Mikhail Katkov

Singularities in the inverse modeling of 2AFC contrast discrimination data

Analytical calculations show that two-alternative force-choice data are not always suitable for specifying the parameters of the underlying discrimination model. Experimentally, we show here that in the case of contrast discrimination in humans, a variety of models spanning a large range of parameters can explain the data within an experimental error. Monte-Carlo simulations indicate that the number of trials in psychophysical experiments is not the limiting factor in estimating the parameters in contrast discrimination. These results can therefore explain the contradictory conclusions made by different groups about the relationship between the response to contrast and the noise amplitude.

Synaptic Correlates of Working Memory Capacity

Psychological studies indicate that human ability to keep information in readily accessible working memory is limited to four items for most people. This extremely low capacity severely limits execution of many cognitive tasks, but its neuronal underpinnings remain unclear. Here we show that in the framework of synaptic theory of working memory, capacity can be analytically estimated to scale with characteristic time of short-term synaptic depression relative to synaptic current time constant. The number of items in working memory can be regulated by external excitation, enabling the system to be tuned to the desired load and to clear the working memory of currently held items to make room for new ones.

Inverse modeling of human contrast response

Mathematical singularities found in the Signal Detection Theory (SDT) based analysis of the 2-Alternative-Forced-Choice (2AFC) method [Katkov, M., Tsodyks, M., & Sagi, D. (2006a). Analysis of two-alternative force-choice Signal Detection Theory model. Journal of Mathematical Psychology, 50, 411-420; Katkov, M., Tsodyks, M., & Sagi, D. (2006b). Singularities in the inverse modeling of 2AFC contrast discrimination data. Vision Research, 46, 256-266; Katkov, M., Tsodyks, M., & Sagi, D. (2007). Singularities explained: Response to Klein. Vision Research, doi:10.1016/j.visres.2006.10.030] imply that contrast discrimination data obtained with the 2AFC method cannot always be used to reliably estimate the parameters of the underlying model (internal response and noise functions) with a reasonable number of trials. Here we bypass this problem with the Identification Task (IT) where observers identify one of N contrasts. We have found that identification data varies significantly between experimental sessions. Stable estimates using individual session data showed Contrast Response Functions (CRF) with high gain in the low contrast regime and low gain in the high contrast regime. Noise Amplitudes (NA) followed a decreasing function of contrast at low contrast levels, and were practically constant above some contrast level. The transition between these two regimes corresponded approximately to the position of the dipper in the Threshold versus Contrast (TvC) curves that were computed using the estimated parameters and independently measured using 2AFC.

Word length effect in free recall of randomly assembled word lists.

In serial recall experiments, human subjects are requested to retrieve a list of words in the same order as they were presented. In a classical study, participants were reported to recall more words from study lists composed of short words compared to lists of long words, the word length effect. The world length effect was also observed in free recall experiments, where subjects can retrieve the words in any order. Here we analyzed a large dataset from free recall experiments of unrelated words, where short and long words were randomly mixed, and found a seemingly opposite effect: long words are recalled better than the short ones. We show that our recently proposed mechanism of associative retrieval can explain both these observations. Moreover, the direction of the effect depends solely on the way study lists are composed.

Effects of long-term representations on free recall of unrelated words

Human memory stores vast amounts of information. Yet recalling this information is often challenging when specific cues are lacking. Here we consider an associative model of retrieval where each recalled item triggers the recall of the next item based on the similarity between their long-term neuronal representations. The model predicts that different items stored in memory have different probability to be recalled depending on the size of their representation. Moreover, items with high recall probability tend to be recalled earlier and suppress other items. We performed an analysis of a large data set on free recall and found a highly specific pattern of statistical dependencies predicted by the model, in particular negative correlations between the number of words recalled and their average recall probability. Taken together, experimental and modeling results presented here reveal complex interactions between memory items during recall that severely constrain recall capacity.

