Life on the Edge: Latching Dynamics in a Potts Neural Network

Abstract

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.

Continuous attractors for dynamic memories

“…The production of sequences of discrete memories can be implemented with a heteroassociative component [31], usually dependent on the time integral of the instantaneous activity, that brings the network out of equilibrium and to the next step in the sequence. A similar effect can be obtained with an adaptation mechanism in a coarse grained model of cortical networks [32], with the difference that in this case the transitions are not imposed, but driven by the correlations between the memories in so-called latching dynamics [33], [34]. Moreover, adaptation-based mechanisms have been used to model the production of random sequences on continuous manifolds [35], and shown to be crucial in determining the balance between retrieval and prediction in a network describing CA3-CA1 interactions [36].…”

Professional or Amateur? The Phonological Output Buffer as a Working Memory Operator

“…To simplify the analysis, we write and assume the component to be very fast, and the very slow, both being driven up by recent activity in patch i . As discussed elsewhere [ 99 ], the dynamical behaviour of the Potts model is complex, different in distinct regions or phases of parameter space. It shows latching dynamics in a wider region, if both inhibitory fast and slow components are included.…”

“…Increasing the number of learned patterns, from to to , the length of the sequence increases, but eventually to the detriment of the quality of retrieval. In [ 99 ], narrow bands are identified in and planes, where lengthy latching sequences co-exist together with good retrieval of each individual attractor visited by the network, both when inhibition is slow and when it is fast. Whichever parameter one considers, in fact, one finds that it can vary only in a narrow range between when latching is limited in duration and when its quality deteriorates.…”

Information Theory in Neuroscience

“…These techniques have potential for a wide range of applications, not least of which is the study of how consciousness emerges from the dynamics of the brain. Other work uses information theory as a tool to investigate different aspects of brain dynamics, from latching in neural networks [ 23 ], to the long-term development dynamics of the human brain studied using functional imaging data [ 24 ], to rapid information processing possibly mediated by the synfire chains [ 25 ] that have been reported in studies of simultaneously-recorded spike trains [ 26 ]. Other studies attempt to bridge between information theory and the theory of inference [ 27 ] and of categorical perception mediated by representation similarity in neural activity [ 28 ].…”