Is the homunculus "aware" of sensory adaptation?

Abstract

Neural activity and perception are both affected by sensory history. The work presented here explores the relationship between the physiological effects of adaptation and their perceptual consequences. Perception is modeled as arising from an encoder-decoder cascade, in which the encoder is defined by the probabilistic response of a population of neurons, and the decoder transforms this population activity into a perceptual estimate. Adaptation is assumed to produce changes in the encoder, and we examine the conditions under which the decoder behavior is consistent with observed perceptual effects in terms of both bias and discriminability. We show that for all decoders, discriminability is bounded from below by the inverse Fisher information. Estimation bias, on the other hand, can arise for a variety of different reasons and can range from zero to substantial. We specifically examine biases that arise when the decoder is fixed, "unaware" of the changes in the encoding population (as opposed to "aware" of the adaptation and changing accordingly). We simulate the effects of adaptation on two well-studied sensory attributes, motion direction and contrast, assuming a gain change description of encoder adaptation. Although we cannot uniquely constrain the source of decoder bias, we find for both motion and contrast that an "unaware" decoder that maximizes the likelihood of the percept given by the preadaptation encoder leads to predictions that are consistent with behavioral data. This model implies that adaptation-induced biases arise as a result of temporary suboptimality of the decoder.

Figure 1

Encoding-decoding framework for adaptation. The encoder represents stimulus s using the stochastic responses of a neural population, r. This mapping is affected by the current adaptation state, and the responses can also affect the adaptation state. Two types of decoders can be considered. (A) An aware decoder knows of the adaptive state of the encoder and can adjust itself accordingly. Note that although the diagram implies that the adaptation state must be transmitted via a separate channel, it might also be possible to encode it directly in the population response. (B) An unaware decoder is fixed and ignores any adaptive changes in the encoder.

Figure 2

Linking estimation to psychophysically measurements. The bold lines correspond to the subject’s average percept as a function of stimulus parameter s. How well the difference δs between stimulus parameters s₁ and s₂ can be discriminated depends on the overlap between the distributions of the estimates ŝ₁ and ŝ₂. The more separated and the narrower the distributions, the better the discriminability, and thus the lower the discrimination threshold. (A) The estimates are unbiased. On average, the estimates ŝ₁ and ŝ₂ are equal to the true parameter values. The discriminability depends on only the standard deviation σ̂ of the estimates. (B) The estimates are biased. Now, the distance between the distributions is scaled by a factor (1 + b′), which represents the linearized distortion factor from stimulus space to estimate space. Discrimination performance is thus controlled by both σ̂ and the derivative of the bias b′(s).

Figure 3

Motion direction adaptation: Psychophysical measurements. (A) Shift in perceived direction as a function of the test direction relative to the adapter direction. Stimuli whose directions are close to the adapter are repelled away from it. Data are replotted from Levinson and Sekuler (1976) (squares—mean of two subjects), Patterson and Becker (1996) (circles—subject MD), and Alais and Blake (1999) (triangles—mean of four subjects). (B) Ratio of discrimination thresholds after and before adaptation. Adaptation induces no change or a modest improvement in discriminability near the adapter direction, but a substantial decrease away from the direction. Data replotted from Phinney, Bowd, and Patterson (1997) (circles—subject AW) and Hol and Treue (2001) (triangles—mean of 10 subjects). All studies used random dot stimuli, but the details of the experiments (e.g., the duration of adaptation) differed.

Figure 4

Model of adaptation in motion direction encoding. (A) Tuning curves before adaptation. (B) Population response for a test stimulus moving in direction θ = 30 degrees (black arrow), before adaptation. The dots illustrate the response of neurons with preferred direction θ_i during one example trial after adaptation. The line represents the mean response. (C) Tuning curves after adaptation at 0 degree. Adaptation induces a gain suppression of neurons selective to the adapter. (D) Population response after adaptation at 0 degree (gray arrow). The responses of cells with preferred directions close to 0 degree respond much less to the test than they did prior to adaptation, whereas the cells with preferred directions larger than the test (e.g., 60 degrees) are not strongly affected. As a result, the population tuning curve seems to shift rightward, away from the adapter. Most fixed (unaware) decoders thus predict a repulsive shift of the direction estimate, in agreement with previous studies (Clifford et al., 2000; Jin et al., 2005).

Figure 5

Bias and discriminability predictions for aware and unaware ML decoder. (Left) Preadaptation (dashed) and postadaptation (solid) estimation bias. (Middle) Preadaptation (dashed) and postadaptation (solid) standard deviation, along with I_F (θ)^−1/2 (dash-dotted) and the Cramér-Rao bound (dotted). (Right) Postadaptation (solid) relative discrimination thresholds ${(\delta \theta )}_{76\%}^{\mathit{post}}/{(\delta \theta )}_{76\%}^{\mathit{pre}}$, along with IF (θ)^−1/2 (dash-dotted) normalized by the pre-adaptation threshold. (A) The aware estimator predicts no perceptual bias. Its standard deviation and discrimination threshold match I_F(θ)^−1/2, which is the Cramér-Rao bound. (B) The unaware estimator is capable of explaining large perceptual biases, as well as increases in thresholds away from the adapter, comparable with the experimental data. In this case, I_F(θ)^−1/2 differs from the Cramér-Rao bound: it provides a meaningful bound for the discrimination threshold but not for the standard deviation of the estimates. Values are based on simulations of 10,000 trials.

