The Urgency Gating Model

Introduction

In decision-making literature, the model most commonly used to explain experimental data is an integrator, with variations being made on the quantity to be integrated. In a study by Cisek et al., an alternative model is proposed, where the neural activity is a product of instantaneous estimation of information and an urgency signal that increases in time [1]. Experiments are performed to distinguish between these two types of models.

Models

Six different types of models are compared side-by-side in this study, but we will mention only two: the pure diffusion integrator model, and the urgency gating model without filtering. The former takes the form of:

$$x_i(t)=g\int_0^t E_i(\tau) d\tau,\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; (1)$$

where $E_i(t)=p_i(t)-0.5+N(t)$ is the evidence present at time $t$. $x_i(t)$ represents the neural activity, $g$ is a gain factor, $N(t)$ is noise, and $p_i(t)$ is the probability of choice $i$ being the correct choice.

The latter is given by:

$$x_i(t)=g\times E_i(t)\times u(t),\; u(t)=t.\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; (2)$$

$E_i(t)$ takes the same form as above, and $u(t)$ here is the urgency signal, which is set to grow linearly in time. While the authors ultimately argue for a filtered form of this urgency gating model -- as this version as is is highly susceptible to noise -- this form is discussed instead for easier comprehension.

The value $p_i$ is an estimation of the subject regarding whether it is likely choice $i$ is correct or not. The experiment conducted is one where tokens that are initially positioned in the middle jump to the left or right one by one. The ``correct" choice is the side which ultimately accumulates the most amount of tokens. Therefore, the current distribution of tokens at each time step provides information regarding which side is more likely to win. This can easily be estimated by assuming that the token jumps are random and unbiased, which is what the subjects are told (but not necessarily true for every trial).

In fact, four different trials were conducted:

(I) The ``easy" trials, where token movements were more correlated with one another.

(II) The ``ambiguous" trials, where token movements are fairly even until late in the trial.

(III) The ``bias-for" trials, where the three initial tokens moved to the correct side, the later three moved to the other, and the rest is an easy trial.

(IV) The ``bias-against" trials, where the three initial tokens moved to the wrong side, the later three moved to the other, and the rest is an easy trial.

The latter two types of trials were used to distinguish between the diffusion model and the urgency gating model. The reason for this setup is that past two-alternative forced choice tasks used constant $E_i(t)$ throughout the trial, in which both models would produce identical results. The bias-for and bias-against trials guarantees different $E_i(t)$ at the beginning of the trial, which would result in different predictions from the two models.

Specifically, in the first three time steps of the bias-for trials, $E_i(t)$ is positive for the diffusion model. In the following three time steps, although $E_i(t)$ decreases, it remains non-negative. The opposite happens for the bias-against trials. Therefore, the diffusion model would predict a shorter reaction time for the bias-for versus bias-against trials. On the other hand, since the instantaneous sensory evidence is similarly zero for both trials at the end of the first six time steps, the urgency model predicts no such difference.

Results

The results were in agreement with the urgency gating model's prediction, where neither the accuracy nor the reaction time of the bias-for versus bias-against trials were significantly different. For further elimination of alternative explanations of the results, see the original paper.

Assuming that the urgency gating model is correct, it can then make another prediction. Using Eq 2 and setting the threshold to a constant value $T$, we have:

$$g\times E_i(t)\times u(t)=T,\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; (3)$$

which would result in $E_i(t)=\frac{T}{g\times t}$. This states that the estimated evidence for choice $i$, $E_i(t)$, decreases as a function of the decision time. Namely, the level of confidence the subject has about choice $i$ decreases as a function of time, which is a natural consequence of having an emergency signal that forces the subject to make a choice later in time. By using a first-order estimate of $E_i(t)$, the authors confirmed that there is indeed a negative relation between $E_i(t)$ and $t$. Altogether, these results argue for the urgency-gating model being the mechanism behind decision making.

Author: Pei-Hsien Liu

References

[1] Cisek, Paul, Geneviève Aude Puskas, and Stephany El-Murr. "Decisions in changing conditions: the urgency-gating model." Journal of Neuroscience 29.37 (2009): 11560-11571.