Ring Attractor Research Articles

Estimating orientation in natural scenes: A spiking neural network model of the insect central complex.

The central complex of insects contains cells, organised as a ring attractor, that encode head direction. The 'bump' of activity in the ring can be updated by idiothetic cues and external sensory information. Plasticity at the synapses between these cells and the ring neurons, that are responsible for bringing sensory information into the central complex, has been proposed to form a mapping between visual cues and the heading estimate which allows for more accurate tracking of the current heading, than if only idiothetic information were used. In Drosophila, ring neurons have well characterised non-linear receptive fields. In this work we produce synthetic versions of these visual receptive fields using a combination of excitatory inputs and mutual inhibition between ring neurons. We use these receptive fields to bring visual information into a spiking neural network model of the insect central complex based on the recently published Drosophila connectome. Previous modelling work has focused on how this circuit functions as a ring attractor using the same type of simple visual cues commonly used experimentally. While we initially test the model on these simple stimuli, we then go on to apply the model to complex natural scenes containing multiple conflicting cues. We show that this simple visual filtering provided by the ring neurons is sufficient to form a mapping between heading and visual features and maintain the heading estimate in the absence of angular velocity input. The network is successful at tracking heading even when presented with videos of natural scenes containing conflicting information from environmental changes and translation of the camera.

Synaptic ring attractor: A unified framework for attractor dynamics and multiple cues integration

Effective cue integration is essential for an animal's survival. The ring attractor network has emerged as a powerful framework for understanding how animals seamlessly integrate various cues. This network not only elucidates neural dynamics within the brain, especially in spatial encoding systems like the heading direction (HD) system, but also sheds light on cue integration within decision-making processes. Yet, many significant phenomena across different fields lack clear explanations. For instance, in physiology, the integration mechanism of Drosophila's compass neuron when confronted with conflicting self-motion cues and external sensory cues with varying gain control settings is not well elucidated. Similarly, in ethology, the decision-making system shows Bayesian integration (BI) under minimal cue conflicts, but shifts to a winner-take-all (WTA) mode as conflicts surpass a certain threshold. To address these gaps, we introduce a ring attractor network with asymmetrical neural connections and synaptic dynamics in this paper. A thorough series of simulations has been conducted to assess its ability to track external cues and integrate conflicting cues. The results from these simulations demonstrate that the proposed model replicates observed neural dynamics and offers a framework for modeling biologically plausible cue integration behaviors. Furthermore, our findings yield several testable predictions that could inform future neuroethological research, providing insights into the role of ring attractor dynamics in the animal brain.

Flexible multitask computation in recurrent networks utilizes shared dynamical motifs

Flexible computation is a hallmark of intelligent behavior. However, little is known about how neural networks contextually reconfigure for different computations. In the present work, we identified an algorithmic neural substrate for modular computation through the study of multitasking artificial recurrent neural networks. Dynamical systems analyses revealed learned computational strategies mirroring the modular subtask structure of the training task set. Dynamical motifs, which are recurring patterns of neural activity that implement specific computations through dynamics, such as attractors, decision boundaries and rotations, were reused across tasks. For example, tasks requiring memory of a continuous circular variable repurposed the same ring attractor. We showed that dynamical motifs were implemented by clusters of units when the unit activation function was restricted to be positive. Cluster lesions caused modular performance deficits. Motifs were reconfigured for fast transfer learning after an initial phase of learning. This work establishes dynamical motifs as a fundamental unit of compositional computation, intermediate between neuron and network. As whole-brain studies simultaneously record activity from multiple specialized systems, the dynamical motif framework will guide questions about specialization and generalization.

Attractors coexistence and representation research of Lotka–Volterra recurrent neural networks by matrix analysis theory

Attractor neural network models have been extensively studied in maintaining brain working memory state, spatial representation, and other brain processing mechanisms. The coexistence of multiple attractors in nonlinear neural network is particularly worth studying. The attractor is a stable state in the dynamic system, and all adjacent states will eventually be pulled to the attractor over time. Attractors can be regarded as the expression of data in low-dimensional state space, and different kinds of attractors can be used to process different information. The coexistence of multiple attractors means that a neural network can store multiple patterns, that is to say different memory mechanisms appear at the same time. Investigating the coexistence and competition of attractors within Lotka–Volterra(LV) recurrent neural networks presents a pivotal avenue for understanding the dynamical underpinnings of complex systems, particularly in the realm of computational neuroscience and ecological modeling. This paper studies the coexistence of different types of attractors in asymmetric Lotka–Volterra recurrent neural networks. Through the weight matrix block and matrix decomposition theory, we obtain the explicit expressions of continuous attractors and discrete attractors. Since neurons have multiple grouping methods, each weight matrix block satisfying certain conditions corresponds to different attractors. Different from traditional symmetric networks, the eigenvalues of the asymmetric weight matrices may be complex, which may correspond to ring attractors. Our research shows that attractors can coexist under certain conditions, depending on the weight matrix and external input. Moreover, through simulation experiments, we show that external input will cause the competition of attractors. Finally, we provide several simulations of attractor coexistence to illustrate our theory.