Figure 6

Predicted bias and discriminability arising from different neural adaptation effects. (A) Sharpening of the tuning curves around the adapter. (B) Repulsive shift of the tuning curves sensitive to the adapter, away from the adapter. (C) Flank suppression of tuning curves for stimuli close to the adapter. (D) Increase in the Fano factor at the adapter (the gray area shows the standard deviation of the spike count at the peak of each tuning curve). Each plot presents the predictions in terms of bias (middle column) and discrimination threshold (right column) for the ML_unaw readout (solid lines). The dash-dotted line on the right column is (I_F)^−1/2. See also Jin et al. (2005); Schwartz et al. (2007).

Figure 7

Contrast adaptation: Psychophysical measurements. Effect of high-contrast adaptation on apparent contrast and contrast discrimination. (A) Bias in apparent contrast as a function of test contrast. Circles represent the data replotted from Langley (2002) (mean of subjects KL and SR; the test and adapter are horizontal gratings; the contrast of the adapter is 88%). Triangles show the data from Ross and Speed (1996) (subject HS, after adaptation to a 90% contrast grating). Perceived contrast decreases after adaptation for all test contrasts. (B) Effect of adaptation on contrast discrimination threshold, as a function of test contrast. Circles: Data replotted from Abbonizio et al. (2002) (mean of subjects KL and GA, after adaptation to 80% contrast as shown in their Figure 1). Triangles: data replotted from Greenlee and Heitger (1988) (subject MWG after adaptation to a 80% contrast grating). At low test contrasts, thresholds increase, while modest improvements can be observed at high contrasts.

Figure 8

Encoding model for contrast adaptation. Contrast adaptation is assumed to produce a rightward shift of the response functions of each neuron. The amount of shift depends on the neuron’s responsivity to the adapting contrast. (A) The contrast response curve averaged over all neurons (dash-dot) also shifts compared to its position before adaptation (solid line) and slightly changes its slope. (B) Scatter plot showing the shift in the distribution of the model neurons’ semisaturation constants (β_i) toward the adapter. Model neurons with low values respond more to the high-contrast adapter and thus shift more.

Figure 9

Bias and discriminability predictions for aware and unaware ML decoders. Bias (left), standard deviation (middle) and discrimination threshold (right) as a function of test contrast, after adaptation to a high-contrast stimulus. Values are based on simulations of 10,000 trials. The dash-dotted line represents (I_F)^−1/2 in the middle panel and (I_F)^−1/2 normalized by the preadaptation threshold in the right panel. (A) The aware ML decoder predicts no bias, but an increase in threshold at low test contrasts and a decrease at high contrasts. (B) The unaware ML decoder predicts a decrease in apparent contrast and an increase in threshold at low contrasts and a decrease at high contrasts. These characteristics are consistent with the experimental results shown in Figure 7. Again, (I_F)^−1/2 is a relevant bound for the discrimination threshold but not for the standard deviation of the estimates.

Figure 10

Effects of different adaptation behaviors on bias and discriminability. (A) A reduction in maximal responses R_i induces a decrease in apparent contrast and an increase in discrimination threshold. (B) An increase in the slopes n_i of the response functions induces a small decrease in apparent contrast at low test contrasts and a strong increase at high contrast. It also induces a reduction in discrimination threshold for low-medium test contrasts and an increase elsewhere. (C) An increase in the Fano factor (dark gray: variability before adaptation, light gray: after adaptation) results in a slight estimation bias at high contrast and a strong threshold elevation. Solid lines: predictions of ML_unaw. Dash-dot: predictions of ML_aw (I_F ^−1/2 in the middle panel, and I_F^−1/2 normalized by the preadaptation threshold in the right panel).

Figure 11

Potential causes of bias in an optimal estimator. Optimal decoders that are aware of changes in the encoding side, unrestricted, and operate in the asymptotic regime can result in unbiased perception. On the contrary, readouts that are either unaware (and thus, temporarily suboptimal), restricted to a particular form (e.g., linear, local connectivity), or operating in a nonasymptotic regime (e.g., a few neurons or high levels of noise) can lead to perceptual biases.

Figure 12

Predictions of different aware decoders on bias and discriminability. (A) Minimum mean square error (MMSE). (B) Optimal linear estimator (OLE). (C) Winner-take-all (WTA). As found with the aware ML readout, these estimators are unable to account for the perceptual biases found in psychophysics: the biases are absent, very small, or of the wrong sign. Only the discrimination threshold of the MMSE follows closely the bound given by $I_F^{-\frac{1}{2}}$ and exhibits a shape that is similar to that of the experimental data.

Figure 13

Predictions of different unaware decoders on bias and discriminability. (A) Minimum mean-square error (MMSE). (B) Optimal linear estimator (OLE). (C) Winner-take-all (WTA). As found with the unaware ML readout, these estimators exhibit biases and discrimination thresholds that are qualitatively comparable with the psychophysics.