A neural microcircuit model for a scalable scale‐invariant representation of time

Liu, Yue; Tiganj, Zoran; Hasselmo, Michael E.; Howard, Marc W.

doi:10.1002/hipo.22994

Cited by 52 publications

(49 citation statements)

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“…Similarly, slow changes in firing rate were observed in the EC of rats during trace eyeblink conditioning across distinct environmental contexts 39 . Computational modeling studies have suggested that properties of calcium non-specific cation current observed in slice are sufficient to generate a spectrum of response decay periods, ranging from brief to prolonged 40,41 . Juxtaposed with work showing spatial responses in navigating rodents [42][43][44] , these findings suggest EC neurons code for "position" in both temporal and spatial domains.…”

Section: Discussionmentioning

confidence: 99%

A temporal record of the past with a spectrum of time constants in the monkey entorhinal cortex

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Episodic memory is believed to be intimately related to our experience of the passage of time. Indeed, neurons in the hippocampus and other brain regions critical to episodic memory code for the passage of time at a range of time scales. The origin of this temporal signal, however, remains unclear. Here, we examined temporal responses in the entorhinal cortex of macaque monkeys as they viewed complex images. Many neurons in the entorhinal cortex were responsive to image onset, showing large deviations from baseline firing shortly after image onset but relaxing back to baseline at different rates. This range of relaxation rates allowed for the time since image onset to be decoded on the scale of seconds. Further, the ensemble carried information about image content suggesting that neurons in the entorhinal cortex carry information not only about when an event took place but also the identity of that event. Taken together, these findings suggest that the primate entorhinal cortex uses a spectrum of time constants to construct a temporal record of the past in support of episodic memory.Episodic memory, the vivid recollection of an event situated in a specific time and place 1 , depends critically on medial temporal lobe (MTL) structures, including the hippocampus and entorhinal cortex (EC) 2-5 . Building on pioneering work demonstrating a spatial code in the hippocampus and entorhinal cortex 6,7 , recent research has shown that hippocampal representations also carry information about the time at which past events took place, suggesting that the MTL maintains a representation of spatiotemporal context in support of episodic memory [8][9][10] . Although a great deal is known about the temporal coding properties of neurons in the hippocampus, the temporal code in the entorhinal cortex, which provides the majority of the cortical input to the hippocampus is less understood, but see [11][12][13][14] .Hippocampal time cells provide a record of recent events including explicit information about when an event occurred. Analogous to hippocampal place cells that fire when an animal is in a circumscribed region of physical space 6, 15 , hippocampal time cells fire during a circumscribed period of time within unfilled delays 8,9,16 . Across studies, there is a remarkable consistency in the properties of hippocampal time cells. Hippocampal time cells peak at a range of times during the delay interval and typically code time with decreasing accuracy as the delay unfolds, as manifest 1 by fewer neurons with peak firing late in the delay and wider time fields later in the delay 12,17,18 . Hippocampal time cells have been observed in a wide range of behavioral paradigms, including tasks with and without explicit memory demands during the delay 17 and experiments in which the animal is fixed in space 19,20 . In addition, it has been shown that different stimuli trigger different time cell sequences 19,20 . Taken together, time cells provide an explicit record of how far in the past an event took place, i.e., the amount of time that h...

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Section: Discussionmentioning

confidence: 99%

A temporal record of the past with a spectrum of time constants in the monkey entorhinal cortex

Bright

Meister

Cruzado

et al. 2019

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“…In vitro slice experiments and modeling works have shown that a spectrum of slow timescales can be obtained in single cells by utilizing the slow dynamics of calcium-dependent currents (Loewenstein and Sompolinsky (2003); Egorov et al (2002); Fransén et al (2002); Mongillo et al (2008); Tiganj et al (2015); Liu et al (2018)). In vivo experiments also showed a spectrum of timescales in cortical dynamics, both on the single cell and the population level.…”

Section: Discussionmentioning

confidence: 99%

“…It should be noted that the geometric series of time constants required by Constraint 1 do not necessarily have to be an emergent property of the network, but can instead be driven by physiological properties of single cells (Loewenstein and Sompolinsky (2003); Fransén et al (2002); Tiganj et al (2015); Liu et al (2018)). Consequently, scale-invariant sequential activity could also be generated by feedforward networks where the neurons in the first layer receive inputs and decay exponentially with a geometric series of intrinsic time constants, and the a.…”

