Papers by Alessandro Treves
Under what conditions can prefrontal cortex direct the composition of brain states, to generate c... more Under what conditions can prefrontal cortex direct the composition of brain states, to generate coherent streams of thoughts? Using a simplified Potts model of cortical dynamics, crudely differentiated into two halves, we show that once activity levels are regulated, so as to disambiguate a single temporal sequence, whether the contents of the sequence are mainly determined by the frontal or by the posterior half, or by neither, depends on statistical parameters that describe its microcircuits. The frontal cortex tends to lead if it has more local attractors, longer-lasting and stronger ones, in order of increasing importance. Its guidance is particularly effective to the extent that posterior cortices do not tend to transition from state to state on their own. The result may be related to prefrontal cortex enforcing its temporally-oriented schemata driving coherent sequences of brain states, unlike the atemporal “context” contributed by the hippocampus. Modelling a mild prefrontal ...
The way grid cells represent space in the rodent brain has been a striking discovery, with theore... more The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Differently from hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute-using two alternative mathematical models-the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple non-congruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.
PLOS Computational Biology, 2005
Behaving in the real world requires flexibly combining and maintaining information about both con... more Behaving in the real world requires flexibly combining and maintaining information about both continuous and discrete variables. In the visual domain, several lines of evidence show that neurons in some cortical networks can simultaneously represent information about the position and identity of objects, and maintain this combined representation when the object is no longer present. The underlying network mechanism for this combined representation is, however, unknown. In this paper, we approach this issue through a theoretical analysis of recurrent networks. We present a model of a cortical network that can retrieve information about the identity of objects from incomplete transient cues, while simultaneously representing their spatial position. Our results show that two factors are important in making this possible: A) a metric organisation of the recurrent connections, and B) a spatially localised change in the linear gain of neurons. Metric connectivity enables a localised retrieval of information about object identity, while gain modulation ensures localisation in the correct position. Importantly, we find that the amount of information that the network can retrieve and retain about identity is strongly affected by the amount of information it maintains about position. This balance can be controlled by global signals that change the neuronal gain. These results show that anatomical and physiological properties, which have long been known to characterise cortical networks, naturally endow them with the ability to maintain a conjunctive representation of the identity and location of objects.
bioRxiv (Cold Spring Harbor Laboratory), Jan 29, 2021
An essential role of the hippocampal region is to integrate information to compute and update rep... more An essential role of the hippocampal region is to integrate information to compute and update representations. How this transpires is highly debated. Many theories hinge on the integration of self-motion signals and the existence of continuous attractor networks (CAN). CAN models hypothesise that neurons coding for navigational correlates-such as position and directionreceive inputs from cells conjunctively coding for position, direction and self-motion. As yet, such conjunctive coding had not been found in the hippocampal region. Here, we report neurons coding for angular and linear velocity, distributed across the medial entorhinal cortex, the presubiculum and the parasubiculum. These self-motion neurons often conjunctively encoded position and/or direction, yet lacked a structured organisation, calling for the revision of current CAN models. These results offer insights as to how linear/angular speed-derivative in time of position/direction-may allow the updating of spatial representations, possibly uncovering a generalised algorithm to update any representation. .
We consider a model of associative storage and retrieval of compositional memories in an extended... more We consider a model of associative storage and retrieval of compositional memories in an extended cortical network. Our model network is comprised of Potts units, which represent patches of cortex, interacting through long-range connections. The critical assumption is that a memory is composed of a limited number of items, each of which has a pre-established representation: storing a new memory only involves acquiring the connections, if novel, among the participating items. The model is shown to have a much lower storage capacity than when it stores simple unitary representations. It is also shown that an input from the hippocampus facilitates associative retrieval. When it is absent, it is advantageous to cue rare rather than frequent items. The implications of these results for emerging trends in empirical research are discussed.
We study latching dynamics in the adaptive Potts model network, through numerical simulations wit... more 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 so 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 Effect of Slow Synaptic Coupling on Populations of Spiking Neurons
Springer eBooks, 1993
We examine the conditions under which a population of spiking neurons with all-to-all excitatory ... more We examine the conditions under which a population of spiking neurons with all-to-all excitatory coupling can fire asynchronously. Synapses with time constants satisfying computed constraints assure the stability of an asynchronous firing state even in the absense of inhibition.
