Feedback plays an interesting role in perceptual learning. The complex pattern of empirical results concerning the role of feedback in perceptual learning rules out both a pure supervised mode and a pure unsupervised mode of learning and leads some researchers to the proposal that feedback may change the learning rate through top-down control but does not act as a teaching signal in perceptual learning (M. H. Herzog & M. Fahle, 1998). In this study, we tested the predictions of an augmented Hebbian reweighting model (AHRM) of perceptual learning (A. Petrov, B. A. Dosher, & Z.-L. Lu, 2005), in which feedback influences the effective rate of learning by serving as an additional input and not as a direct teaching signal. We investigated the interactions between feedback and training accuracy in a Gabor orientation identification task over six training days. The accelerated stochastic approximation method was used to track threshold contrasts at particular performance accuracy levels throughout training. Subjects were divided into 4 groups: high training accuracy (85% correct) with and without feedback, and low training accuracy (65%) with and without feedback. Contrast thresholds improved in the high training accuracy condition, independent of the feedback condition. However, thresholds improved in the low training accuracy condition only in the presence of feedback but not in the absence of feedback. The results are both qualitatively and quantitatively consistent with the predictions of the augmented Hebbian learning model and are not consistent with pure supervised error correction or pure Hebbian learning models.

*ad hoc*extensions also fail.” Herzog and Fahle (1998) suggested that feedback changes the learning rate through (unspecified) top-down control but does not act as a teaching signal in perceptual learning (also see Shibata et al., 2009).

*d*′ levels and learning dynamics were comparable to those obtained for observers with feedback (Petrov et al., 2005). Petrov et al. (2006) found that the AHRM, which tracks the external feedback when available, or else reinforces the model's own response, along with a criterion control bias input, can account for all the experimental results.

*c*is the signal contrast,

*L*

_{0}is the background luminance, set in the middle of the dynamic range of the display (

*L*

_{min}= 1 cd/m

^{2};

*L*

_{max}= 53 cd/m

^{2}),

*f*= 1.29 c/d is the center spatial frequency of the Gabor, and

*σ*= 0.77 deg is the standard deviation of the Gaussian window. The Gabors were rendered on a 64 × 64 pixel grid, extending 3.09° × 3.09° of visual angle (Figure 2).

^{1}

*ϕ*, stimulus contrasts in the first two trials are given by

*n*is the trial number,

*c*

_{ n }is the stimulus contrast in trial

*n*,

*Z*

_{ n }= 0 (incorrect) or 1 (correct) is the response accuracy in trial

*n*,

*c*

_{ n+1}is the stimulus contrast for the next trial, and

*s*is the pre-chosen step size at the beginning of the trial sequence. From the third trial onward, the sequence is “accelerated”:

*m*

_{shift}is the number of shifts in response category (switches from consecutive correct responses to incorrect responses and vice versa). In an influential review of adaptive psychophysical procedures, Treutwein (1995) recommended the accelerated stochastic approximation procedure as the best available procedure for measuring thresholds. Simulation studies prior to the experiments suggest that the optimal

*s*is the same as

*c*

_{1}and the optimal

*c*

_{1}is the threshold, which can be estimated from a QUEST procedure (see below).

*d*′ curves with and without feedback (Petrov et al., 2005, 2006). Detailed descriptions of the augmented Hebbian reweighting model can be found in Petrov et al. (2005, 2006). Here, we briefly review the major computations in the model.