Singularities explained: Response to Klein

Klein [Klein, A. S. (2006). Separating transducer nonlinearities and multiplicative noise in contrast discrimination. Vision Research, 46, 4279–4293] questions the existence of intrinsic singularities in two-alternative force-choice (2AFC) Signal Detection Theory (SDT) models, suggesting that the singularities found in Katkov et al. [Katkov, M., Tsodyks, M., & Sagi, D. (2006a). Singularities in the inverse modeling of 2AFC contrast discrimination data. Vision Research, 46, 259–266; Katkov, M., Tsodyks, M., & Sagi, D. (2006b). Analysis of two-alternative force-choice Signal Detection Theory model. Journal of Mathematical Psychology, 50, 411–420] are due to discarding higher order terms in the Taylor expansion of d′ and/or limited to steep psychometric functions. Here we provide some simple intuitive examples that illustrate the results described in Katkov et al. (2006a, 2006b). We show, for the constant noise model, that singularities exist when exact values of d′ are computed and that the singularities are not limited to steep psychometric functions. In these cases the disambiguation of the different models requires millions of trials.

Neural Network Model of Memory Retrieval

Human memory can store large amount of information. Nevertheless, recalling is often a challenging task. In a classical free recall paradigm, where participants are asked to repeat a briefly presented list of words, people make mistakes for lists as short as 5 words. We present a model for memory retrieval based on a Hopfield neural network where transition between items are determined by similarities in their long-term memory representations. Meanfield analysis of the model reveals stable states of the network corresponding (1) to single memory representations and (2) intersection between memory representations. We show that oscillating feedback inhibition in the presence of noise induces transitions between these states triggering the retrieval of different memories. The network dynamics qualitatively predicts the distribution of time intervals required to recall new memory items observed in experiments. It shows that items having larger number of neurons in their representation are statistically easier to recall and reveals possible bottlenecks in our ability of retrieving memories. Overall, we propose a neural network model of information retrieval broadly compatible with experimental observations and is consistent with our recent graphical model (Romani et al., 2013).

Decision criteria in dual discrimination tasks estimated using external-noise methods

According to classical signal detection theory (SDT), in simple detection or discrimination tasks, observers use a decision parameter based on their noisy internal response to set a boundary between “yes” and “no” responses. Experimental paradigms where performance is limited by internal noise cannot be used to provide an unambiguous measure of the decision criterion and its variability. Here, unidimensional external noise is used to estimate a criterion and its variability in stimulus space. Within this paradigm, the criterion is defined as the stimulus value separating the two response alternatives. This paradigm allows the assessment of interactions between criteria assigned to different targets in dual tasks. Previous studies suggested that observers’ criteria interacted or even collapsed to one (hence, nonoptimal) criterion. An alternative interpretation of those results is that observers equated their false alarm (FA) rates. The external-noise method enables the confrontation of the two hypotheses. It is shown that the variability of observers’ criterion in stimulus space is about 1.6 times their measured sensory threshold, suggesting that the presence of external noise increases decision uncertainty. Observers’ stimulus criterion settings are close to SDT predictions in single tasks, but not in dual tasks where the two criteria tend to “attract” each other. Observers maintain distinct FA rates even when SDT predicts equal rates. Observers trained in psychophysics or provided with basic notions of SDT exemplified with the present experimental design manage to better separate their criteria in some conditions.

Lateral facilitation--no effect on the target noise level.

The detection threshold of a centrally placed Gabor target is reduced in the presence of aligned high-contrast Gabor patches that are optimally spaced from the target (Polat & Sagi, 1993). Here we determined whether threshold reduction is due to signal enhancement or to decreased signal response variability (internal noise), using a recently developed analysis for a Signal Detection Theory (SDT)-based contrast-identification paradigm (Katkov, Tsodyks, & Sagi, 2007a). We found that flankers did not affect internal noise, but instead caused increased target response when collinear with it, in agreement with the lateral facilitation effect. Based on these results, we concluded that lateral facilitation can be explained by signal enhancement only, and that uncertainty-based models do not provide a satisfactory description of the data.

Memory States and Transitions between Them in Attractor Neural Networks

Human memory is capable of retrieving similar memories to a just retrieved one. This associative ability is at the base of our everyday processing of information. Current models of memory have not been able to underpin the mechanism that the brain could use in order to actively exploit similarities between memories. The current idea is that to induce transitions in attractor neural networks, it is necessary to extinguish the current memory. We introduce a novel mechanism capable of inducing transitions between memories where similarities between memories are actively exploited by the neural dynamics to retrieve a new memory. Populations of neurons that are selective for multiple memories play a crucial role in this mechanism by becoming attractors on their own. The mechanism is based on the ability of the neural network to control the excitation-inhibition balance.