A nonlinear updating algorithm captures suboptimal inference in the presence of signal-dependent noise

Context-dependence of deterministic and nondeterministic contributions to closed-loop steering control

In natural circumstances, sensory systems operate in a closed loop with motor output, whereby actions shape subsequent sensory experiences. A prime example of this is the sensorimotor processing required to align one's direction of travel, or heading, with one's goal, a behavior we refer to as steering. In steering, motor outputs work to eliminate errors between the direction of heading and the goal, modifying subsequent errors in the process. The closed-loop nature of the behavior makes it challenging to determine how deterministic and nondeterministic processes contribute to behavior. We overcome this by applying a nonparametric, linear kernel-based analysis to behavioral data of monkeys steering through a virtual environment in two experimental contexts. In a given context, the results were consistent with previous work that described the transformation as a second-order linear system. Classically, the parameters of such second-order models are associated with physical properties of the limb such as viscosity and stiffness that are commonly assumed to be approximately constant. By contrast, we found that the fit kernels differed strongly across tasks in these and other parameters, suggesting context-dependent changes in neural and biomechanical processes. We additionally fit residuals to a simple noise model and found that the form of the noise was highly conserved across both contexts and animals. Strikingly, the fitted noise also closely matched that found previously in a human steering task. Altogether, this work presents a kernel-based analysis that characterizes the context-dependence of deterministic and non-deterministic components of a closed-loop sensorimotor task.

Neural structure of a sensory decoder for motor control

The transformation of sensory input to motor output is often conceived as a decoder operating on neural representations. We seek a mechanistic understanding of sensory decoding by mimicking neural circuitry in the decoder's design. The results of a simple experiment shape our approach. Changing the size of a target for smooth pursuit eye movements changes the relationship between the variance and mean of the evoked behavior in a way that contradicts the regime of "signal-dependent noise" and defies traditional decoding approaches. A theoretical analysis leads us to propose a circuit for pursuit that includes multiple parallel pathways and multiple sources of variation. Behavioral and neural responses with biomimetic statistics emerge from a biologically-motivated circuit model with noise in the pathway that is dedicated to flexibly adjusting the strength of visual-motor transmission. Our results demonstrate the power of re-imagining decoding as processing through the parallel pathways of neural systems.

Validating model-based Bayesian integration using prior-cost metamers

There are two competing views on how humans make decisions under uncertainty. Bayesian decision theory posits that humans optimize their behavior by establishing and integrating internal models of past sensory experiences (priors) and decision outcomes (cost functions). An alternative hypothesis posits that decisions are optimized through trial and error without explicit internal models for priors and cost functions. To distinguish between these possibilities, we introduce a paradigm that probes the sensitivity of humans to transitions between prior-cost pairs that demand the same optimal policy (metamers) but distinct internal models. We demonstrate the utility of our approach in two experiments that were classically explained by Bayesian theory. Our approach validates the Bayesian learning strategy in an interval timing task but not in a visuomotor rotation task. More generally, our work provides a domain-general approach for testing the circumstances under which humans explicitly implement model-based Bayesian computations.

Expectancy-based rhythmic entrainment as continuous Bayesian inference

When presented with complex rhythmic auditory stimuli, humans are able to track underlying temporal structure (e.g., a "beat"), both covertly and with their movements. This capacity goes far beyond that of a simple entrained oscillator, drawing on contextual and enculturated timing expectations and adjusting rapidly to perturbations in event timing, phase, and tempo. Previous modeling work has described how entrainment to rhythms may be shaped by event timing expectations, but sheds little light on any underlying computational principles that could unify the phenomenon of expectation-based entrainment with other brain processes. Inspired by the predictive processing framework, we propose that the problem of rhythm tracking is naturally characterized as a problem of continuously estimating an underlying phase and tempo based on precise event times and their correspondence to timing expectations. We present two inference problems formalizing this insight: PIPPET (Phase Inference from Point Process Event Timing) and PATIPPET (Phase and Tempo Inference). Variational solutions to these inference problems resemble previous "Dynamic Attending" models of perceptual entrainment, but introduce new terms representing the dynamics of uncertainty and the influence of expectations in the absence of sensory events. These terms allow us to model multiple characteristics of covert and motor human rhythm tracking not addressed by other models, including sensitivity of error corrections to inter-event interval and perceived tempo changes induced by event omissions. We show that positing these novel influences in human entrainment yields a range of testable behavioral predictions. Guided by recent neurophysiological observations, we attempt to align the phase inference framework with a specific brain implementation. We also explore the potential of this normative framework to guide the interpretation of experimental data and serve as building blocks for even richer predictive processing and active inference models of timing.

Discrimination of Regular and Irregular Rhythms Explained by a Time Difference Accumulation Model

Perceiving the temporal regularity in a sequence of repetitive sensory events facilitates the preparation and execution of relevant behaviors with tight temporal constraints. How we estimate temporal regularity from repeating patterns of sensory stimuli is not completely understood. We developed a decision-making task in which participants had to decide whether a train of visual, auditory, or tactile pulses, had a regular or an irregular temporal pattern. We tested the hypothesis that subjects categorize stimuli as irregular by accumulating the time differences between the predicted and observed times of sensory pulses defining a temporal rhythm. Results suggest that instead of waiting for a single large temporal deviation, participants accumulate timing-error signals and judge a pattern as irregular when the amount of evidence reaches a decision threshold. Model fits of bounded integration showed that this accumulation occurs with negligible leak of evidence. Consistent with previous findings, we show that participants perform better when evaluating the regularity of auditory pulses, as compared with visual or tactile stimuli. Our results suggest that temporal regularity is estimated by comparing expected and measured pulse onset times, and that each prediction error is accumulated towards a threshold to generate a behavioral choice.

A neural circuit model for human sensorimotor timing

Humans and animals can effortlessly coordinate their movements with external stimuli. This capacity indicates that sensory inputs can rapidly and flexibly reconfigure the ongoing dynamics in the neural circuits that control movements. Here, we develop a circuit-level model that coordinates movement times with expected and unexpected temporal events. The model consists of two interacting modules, a motor planning module that controls movement times and a sensory anticipation module that anticipates external events. Both modules harbor a reservoir of latent dynamics, and their interaction forms a control system whose output is adjusted adaptively to minimize timing errors. We show that the model’s output matches human behavior in a range of tasks including time interval production, periodic production, synchronization/continuation, and Bayesian time interval reproduction. These results demonstrate how recurrent interactions in a simple and modular neural circuit could create the dynamics needed to control timing behavior.

We can flexibly coordinate our movements with external stimuli, but no circuit-level model exists to explain this ability. Inspired by fundamental concepts in control theory, the authors construct a modular neural circuit that captures human behavior in a wide range of temporal coordination tasks.

Internal models of sensorimotor integration regulate cortical dynamics

Sensorimotor control during overt movements is characterized in terms of three building blocks: a controller, a simulator, and a state estimator. We asked whether the same framework could explain the control of internal states in the absence of movements. Recently, it was shown that the brain controls the timing of future movements by adjusting an internal speed command. We trained monkeys in a novel task in which the speed command had to be controlled dynamically based on the timing of a sequence of flashes. Recordings from the frontal cortex provided evidence that the brain updates the internal speed command after each flash based on the error between the timing of the flash and the anticipated timing of the flash derived from a simulated motor plan. These findings suggest that cognitive control of internal states may be understood in terms of the same computational principles as motor control.