Drift-diffusion models for multiple-alternative forced-choice decision making

Embodied sequential sampling models and dynamic neural fields for decision-making: Why hesitate between two when a continuum is the answer

As two alternative options in a forced choice task are separated by design, two classes of computational models of decision-making have thrived independently in the literature for nearly five decades. While sequential sampling models (SSM) focus on response times and keypresses in binary decisions in experimental paradigms, dynamic neural fields (DNF) focus on continuous sensorimotor dimensions and tasks found in perception and robotics. Recent attempts have been made to address limitations in their application to other domains, but strong similarities and compatibility between prominent models from both classes were hardly considered. This article is an attempt at bridging the gap between these classes of models, and simultaneously between disciplines and paradigms relying on binary or continuous responses. A unifying formulation of representative SSM and DNF equations is proposed, varying the number of units which interact and compete to reach a decision. The embodiment of decisions is also considered by coupling cognitive and sensorimotor processes, enabling the model to generate decision trajectories at trial level. The resulting mechanistic model is therefore able to target different paradigms (forced choices or continuous response scales) and measures (final responses or dynamics). The validity of the model is assessed statistically by fitting empirical distributions obtained from human participants in moral decision-making mouse-tracking tasks, for which both dichotomous and nuanced responses are meaningful. Comparing equations at the theoretical level, and model parametrizations at the empirical level, the implications for psychological decision-making processes, as well as the fundamental assumptions and limitations of models and paradigms are discussed.

Evidence or Confidence: What Is Really Monitored during a Decision?

Assessing our confidence in the choices we make is important to making adaptive decisions, and it is thus no surprise that we excel in this ability. However, standard models of decision-making, such as the drift-diffusion model (DDM), treat confidence assessment as a post hoc or parallel process that does not directly influence the choice, which depends only on accumulated evidence. Here, we pursue the alternative hypothesis that what is monitored during a decision is an evolving sense of confidence (that the to-be-selected option is the best) rather than raw evidence. Monitoring confidence has the appealing consequence that the decision threshold corresponds to a desired level of confidence for the choice, and that confidence improvements can be traded off against the resources required to secure them. We show that most previous findings on perceptual and value-based decisions traditionally interpreted from an evidence-accumulation perspective can be explained more parsimoniously from our novel confidence-driven perspective. Furthermore, we show that our novel confidence-driven DDM (cDDM) naturally generalizes to decisions involving any number of alternative options - which is notoriously not the case with traditional DDM or related models. Finally, we discuss future empirical evidence that could be useful in adjudicating between these alternatives.

Reference-free Bayesian model for pointing errors of typein neurosurgical planning

PURPOSE

Many neurosurgical planning tasks rely on identifying points of interest in volumetric images. Often, these points require significant expertise to identify correctly as, in some cases, they are not visible but instead inferred by the clinician. This leads to a high degree of variability between annotators selecting these points. In particular, errors of type are when the experts fundamentally select different points rather than the same point with some inaccuracy. This complicates research as their mean may not reflect any of the experts' intentions nor the ground truth.

METHODS

We present a regularised Bayesian model for measuring errors of type in pointing tasks. This model is reference-free; in that it does not require a priori knowledge of the ground truth point but instead works on the basis of the level of consensus between multiple annotators. We apply this model to simulated data and clinical data from transcranial magnetic stimulation for chronic pain.

RESULTS

Our model estimates the probabilities of selecting the correct point in the range of 82.6[Formula: see text]88.6% with uncertainties in the range of 2.8[Formula: see text]4.0%. This agrees with the literature where ground truth points are known. The uncertainty has not previously been explored in the literature and gives an indication of the dataset's strength.

CONCLUSIONS

Our reference-free Bayesian framework easily models errors of type in pointing tasks. It allows for clinical studies to be performed with a limited number of annotators where the ground truth is not immediately known, which can be applied widely for better understanding human errors in neurosurgical planning.