Innovative Exploration of a Bio-Inspired Sensor Fusion Algorithm: Enhancing Micro Satellite Functionality through Touretsky's Decentralized Neural Networks

Insect-inspired sensor fusion algorithms have presented a promising avenue in the development of robust and efficient systems, owing to the insects' ability to process numerous streams of noisy sensory data. The ring attractor neural network architecture has been identified as a noteworthy model for the optimal integration of diverse insect sensors. Expanding on this, our research presents an innovative bio-inspired ring attractor neural network architecture designed to augment the performance of microsatellite attitude determination systems through the fusion of data from multiple gyroscopic sensors.Extensive simulations using a nonlinear model of the microsatellite, while incorporating specific navigational disturbances, have been conducted to ascertain the viability and effectiveness of this approach. The results obtained have been superior to those of alternative methodologies, thus highlighting the potential of our proposed bio-inspired fusion technique. The findings indicate that this approach could significantly improve the accuracy and robustness of microsatellite systems across a wide range of applications.

Transforming a head direction signal into a goal-oriented steering command.

To navigate, we must continuously estimate the direction we are headed in, and we must correct deviations from our goal1. Direction estimation is accomplished by ring attractor networks in the head direction system2,3. However, we do not fully understand how the sense of direction is used to guide action. Drosophila connectome analyses4,5 reveal three cell populations (PFL3R, PFL3L and PFL2) that connect the head direction system to the locomotor system. Here we use imaging, electrophysiology and chemogenetic stimulation during navigation to show how these populations function. Each population receives a shifted copy of the head direction vector, such that their three reference frames are shifted approximately 120° relative to each other. Each cell type then compares its own head direction vector with a common goal vector; specifically, it evaluates the congruence of these vectors via a nonlinear transformation. The output of all three cell populations is then combined to generate locomotor commands. PFL3R cells are recruited when the fly is oriented to the left of its goal, and their activity drives rightward turning; the reverse is true for PFL3L. Meanwhile, PFL2 cells increase steering speed, and are recruited when the fly is oriented far from its goal. PFL2 cells adaptively increase the strength of steering as directional error increases, effectively managing the tradeoff between speed and accuracy. Together, our results show how a map of space in the brain can be combined with an internal goal to generate action commands, via a transformation from world-centric coordinates to body-centric coordinates.

Ring Attractors as the Basis of a Biomimetic Navigation System.

The ability to navigate effectively in a rich and complex world is crucial for the survival of all animals. Specialist neural structures have evolved that are implicated in facilitating this ability, one such structure being the ring attractor network. In this study, we model a trio of Spiking Neural Network (SNN) ring attractors as part of a bio-inspired navigation system to maintain an internal estimate of planar translation of an artificial agent. This estimate is dynamically calibrated using a memory recall system of landmark-free allotheic multisensory experiences. We demonstrate that the SNN-based ring attractor system can accurately model motion through 2D space by integrating ideothetic velocity information and use recalled allothetic experiences as a positive corrective mechanism. This SNN based navigation system has potential for use in mobile robotics applications where power supply is limited and external sensory information is intermittent or unreliable.

Ring attractor bio-inspired neural network for social robot navigation.

We introduce a bio-inspired navigation system for a robot to guide a social agent to a target location while avoiding static and dynamic obstacles. Robot navigation can be accomplished through a model of ring attractor neural networks. This connectivity pattern between neurons enables the generation of stable activity patterns that can represent continuous variables such as heading direction or position. The integration of sensory representation, decision-making, and motor control through ring attractor networks offers a biologically-inspired approach to navigation in complex environments. The navigation system is divided into perception, planning, and control stages. Our approach is compared to the widely-used Social Force Model and Rapidly Exploring Random Tree Star methods using the Social Individual Index and Relative Motion Index as metrics in simulated experiments. We created a virtual scenario of a pedestrian area with various obstacles and dynamic agents. The results obtained in our experiments demonstrate the effectiveness of this architecture in guiding a social agent while avoiding obstacles, and the metrics used for evaluating the system indicate that our proposal outperforms the widely used Social Force Model. Our approach points to improving safety and comfort specifically for human-robot interactions. By integrating the Social Individual Index and Relative Motion Index, this approach considers both social comfort and collision avoidance features, resulting in better human-robot interactions in a crowded environment.