*A*(

*θ*,

*f*) of each of the 35 representation units encodes the normalized spectral energy in the corresponding orientation and frequency channel. First, units tuned to different orientations (

*θ*∈ {0°, 15°, 30°, 45°, 60°, 75°, 90°}; half-amplitude full-bandwidth

*h*

_{ θ }= 30°), spatial frequencies (

*f*∈ {0.7, 1, 1.4, 2, 2.8 c/d};

*h*

_{ f }= 1 octave for spatial frequency), and spatial phases (

*ϕ*∈ {0°, 90°, 180°, 270°}) compute a set of retinotopic

*phase-sensitive maps S*(

*x*,

*y*,

*θ*,

*f*,

*ϕ*) of the input image

*I*(

*x*,

*y*):

*I*(

*x*,

*y*) is convolved with all the 140 tuned units via fast Fourier transformation. The output images are then rectified by a half-squaring operator to generate phase-sensitive maps, which can be interpreted as activation patterns across a large retinotopic population of “simple cells” (Heeger, 1992). Because spatial phase is not relevant in this task (and to simplify the representations), the model aggregates across phases in channel at each spatial location and uses shunting inhibition to obtain normalized outputs (Heeger, 1992):

*ɛ*

_{1}represents a Gaussian-distributed internal noise source with mean 0 and standard deviation

*σ*

_{1}, the normalization pool

*N*(

*f*) is assumed to be essentially independent of orientation and modestly tuned for spatial frequency,

*a*is a scaling factor, and

*k*is the saturation constant that is relevant only at near-zero contrasts.

*W*

_{ r }with full-width at half-height

*h*

_{ r }= 2.0 degrees, commensurate with the size of the target Gabor:

*ɛ*

_{2}represents another Gaussian-distributed noise source with mean 0 and standard deviation

*σ*

_{2}.

*γ*was used to limit the dynamic range of the representation units:

*w*

_{ i }and the current top-down bias

*b*:

*ɛ*

_{ d }with mean 0 and standard deviation

*σ*

_{ d }models the random fluctuations in the decision-making process.

*o*′ is negative, and a “right” response if

*o*′ is positive.

*F*adds to the early input

*u*driving the decision unit, which changes its activation to a new, late level

*o*according to the following equation:

*w*

_{ f }on the feedback input. The late activation is driven to ±

*A*

_{max}= ±1 when feedback

*F*= ±1 is present and the feedback weight is relatively high. Lower feedback weights may simply shift the activation slightly. When no feedback signal is present (

*F*= 0), the late decision activation is the same as the early decision activation (

*o*=

*o*′), which typically is in the intermediate range. In other words, the model uses the internal response of the observer to update the weights: the weights still move in the correct direction on average because the activation of the decision unit correlates with the correct stimulus classification.

*w*

_{ i }of the connections between the sensory units

*i*and the decision unit. The Hebbian rule is exactly the same with and without feedback. Each weight change depends on the activation

*a*

_{ i }of the presynaptic sensory unit and the activation

*o*of the postsynaptic decision unit relative to the baseline

*o*by its long-term average

*δ*

_{ i }tracks systematic stimulus-response correlations rather than mere response bias.

*b*with weight

*w*

_{ b }(Equation 9). Observers are assumed to approximately equalize the frequencies of recent “Left” and “Right” responses to approximately match the presentation probabilities in the experiment. The bias

*b*(

*t*+ 1) on each successive trial equals the current weighted running average

*r*(

*t*), discounting the distant past exponentially with a time constant of 50 trials (

*ρ*= 0.02):

*w*

_{ b }in the model. For example, Petrov et al. (2006) found a higher weight on adaptive criterion control in the presence of feedback. Although their effects may interact in subtle ways, the bias and the feedback inputs are structurally separate—the former tracks the model's own response

*R*, whereas the latter tracks the external feedback signal

*F*.

*a*), one for each group, internal multiplicative noise (

*σ*

_{2}), decision noise (

*σ*

_{ d }), and learning rate

*η*, were adjusted to fit the experimental data. Three parameters, orientation tuning bandwidth (

*h*

_{ θ }), frequency tuning bandwidth (

*h*

_{ f }), and radial kernel width (

*h*

_{ r }) were set a priori based on publications in the literature. All other parameters were set a priori based on Petrov et al. (2005). The scaling factors and internal noises allow a match to the overall performance shown in the initial performance measure. Critically, a single learning rate

*η*was used to model the learning curves in all four experimental conditions, and the predicted differences between conditions entirely reflect differential effectiveness of Hebbian learning and feedback in these conditions.

