An autoassociative network of Potts units, coupled via tensor connections, has been proposed and analysed as an effective model of an extensive cortical network with distinct short-and long-range synaptic connections, but it has not been clarified in what sense it can be regarded as an effective model. We draw here the correspondence between the two, which indicates the need to introduce a local feedback term in the reduced model, i.e., in the Potts network. An effective model allows the study of phase transitions. As an example, we study the storage capacity of the Potts network with this additional term, the local feedback w, which contributes to drive the activity of the network towards one of the stored patterns. The storage capacity calculation, performed using replica tools, is limited to fully connected networks, for which a Hamiltonian can be defined. To extend the results to the case of intermediate partial connectivity, we also derive the self-consistent signal-to-noise analysis for the Potts network; and finally we discuss implications for semantic memory in humans.
Abstract:We study latching dynamics in the adaptive Potts model network, through numerical simulations with randomly and also weakly correlated patterns, and we focus on comparing its slowly and fast adapting regimes. A measure, Q, is used to quantify the quality of latching in the phase space spanned by the number of Potts states S, the number of connections per Potts unit C and the number of stored memory patterns p. We find narrow regions, or bands in phase space, where distinct pattern retrieval and duration of latching combine to yield the highest values of Q. The bands are confined by the storage capacity curve, for large p, and by the onset of finite latching, for low p. Inside the band, in the slowly adapting regime, we observe complex structured dynamics, with transitions at high crossover between correlated memory patterns; while away from the band latching, transitions lose complexity in different ways: below, they are clear-cut but last such few steps as to span a transition matrix between states with few asymmetrical entries and limited entropy; while above, they tend to become random, with large entropy and bi-directional transition frequencies, but indistinguishable from noise. Extrapolating from the simulations, the band appears to scale almost quadratically in the p-S plane, and sublinearly in p-C. In the fast adapting regime, the band scales similarly, and it can be made even wider and more robust, but transitions between anti-correlated patterns dominate latching dynamics. This suggest that slow and fast adaptation have to be integrated in a scenario for viable latching in a cortical system. The results for the slowly adapting regime, obtained with randomly correlated patterns, remain valid also for the case with correlated patterns, with just a simple shift in phase space.
The central tendency bias, or contraction bias is a phenomenon where the judgment of the magnitude of items held in working memory is biased towards the average of past observations. This phenomenon has been first described more than a century ago [1] and since then, has been replicated in various decision making tasks in humans [2–10], and rodents [11, 12]. Contraction bias is assumed to be an optimal strategy by the brain, given the noisy nature of working memory. From a Bayesian perspective [7], the progressive shift of the noisy memory towards the mean of a prior distribution built from past sensory experience helps with more accurate estimates of the memory. In this work, we propose an alternative account, via short-term history biases (serial dependence) [12–15]. Our model is motivated and inspired by recent results from an auditory delayed-discrimination task in rats, where the posterior parietal cortex (PPC) has been shown to be critical to these memory effects [12]. The dynamics of our model suggests that contraction bias can emerge as a result of a volatile working memory content which makes it susceptible to shifting to the past sensory experience. The errors, at the level of individual trials, are sampled from the full distribution of the stimuli, and are not due to a gradual shift of the memory towards the distribution’s mean. Our model explains both short-term history biases, as well as contraction bias towards the sensory mean for the averaged performance. The results are consistent with the role of the PPC in encoding such sensory history biases, and provide predictions of performance across different stimulus distributions and timings, delay intervals, as well as neuronal dynamics in putative working memory areas.
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