Dynamics of Optimal Cue Integration with Time-Varying Delay in the Insects’ Navigation System

Neural networks with a ring structure are considered biologically plausible and have the ability of enforcing unique and persistent heading representations, yielding realistic homing behaviors. Recent studies have found that insects optimally integrate sensory information from the environment for head direction by using ring attractor networks. Optimal cue integration as the basic component of a complex insect navigation system proves to consist of a ring attractor network that is coupled by some integration neurons and some uniform inhibition neurons. The dynamics of the coupled mechanisms between neurons in optimal cue integration determine whether the insects’ homing capability is affected by environmental noises. Furthermore, time delays caused by communication between different kinds of neurons may induce complex dynamical properties. These dynamical behaviors are essential for understanding the neural mechanisms of insect homing behaviors, but there is a lack of relevant research on the dynamics of optimal cue integration with time-varying delay in the insects’ navigation system. In this paper, we discuss the dynamical properties of optimal cue integration with time-varying delay and show that it is asymptotically stable and leads to a unique insect home direction. These results are critical in providing the theoretical basis for further research on insect homing behaviors and the establishment of autonomous robots that mimic insect navigation mechanisms in the future.

Neural dynamics and architecture of the heading direction circuit in zebrafish

Animals generate neural representations of their heading direction. Notably, in insects, heading direction is topographically represented by the activity of neurons in the central complex. Although head direction cells have been found in vertebrates, the connectivity that endows them with their properties is unknown. Using volumetric lightsheet imaging, we find a topographical representation of heading direction in a neuronal network in the zebrafish anterior hindbrain, where a sinusoidal bump of activity rotates following directional swims of the fish and is otherwise stable over many seconds. Electron microscopy reconstructions show that, although the cell bodies are located in a dorsal region, these neurons arborize in the interpeduncular nucleus, where reciprocal inhibitory connectivity stabilizes the ring attractor network that encodes heading. These neurons resemble those found in the fly central complex, showing that similar circuit architecture principles may underlie the representation of heading direction across the animal kingdom and paving the way to an unprecedented mechanistic understanding of these networks in vertebrates.

Sensory fusion in the hoverfly righting reflex

We study how falling hoverflies use sensory cues to trigger appropriate roll righting behavior. Before being released in a free fall, flies were placed upside-down with their legs contacting the substrate. The prior leg proprioceptive information about their initial orientation sufficed for the flies to right themselves properly. However, flies also use visual and antennal cues to recover faster and disambiguate sensory conflicts. Surprisingly, in one of the experimental conditions tested, hoverflies flew upside-down while still actively flapping their wings. In all the other conditions, flies were able to right themselves using two roll dynamics: fast (sim 50ms) and slow (sim 110ms) in the presence of consistent and conflicting cues, respectively. These findings suggest that a nonlinear sensory integration of the three types of sensory cues occurred. A ring attractor model was developed and discussed to account for this cue integration process.

Navigation and the efficiency of spatial coding: insights from closed-loop simulations

Spatial learning is critical for survival and its underlying neuronal mechanisms have been studied extensively. These studies have revealed a wealth of information about the neural representations of space, such as place cells and boundary cells. While many studies have focused on how these representations emerge in the brain, their functional role in driving spatial learning and navigation has received much less attention. We extended an existing computational modeling tool-chain to study the functional role of spatial representations using closed-loop simulations of spatial learning. At the heart of the model agent was a spiking neural network that formed a ring attractor. This network received inputs from place and boundary cells and the location of the activity bump in this network was the output. This output determined the movement directions of the agent. We found that the navigation performance depended on the parameters of the place cell input, such as their number, the place field sizes, and peak firing rate, as well as, unsurprisingly, the size of the goal zone. The dependence on the place cell parameters could be accounted for by just a single variable, the overlap index, but this dependence was nonmonotonic. By contrast, performance scaled monotonically with the Fisher information of the place cell population. Our results therefore demonstrate that efficiently encoding spatial information is critical for navigation performance.

