Fig 1.
Two dots of different color are shown in rapid succession. For certain spatial and temporal distances, the perception is that of the first dot moving to the position of the second dot while abruptly changing color somewhere along the path.
Fig 2.
Backward temporal masking with a single dynamical neuron.
(A) Neuron circuit with excitatory self-feedback, Eq (3), illustrates backward temporal sensory masking. w1 = w2 = 1.5, τ = 1. (B) Positive feedback creates two stable equilibria at y* = ±1 (top trace). These form the minima of a gradient-descent function V(y) (bottom trace). (C) Depending on the interval between a priming and a countering stimulus of opposite polarity, masking can occur. (D) The effectiveness of the masking stimulus also depends on its amplitude.
Fig 3.
A four-neuron model for demonstrating stimulus-response arrival order reversals.
(A) The model. See below Eq (6) for parameter values. (B) A Scan over stimuli intervals Δtin = tin,b − tin,a showing the influence on response times RTa = tout,a − tin,a (red), RTb = tout,b − tin,b (blue) and the response time interval Δtout = tout,b − tout,a (black). For a certain central region of the input interval, there exists a reversal of the order in which responses happen, compared to the order in which the stimuli were applied. (C) Scan over stimuli intervals and amplitude ratios, illustrating how temporal and amplitude-related stimuli characteristics influence their temporal perception. (D) Detailed signals for tin,b ≫ tin,a such that the output order corresponds to the input order. (E) Detailed signals in the input-output reversal regime, where Δtin > 0 and Δtout < 0.
Fig 4.
An abstract one-dimensional three-pixel visual system, illustrating the phi phenomenon.
(A) The circuit. Outputs ya, yb and yc separately respond to inputs xa, xb and xc respectively, corresponding to perception when above a certain threshold. Weights and τ-values of the a and c-chains are identical as those indicated in the b-chain. (B) Long distance weakly coupled feedforward priming units pa, pb and pc (middle graph) with fast activation and slow decay enable sensitivity to recent inputs to be carried to adjacent output units. (C) If the input pulses on xa and xc are temporally sufficiently separated, the decayed priming signals pa and pc are unable to evoke a response from the middle output yb. (D) When inputs xa and xc are stimulated adequately fast after one another, the priming signals combine and a ghost percept on yb appears. This ghost happens after ya and before yc cross the threshold in opposite directions. The ghost appears without the presence of an input stimulus on xb.
Fig 5.
Illustration of the color phi phenomenon via an echo state network.
A large randomly connected network of neurons, also called a reservoir, interacts in a complicated and unknown way in response to an input stimulus. The connections between the neurons in the network remain fixed for the duration of the experiment. The desired output response is constructed from a linear combination of the responses of the individual neurons that form the network. After training, the ESN can generalize to novel input data.
Fig 6.
(top) Training input, (second graph) states of the first ten neurons, (third graph) desired output used to calculate the readout layer, (bottom graph) actual output calculated by the readout layer from the neuron states after training.
Fig 7.
Echo state network during testing for the color phi phenomenon.
(A) (top) Stimuli jumping between left-red and right-blue with decreasing intervals, (middle graph) ideal response with low middle output, (bottom graph) actual output showing CPP near n ≈ 3490. (B) Zoom-in of (A). The vertical dashed green line in the bottom graph indicates the time at which the CPP occurs.
Fig 8.
Some characteristics of the ESNs that do (Nwith = 1867) and do not (Nwithout = 98133) show the CPP.
(A) Distribution of neuron α-timescales, (B) magnitude of the reservoir matrix eigenvalues, (C) ratio of excitatory to inhibitory synapses, (D) number of positive long distance feedforward connections.
Fig 9.
Fraction of ESNs that show the CPP as a function of several network parameters.
(A) Reservoir sparsity, (B) input sparsity, (C) spectral radius, (D) input scaling. Each point represents n = 200 tested networks. The error bars are estimated at the 95% confidence interval. Non-varied parameters kept as described in the text.