**We studied how learning changes the processing of a low-level Gabor stimulus, using a classification-image method (psychophysical reverse correlation) and a task where observers discriminated between slight differences in the phase (relative alignment) of a target Gabor in visual noise. The method estimates the internal “template” that describes how the visual system weights the input information for decisions. One popular idea has been that learning makes the template more like an ideal Bayesian weighting; however, the evidence has been indirect. We used a new regression technique to directly estimate the template weight change and to test whether the direction of reweighting is significantly different from an optimal learning strategy. The subjects trained the task for six daily sessions, and we tested the transfer of training to a target in an orthogonal orientation. Strong learning and partial transfer were observed. We tested whether task precision (difficulty) had an effect on template change and transfer: Observers trained in either a high-precision (small, 60° phase difference) or a low-precision task (180°). Task precision did not have an effect on the amount of template change or transfer, suggesting that task precision per se does not determine whether learning generalizes. Classification images show that training made observers use more task-relevant features and unlearn some irrelevant features. The transfer templates resembled partially optimized versions of templates in training sessions. The template change direction resembles ideal learning significantly but not completely. The amount of template change was highly correlated with the amount of learning.**

*x*in the Gabor

**g**

*in phase*

_{ϕ}*ϕ*was defined as where

*a*is the contrast of the Gabor,

*σ*is the width of the Gaussian envelope (here 0.17°), and

_{x}*λ*is the cycle length of the sinusoid (0.25°). The vector of white random noise values

**n**

*and the mean luminance*

_{t}*I*

_{m}were then added to this pattern, which defined the contrast of oriented lines. After that, the lines were windowed by a one-dimensional Gaussian function at the orientation orthogonal to the Gabor function. The resulting stimulus (without noise) is the standard two-dimensional Gabor (a two-dimensional Gaussian multiplied by a one-dimensional sinusoid; see Figure 2, for example). The noise had the same contrast energy in each line. The Gabor stimuli (and lines) were oriented globally at either 45° or 135°.

*c*

_{1}and the transfer session

*c*to change between the initial session and the last training session

_{t}*c*

_{6}:

*τ*= (

*c*

_{1}−

*c*)/(

_{t}*c*

_{1}−

*c*

_{6}). A value of 1 means that any decrease in the contrast threshold is fully transferred; 0 means no transfer.

**s**

*was randomly either a Gabor with a positive phase shift*

_{t}**g**

*or a Gabor with a negative phase shift*

_{ϕ}**g**

_{−}

*, added to a Gaussian-distributed external noise*

_{ϕ}**n**

*. We assume that the internal response*

_{t}*r*on experimental trial

_{t}*t*is dependent on the cross-correlation between the noisy stimulus

**s**

*and the internal template*

_{t}**w**. In addition, we modeled the effect of internal noise by adding a random Gaussian-distributed noise

*e*

_{t}:

*i*is given when the response falls between criteria

*c*and

_{i}*c*

_{i}_{+1}. Since there were only two possible target stimuli (

**g**

*and*

_{ϕ}**g**

_{−}

*), the cross-correlation between the target and the template has only two values. We used a dummy variable*

_{ϕ}*o*to represent the match in trial

_{t}*t*and used only external random noise in the regression analysis. This ensures that target shapes cannot bias template estimates.

*c*, the expectation for a positive, “positive phase shift” response is where Φ is the cumulative normal distribution function. A generalized linear ordinal probit model (linear regression with a nonlinear Gaussian link function) can be used to solve this kind of regression with multiple criteria—i.e., estimate the unknown template weights

_{i}**w**from the known stimulus values and responses (for a review, see Knoblauch & Maloney, 2012). We used 24 regressors to estimate the internal weights (classification image), one regressor to estimate the constant target-stimulus match, and three regressors for the internal criteria that correspond to the four response alternatives.

**ŵ**

*for each session*

_{k}*k*.

*k*= 1, 2, …, 12 of the session, representing the time dimension. This will then give the direction of the change in the course of learning. The data were made zero mean by subtracting the template average. Then we regressed these templates with a linear, zero-mean session index, using the regress function of MATLAB.