Population dynamics of head-direction neurons during drift and reorientation

The head direction (HD) system functions as the brain’s internal compass1,2, classically formalized as a one-dimensional ring attractor network3,4. In contrast to a globally consistent magnetic compass, the HD system does not have a universal reference frame. Instead, it anchors to local cues, maintaining a stable offset when cues rotate5–8 and drifting in the absence of referents5,8–10. However, questions about the mechanisms that underlie anchoring and drift remain unresolved and are best addressed at the population level. For example, the extent to which the one-dimensional description of population activity holds under conditions of reorientation and drift is unclear. Here we performed population recordings of thalamic HD cells using calcium imaging during controlled rotations of a visual landmark. Across experiments, population activity varied along a second dimension, which we refer to as network gain, especially under circumstances of cue conflict and ambiguity. Activity along this dimension predicted realignment and drift dynamics, including the speed of network realignment. In the dark, network gain maintained a ‘memory trace’ of the previously displayed landmark. Further experiments demonstrated that the HD network returned to its baseline orientation after brief, but not longer, exposures to a rotated cue. This experience dependence suggests that memory of previous associations between HD neurons and allocentric cues is maintained and influences the internal HD representation. Building on these results, we show that continuous rotation of a visual landmark induced rotation of the HD representation that persisted in darkness, demonstrating experience-dependent recalibration of the HD system. Finally, we propose a computational model to formalize how the neural compass flexibly adapts to changing environmental cues to maintain a reliable representation of HD. These results challenge classical one-dimensional interpretations of the HD system and provide insights into the interactions between this system and the cues to which it anchors.

Bayesian inference in ring attractor networks

Working memories are thought to be held in attractor networks in the brain. These attractors should keep track of the uncertainty associated with each memory, so as to weigh it properly against conflicting new evidence. However, conventional attractors do not represent uncertainty. Here, we show how uncertainty could be incorporated into an attractor, specifically a ring attractor that encodes head direction. First, we introduce a rigorous normative framework (the circular Kalman filter) for benchmarking the performance of a ring attractor under conditions of uncertainty. Next, we show that the recurrent connections within a conventional ring attractor can be retuned to match this benchmark. This allows the amplitude of network activity to grow in response to confirmatory evidence, while shrinking in response to poor-quality or strongly conflicting evidence. This "Bayesian ring attractor" performs near-optimal angular path integration and evidence accumulation. Indeed, we show that a Bayesian ring attractor is consistently more accurate than a conventional ring attractor. Moreover, near-optimal performance can be achieved without exact tuning of the network connections. Finally, we use large-scale connectome data to show that the network can achieve near-optimal performance even after we incorporate biological constraints. Our work demonstrates how attractors can implement a dynamic Bayesian inference algorithm in a biologically plausible manner, and it makes testable predictions with direct relevance to the head direction system as well as any neural system that tracks direction, orientation, or periodic rhythms.

Multiple bumps can enhance robustness to noise in continuous attractor networks.

A central function of continuous attractor networks is encoding coordinates and accurately updating their values through path integration. To do so, these networks produce localized bumps of activity that move coherently in response to velocity inputs. In the brain, continuous attractors are believed to underlie grid cells and head direction cells, which maintain periodic representations of position and orientation, respectively. These representations can be achieved with any number of activity bumps, and the consequences of having more or fewer bumps are unclear. We address this knowledge gap by constructing 1D ring attractor networks with different bump numbers and characterizing their responses to three types of noise: fluctuating inputs, spiking noise, and deviations in connectivity away from ideal attractor configurations. Across all three types, networks with more bumps experience less noise-driven deviations in bump motion. This translates to more robust encodings of linear coordinates, like position, assuming that each neuron represents a fixed length no matter the bump number. Alternatively, we consider encoding a circular coordinate, like orientation, such that the network distance between adjacent bumps always maps onto 360 degrees. Under this mapping, bump number does not significantly affect the amount of error in the coordinate readout. Our simulation results are intuitively explained and quantitatively matched by a unified theory for path integration and noise in multi-bump networks. Thus, to suppress the effects of biologically relevant noise, continuous attractor networks can employ more bumps when encoding linear coordinates; this advantage disappears when encoding circular coordinates. Our findings provide motivation for multiple bumps in the mammalian grid network.

Learning accurate path integration in ring attractor models of the head direction system.

