We have previously described a psychophysical paradigm for investigating rapid learning of relevant visual information in detection tasks (M. P. Eckstein, C. K. Abbey, B. T. Pham, & S. S. Shimozaki, 2004). This paradigm uses blocked trials with a set of possible target profiles, and it has demonstrated learning effects after a single trial. When targets are masked by Gaussian luminance noise, there exists a Bayesian ideal observer that also exhibits learning effects over the trials within a block. In this work, we investigate the effect of target contrast and the effect of the information to be learned in the target profile set. Absolute efficiency tracks target contrast closely and ranges from approximately 10% to 25% in these experiments. To disambiguate learning from other effects contributing to absolute efficiency, we define a measure of learning efficiency that measures the observed improvement over a block of trials against the total improvement expected in the ideal observer. We find significant positive trends in learning efficiency both over contrast and the within-block trial number. We find that a two-feature profile set containing orientation and polarity differences leads to a greater within-block gain in performance than a one-feature profile set that contains only orientation differences. However, this apparent difference disappears when efficiency is compared. Lastly, we show that the disparity between task performance and accumulated knowledge of the target profile can be largely explained by a model that only allows learning to occur in trials the observer performs correctly.

_{Loc}) by reducing the influence of irrelevant sensory input. Therefore, improved performance in later trials is a sign of learning.

_{Id}) before any localization trials have occurred must be at chance levels. If PC

_{Id}is significantly above chance performance at some later trial, then the subject must have acquired some knowledge of the target profile during the localization process.

_{Loc}. While learning the identity of the target is sufficient to cause improved performance in later localization trials, it is not necessary. It is possible to imagine an observer that shows improved performance without actually learning about the target profile. For example, imagine the following extreme case in which an observer simply ignores the stimulus in the first trial of a block—responding by guessing—and then does use the stimuli in the second trial. Performance in the first trial will be at chance levels, and the observer will have no rational basis for updating the priors. As a result, the observer will be just as uncertain in the second trial as the first. However, in the second trial the observer uses the stimulus and hence will show improved performance. This performance improvement occurs without any updating of priors between the two trials.

_{Id}that are significantly greater than chance demonstrate learning that occurs over the localization trials of a block. We use identification performance after the 4th learning trial to establish the presence of a learning effect and then attribute the changes in localization performance over the 4 trials in a block to this effect.

*t*within a block (here

*t*= 1,…,4), let the image vector

**g**

_{ t}(256 × 256 pixels) contain the intensities of all pixels in a localization stimulus with the mean background intensity subtracted, and let

**g**

_{ t,m}be independent sub-regions (50 × 50 pixels) centered on each possible location (here,

*m*= 1,…, 8). The ideal observer selects the location that maximizes the posterior probability of being the target location. For forced-choice tasks with equi-probable randomized locations, an equivalent strategy is to choose the target location,

_{ t}, that maximizes the likelihood of the stimulus,

*p*(

**g**

_{ t}∣

*m*). This in turn is equivalent to maximizing the likelihood of the sub-region around the target location

*j*index the possible target profiles (

*j*= 1,…,

*N,*with

*N*= 4 in this work), then

*π*

_{ t,j}is the prior probability of target

*j*in trial

*t*. In the first trial, all target profiles are equally probable, and hence

*π*

_{1 ,j}= 1/

*N*. Incorporating the sum over target profiles gives a likelihood defined by

*p*(

**g**

_{ t,m}∣

*m, j*) is the likelihood of

**g**

_{ t,m}given target profile

*j*at location

*m*.

*m*

_{ t,true}be the index denoting the actual location of the target in the

*t*th trial. For

*t*> 1, the ideal observer weights the various target profiles according to

*Q*is a normalization constant necessary for the priors to sum to unity across

*j*. With this rule, the prior probability of trial

*t*+ 1 is the posterior probability from trial

*t*. The ideal observer performs the identification task after

*t*trials by choosing the target index with the largest posterior probability,

*b*= 1,..,

*B,*where

*B*is the number of blocks. We have omitted this subscript for clarity.

*p*(

**g**

_{ t,m}∣

*m,*

*j*), in Equations 2 and 3 has so far been left general. In this work, we use Gaussian white noise with variance

*σ*

^{2}to mask the appearance of the target in the stimulus. Let us denote by the vector

**s**

_{ j}the profile of the

*j*th target, which serves as the conditional mean of the observed sub-region. This gives a multivariate Gaussian function for the likelihood term,

*P*is the number of pixels in each sub-region and the ∣∣ ∣∣ indicates the vector magnitude of its argument.

