Fig 1.
Hierarchical decision-making task.
(A) Stimulus display. Participants had to identify which of the 8 lower-level nodes delivered a positive reward and ended the trial. Directing the gaze to a node from the top three levels of the decision tree and pressing a key triggered a short pulse of random-dot motion. The direction (left or right) and strength of motion assigned to each internal node were randomly selected in each trial. The target could be identified by following the correct direction of motion at each bifurcation from the root node to a leaf node. Participants were free to explore the decision tree as they wished to maximize the number of points earned. (B–C) Correct direction of motion at each internal node for two example trials. The true direction of motion is indicated by the horizontal arrows shown below each internal node. The numbers assigned to the nodes do not represent spatial positions but depend on the correct direction of motion at each bifurcation (as explained in the next panel). (D) Adopted nomenclature. Levels 1 to 3 are internal nodes. The leaf nodes are those at the lowest level of the decision tree. Nodes are numbered depending on the correct direction of motion at each bifurcation. If rightwards were the correct direction of motion at every bifurcation (as indicated by the horizontal arrows), the number assigned to each node would increase from top to bottom and from left to right, as indicated in the panel. (E) Example of sequence of choices from two representative trials. The vertical arrows indicate when a node of the decision tree was queried. The numbers above the arrows identify the node that was queried, following the convention described in panel D.
Fig 2.
Transition probabilities between nodes of the decision tree.
(A) In all the panels, the nodes of the decision tree were re-arranged following the convention depicted in Fig 1D. The re-arrangement can be interpreted as-if rightward were the true direction of motion at every bifurcation (indicated here by the right-pointing arrows). (B-E) Red lines identify the most frequent transitions between pairs of nodes. Transitions from nodes at levels 1–3 are shown in panel B–D, and transitions from leaf nodes are shown in panel E. The width of the line from node x to node y is proportional to the probability of transitioning from x to y given that last query was to node x. Unlikely transitions (conditional probability < 0.075) were omitted. (B–D) After querying an internal node, the more frequent actions were choosing one of the two child-nodes, or re-querying the same node. The ribbon corresponds to re-queries. Because of the notation convention, the true direction of motion is rightward at every internal node. (E) From left to right, transitions from leaf nodes 8 to 14. We excluded the target (node 15) since querying it terminates the trial.
Fig 3.
Motion choices depend on motion strength and tree level.
The top row shows the proportion of correct motion choices as a function of motion strength. The bottom row shows the proportion of queries that were followed by another query at the same node. Solid curves are fits of a detection model. Decisions made at different levels of the decision tree are displayed in different colors. Each column shows data from one participant (S1 to S4). Error bars indicate s.e.m.
Fig 4.
A simple detection model explains the motion choices.
(A) Distributions from which the momentary motion evidence were sampled. The momentary motion evidence is normally distributed, with mean and variance that scale linearly with motion strength. The sign of the mean depends on motion direction. The slopes were fit independently for each participant (here we show the distributions from participant 1). The decision is made comparing an evidence sample against two criteria located at ±Φ. The criterion is given by the product of a base criterion, ϕℓ, and a term that decays exponentially with the number of successive queries made at the node (nq). (B) Base criterion for every participant and level of the decision tree, obtained from the best-fitting model. (C) The criterion, Φ, approaches zero exponentially as the number of successive queries at a node (nq) increases. Decay rate is determined by λ. Each curve depicts the best-fitting exponential function for each participant. (D) Frequency of re-queries, as a function of the number of previous successive queries at the node (nq). This proportion decreases with nq and with the level of the decision in the tree (indicated by the different colors). Solid lines are predictions from the detection model. Only the lower motion strengths (below 25.6%) were included in this analysis. Error bars indicate s.e.m. across participants.
Fig 5.
Only motion information from the last query informs the left/right choice.
(A) Influence of motion energy residuals on the decision to descend levels through the left or right branch. The residuals were calculated by applying a filter to the sequence of random dots and subtracting the mean of all stimuli of the same motion strength and direction. Positive (negative) residuals indicate an excess of motion in rightward (leftward) direction. For left/right choices made after a single query, the motion energy residuals were positive for rightward choices and negative for leftward choices. (B) As panel A, except that we analyze the left/right choices made after two successive queries of the same internal node. The two panels show the motion energy residuals obtained from the first and second queries, sorted by the left/right choice made after the second one. Only the motion energy residuals from the second presentation distinguished between leftward and rightward choices, which indicates that the motion information from the first query did not influence the ultimate choice. Shading indicates s.e.m. The latency introduced by the impulse response of the motion energy filters explain the offset between the time of stimulus presentation (gray horizontal bars) and the onset of motion selectivity (Methods).
Fig 6.
Comparison of average reward and number of queries between data and models.
(A) Average reward per trial obtained by the participants, the Bayesian model and the heuristic model. Error bars indicate s.e.m. across trials. (B) Average number of queries per level and of errors at leaf nodes. The averages were first calculated per participant and then across participants. Error bars indicate s.e.m. across participants. The predictions of the Bayesian model (Heuristic model) are based on 2,000 (50,000) simulated trials per participants.
Fig 7.
Distribution of actions after the query of internal and leaf nodes.
The left column shows the types of action selected after a query of an internal node, and the right column shows those selected after an error at a leaf node. Panels A–H represent different datasets, identified in each panel. We sorted the actions that follow the query of an internal node into 3 categories: on-path queries, off-path queries, and queries that cannot be classified as neither on- nor off-path (‘other’). We sorted the actions that follow an error at a leaf node into 6 categories: choosing the child node that is in the true direction of motion (‘correct child’), the other child node (‘incorrect child’), querying the same node again (‘re-query’), other nodes at the same level excluding re-queries (‘other, same level’), nodes of lower level that are not direct child nodes (‘other, lower level’), and nodes located at higher levels of the decision tree (‘higher level’).
Fig 8.
Participants and heuristic model made similar transitions between levels.
Transition frequencies between levels of the decision tree, obtained by grouping all nodes from the same level. The top row shows the transitions before making an error at a leaf node. The bottom row shows the transition after at least one error at a leaf node. The width of the red lines is proportional to the transition frequency. The dashed lines are placeholders for infrequent transitions. The last column corresponds to a Bayesian model in which the cost of querying internal nodes was reduced to 30% of its true value. In each of the 8 panels, transitions to a lower level are shown on the right, and transitions to a higher level are shown on the left. The ribbon identifies transitions between nodes at the same level of the decision tree (including re-queries). Transition probabilities were first calculated per participant, and then averaged across participant (see Methods).
Fig 9.
Motion strength and tree level influence which node is blamed for an error.
Panels A-C show the predictions of the heuristic model and panels D-F correspond to the behavioral data. (A) Proportion of errors for which the blame was assigned to a node with the motion strength indicated in the abscissa, given that a node with that motion strength was in the error-path. Note that proportions do not need to add to 1 since the error-path can contain up to three different values of motion strength. (B) Proportion of errors that were followed by an on-path query to a node of level ℓ, given that level ℓ of the error-path had the motion strength indicated in the abscissa. For example, if the root node had the weakest possible motion strength, the probability that an on-path query is made at that node is ∼0.23. (C) Proportion of errors that were followed by an off-path query from a node of level ℓ, given that level ℓ of the error-path had the motion strength indicated in the abscissa. For example, if the root (level 1) node had the weakest possible motion strength, there is a ∼0.25 chance that the root node is blamed for the error and an off-path query is made to its child that was not on the error path. Proportions were first calculated per participant and then averaged across participants.