Modeling evidence accumulation decision processes using integral equations: Urgency-gating and collapsing boundaries

The Tweedledum and Tweedledee of dynamic decisions: Discriminating between diffusion decision and accumulator models

Theories of dynamic decision-making are typically built on evidence accumulation, which is modeled using racing accumulators or diffusion models that track a shifting balance of support over time. However, these two types of models are only two special cases of a more general evidence accumulation process where options correspond to directions in an accumulation space. Using this generalized evidence accumulation approach as a starting point, I identify four ways to discriminate between absolute-evidence and relative-evidence models. First, an experimenter can look at the information that decision-makers considered to identify whether there is a filtering of near-zero evidence samples, which is characteristic of a relative-evidence decision rule (e.g., diffusion decision model). Second, an experimenter can disentangle different components of drift rates by manipulating the discriminability of the two response options relative to the stimulus to delineate the balance of evidence from the total amount of evidence. Third, a modeler can use machine learning to classify a set of data according to its generative model. Finally, machine learning can also be used to directly estimate the geometric relationships between choice options. I illustrate these different approaches by applying them to data from an orientation-discrimination task, showing converging conclusions across all four methods in favor of accumulator-based representations of evidence during choice. These tools can clearly delineate absolute-evidence and relative-evidence models, and should be useful for comparing many other types of decision theories.

Graded decisions in the human brain

Decision-makers objectively commit to a definitive choice, yet at the subjective level, human decisions appear to be associated with a degree of uncertainty. Whether decisions are definitive (i.e., concluding in all-or-none choices), or whether the underlying representations are graded, remains unclear. To answer this question, we recorded intracranial neural signals directly from the brain while human subjects made perceptual decisions. The recordings revealed that broadband gamma activity reflecting each individual's decision-making process, ramped up gradually while being graded by the accumulated decision evidence. Crucially, this grading effect persisted throughout the decision process without ever reaching a definite bound at the time of choice. This effect was most prominent in the parietal cortex, a brain region traditionally implicated in decision-making. These results provide neural evidence for a graded decision process in humans and an analog framework for flexible choice behavior.

The neural implausibility of the diffusion decision model doesn't matter for cognitive psychometrics, but the Ornstein-Uhlenbeck model is better

In cognitive psychometrics, the parameters of cognitive models are used as measurements of the processes underlying observed behavior. In decision making, the diffusion decision model (DDM) is by far the most commonly used cognitive psychometric tool. One concern when using this model is that more recent theoretical accounts of decision-making place more emphasis on neural plausibility, and thus incorporate many assumptions not found in the DDM. One such model is the Ising Decision Maker (IDM), which builds from the assumption that two pools of neurons with self-excitation and mutual inhibition receive perceptual input from external excitatory fields. In this study, we investigate whether the lack of such mechanisms in the DDM compromises its ability to measure the processes it does purport to measure. We cross-fit the DDM and IDM, and find that the conclusions of DDM would be mostly consistent with those from an analysis using a more neurally plausible model. We also show that the Ornstein-Uhlenbeck Model (OUM) model, a variant of the DDM that includes the potential for leakage (or self-excitation), reaches similar conclusions to the DDM regarding the assumptions they share, while also sharing an interpretation with the IDM in terms of self-excitation (but not leakage). Since the OUM is relatively easy to fit to data, while being able to capture more neurally plausible mechanisms, we propose that it be considered an alternative cognitive psychometric tool to the DDM.

Attribute latencies causally shape intertemporal decisions

Intertemporal choices - decisions that play out over time - pervade our life. Thus, how people make intertemporal choices is a fundamental question. Here, we investigate the role of attribute latency (the time between when people start to process different attributes) in shaping intertemporal preferences using five experiments with choices between smaller-sooner and larger-later rewards. In the first experiment, we identify attribute latencies using mouse-trajectories and find that they predict individual differences in choices, response times, and changes across time constraints. In the other four experiments we test the causal link from attribute latencies to choice, staggering the display of the attributes. This changes attribute latencies and intertemporal preferences. Displaying the amount information first makes people more patient, while displaying time information first does the opposite. These findings highlight the importance of intra-choice dynamics in shaping intertemporal choices and suggest that manipulating attribute latency may be a useful technique for nudging.