Hippocampus, Jul 24, 2019
Nearby grid cells have been observed to express a remarkable degree of long-range order, which is... more Nearby grid cells have been observed to express a remarkable degree of long-range order, which is often idealized as extending potentially to infinity. Yet their strict periodic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.
arXiv (Cornell University), Jul 6, 2023
Parametric approaches to grammatical diversity range from Chomsky's 1981 classical Principles & P... more Parametric approaches to grammatical diversity range from Chomsky's 1981 classical Principles & Parameters model to minimalist reinterpretations: in some proposals of the latter framework, parameters need not be an extensional list given at the initial state S0 of the mind, but can be constructed through a bio-program in the course of language development. In this contribution we pursue this lead and discuss initial data and ideas relevant for the elaboration of three sets of questions: 1) how can binary parameters be conceivably implemented in cortical and subcortical circuitry in the human brain? 2) how can parameter mutations be taken to occur? 3) given the distribution of parameter values across languages and their implications, can multi-parental models of language phylogenies, departing from ultrametricity, also account for some of the available evidence?
Facial Expressions, Computational Perspectives
Encyclopedia of the Mind, Mar 1, 2013
bioRxiv (Cold Spring Harbor Laboratory), Oct 10, 2022
We consider a model of associative storage and retrieval of compositional memories in an extended... more We consider a model of associative storage and retrieval of compositional memories in an extended cortical network. Our model network is comprised of Potts units, which represent patches of cortex, interacting through long-range connections. The critical assumption is that a memory is composed of a limited number of items, each of which has a pre-established representation: storing a new memory only involves acquiring the connections, if novel, among the participating items. The model is shown to have a much lower storage capacity than when it stores simple unitary representations. It is also shown that an input from the hippocampus facilitates associative retrieval. When it is absent, it is advantageous to cue rare rather than frequent items. The implications of these results for emerging trends in empirical research are discussed.
Neural Computation, Dec 1, 2019
The way grid cells represent space in the rodent brain has been a striking discovery, with theore... more The way grid cells represent space in the rodent brain has been a striking discovery, with theoretical implications still unclear. Differently from hippocampal place cells, which are known to encode multiple, environment-dependent spatial maps, grid cells have been widely believed to encode space through a single low dimensional manifold, in which coactivity relations between different neurons are preserved when the environment is changed. Does it have to be so? Here, we compute-using two alternative mathematical models-the storage capacity of a population of grid-like units, embedded in a continuous attractor neural network, for multiple spatial maps. We show that distinct representations of multiple environments can coexist, as existing models for grid cells have the potential to express several sets of hexagonal grid patterns, challenging the view of a universal grid map. This suggests that a population of grid cells can encode multiple non-congruent metric relationships, a feature that could in principle allow a grid-like code to represent environments with a variety of different geometries and possibly conceptual and cognitive spaces, which may be expected to entail such context-dependent metric relationships.
Entropy, Oct 26, 2018
A statistical analysis of semantic memory should reflect the complex, multifactorial structure of... more A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through "factors" that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a dataset of nouns. We find that such correlations reduce the storage capacity of a Potts network to a limited extent, so that the number of concepts that can be stored and retrieved in a large, human-scale cortical network may still be of order 10 7 , as originally estimated without correlations. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving's remember/know paradigms.
Oxford University Press eBooks, Nov 3, 2016
AIMS neuroscience, 2020
Are the grid cells discovered in rodents relevant to human cognition? Following up on two seminal... more Are the grid cells discovered in rodents relevant to human cognition? Following up on two seminal studies by others, we aimed to check whether an approximate 6-fold, grid-like symmetry shows up in the cortical activity of humans who "navigate" between vowels, given that vowel space can be approximated with a continuous trapezoidal 2D manifold, spanned by the first and second formant frequencies. We created 30 vowel trajectories in the assumedly flat central portion of the trapezoid. Each of these trajectories had a duration of 240 milliseconds, with a steady start and end point on the perimeter of a "wheel". We hypothesized that if the neural representation of this "box" is similar to that of rodent grid units, there should be an at least partial hexagonal (6-fold) symmetry in the EEG response of participants who navigate it. We have not found any dominant n-fold symmetry, however, but instead, using PCAs, we find indications that the vowel representation may reflect phonetic features, as positioned on the vowel manifold. The suggestion, therefore, is that vowels are encoded in relation to their salient sensory-perceptual variables, and are not assigned to arbitrary gridlike abstract maps. Finally, we explored the relationship between the first PCA eigenvector and putative vowel attractors for native Italian speakers, who served as the subjects in our study.