Ring attractor models for angular path integration have received strong experimental support. To function as integrators, head direction circuits require precisely tuned connectivity, but it is currently unknown how such tuning could be achieved. Here, we propose a network model in which a local, biologically plausible learning rule adjusts synaptic efficacies during development, guided by supervisory allothetic cues. Applied to the Drosophila head direction system, the model learns to path-integrate accurately and develops a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading in flies, and where the network remaps to integrate with different gains in rodents. Our model predicts that path integration requires self-supervised learning during a developmental phase, and proposes a general framework to learn to path-integrate with gain-1 even in architectures that lack the physical topography of a ring.

Online learning for orientation estimation during translation in an insect ring attractor network

Insect neural systems are a promising source of inspiration for new navigation algorithms, especially on low size, weight, and power platforms. There have been unprecedented recent neuroscience breakthroughs with Drosophila in behavioral and neural imaging experiments as well as the mapping of detailed connectivity of neural structures. General mechanisms for learning orientation in the central complex (CX) of Drosophila have been investigated previously; however, it is unclear how these underlying mechanisms extend to cases where there is translation through an environment (beyond only rotation), which is critical for navigation in robotic systems. Here, we develop a CX neural connectivity-constrained model that performs sensor fusion, as well as unsupervised learning of visual features for path integration; we demonstrate the viability of this circuit for use in robotic systems in simulated and physical environments. Furthermore, we propose a theoretical understanding of how distributed online unsupervised network weight modification can be leveraged for learning in a trajectory through an environment by minimizing orientation estimation error. Overall, our results may enable a new class of CX-derived low power robotic navigation algorithms and lead to testable predictions to inform future neuroscience experiments.

Plasticity between visual input pathways and the head direction system.

Animals can maintain a stable sense of direction even when they navigate in novel environments, but how the animal's brain interprets and encodes unfamiliar sensory information in its navigation system to maintain a stable sense of direction is a mystery. Recent studies have suggested that distinct brain structures of mammals and insects have evolved to solve this common problem with strategies that share computational principles; specifically, a network structure called a ring attractor maintains the sense of direction. Initially, in a novel environment, the animal's sense of direction relies on self-motion cues. Over time, the mapping from visual inputs to head direction cells, responsible for the sense of direction, is established via experience-dependent plasticity. Yet the mechanisms that facilitate acquiring a world-centered sense of direction, how many environments can be stored in memory, and what visual features are selected, all remain unknown. Thanks to recent advances in large scale physiological recording, genetic tools, and theory, these mechanisms may soon be revealed.

Electrocorticography reveals thalamic control of cortical dynamics following traumatic brain injury

The return of consciousness after traumatic brain injury (TBI) is associated with restoring complex cortical dynamics; however, it is unclear what interactions govern these complex dynamics. Here, we set out to uncover the mechanism underlying the return of consciousness by measuring local field potentials (LFP) using invasive electrophysiological recordings in patients recovering from TBI. We found that injury to the thalamus, and its efferent projections, on MRI were associated with repetitive and low complexity LFP signals from a highly structured phase space, resembling a low-dimensional ring attractor. But why do thalamic injuries in TBI patients result in a cortical attractor? We built a simplified thalamocortical model, which connotes that thalamic input facilitates the formation of cortical ensembles required for the return of cognitive function and the content of consciousness. These observations collectively support the view that thalamic input to the cortex enables rich cortical dynamics associated with consciousness.

Funneled energy landscape unifies principles of protein binding and evolution

Most proteins have evolved to spontaneously fold into native structure and specifically bind with their partners for the purpose of fulfilling biological functions. According to Darwin, protein sequences evolve through random mutations, and only the fittest survives. The understanding of how the evolutionary selection sculpts the interaction patterns for both biomolecular folding and binding is still challenging. In this study, we incorporated the constraint of functional binding into the selection fitness based on the principle of minimal frustration for the underlying biomolecular interactions. Thermodynamic stability and kinetic accessibility were derived and quantified from a global funneled energy landscape that satisfies the requirements of both the folding into the stable structure and binding with the specific partner. The evolution proceeds via a bowl-like evolution energy landscape in the sequence space with a closed-ring attractor at the bottom. The sequence space is increasingly reduced until this ring attractor is reached. The molecular-interaction patterns responsible for folding and binding are identified from the evolved sequences, respectively. The residual positions participating in the interactions responsible for folding are highly conserved and maintain the hydrophobic core under additional evolutionary constraints of functional binding. The positions responsible for binding constitute a distributed network via coupling conservations that determine the specificity of binding with the partner. This work unifies the principles of protein binding and evolution under minimal frustration and sheds light on the evolutionary design of proteins for functions.