Of Rodents and Primates: Time-Variant Gain in Drift-Diffusion Decision Models

Sequential sampling models of decision-making involve evidence accumulation over time and have been successful in capturing choice behaviour. A popular model is the drift-diffusion model (DDM). To capture the finer aspects of choice reaction times (RTs), time-variant gain features representing urgency signals have been implemented in DDM that can exhibit slower error RTs than correct RTs. However, time-variant gain is often implemented on both DDM's signal and noise features, with the assumption that increasing gain on the drift rate (due to urgency) is similar to DDM with collapsing decision bounds. Hence, it is unclear whether gain effects on just the signal or noise feature can lead to a different choice behaviour. This work presents an alternative DDM variant, focusing on the implications of time-variant gain mechanisms, constrained by model parsimony. Specifically, using computational modelling of choice behaviour of rats, monkeys, and humans, we systematically showed that time-variant gain only on the DDM's noise was sufficient to produce slower error RTs, as in monkeys, while time-variant gain only on drift rate leads to faster error RTs, as in rodents. We also found minimal effects of time-variant gain in humans. By highlighting these patterns, this study underscores the utility of group-level modelling in capturing general trends and effects consistent across species. Thus, time-variant gain on DDM's different components can lead to different choice behaviours, shed light on the underlying time-variant gain mechanisms for different species, and can be used for systematic data fitting.

Supplementary Information

The online version contains supplementary material available at 10.1007/s42113-023-00194-1.

Expressions for Bayesian confidence of drift diffusion observers in fluctuating stimuli tasks

We introduce a new approach to modelling decision confidence, with the aim of enabling computationally cheap predictions while taking into account, and thereby exploiting, trial-by-trial variability in stochastically fluctuating stimuli. Using the framework of the drift diffusion model of decision making, along with time-dependent thresholds and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of "pipeline" evidence that has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli that change over the course of a trial with normally-distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions contain only a small number of standard functions, and require evaluating only once per trial, making trial-by-trial modelling of confidence data in stochastically fluctuating stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns.

"Reliable organisms from unreliable components" revisited: the linear drift, linear infinitesimal variance model of decision making

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann's (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann's problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann's problem do not address the main theoretical question that historically motivated research in this area.

Multiphasic value biases in fast-paced decisions

Perceptual decisions are biased toward higher-value options when overall gains can be improved. When stimuli demand immediate reactions, the neurophysiological decision process dynamically evolves through distinct phases of growing anticipation, detection, and discrimination, but how value biases are exerted through these phases remains unknown. Here, by parsing motor preparation dynamics in human electrophysiology, we uncovered a multiphasic pattern of countervailing biases operating in speeded decisions. Anticipatory preparation of higher-value actions began earlier, conferring a 'starting point' advantage at stimulus onset, but the delayed preparation of lower-value actions was steeper, conferring a value-opposed buildup-rate bias. This, in turn, was countered by a transient deflection toward the higher-value action evoked by stimulus detection. A neurally-constrained process model featuring anticipatory urgency, biased detection, and accumulation of growing stimulus-discriminating evidence, successfully captured both behavior and motor preparation dynamics. Thus, an intricate interplay of distinct biasing mechanisms serves to prioritise time-constrained perceptual decisions.

Humans utilize sensory evidence of others' intended action to make online decisions

We often acquire sensory information from another person's actions to make decisions on how to move, such as when walking through a crowded hallway. Past interactive decision-making research has focused on cognitive tasks that did not allow for sensory information exchange between humans prior to a decision. Here, we test the idea that humans accumulate sensory evidence of another person's intended action to decide their own movement. In a competitive sensorimotor task, we show that humans exploit time to accumulate sensory evidence of another's intended action and utilize this information to decide how to move. We captured this continuous interactive decision-making behaviour with a drift-diffusion model. Surprisingly, aligned with a 'paralysis-by-analysis' phenomenon, we found that humans often waited too long to accumulate sensory evidence and failed to make a decision. Understanding how humans engage in interactive and online decision-making has broad implications that spans sociology, athletics, interactive technology, and economics.