuclei, striatum, and motor thalamus exhibit periodic activity, with different time courses depending on the brain region. Since electrical stimulation or inactivation of recording sites changes the reaction time to stimulus omission, these neuronal activities must be involved in periodic temporal processing. Future research is needed to elucidate the mechanism of rhythm perception, which appears to be processed by both cortico-cerebellar and cortico-basal ganglia pathways.

Effective connectivity in a duration selective cortico-cerebellar network

How the human brain represents millisecond unit of time is far from clear. A recent neuroimaging study revealed the existence in the human premotor cortex of a topographic representation of time i.e., neuronal units selectively responsive to specific durations and topographically organized on the cortical surface. By using high resolution functional Magnetic Resonance Images here, we go beyond this previous work, showing duration preferences across a wide network of cortical and subcortical brain areas: from cerebellum to primary visual, parietal, premotor and prefrontal cortices. Most importantly, we identify the effective connectivity structure between these different brain areas and their duration selective neural units. The results highlight the role of the cerebellum as the network hub and that of medial premotor cortex as the final stage of duration recognition. Interestingly, when a specific duration is presented, only the communication strength between the units selective to that specific duration and to the neighboring durations is affected. These findings link for the first time, duration preferences within single brain region with connectivity dynamics between regions, suggesting a communication mode that is partially duration specific.

Prediction during language comprehension: what is next?

Prediction is often regarded as an integral aspect of incremental language comprehension, but little is known about the cognitive architectures and mechanisms that support it. We review studies showing that listeners and readers use all manner of contextual information to generate multifaceted predictions about upcoming input. The nature of these predictions may vary between individuals owing to differences in language experience, among other factors. We then turn to unresolved questions which may guide the search for the underlying mechanisms. (i) Is prediction essential to language processing or an optional strategy? (ii) Are predictions generated from within the language system or by domain-general processes? (iii) What is the relationship between prediction and memory? (iv) Does prediction in comprehension require simulation via the production system? We discuss promising directions for making progress in answering these questions and for developing a mechanistic understanding of prediction in language.

Cerebellar contributions across behavioural timescales: a review from the perspective of cerebro-cerebellar interactions

Performing successful adaptive behaviour relies on our ability to process a wide range of temporal intervals with certain precision. Studies on the role of the cerebellum in temporal information processing have adopted the dogma that the cerebellum is involved in sub-second processing. However, emerging evidence shows that the cerebellum might be involved in suprasecond temporal processing as well. Here we review the reciprocal loops between cerebellum and cerebral cortex and provide a theoretical account of cerebro-cerebellar interactions with a focus on how cerebellar output can modulate cerebral processing during learning of complex sequences. Finally, we propose that while the ability of the cerebellum to support millisecond timescales might be intrinsic to cerebellar circuitry, the ability to support supra-second timescales might result from cerebellar interactions with other brain regions, such as the prefrontal cortex.

Belief embodiment through eye movements facilitates memory-guided navigation

Neural network models optimized for task performance often excel at predicting neural activity but do not explain other properties such as the distributed representation across functionally distinct areas. Distributed representations may arise from animals' strategies for resource utilization, however, fixation-based paradigms deprive animals of a vital resource: eye movements. During a naturalistic task in which humans use a joystick to steer and catch flashing fireflies in a virtual environment lacking position cues, subjects physically track the latent task variable with their gaze. We show this strategy to be true also during an inertial version of the task in the absence of optic flow and demonstrate that these task-relevant eye movements reflect an embodiment of the subjects' dynamically evolving internal beliefs about the goal. A neural network model with tuned recurrent connectivity between oculomotor and evidence-integrating frontoparietal circuits accounted for this behavioral strategy. Critically, this model better explained neural data from monkeys' posterior parietal cortex compared to task-optimized models unconstrained by such an oculomotor-based cognitive strategy. These results highlight the importance of unconstrained movement in working memory computations and establish a functional significance of oculomotor signals for evidence-integration and navigation computations via embodied cognition.

Long- and short-term history effects in a spiking network model of statistical learning

The statistical structure of the environment is often important when making decisions. There are multiple theories of how the brain represents statistical structure. One such theory states that neural activity spontaneously samples from probability distributions. In other words, the network spends more time in states which encode high-probability stimuli. Starting from the neural assembly, increasingly thought of to be the building block for computation in the brain, we focus on how arbitrary prior knowledge about the external world can both be learned and spontaneously recollected. We present a model based upon learning the inverse of the cumulative distribution function. Learning is entirely unsupervised using biophysical neurons and biologically plausible learning rules. We show how this prior knowledge can then be accessed to compute expectations and signal surprise in downstream networks. Sensory history effects emerge from the model as a consequence of ongoing learning.

