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Head direction network. HD cells excite their close neighbours strongly and more distant neighbours less strongly, and this selfexcitation creates the HD activity bump. The HD cells also excite the asymmetric AHV cells using a similar neighbourhood relation. The left turn AHV cells then project back to the HD cells with an offset in one direction ( " leftwards " ) and the right turn AHV cells project back to the HD cells with offset in the other direction ( " rightwards " ). These  

Head direction network. HD cells excite their close neighbours strongly and more distant neighbours less strongly, and this selfexcitation creates the HD activity bump. The HD cells also excite the asymmetric AHV cells using a similar neighbourhood relation. The left turn AHV cells then project back to the HD cells with an offset in one direction ( " leftwards " ) and the right turn AHV cells project back to the HD cells with offset in the other direction ( " rightwards " ). These  

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Continuous attractor networks require calibration. Computational models of the head direction (HD) system of the rat usually assume that the connections that maintain HD neuron activity are pre-wired and static. Ongoing activity in these models relies on precise continuous attractor dynamics. It is currently unknown how such connections could be so...

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... The generation of HD tuning is believed to involve AHV cells in ring attractor models. [9,50] A recent report showed that AHV cells can be found alongside HD cells in the neighboring motor cortex. [51] Therefore, we hypothesized AHV cells should be present in the S1. ...
... Along with RS/ putative excitatory HD cells, all basic components of a theorized ring attractor are present within the S1 for de novo HD signal generation. [50] However, none of the examined brain areas exhibiting HD tuning is independent of the canonical HD circuit; [51,[84][85][86][87] It is currently unknown whether our S1 HD cells are dependent on the canonical HD circuit, since FS HD cells appear to have many different physiological properties compared to canonical HD cells. In our previous report, we suggested that S1 spatial selectivity is likely to be an efferent copy inherited from elsewhere, possibly from motor areas, given their extensive functional and anatomical connections. ...
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Head direction (HD) cells form a fundamental component in the brain's spatial navigation system and are intricately linked to spatial memory and cognition. Although HD cells have been shown to act as an internal neuronal compass in various cortical and subcortical regions, the neural substrate of HD cells is incompletely understood. It is reported that HD cells in the somatosensory cortex comprise regular‐spiking (RS, putative excitatory) and fast‐spiking (FS, putative inhibitory) neurons. Surprisingly, somatosensory FS HD cells fire in bursts and display much sharper head‐directionality than RS HD cells. These FS HD cells are nonconjunctive, rarely theta rhythmic, sparsely connected and enriched in layer 5. Moreover, sharply tuned FS HD cells, in contrast with RS HD cells, maintain stable tuning in darkness; FS HD cells’ coexistence with RS HD cells and angular head velocity (AHV) cells in a layer‐specific fashion through the somatosensory cortex presents a previously unreported configuration of spatial representation in the neocortex. Together, these findings challenge the notion that FS interneurons are weakly tuned to sensory stimuli, and offer a local circuit organization relevant to the generation and transmission of HD signaling in the brain. Head direction cells act as an internal neuronal compass in the brain's spatial navigation system. However, the neuronal substrate of head direction cells remains poorly understood. Long and co‐workers first identify sharply tuned fast‐spiking head direction cells in somatosensory cortex that fire in bursts. Their findings uncover the cellular basis for somatosensory head direction cells different from their classical hippocampal counterpart.
... Other models have explored more biologically plausible architectures with spiking neural networks (e.g. [27,31,32,37,38]). For the purpose of modelling, the attractor is assumed to substitute not only the entire generative circuitry for HD signals (i.e. ...
