Higher cognitive capacities, such as navigating complex environments or learning new languages, rely on the possibility to memorize, in the brain, continuous noisy variables. Memories are generally understood to be realized, e.g. in the cortex and in the hippocampus, as configurations of activity towards which specific populations of neurons are “attracted”, i.e towards which they dynamically converge, if properly cued. Distinct memories are thus considered as separate attractors of the dynamics, embedded within the same neuronal connectivity structure. But what if the underlying variables are continuous, such as a position in space or the resonant frequency of a phoneme? If such variables are continuous and the experience to be retained in memory has even a minimal temporal duration, highly correlated, yet imprecisely determined values of those variables will occur at successive time instants. And if memories are idealized as point-like in time, still distinct memories will be highly correlated. How does the brain self-organize to deal with noisy correlated memories? In this thesis, we try to approach the question along three interconnected itineraries. In Part II we first ask the opposite: we derive how many uncorrelated memories a network of neurons would be able to precisely store, as discrete attractors, if the neurons were optimally connected. Then, we compare the results with those obtained when memories are allowed to be retrieved imprecisely and connections are based on self-organization. We find that a simple strategy is available in the brain to facilitate the storage of memories: it amounts to making them more sparse, i.e. to silencing those neurons which are not very active in the configuration of activity to be memorized. We observe that the more the distribution of activity in the memory is complex, the more this strategy leads to store a higher number of memories, as compared with the maximal load in networks endowed with the theoretically optimal connection weights. In part III we ask, starting from experimental observations of spatially selective cells in quasi-realistic environments, how can the brain store, as a continuous attractor, complex and irregular spatial information. We find indications that while continuous attractors, per se, are too brittle to deal with irregularities, there seem to be other mathematical objects, which we refer to as quasi-attractive continuous manifolds, which may have this function. Such objects, which emerge as soon as a tiny amount of quenched irregularity is introduced in would-be continuous attractors, seem to persist over a wide range of noise levels and then break up, in a phase transition, when the variability reaches a critical threshold, lying just above that seen in the experimental measurements. Moreover, we find that the operational range is squeezed from behind, as it were, by a third phase, in which the spatially selective units cannot dynamically converge towards a localized state. Part IV, which is more exploratory, is motivated by the frequency characteristics of vowels. We hypothesize that also phonemes of different languages could be stored as separate fixed points in the brain through a sort of two-dimensional cognitive map. In our preliminary results, we show that a continuous quasi-attractor model, trained with noisy recorded vowels, can effectively learn them through a self-organized procedure and retrieve them separately, as fixed points on a quasi-attractive manifold. Overall, this thesis attempts to contribute to the search for general principles underlying memory, intended as an emergent collective property of networks in the brain, based on self-organization, imperfections and irregularities.

Memories, attractors, space and vowels / Schonsberg, Francesca. - (2021 Jul 15).

Memories, attractors, space and vowels

Schonsberg, Francesca
2021-07-15

Abstract

Higher cognitive capacities, such as navigating complex environments or learning new languages, rely on the possibility to memorize, in the brain, continuous noisy variables. Memories are generally understood to be realized, e.g. in the cortex and in the hippocampus, as configurations of activity towards which specific populations of neurons are “attracted”, i.e towards which they dynamically converge, if properly cued. Distinct memories are thus considered as separate attractors of the dynamics, embedded within the same neuronal connectivity structure. But what if the underlying variables are continuous, such as a position in space or the resonant frequency of a phoneme? If such variables are continuous and the experience to be retained in memory has even a minimal temporal duration, highly correlated, yet imprecisely determined values of those variables will occur at successive time instants. And if memories are idealized as point-like in time, still distinct memories will be highly correlated. How does the brain self-organize to deal with noisy correlated memories? In this thesis, we try to approach the question along three interconnected itineraries. In Part II we first ask the opposite: we derive how many uncorrelated memories a network of neurons would be able to precisely store, as discrete attractors, if the neurons were optimally connected. Then, we compare the results with those obtained when memories are allowed to be retrieved imprecisely and connections are based on self-organization. We find that a simple strategy is available in the brain to facilitate the storage of memories: it amounts to making them more sparse, i.e. to silencing those neurons which are not very active in the configuration of activity to be memorized. We observe that the more the distribution of activity in the memory is complex, the more this strategy leads to store a higher number of memories, as compared with the maximal load in networks endowed with the theoretically optimal connection weights. In part III we ask, starting from experimental observations of spatially selective cells in quasi-realistic environments, how can the brain store, as a continuous attractor, complex and irregular spatial information. We find indications that while continuous attractors, per se, are too brittle to deal with irregularities, there seem to be other mathematical objects, which we refer to as quasi-attractive continuous manifolds, which may have this function. Such objects, which emerge as soon as a tiny amount of quenched irregularity is introduced in would-be continuous attractors, seem to persist over a wide range of noise levels and then break up, in a phase transition, when the variability reaches a critical threshold, lying just above that seen in the experimental measurements. Moreover, we find that the operational range is squeezed from behind, as it were, by a third phase, in which the spatially selective units cannot dynamically converge towards a localized state. Part IV, which is more exploratory, is motivated by the frequency characteristics of vowels. We hypothesize that also phonemes of different languages could be stored as separate fixed points in the brain through a sort of two-dimensional cognitive map. In our preliminary results, we show that a continuous quasi-attractor model, trained with noisy recorded vowels, can effectively learn them through a self-organized procedure and retrieve them separately, as fixed points on a quasi-attractive manifold. Overall, this thesis attempts to contribute to the search for general principles underlying memory, intended as an emergent collective property of networks in the brain, based on self-organization, imperfections and irregularities.
15-lug-2021
Treves, Alessandro
Schonsberg, Francesca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/123841
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