Human acute microelectrode array recordings with broad cortical access, single-unit resolution, and parallel behavioral monitoring

There are vast gaps in our understanding of the organization and operation of the human nervous system at the level of individual neurons and their networks. Here, we report reliable and robust acute multichannel recordings using planar microelectrode arrays (MEAs) implanted intracortically in awake brain surgery with open craniotomies that grant access to large parts of the cortical hemisphere. We obtained high-quality extracellular neuronal activity at the microcircuit, local field potential level and at the cellular, single-unit level. Recording from the parietal association cortex, a region rarely explored in human single-unit studies, we demonstrate applications on these complementary spatial scales and describe traveling waves of oscillatory activity as well as single-neuron and neuronal population responses during numerical cognition, including operations with uniquely human number symbols. Intraoperative MEA recordings are practicable and can be scaled up to explore cellular and microcircuit mechanisms of a wide range of human brain functions.

Intrinsic timescales in the visual cortex change with selective attention and reflect spatial connectivity

Intrinsic timescales characterize dynamics of endogenous fluctuations in neural activity. Variation of intrinsic timescales across the neocortex reflects functional specialization of cortical areas, but less is known about how intrinsic timescales change during cognitive tasks. We measured intrinsic timescales of local spiking activity within columns of area V4 in male monkeys performing spatial attention tasks. The ongoing spiking activity unfolded across at least two distinct timescales, fast and slow. The slow timescale increased when monkeys attended to the receptive fields location and correlated with reaction times. By evaluating predictions of several network models, we found that spatiotemporal correlations in V4 activity were best explained by the model in which multiple timescales arise from recurrent interactions shaped by spatially arranged connectivity, and attentional modulation of timescales results from an increase in the efficacy of recurrent interactions. Our results suggest that multiple timescales may arise from the spatial connectivity in the visual cortex and flexibly change with the cognitive state due to dynamic effective interactions between neurons.

Comparing representations and computations in single neurons versus neural networks

Single-neuron-level explanations have been the gold standard in neuroscience for decades. Recently, however, neural-network-level explanations have become increasingly popular. This increase in popularity is driven by the fact that the analysis of neural networks can solve problems that cannot be addressed by analyzing neurons independently. In this opinion article, I argue that while both frameworks employ the same general logic to link physical and mental phenomena, in many cases the neural network framework provides better explanatory objects to understand representations and computations related to mental phenomena. I discuss what constitutes a mechanistic explanation in neural systems, provide examples, and conclude by highlighting a number of the challenges and considerations associated with the use of analyses of neural networks to study brain function.

Influence of Recent Trial History on Interval Timing

Interval timing is involved in a variety of cognitive behaviors such as associative learning and decision-making. While it has been shown that time estimation is adaptive to the temporal context, it remains unclear how interval timing behavior is influenced by recent trial history. Here we found that, in mice trained to perform a licking-based interval timing task, a decrease of inter-reinforcement interval in the previous trial rapidly shifted the time of anticipatory licking earlier. Optogenetic inactivation of the anterior lateral motor cortex (ALM), but not the medial prefrontal cortex, for a short time before reward delivery caused a decrease in the peak time of anticipatory licking in the next trial. Electrophysiological recordings from the ALM showed that the response profiles preceded by short and long inter-reinforcement intervals exhibited task-engagement-dependent temporal scaling. Thus, interval timing is adaptive to recent experience of the temporal interval, and ALM activity during time estimation reflects recent experience of interval.

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.

The Grossberg Code: Universal Neural Network Signatures of Perceptual Experience

Two universal functional principles of Grossberg’s Adaptive Resonance Theory decipher the brain code of all biological learning and adaptive intelligence. Low-level representations of multisensory stimuli in their immediate environmental context are formed on the basis of bottom-up activation and under the control of top-down matching rules that integrate high-level, long-term traces of contextual configuration. These universal coding principles lead to the establishment of lasting brain signatures of perceptual experience in all living species, from aplysiae to primates. They are re-visited in this concept paper on the basis of examples drawn from the original code and from some of the most recent related empirical findings on contextual modulation in the brain, highlighting the potential of Grossberg’s pioneering insights and groundbreaking theoretical work for intelligent solutions in the domain of developmental and cognitive robotics.

A virtual reality time reproduction task for rodents

Estimates of the duration of time intervals and other magnitudes exhibit characteristic biases that likely result from error minimization strategies. To investigate such phenomena, magnitude reproduction tasks are used with humans and other primates. However, such behavioral tasks do not exist for rodents, one of the most important animal orders for neuroscience. We, therefore, developed a time reproduction task that can be used with rodents. It involves an animal reproducing the duration of a timed visual stimulus by walking along a corridor. The task was implemented in virtual reality, which allowed us to ensure that the animals were actually estimating time. The hallway did not contain prominent spatial cues and movement could be de-correlated from optic flow, such that the animals could not learn a mapping between stimulus duration and covered distance. We tested the reproduction of durations of several seconds in three different stimulus ranges. The gerbils reproduced the durations with a precision similar to experiments on humans. Their time reproductions also exhibited the characteristic biases of magnitude estimation experiments. These results demonstrate that our behavioral paradigm provides a means to study time reproduction in rodents.