**g**

_{ t}, and Equation 3 gives the identification response. These responses can be used in Monte Carlo simulations to evaluate ideal observer performance and determine target energy thresholds needed to equate the ideal observer to human–observer performance. This process is used frequently in this work to compute the efficiency of human observer performance (Barlow, 1980; Tanner & Birdsall, 1958). If we let

*E*

_{exp}be target energy in a blocked learning experiment and let

*E*

_{IO}(PC,

*i*) be the target energy required for the ideal observer to achieve a performance of PC in learning trial

*i,*then the observer efficiency is computed as

_{i}is the observed PC in learning trial

*i*. Implementation of the ideal observer through lookup tables derived from Monte Carlo simulations is described in the Methods section.

_{1}) of 0.98 can only achieve a PC difference of 0.02 or less regardless of how effective learning is for the task. Similarly, imagine target contrast is manipulated so that average localization PC is 0.145 when there is no uncertainty about signal type. In this case, again, the maximum PC difference achievable is 0.02 (recall that chance performance for 8AFC is PC = 0.125). Mid-range values of PC

_{1}are less constrained by these effects and can be considerably higher.

_{1}, the observer will often go from a state of total uncertainty about the identity of the target before the first trial to almost total certainty after it. Thus, the observer has effectively resolved nearly all uncertainty about the target profile in one trial. The PC difference assigns a modest score to what is effectively near-total learning of target identity.

_{loc}above.

^{2}. Viewing distance was not constrained, but observers maintained a comfortable viewing distance of approximately 40 cm.

*SE*< 0.0016).

_{targ}be the targeted value of proportion correct, and let PC

_{lo}and PC

_{hi}be values from the lookup table that bracket it, with corresponding contrasts

*C*

_{lo}and

*C*

_{hi}. Linear interpolation yields a threshold contrast of

*A*

_{pix}, in units of degrees

^{2}; the stimulus duration,

*T,*in seconds; and the sum of squared pixel intensities averaged across all target profiles at a nominal contrast of 1, SS

_{ave}. Conversion to signal energy is given by

^{2}sec. For the experiments reported here, the average target sum of squares is SS

_{ave}= 82.84, the area of a pixel in degrees is

*A*

_{pix}= 0.001847 deg

^{2}(for pixel area of 0.09 mm

^{2}and 40 cm viewing distance), and the stimulus duration is

*T*= 0.2 s. Thus, the conversion to threshold energy is

*E*= 0.0306

*C*

^{2}. Efficiency with respect to the ideal observer is then computed according to Equation 6, and learning efficiency is computed using this approach according to Equation 9.

_{ID}= 1) and is also consistent with the larger effects of measurement error at very high levels of PC (0.969 ± 0.011).

*t*-test,

*df*= 3,

*p*< 0.022 (LT2), 0.006 (LT3), and 0.013 (LT4)), and a linear trend in learning trials averaged across contrasts was also significant (one-tailed

*t*-test,

*df*= 3,

*p*< 0.014). Significance of the trend in learning trials was greater when averaging was restricted to the three highest contrasts (

*p*< 0.001). In contrast, absolute efficiency is significant at all contrasts with no significant learning trial effect.

_{Loc}) over learning trials seen in Figure 5A, where the largest effects are found at mid-range target contrast. Observers are most effectively incorporating prior experience at high contrast when the information gleaned from that experience is the highest quality.

*t*-test,

*df*= 3,

*p*< 0.001). Significant effects from an incorrect localization persist throughout the learning trials and the identification task (

*p*< 0.001 (LT3), 0.002 (LT4), and 0.003 (ID)).

*p*< 0.042 for the one-polarity stimuli,

*p*< 0.001 for the two-polarity stimuli: paired

*t*-test two-tailed,

*df*= 3). However, the two-polarity stimuli show a substantially larger effect. The average difference in proportion correct between Trial 4 and Trial 1 is 0.091 (±0.004) for the two-polarity stimuli as opposed to 0.033 (±0.010) for the one-polarity stimuli. This difference is primarily due to the first trial, where PC for the two-polarity stimuli is significantly lower (

*p*< 0.001) than the one-polarity stimuli. There is also a significant difference (

*p*< 0.027) in identification performance after Trial 4. In this case, two-polarity stimuli result in higher average performance by 0.079 (±0.019) units of PC.

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