Temporal order judgment of multisensory stimuli in rat and human

We do not fully understand the resolution at which temporal information is processed by different species. Here we employed a temporal order judgment (TOJ) task in rats and humans to test the temporal precision with which these species can detect the order of presentation of simple stimuli across two modalities of vision and audition. Both species reported the order of audiovisual stimuli when they were presented from a central location at a range of stimulus onset asynchronies (SOA)s. While both species could reliably distinguish the temporal order of stimuli based on their sensory content (i.e., the modality label), rats outperformed humans at short SOAs (less than 100 ms) whereas humans outperformed rats at long SOAs (greater than 100 ms). Moreover, rats produced faster responses compared to humans. The reaction time data further revealed key differences in decision process across the two species: at longer SOAs, reaction times increased in rats but decreased in humans. Finally, drift-diffusion modeling allowed us to isolate the contribution of various parameters including evidence accumulation rates, lapse and bias to the sensory decision. Consistent with the psychophysical findings, the model revealed higher temporal sensitivity and a higher lapse rate in rats compared to humans. These findings suggest that these species applied different strategies for making perceptual decisions in the context of a multimodal TOJ task.

Informational Entropy Threshold as a Physical Mechanism for Explaining Tree-like Decision Making in Humans

While approaches based on physical grounds (such as the drift-diffusion model-DDM) have been exhaustively used in psychology and neuroscience to describe perceptual decision making in humans, similar approaches to complex situations, such as sequential (tree-like) decisions, are still scarce. For such scenarios that involve a reflective prospection of future options, we offer a plausible mechanism based on the idea that subjects can carry out an internal computation of the uncertainty about the different options available, which is computed through the corresponding Shannon entropy. When the amount of information gathered through sensory evidence is enough to reach a given threshold in the entropy, this will trigger the decision. Experimental evidence in favor of this entropy-based mechanism was provided by exploring human performance during navigation through a maze on a computer screen monitored with the help of eye trackers. In particular, our analysis allows us to prove that (i) prospection is effectively used by humans during such navigation tasks, and an indirect quantification of the level of prospection used is attainable; in addition, (ii) the distribution of decision times during the task exhibits power-law tails, a feature that our entropy-based mechanism is able to explain, unlike traditional (DDM-like) frameworks.

Multi-sensory feedback improves spatially compatible sensori-motor responses

To interact with machines, from computers to cars, we need to monitor multiple sensory stimuli, and respond to them with specific motor actions. It has been shown that our ability to react to a sensory stimulus is dependent on both the stimulus modality, as well as the spatial compatibility of the stimulus and the required response. However, the compatibility effects have been examined for sensory modalities individually, and rarely for scenarios requiring individuals to choose from multiple actions. Here, we compared response time of participants when they had to choose one of several spatially distinct, but compatible, responses to visual, tactile or simultaneous visual and tactile stimuli. We observed that the presence of both tactile and visual stimuli consistently improved the response time relative to when either stimulus was presented alone. While we did not observe a difference in response times of visual and tactile stimuli, the spatial stimulus localization was observed to be faster for visual stimuli compared to tactile stimuli.

Signal neutrality, scalar property, and collapsing boundaries as consequences of a learned multi-timescale strategy

We postulate that three fundamental elements underlie a decision making process: perception of time passing, information processing in multiple timescales and reward maximisation. We build a simple reinforcement learning agent upon these principles that we train on a random dot-like task. Our results, similar to the experimental data, demonstrate three emerging signatures. (1) signal neutrality: insensitivity to the signal coherence in the interval preceding the decision. (2) Scalar property: the mean of the response times varies widely for different signal coherences, yet the shape of the distributions stays almost unchanged. (3) Collapsing boundaries: the “effective” decision-making boundary changes over time in a manner reminiscent of the theoretical optimal. Removing the perception of time or the multiple timescales from the model does not preserve the distinguishing signatures. Our results suggest an alternative explanation for signal neutrality. We propose that it is not part of motor planning. It is part of the decision-making process and emerges from information processing on multiple timescales.