arXiv (Cornell University), 2008
Multielectrode arrays allow recording of the activity of many single neurons, from which correlat... more Multielectrode arrays allow recording of the activity of many single neurons, from which correlations can be calculated. The functional roles of correlations can be revealed by the measures of the information conveyed by neuronal activity; a simple formula has been shown to discriminate the information transmitted by individual spikes from the positive or negative contributions due to correlations (Panzeri et al, Proc. Roy. Soc. B., 266: 1001-1012 (1999)). The formula quantifies the corrections to the single-unit instantaneous information rate which result from correlations in spike emission between pairs of neurons. Positive corrections imply synergy, while negative corrections indicate redundancy. Here, this analysis, previously applied to recordings from small ensembles, is developed further by considering a model of a large ensemble, in which correlations among the signal and noise components of neuronal firing are small in absolute value and entirely random in origin. Even such small random correlations are shown to lead to large possible synergy or redundancy, whenever the time window for extracting information from neuronal firing extends to the order of the mean interspike interval. In addition, a sample of recordings from rat barrel cortex illustrates the mean time window at which such 'corrections' dominate when correlations are, as often in the real brain, neither random nor small. The presence of this kind of correlations for a large ensemble of cells restricts further the time of validity of the expansion, unless what is decodable by the receiver is also taken into account.
Nature Communications, Apr 7, 2022
An essential role of the hippocampal region is to integrate information to compute and update rep... more An essential role of the hippocampal region is to integrate information to compute and update representations. How this transpires is highly debated. Many theories hinge on the integration of self-motion signals and the existence of continuous attractor networks (CAN). CAN models hypothesise that neurons coding for navigational correlatessuch as position and directionreceive inputs from cells conjunctively coding for position, direction, and selfmotion. As yet, very little data exist on such conjunctive coding in the hippocampal region. Here, we report neurons coding for angular and linear velocity, uniformly distributed across the medial entorhinal cortex (MEC), the presubiculum and the parasubiculum, except for MEC layer II. Self-motion neurons often conjunctively encoded position and/or direction, yet lacked a structured organisation. These results offer insights as to how linear/angular speedderivative in time of position/directionmay allow the updating of spatial representations, possibly uncovering a generalised algorithm to update any representation.
PLOS Computational Biology, Mar 21, 2008
Behaving in the real world requires flexibly combining and maintaining information about both con... more Behaving in the real world requires flexibly combining and maintaining information about both continuous and discrete variables. In the visual domain, several lines of evidence show that neurons in some cortical networks can simultaneously represent information about the position and identity of objects, and maintain this combined representation when the object is no longer present. The underlying network mechanism for this combined representation is, however, unknown. In this paper, we approach this issue through a theoretical analysis of recurrent networks. We present a model of a cortical network that can retrieve information about the identity of objects from incomplete transient cues, while simultaneously representing their spatial position. Our results show that two factors are important in making this possible: A) a metric organisation of the recurrent connections, and B) a spatially localised change in the linear gain of neurons. Metric connectivity enables a localised retrieval of information about object identity, while gain modulation ensures localisation in the correct position. Importantly, we find that the amount of information that the network can retrieve and retain about identity is strongly affected by the amount of information it maintains about position. This balance can be controlled by global signals that change the neuronal gain. These results show that anatomical and physiological properties, which have long been known to characterise cortical networks, naturally endow them with the ability to maintain a conjunctive representation of the identity and location of objects.
Part 3. Coding and representation
Oxford University Press eBooks, May 14, 2009
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Papers by Alessandro Treves