Section: A Special Case: Laplace and Inverse Laplace Transformsmentioning

confidence: 99%

“…As the activation spreads across the chain, the spread in time accumulates. However, as can be shown via the Central Limit theorem, the sequential activity is not scale-invariant because peak time of the ith unit goes up linearly in i but the width of the peak goes up with √ i (Liu et al (2018)). Here we show that the eigenvalues and eigenvectors of the connectivity matrix of this simple model (Eq.…”

Section: Simple Feedforward Chaining Modelmentioning

confidence: 99%

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Generation of scale-invariant sequential activity in linear recurrent networks

Liu

Howard

2019

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Sequential neural activity has been observed in many parts of the brain and has been proposed as a neural mechanism for memory. The natural world expresses temporal relationships at a wide range of scales. Because we cannot know the relevant scales a priori it is desirable that memory, and thus the generated sequences, are scale-invariant. Although recurrent neural network models have been proposed as a mechanism for generating sequences, the requirements for scale-invariant sequences are not known. This paper reports the constraints that enable a linear recurrent neural network model to generate scale-invariant sequential activity. A straightforward eigendecomposition analysis results in two independent conditions that are required for scale-invariance. First the eigenvalues of the network must be geometrically spaced. Second, the eigenvectors must be related to one another via translation. These constraints, along with considerations on initial conditions, provide a general recipe to build linear recurrent neural networks that support scale-invariant sequential activity.(2016); Tiganj et al. (2018)). The firing fields of time cells that fire later in the delay period are wider than the firing fields of time cells that fire earlier in the delay period.Many researchers have studied recurrent neural networks that generate sequential activity (Goldman (2009); Rajan et al. (2016); Wang et al. (2018)), but not many of these works considered scale-invariant sequences (but see Voelker and Eliasmith (2018)). In this paper we seek to identify general constraints on the network connectivity for the generation of scale-invariant neural sequences in recurrent neural networks. We study a linear network of interacting neurons. The f-I curve of many neurons are observed to be largely linear (e.g. Chance et al. (2002)). The learning dynamics of linear feedforward neural networks exhibit many similarities compared to their non-linear counterparts (Saxe et al. (2013)). Therefore linear neural networks provide a good model for studying systems-level properties of real neuronal circuits.The paper is organized as follows. In Section 2 the network constraints for the generation of scale-invariant neural sequences are derived analytically. In Section 3 two example networks with different single cell dynamics are constructed to illustrate the mathematical result. In Section 4, we compare the eigenvectors and eigenvalues of a chaining model and a random recurrent network with those of the examples in Section 3. It is shown that neither of these networks satisfy the structural constraints derived from Section 2, therefore neither of them support sequential neural activity that is scale-invariant.

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“…Computational modeling has addressed the mechanism for generation of time cells. One type of model uses a mechanism similar to a Laplace transform (Howard et al, 2014;Liu, Tiganj, Hasselmo, & Howard, 2018), in which neurons exhibit exponential decay relative to a temporal cue (Tiganj, Hasselmo, & Howard, 2015). This model is supported by the existence of both time cells and neurons that show exponential decay of firing rate over time intervals (Tahvildari, Fransen, Alonso, & Hasselmo, 2007;Tsao et al, 2018).…”

Section: Data Supports Neural Coding Of Timementioning

confidence: 99%

Overview of computational models of hippocampus and related structures: Introduction to the special issue

et al. 2020

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Extensive computational modeling has focused on the hippocampal formation and associated cortical structures. This overview describes some of the factors that have motivated the strong focus on these structures, including major experimental findings and their impact on computational models. This overview provides a framework for describing the topics addressed by individual articles in this special issue of the journal Hippocampus.

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A neural microcircuit model for a scalable scale‐invariant representation of time

Cited by 52 publications

References 58 publications

A temporal record of the past with a spectrum of time constants in the monkey entorhinal cortex

A temporal record of the past with a spectrum of time constants in the monkey entorhinal cortex

Generation of scale-invariant sequential activity in linear recurrent networks

Overview of computational models of hippocampus and related structures: Introduction to the special issue

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