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Environmental information is required to stabilize estimates of head direction (HD) based on angular path integration. However, it is unclear how this happens in real-world (visually complex) environments. We present a computational model of how visual feedback can stabilize HD information in environments that contain multiple cues of varying stability and directional specificity. We show how combinations of feature-specific visual inputs can generate a stable unimodal landmark bearing signal, even in the presence of multiple cues and ambiguous directional specificity. This signal is associated with the retrosplenial HD signal (inherited from thalamic HD cells) and conveys feedback to the subcortical HD circuitry. The model predicts neurons with a unimodal encoding of the egocentric orientation of the array of landmarks, rather than any one particular landmark. The relationship between these abstract landmark bearing neurons and head direction cells is reminiscent of the relationship between place cells and grid cells. Their unimodal encoding is formed from visual inputs via a modified version of Oja’s Subspace Algorithm. The rule allows the landmark bearing signal to disconnect from directionally unstable or ephemeral cues, incorporate newly added stable cues, support orientation across many different environments (high memory capacity), and is consistent with recent empirical findings on bidirectional HD firing reported in the retrosplenial cortex. Our account of visual feedback for HD stabilization provides a novel perspective on neural mechanisms of spatial navigation within richer sensory environments, and makes experimentally testable predictions.
... The underlying circuit therefore combines idiothetic and allothetic information into a coherent heading signal. Overall, this neuronal activity appears to constitute an internal encoding of heading in the insect's CX, which closely resembles the hypothetical ring attractor (Amari, 1977) proposed by Skaggs et al., 1995 to account for the rat 'head direction' cells (Taube et al., 1990;Blair and Sharp, 1995;Redish et al., 1996;Stackman and Taube, 1998;Goodridge et al., 1998;Goodridge and Touretzky, 2000;Sharp et al., 2001;Taube and Bassett, 2003;Stratton et al., 2010). That is, the activity has the following key properties associated with ring attractors: input to the circuit results in a single localised 'bump' of activity -centred in one subset of the neurons -while other neuronal units are silenced; the activity 'bump' can move around the attractor space, which forms a ring, in a manner that consistently tracks some property of the input; and the 'bump' of activity is maintained for some time after all input is removed. ...
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... The underlying circuit therefore combines idiothetic and allothetic information into a coherent heading signal. Overall, this neuronal activity appears to constitute an internal encoding of heading in the insect's CX, which closely resembles the hypothetical ring attractor (Amari, 1977) proposed by Skaggs et al., 1995 to account for the rat 'head direction' cells (Taube et al., 1990;Blair and Sharp, 1995;Redish et al., 1996;Stackman and Taube, 1998;Goodridge et al., 1998;Goodridge and Touretzky, 2000;Sharp et al., 2001;Taube and Bassett, 2003;Stratton et al., 2010). That is, the activity has the following key properties associated with ring attractors: input to the circuit results in a single localised 'bump' of activity -centred in one subset of the neurons -while other neuronal units are silenced; the activity 'bump' can move around the attractor space, which forms a ring, in a manner that consistently tracks some property of the input; and the 'bump' of activity is maintained for some time after all input is removed. ...
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Recent studies of the Central Complex in the brain of the fruit fly have identified neurons with activity that tracks the animal’s heading direction. These neurons are part of a neuronal circuit with dynamics resembling those of a ring attractor. The homologous circuit in other insects has similar topographic structure but with significant structural and connectivity differences. We model the connectivity patterns of two insect species to investigate the effect of these differences on the dynamics of the circuit. We illustrate that the circuit found in locusts can also operate as a ring attractor but differences in the inhibition pattern enable the fruit fly circuit to respond faster to heading changes while additional recurrent connections render the locust circuit more tolerant to noise. Our findings demonstrate that subtle differences in neuronal projection patterns can have a significant effect on circuit performance and illustrate the need for a comparative approach in neuroscience.
... The underlying circuit therefore combines idiothetic and allothetic information into a coherent heading signal. Overall, this neuronal activity appears to constitute an internal encoding of heading in the insect's CX, which closely resembles the hypothetical ring attractor (Amari, 1977) proposed by Skaggs et al., 1995 to account for the rat 'head direction' cells (Taube et al., 1990;Blair and Sharp, 1995;Redish et al., 1996;Stackman and Taube, 1998;Goodridge et al., 1998;Goodridge and Touretzky, 2000;Sharp et al., 2001;Taube and Bassett, 2003;Stratton et al., 2010). That is, the activity has the following key properties associated with ring attractors: input to the circuit results in a single localised 'bump' of activity -centred in one subset of the neurons -while other neuronal units are silenced; the activity 'bump' can move around the attractor space, which forms a ring, in a manner that consistently tracks some property of the input; and the 'bump' of activity is maintained for some time after all input is removed. ...