Cortical feedback loops bind distributed representations of working memory

Working memory—the brain’s ability to internalize information and use it flexibly to guide behaviour—is an essential component of cognition. Although activity related to working memory has been observed in several brain regions^1–3, how neural populations actually represent working memory^4–7 and the mechanisms by which this activity is maintained^8–12 remain unclear^13–15. Here we describe the neural implementation of visual working memory in mice alternating between a delayed non-match-to-sample task and a simple discrimination task that does not require working memory but has identical stimulus, movement and reward statistics. Transient optogenetic inactivations revealed that distributed areas of the neocortex were required selectively for the maintenance of working memory. Population activity in visual area AM and premotor area M2 during the delay period was dominated by orderly low-dimensional dynamics^16,17 that were, however, independent of working memory. Instead, working memory representations were embedded in high-dimensional population activity, present in both cortical areas, persisted throughout the inter-stimulus delay period, and predicted behavioural responses during the working memory task. To test whether the distributed nature of working memory was dependent on reciprocal interactions between cortical regions^18–20, we silenced one cortical area (AM or M2) while recording the feedback it received from the other. Transient inactivation of either area led to the selective disruption of inter-areal communication of working memory. Therefore, reciprocally interconnected cortical areas maintain bound high-dimensional representations of working memory.

Experiments in mice alternating between a visual working memory task and a task that is independent of working memory provide insight into the neural representation of working memory and the distributed nature of its maintenance.

Implicit Versus Explicit Timing-Separate or Shared Mechanisms?

Time implicitly shapes cognition, but time is also explicitly represented, for instance, in the form of durations. Parsimoniously, the brain could use the same mechanisms for implicit and explicit timing. Yet, the evidence has been equivocal, revealing both joint versus separate signatures of timing. Here, we directly compared implicit and explicit timing using magnetoencephalography, whose temporal resolution allows investigating the different stages of the timing processes. Implicit temporal predictability was induced in an auditory paradigm by a manipulation of the foreperiod. Participants received two consecutive task instructions: discriminate pitch (indirect measure of implicit timing) or duration (direct measure of explicit timing). The results show that the human brain efficiently extracts implicit temporal statistics of sensory environments, to enhance the behavioral and neural responses to auditory stimuli, but that those temporal predictions did not improve explicit timing. In both tasks, attentional orienting in time during predictive foreperiods was indexed by an increase in alpha power over visual and parietal areas. Furthermore, pretarget induced beta power in sensorimotor and parietal areas increased during implicit compared to explicit timing, in line with the suggested role for beta oscillations in temporal prediction. Interestingly, no distinct neural dynamics emerged when participants explicitly paid attention to time, compared to implicit timing. Our work thus indicates that implicit timing shapes the behavioral and sensory response in an automatic way and is reflected in oscillatory neural dynamics, whereas the translation of implicit temporal statistics to explicit durations remains somewhat inconclusive, possibly because of the more abstract nature of this task.

Prediction-error neurons in circuits with multiple neuron types: Formation, refinement, and functional implications

An influential idea in neuroscience is that neural circuits do not only passively process sensory information but rather actively compare them with predictions thereof. A core element of this comparison is prediction-error neurons, the activity of which only changes upon mismatches between actual and predicted sensory stimuli. While it has been shown that these prediction-error neurons come in different variants, it is largely unresolved how they are simultaneously formed and shaped by highly interconnected neural networks. By using a computational model, we study the circuit-level mechanisms that give rise to different variants of prediction-error neurons. Our results shed light on the formation, refinement, and robustness of prediction-error circuits, an important step toward a better understanding of predictive processing.

Predictable sensory stimuli do not evoke significant responses in a subset of cortical excitatory neurons. Some of those neurons, however, change their activity upon mismatches between actual and predicted stimuli. Different variants of these prediction-error neurons exist, and they differ in their responses to unexpected sensory stimuli. However, it is unclear how these variants can develop and coexist in the same recurrent network and how they are simultaneously shaped by the astonishing diversity of inhibitory interneurons. Here, we study these questions in a computational network model with three types of inhibitory interneurons. We find that balancing excitation and inhibition in multiple pathways gives rise to heterogeneous prediction-error circuits. Dependent on the network’s initial connectivity and distribution of actual and predicted sensory inputs, these circuits can form different variants of prediction-error neurons that are robust to network perturbations and generalize to stimuli not seen during learning. These variants can be learned simultaneously via homeostatic inhibitory plasticity with low baseline firing rates. Finally, we demonstrate that prediction-error neurons can support biased perception, we illustrate a number of functional implications, and we discuss testable predictions.

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.

Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system's dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain.