Time scales of representation in the human brain: weighing past information to predict future events

Abstract

The estimates that humans make of statistical dependencies in the environment and therefore their representation of uncertainty crucially depend on the integration of data over time. As such, the extent to which past events are used to represent uncertainty has been postulated to vary over the cortex. For example, primary visual cortex responds to rapid perturbations in the environment, while frontal cortices involved in executive control encode the longer term contexts within which these perturbations occur. Here we tested whether primary and executive regions can be distinguished by the number of past observations they represent. This was based on a decay-dependent model that weights past observations from a Markov process and Bayesian Model Selection to test the prediction that neuronal responses are characterized by different decay half-lives depending on location in the brain. We show distributions of brain responses for short and long term decay functions in primary and secondary visual and frontal cortices, respectively. We found that visual and parietal responses are released from the burden of the past, enabling an agile response to fluctuations in events as they unfold. In contrast, frontal regions are more concerned with average trends over longer time scales within which local variations are embedded. Specifically, we provide evidence for a temporal gradient for representing context within the prefrontal cortex and possibly beyond to include primary sensory and association areas.

Keywords: Bayesian model selection; Bayesian spatial models; functional MRI; information theory; surprise; uncertainty.

Figure 1

Information theoretic indices. A sample from a Bernoulli process, e.g., a sequence of coin tosses, over 40 events (top panel), schematic showing differences in the estimated probability of Heads, given past samples (middle panel) and a typical IT measure, i.e., “surprise,” used in a computational model to quantify subject responses (lower panel). Short (STS) or long time scale (LTS), i.e., integration over few or many past events, are shown by the blue and red traces, respectively. The differences between the two processes are best appreciated by considering the 28th event (indicated by the vertical dotted line). The estimated probability of Heads is low for the STS as it is the first Head in five events. By contrast, many samples have occurred over a longer period, which is reflected in the estimate using the LTS. STS is therefore sensitive to local changes (over events) in the process, whereas the LTS averages these out. This is seen again when considering a function of the estimated probability of Heads, e.g., the negative log of this estimate, i.e., the surprise. For the STS the probability of Heads is low and therefore the surprise is high compared to the LTS that estimates the coin to be approximately fair.

Figure 2

Simulations. (A) A sample of simulated RT data from a single subject over one block is shown, along with the model fit (for the most probable half-life, see next figure). (B) The object of estimation is to quantify evidence for a range of half-life values. The model evidence, given RT data, shows an optimum for τ = 4, which concurs with the true value, i.e., that used to generate these data. (C) The most probable decay function over past events is shown, whose value is characteristically halved with every four events into the past. (D) Simulation of spatial data. A square region is partitioned into three areas (labels), corresponding to three different generative models. Data are generated at each pixel depending on the sampled input, u (see Figure 3A), and label assigned to it. The objective is to recover the true pattern of labels, given only these data, i.e., without direct knowledge of the true labels. The true pattern of labels is along the top row, while the estimated probability of belonging to a label is shown below, which is thresholded to give a binary map along the lower row.

Figure 3

Reaction time (RT), functional fMRI data, and model evidence. (A) Generative model of the process leading to a measured response, e.g., RT or fMRI data. Each node defines a random variable and arrows connecting nodes signify dependence. A sample from a random process, u, is used to construct IT indices, given a known half-life, and included in a design matrix used to generate data from a GLM. (B) RT data from a single subject over one experimental block along with model fit (for the optimal half-life). (C) Model evidence for the decay half-life for RT data. The greatest support, given the data, was found for τ = 4. (D) Exceedance probability maps (EPM) of fMRI data reveal regions where the greatest evidence for each of the two IT models (model 2: τ = 1; model 3: τ = 4) was observed (short time scale, STS model along the top). In line with theoretical accounts, evidence for short time scales was predominantly in primary and secondary visual cortex (cross hairs centrered on coordinate [0, −79, 4] MNI space) and superior parietal cortex. In addition, we found evidence for this in anterior prefrontal cortex (coordinates, [0, 50, 7]), whereas the largest evidence for long time scales was found in orbitofrontal cortex (coordinates, [6, 38, −14]). Both regions are color coded and shown in greater detail in (E). (E) Overlay of EPMs for both STS and LTS, illustrating the partitioning of prefrontal cortex according to progressively longer time scales. (F) A histogram of the EPM from the voxel containing the maximal value from both regions in (E) are shown on the far right, along with the expected probability to its left.