Article
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Recent studies of the Central Complex in the brain of the fruit fly have identified neurons with activity that tracks the animal’s heading direction. These neurons are part of a neuronal circuit with dynamics resembling those of a ring attractor. The homologous circuit in other insects has similar topographic structure but with significant structural and connectivity differences. We model the connectivity patterns of two insect species to investigate the effect of these differences on the dynamics of the circuit. We illustrate that the circuit found in locusts can also operate as a ring attractor but differences in the inhibition pattern enable the fruit fly circuit to respond faster to heading changes while additional recurrent connections render the locust circuit more tolerant to noise. Our findings demonstrate that subtle differences in neuronal projection patterns can have a significant effect on circuit performance and illustrate the need for a comparative approach in neuroscience.
... The detailed mapping of the HD neuronal circuits gave rise to a Spiking Neural Network (SNN) model in which persistent activity is realized through cross-inhibition rather than through recurrent excitation, as previously assumed (Song and Wang, 2005). The function of the HD network is to act as a neural integrator that is supervised by visual signals (Hahnloser, 2003) and supposedly is calibrated through angular velocity signals (Stratton et al., 2010). ...
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In this work, we present a neuromorphic architecture for head pose estimation and scene representation for the humanoid iCub robot. The spiking neuronal network is fully realized in Intel's neuromorphic research chip, Loihi, and precisely integrates the issued motor commands to estimate the iCub's head pose in a neuronal path-integration process. The neuromorphic vision system of the iCub is used to correct for drift in the pose estimation. Positions of objects in front of the robot are memorized using on-chip synaptic plasticity. We present real-time robotic experiments using 2 degrees of freedom (DoF) of the robot's head and show precise path integration, visual reset, and object position learning on-chip. We discuss the requirements for integrating the robotic system and neuromorphic hardware with current technologies.
... FS HD cells fired with ISI shorter than 218 20 ms. 219 Somatosensory angular head velocity cells 220The generation of HD selectivity is believed to involve AHV cells in proposed ring 221 attractor models(Stratton et al., 2010;Zhang, 1996). A recent report showed that AHV222 cells can be found alongside HD cells in the neighboring motor cortex (Mehlman et al., 223 2019 ...
... FS cells). Along with RS/ 358 putative excitatory HD cells, all basic components of a theorized ring attractor are 359 available within the S1HL for de novo HD signal generation(Stratton et al., 2010). ...
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Head direction (HD) information is intricately linked to spatial navigation and cognition. We recently reported the co-existence of all currently recognized spatial cell types can be found in the hindlimb primary somatosensory cortex (S1HL). In this study, we carried out an in-depth characterization of HD cells in S1HL. We show fast-spiking (FS), putative inhibitory neurons are over-represented in and sharply tuned to HD compared to regular-spiking (RS), putative excitatory neurons. These FS HD cells are non-conjunctive, rarely theta modulated, not locally connected and are enriched in layer 4/5a. Their co-existence with RS HD cells and angular head velocity (AHV) cells in a layer-specific fashion through the S1HL presents a previously unreported organization of spatial circuits. These findings challenge the notion that FS, putative inhibitory interneurons are weakly tuned to external stimuli in general and present a novel local network configuration not reported in other parts of the brain.
... 29 Notably, the heading signal (the activity 'bump') is maintained even when the visual stimulus is 30 removed, and it moves relative to the (no longer visible) cue as the animal walks in darkness [18]. 31 The underlying circuit therefore combines idiothetic and allothetic information into a coherent 32 heading signal. Overall, this neuronal activity appears to constitute an internal encoding of heading 33 in the insect's CX, which closely resembles the hypothetical ring attractor [21] proposed by Skaggs 34 et al. in 1995 [22] to account for the rat 'head direction' cells [23][24][25][26][27][28][29][30][31]. ...
... 31 The underlying circuit therefore combines idiothetic and allothetic information into a coherent 32 heading signal. Overall, this neuronal activity appears to constitute an internal encoding of heading 33 in the insect's CX, which closely resembles the hypothetical ring attractor [21] proposed by Skaggs 34 et al. in 1995 [22] to account for the rat 'head direction' cells [23][24][25][26][27][28][29][30][31]. 35 In recent years, several computational models of the fly's CX heading tracking circuit have been 36 presented. ...