Parameter | Value | ||||
---|---|---|---|---|---|

Parameters set a priori | Orientation spacing | Δθ = 15° | |||

Spatial frequency spacing | Δf = 0.5 oct | ||||

Maximum activation level | A _{max} = 1 | ||||

Weight bounds | w _{min/max} = ±1 | ||||

Running average rate | ρ = 0.02 | ||||

Activation function gain | γ = 5 | ||||

Bias weight | w _{ b } = 2.2 | ||||

Normalization constant | k = 0 | ||||

Internal additive noise | σ _{1} = 0 | ||||

Initial weight scaling factor | w _{ini} = 0.169 | ||||

Feedback weight | w _{ f } = 1.0 | ||||

Parameters constrained by published data | Orientation tuning bandwidth | h _{ θ } = 30° | |||

Frequency tuning bandwidth | h _{ f } = 1.0 oct | ||||

Radial kernel width | h _{ r } = 2.0 dva | ||||

Parameters optimized to fit the present data | 65% w | 65% wo | 85% w | 85% wo | |

Representation scaling factor | a = 0.090 | 0.085 | 0.14 | 0.18 | |

Internal multiplicative noise | σ _{2} = 0.16 | ||||

Decision noise | σ _{ d } = 0.20 | ||||

Learning rate | η = 0.00025 |

*w*

_{ i }= (

*θ*

_{ i }/30°)

*w*

_{init}, reflecting general prior knowledge about orientation. The weights were fixed. Six out of the seven “free-to-vary” parameters, four

*a*s,

*σ*

_{2}, and

*σ*

_{ d }, were adjusted, with two of them (internal multiplicative noise and decision noise) restricted to be the same for all 4 groups. The scaling factor was free to vary among the groups such that the model performance can match that of the human observers in the beginning of the experiment, and so reflects small random differences in performance level for these randomly assigned groups.

*c*

_{ τ }

^{measured}and

*c*

_{ τ }

^{theoretical}represent measured and model-generated contrast thresholds, and

*p*< 0.01). However, for observers in the low training accuracy (65% correct) condition, perceptual learning depended on the availability of trial-by-trial feedback—only observers in the trial-by-trial feedback condition exhibited significant threshold reduction (

*p*< 0.01); observers in the no-feedback condition did not show significant threshold reduction (

*p*> 0.10).

*SD*), 0.00 ± 0.04, −0.10 ± 0.04, −0.09 ± 0.04. Analysis of variance on the slopes found significant differences among the four different groups (

*p*< 0.001). Tukey post-hoc analysis (

*α*= 0.05) identified a significant difference only between the 65% training accuracy without feedback group and all other three groups; there was no significant difference among those three. Consistent with Herzog and Fahle (1998) and Petrov et al. (2006), we conclude that the patterns of results are not consistent with either a pure supervised or a pure unsupervised learning model.

*SD*), −0.02 ± 0.04, −0.12 ± 0.02, −0.08 ± 0.02. Analysis of variance on the simulation results identified significant differences among the four different groups (

*p*< 0.001). Tukey post-hoc analysis (

*α*= 0.05) identified a significant difference only between the 65% training accuracy group without feedback and all other three groups; there was no significant difference among those three.

*c*

_{ideal}(

*Pc*), at both 65% and 85% correct performance levels. The sampling efficiency of the human observer was then calculated as (Barlow, 1956)

^{1}Lu, Jeon, and Dosher (2004) measured the window of temporal integration in an external noise study and concluded that the full width of the perceptual temporal window at half-maximum height is 120 ms. Therefore, the three signal and external noise images, each lasting 33 ms, were merged into a single image by the perceptual system through temporal integration.