Large increases in visuomotor feedback gains occur during initial adaptation to novel dynamics, which we propose are due to increased internal model uncertainty. That is, large errors indicate increased uncertainty in our prediction of the environment, increasing feedback gains and co-contraction as a coping mechanism. Our previous work showed distinct patterns of visuomotor feedback gains during abrupt or gradual adaptation to a force field, suggesting two complementary processes: reactive feedback gains increasing with internal model uncertainty and the gradual learning of predictive feedback gains tuned to the environment. Here we further investigate what drives these changes visuomotor feedback gains in learning, by separating the effects of internal model uncertainty from visual error signal through removal of visual error information. Removing visual error information suppresses the visuomotor feedback gains in all conditions, but the pattern of modulation throughout adaptation is unaffected. Moreover, we find increased muscle co-contraction in both abrupt and gradual adaptation protocols, demonstrating that visuomotor feedback responses are independent from the level of co-contraction. Our result suggests that visual feedback benefits motor adaptation tasks through higher visuomotor feedback gains, but when it is not available participants adapt at a similar rate through increased co-contraction. We have demonstrated a direct connection between learning and predictive visuomotor feedback gains, independent from visual error signals. This further supports our hypothesis that internal model uncertainty drives initial increases in feedback gains.

Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing not just how features (e.g., colors) are distributed but also where they are and which other features they are combined with. Using a Bayesian computational model, we recovered probabilistic representations used by human observers to search for odd stimuli among distractors. Importantly, we found that the brain integrates information between feature dimensions and spatial locations, leading to more precise representations compared to when information integration is not possible. We also uncovered representational asymmetries and biases, showing their spatial organization and explain how this structure argues against “summary statistics” accounts of visual representations. Our results confirm that probabilistically encoded visual features are bound with other features and to particular locations, providing a powerful demonstration of how probabilistic representations can be a foundation for higher-level vision.

Biological neural networks are often modeled as systems of coupled, nonlinear, ordinary or partial differential equations. The number of differential equations used to model a network increases with the size of the network and the level of detail used to model individual neurons and synapses. As one scales up the size of the simulation, it becomes essential to utilize powerful computing platforms. While many tools exist that solve these equations numerically, they are often platform-specific. Further, there is a high barrier of entry to developing flexible platform-independent general-purpose code that supports hardware acceleration on modern computing architectures such as GPUs/TPUs and Distributed Platforms. TensorFlow is a Python-based open-source package designed for machine learning algorithms. However, it is also a scalable environment for a variety of computations, including solving differential equations using iterative algorithms such as Runge-Kutta methods. In this article and the accompanying tutorials, we present a simple exposition of numerical methods to solve ordinary differential equations using Python and TensorFlow. The tutorials consist of a series of Python notebooks that, over the course of five sessions, will lead novice programmers from writing programs to integrate simple one-dimensional ordinary differential equations using Python to solving a large system (1000’s of differential equations) of coupled conductance-based neurons using a highly parallelized and scalable framework. Embedded with the tutorial is a physiologically realistic implementation of a network in the insect olfactory system. This system, consisting of multiple neuron and synapse types, can serve as a template to simulate other networks.

Representational similarity analysis (RSA) tests models of brain computation by investigating how neural activity patterns reflect experimental conditions. Instead of predicting activity patterns directly, the models predict the geometry of the representation, as defined by the representational dissimilarity matrix (RDM), which captures how similar or dissimilar different activity patterns associated by different experimental conditions are. RSA therefore first quantifies the representational geometry by calculating a dissimilarity measure for each pair of conditions, and then compares the estimated representational dissimilarities to those predicted by each model. Here we address two central challenges of RSA: First, dissimilarity measures such as the Euclidean, Mahalanobis, and correlation distance, are biased by measurement noise, which can lead to incorrect inferences. Unbiased dissimilarity estimates can be obtained by crossvalidation, at the price of increased variance. Second, the pairwise dissimilarity estimates are not statistically independent, and ignoring this dependency makes model comparison statistically suboptimal. We present an analytical expression for the mean and (co)variance of both biased and unbiased estimators of the squared Euclidean and Mahalanobis distance, allowing us to quantify the bias-variance trade-off. We also use the analytical expression of the covariance of the dissimilarity estimates to whiten the RDM estimation errors. This results in a new criterion for RDM similarity, the whitened unbiased RDM cosine similarity (WUC), which allows for near-optimal model selection combined with robustness to correlated measurement noise.