Preprint
Full-text available
Recent studies of the Central Complex in the brain of the fruit fly Drosophila melanogaster have identified neurons with localised activity that tracks the animal's heading direction. These neurons are part of a neuronal circuit with dynamics resembling those of a ring attractor. Other insects have a homologous circuit sharing a generally similar topographic structure but with significant structural and connectivity differences. In this study, we model the precise connectivity patterns in two insect species to investigate the effect of the differences on the dynamics of the circuit. We illustrate that the circuit found in locusts can also operate as a ring attractor and we explore the role and robustness of the connectivity parameters. We identify differences that enable the fruit fly circuit to respond faster to changes of heading while they render the locust circuit more tolerant to noise. Our findings demonstrate that subtle differences in neuronal projection patterns can have a significant effect on the circuit performance and emphasise the need for a comparative approach in neuroscience.
... The internal organization of the HD circuit therefore appears to be in place before its ability to represent heading direction is manifested. Our results provide new constraints on models of continuous attractor network development, as they demonstrate that the rigid coupling of spatial relationships across directional nodes is not extracted from the structure of sensory input through a learning process [22,23], but instead likely arises through internal, self-organized processes during development (with possible further refinement through learning [24]). This finding may also generalize to other putative attractor networks such as grid cells [25][26][27][28], which display strong coupling as soon as they can be detected in young animals [29], and the recently discovered neural representation of direction in Drosophila [30][31][32][33]. ...
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Head direction (HD) cells are neurons found in an extended cortical and subcortical network that signal the orientation of an animal's head relative to its environment [1-3]. They are a fundamental component of the wider circuit of spatially responsive hippocampal formation neurons that make up the neural cognitive map of space [4]. During post-natal development, HD cells are the first among spatially modulated neurons in the hippocampal circuit to exhibit mature firing properties [5, 6], but before eye opening, HD cell responses in rat pups have low directional information and are directionally unstable [7, 8]. Using Bayesian decoding of HD cell ensemble activity recorded in the anterodorsal thalamic nucleus (ADN), we characterize this instability and identify its source: under-signaling of angular head velocity, which incompletely shifts the directional signal in proportion to head turns. We find evidence that geometric cues (the corners of a square environment) can be used to mitigate this under-signaling and, thereby, stabilize the directional signal even before eye opening. Crucially, even when directional firing cannot be stabilized, ensembles of unstable HD cells show short-timescale (1-10 s) temporal and spatial couplings consistent with an adult-like HD network. The HD network is widely modeled as a continuous attractor whose output is one coherent activity peak, updated during movement by angular head velocity signals and anchored by landmark cues [9-11]. Our findings present strong evidence for this model, and they demonstrate that the required network circuitry is in place and functional early during development, independent of reference to landmark information.
... Such observations suggest that EB neurons exhibit functional properties similar to those observed in the head-direction cells of rodents [15][16][17][18][19][20][21][22][23] . Although several theoretical studies for rodents 19,[24][25][26][27][28][29] and insects 30,31 have provided valuable insights into how the head-direction system or motion integration may work, these studies are based on hypothetical network structures. Moreover, the single-cell-level connectomes of related brain regions in rodents and in most insects (except for Drosophila) are not available. ...
... The mechanism underlying angular path integration has also been addressed in a number of computational models of rodent head-direction system 19,[24][25][26][27][28][29] . However, these models have been proposed on a more abstract level without the availability of single-cell-level connectomes. ...
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Maintaining spatial orientation when carrying out goal-directed movements requires an animal to perform angular path integration. Such functionality has been recently demonstrated in the ellipsoid body (EB) of fruit flies, though the precise circuitry and underlying mechanisms remain unclear. We analyze recently published cellular-level connectomic data and identify the unique characteristics of the EB circuitry, which features coupled symmetric and asymmetric rings. By constructing a spiking neural circuit model based on the connectome, we reveal that the symmetric ring initiates a feedback circuit that sustains persistent neural activity to encode information regarding spatial orientation, while the asymmetric rings are capable of integrating the angular path when the body rotates in the dark. The present model reproduces several key features of EB activity and makes experimentally testable predictions, providing new insight into how spatial orientation is maintained and tracked at the cellular level.