Two sources of uncertainty independently modulate temporal expectancy

The environment is shaped by two sources of temporal uncertainty: the discrete probability of whether an event will occur and-if it does-the continuous probability of when it will happen. These two types of uncertainty are fundamental to every form of anticipatory behavior including learning, decision-making, and motor planning. It remains unknown how the brain models the two uncertainty parameters and how they interact in anticipation. It is commonly assumed that the discrete probability of whether an event will occur has a fixed effect on event expectancy over time. In contrast, we first demonstrate that this pattern is highly dynamic and monotonically increases across time. Intriguingly, this behavior is independent of the continuous probability of when an event will occur. The effect of this continuous probability on anticipation is commonly proposed to be driven by the hazard rate (HR) of events. We next show that the HR fails to account for behavior and propose a model of event expectancy based on the probability density function of events. Our results hold for both vision and audition, suggesting independence of the representation of the two uncertainties from sensory input modality. These findings enrich the understanding of fundamental anticipatory processes and have provocative implications for many aspects of behavior and its neural underpinnings.

Flexible categorization in perceptual decision making

Perceptual decisions rely on accumulating sensory evidence. This computation has been studied using either drift diffusion models or neurobiological network models exhibiting winner-take-all attractor dynamics. Although both models can account for a large amount of data, it remains unclear whether their dynamics are qualitatively equivalent. Here we show that in the attractor model, but not in the drift diffusion model, an increase in the stimulus fluctuations or the stimulus duration promotes transitions between decision states. The increase in the number of transitions leads to a crossover between weighting mostly early evidence (primacy) to weighting late evidence (recency), a prediction we validate with psychophysical data. Between these two limiting cases, we found a novel flexible categorization regime, in which fluctuations can reverse initially-incorrect categorizations. This reversal asymmetry results in a non-monotonic psychometric curve, a distinctive feature of the attractor model. Our findings point to correcting decision reversals as an important feature of perceptual decision making.

Robust parallel decision-making in neural circuits with nonlinear inhibition

Animals frequently need to choose the best alternative from a set of possibilities, whether it is which direction to swim in or which food source to favor. How long should a network of neurons take to choose the best of N options? Theoretical results suggest that the optimal time grows as log(N), if the values of each option are imperfectly perceived. However, standard self-terminating neural network models of decision-making cannot achieve this optimal behavior. We show how using certain additional nonlinear response properties in neurons, which are ignored in standard models, results in a decision-making architecture that both achieves the optimal scaling of decision time and accounts for multiple experimentally observed features of neural decision-making.

An elemental computation in the brain is to identify the best in a set of options and report its value. It is required for inference, decision-making, optimization, action selection, consensus, and foraging. Neural computing is considered powerful because of its parallelism; however, it is unclear whether neurons can perform this max-finding operation in a way that improves upon the prohibitively slow optimal serial max-finding computation (which takes ∼N⁡log(N) time for N noisy candidate options) by a factor of N, the benchmark for parallel computation. Biologically plausible architectures for this task are winner-take-all (WTA) networks, where individual neurons inhibit each other so only those with the largest input remain active. We show that conventional WTA networks fail the parallelism benchmark and, worse, in the presence of noise, altogether fail to produce a winner when N is large. We introduce the nWTA network, in which neurons are equipped with a second nonlinearity that prevents weakly active neurons from contributing inhibition. Without parameter fine-tuning or rescaling as N varies, the nWTA network achieves the parallelism benchmark. The network reproduces experimentally observed phenomena like Hick’s law without needing an additional readout stage or adaptive N-dependent thresholds. Our work bridges scales by linking cellular nonlinearities to circuit-level decision-making, establishes that distributed computation saturating the parallelism benchmark is possible in networks of noisy, finite-memory neurons, and shows that Hick’s law may be a symptom of near-optimal parallel decision-making with noisy input.