**w*** with the measured templates by subtracting the mean of all classification images

**ŵ**

*. The magnitude of the classification images estimated with the generalized linear model is dependent on the internal noise level (Knoblauch & Maloney, 2008; Kurki, Saarinen, & Hyvärinen, 2014). We scaled the ideal template with an internal noise estimate*

_{k}*ê*in order to make the template magnitudes comparable. The internal noise estimate was the mean of the four last sessions, based on the observation that the internal noise level saturated after about two sessions.

**d*** was estimated using where

*k*is the session index. The learning direction was then compared with the ideal learning direction by computing the dot product between the ideal and the observed

**d̂**template change vectors, both normalized to a unit length, divided by the vector length |

**d̂**|. We refer to this measure as the change optimality index

*δ*:

*t*(5) = 3.18,

*p*= 0.025; high-precision:

*t*(5) = 4.66,

*p*= 0.0056. Every individual observer had a lower threshold in the final session (for individual data, see Table 1).

*t*(5) = 0.626,

*p*= 0.56. In the low-precision condition, the contrast threshold in the transfer session (seventh) was about 41% higher than in the final (sixth) learning session, but also 41% lower than the initial threshold. Neither difference was statistically significant:

*t*(5) = −1.59,

*p*= 0.17;

*t*(5) = 1.55,

*p*= 0.18. In the high-precision condition the transfer threshold was about 43% higher than the final threshold and about 43% lower than the initial threshold. Both of these differences were significant:

*t*(5) = −3.44,

*p*= 0.018;

*t*(5) = 3.76,

*p*= 0.013.

*t*(5) = −3.95,

*p*= 0.010. In the high-precision condition the increase was 119%, from 21% to 46%,

*t*(5) = −3.22,

*p*= 0.023. There was not a statistically significant difference between conditions in sampling efficiency,

*F*(1, 10) = 0.55,

*p*= 0.66 (repeated-measures ANOVA, with session as the within-subject variable. We also estimated absolute efficiency change by comparing the squared ratio of observed

*d*′ and ideal-observer's

*d*′. The data are shown in Table 1. On average (across the sessions and subjects), absolute efficiency was 8.9% in the low-precision condition and 7.7% in the high-precision condition.

*F*(1, 10) = 5.34,

*p*= 0.043 (repeated-measures ANOVA). The average internal noise level in the high-precision condition dropped during training sessions by 54%,

*t*(5) = 5.44,

*p*= 0.003, whereas the change in the low-precision condition was small (11%) and not statistically significant,

*t*(5) = 1.22,

*p*= 0.28. The level of internal noise in the transfer condition remained almost constant in the low-precision condition; in the high-precision condition it was slightly higher than in the last training session, but the increase was not statistically significant,

*t*(5) = −0.967,

*p*= 0.378.

*δ*

_{1}and

*δ*

_{o}) are shown in Table 2. The mean correlation across the subjects is 0.47 in the low-precision condition and 0.53 in the high-precision condition. We also calculated the session-wise projections of the templates on the template change vector (Figure 9, insets). This shows how much the template changes from one session to the next along the direction of learning. The inset also shows the projections of the ideal template and the transfer template. In most cases the template projection on the learning vector increases systematically with the session number (time), suggesting that the regression captures how the weights change with learning. The projection of the ideal template on the estimated template change vector is typically quite high in absolute terms, implying that the direction is quite close to ideal, and typically much higher than the last template. This implies that template weights are still quite far from the ideal template. Projection of the transfer template is most often about halfway between the last and the first template, but there is considerable variation in the amount of transfer between the subjects.

*ρ*= 0.87,

*p*= 0.0001. However, linear estimates have less estimation error, as can be seen from the estimated confidence intervals.

*l*for each observer, namely the distance between the projection of the first and the last training templates on the template change vector (using the linear regression estimate). The data are shown in Table 2. The amount of template change was highly correlated with the percentage of threshold decrease,

*ρ*= 0.62,

*p*= 0.030.

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