Extended Data Fig. 1: FINDR can be used to distinguish between the dynamical systems hypotheses of perceptual decision-making.

In these hypotheses, the decision process is represented by the state of a dynamical system, which we refer to as the “decision variable (z)” and is depicted as two-dimensional here but may have fewer or more dimensions. An attractor is a set of states for which the dynamical system tends to move toward, from a variety of starting states. When z is in an attractor state, small perturbations away from the attractor tend to return the system toward the attractor. An attractor can implement the commitment to a choice and the maintenance of the choice in working memory. a, In all these hypotheses, the attractors are implemented by the autonomous dynamics, which corresponds to the deterministic dynamics F in the absence of inputs and depends only on z itself. In the bistable attractors hypothesis, there are two discrete attractors, each of which corresponds to a choice alternative. In the DDM line attractor hypothesis, the autonomous dynamics form not only two discrete attractors but also a line attractor in between. The intervening line attractor allows an analog memory of the accumulated evidence when noise is relatively small. In the line attractor hypothesis with non-normal dynamics, the autonomous dynamics form a line attractor, and a separate readout mechanism is necessary for the commitment to a discrete choice. b, The autonomous speed is the magnitude of the autonomous dynamics. A dark region corresponds to a steady state, which can be an attractor, repeller, or saddle point. In the bistable attractors hypothesis, the left and right steady states are each centered on an attractor, and the middle is a saddle point. In both the DDM line attractor hypothesis and the hypothesis that has non-normal dynamics with a line attractor, the steady states correspond to attractors. c-d, Input dynamics corresponding to a left and right auditory pulse, respectively. Here we show the “effective” input dynamics, which is multiplied by the frequency p(u | z) to account for the pulsatile nature and the statistics of the stimuli in our task (in contrast to Fig. 1e, in which the input dynamics were presented without the multiplication of the frequency, which is appropriate for stimuli that are continuous over time). Whereas in the bistable attractor and DDM line attractor, the inputs are aligned to the attractors, in the hypothesis that has non-normal dynamics with a line attractor, the inputs are not aligned. e, The input speed is the average of the magnitude of the average left input dynamics and the magnitude of the average right input dynamics. f, We simulated spikes that follow the bistable attractor dynamics in a-e to create a synthetic dataset with the number of trials, number of neurons, and firing rates that are typical of the values observed in our datasets. Then, we fit FINDR to this synthetic dataset from random initial parameters. The autonomous and input dynamics inferred by FINDR qualitatively match the bistable attractors hypothesis. g-h, FINDR-inferred dynamics qualitatively match the dynamics in Fig. 1f–h and a–e. In panel g, the sample zone covers the entirety of the plotted area.