Finding the way with a noisy brain

Human navigation strategies and their errors result from dynamic interactions of spatial uncertainties

Goal-directed navigation requires continuously integrating uncertain self-motion and landmark cues into an internal sense of location and direction, concurrently planning future paths, and sequentially executing motor actions. Here, we provide a unified account of these processes with a computational model of probabilistic path planning in the framework of optimal feedback control under uncertainty. This model gives rise to diverse human navigational strategies previously believed to be distinct behaviors and predicts quantitatively both the errors and the variability of navigation across numerous experiments. This furthermore explains how sequential egocentric landmark observations form an uncertain allocentric cognitive map, how this internal map is used both in route planning and during execution of movements, and reconciles seemingly contradictory results about cue-integration behavior in navigation. Taken together, the present work provides a parsimonious explanation of how patterns of human goal-directed navigation behavior arise from the continuous and dynamic interactions of spatial uncertainties in perception, cognition, and action.

The potential underlying mechanisms during learning flights

Hymenopterans, such as bees and wasps, have long fascinated researchers with their sinuous movements at novel locations. These movements, such as loops, arcs, or zigzags, serve to help insects learn their surroundings at important locations. They also allow the insects to explore and orient themselves in their environment. After they gained experience with their environment, the insects fly along optimized paths guided by several guidance strategies, such as path integration, local homing, and route-following, forming a navigational toolkit. Whereas the experienced insects combine these strategies efficiently, the naive insects need to learn about their surroundings and tune the navigational toolkit. We will see that the structure of the movements performed during the learning flights leverages the robustness of certain strategies within a given scale to tune other strategies which are more efficient at a larger scale. Thus, an insect can explore its environment incrementally without risking not finding back essential locations.

No Need for Landmarks: An Embodied Neural Controller for Robust Insect-Like Navigation Behaviors

Bayesian filters have been considered to help refine and develop theoretical views on spatial cell functions for self-localization. However, extending a Bayesian filter to reproduce insect-like navigation behaviors (e.g., home searching) remains an open and challenging problem. To address this problem, we propose an embodied neural controller for self-localization, foraging, backward homing (BH), and home searching of an advanced mobility sensor (AMOS)-driven insect-like robot. The controller, comprising a navigation module for the Bayesian self-localization and goal-directed control of AMOS and a locomotion module for coordinating the 18 joints of AMOS, leads to its robust insect-like navigation behaviors. As a result, the proposed controller enables AMOS to perform robust foraging, BH, and home searching against various levels of sensory noise, compared to conventional controllers. Its implementation relies only on self-localization and heading perception, rather than global positioning and landmark guidance. Interestingly, the proposed controller makes AMOS achieve spiral searching patterns comparable to those performed by real insects. We also demonstrated the performance of the controller for real-time indoor and outdoor navigation in a real insect-like robot without any landmark and cognitive map.

Anesthesia disrupts distance, but not direction, of path integration memory

Solitary foraging insects, such as ants, maintain an estimate of the direction and distance to their starting location as they move away from it, in a process known as path integration. This estimate, commonly known as the "home vector," is updated continuously as the ant moves^1-4 and is reset as soon as it enters its nest,⁵ yet ants prevented from returning to their nest can still use their home vector when released several hours later.^6,7 This conjunction of fast update and long persistence of the home vector memory does not directly map to existing accounts of short-, mid-, and long-term memory;^2,8-12 hence, the substrate of this memory remains unknown. Chill-coma anesthesia^13-15 has previously been shown to affect associative memory retention in fruit flies^14,16 and honeybees.^9,17,18 We investigate the nature of path integration memory by anesthetizing ants after they have accumulated home vector information and testing if the memory persists on recovery. We show that after anesthesia the memory of the distance ants have traveled is degraded, but the memory of the direction is retained. We also show that this is consistent with models of path integration that maintain the memory in a redundant Cartesian coordinate system and with the hypothesis that chill-coma produces a proportional reduction of the memory, rather than a subtractive reduction or increase of noise. The observed effect is not compatible with a memory based on recurrent circuit activity and points toward an activity-dependent molecular process as the basis of path integration memory.

A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection

Flexible behaviors over long timescales are thought to engage recurrent neural networks in deep brain regions, which are experimentally challenging to study. In insects, recurrent circuit dynamics in a brain region called the central complex (CX) enable directed locomotion, sleep, and context- and experience-dependent spatial navigation. We describe the first complete electron microscopy-based connectome of the Drosophila CX, including all its neurons and circuits at synaptic resolution. We identified new CX neuron types, novel sensory and motor pathways, and network motifs that likely enable the CX to extract the fly's head direction, maintain it with attractor dynamics, and combine it with other sensorimotor information to perform vector-based navigational computations. We also identified numerous pathways that may facilitate the selection of CX-driven behavioral patterns by context and internal state. The CX connectome provides a comprehensive blueprint necessary for a detailed understanding of network dynamics underlying sleep, flexible navigation, and state-dependent action selection.

The Critical Role of Head Movements for Spatial Representation During Bumblebees Learning Flight

Bumblebees perform complex flight maneuvers around the barely visible entrance of their nest upon their first departures. During these flights bees learn visual information about the surroundings, possibly including its spatial layout. They rely on this information to return home. Depth information can be derived from the apparent motion of the scenery on the bees' retina. This motion is shaped by the animal's flight and orientation: Bees employ a saccadic flight and gaze strategy, where rapid turns of the head (saccades) alternate with flight segments of apparently constant gaze direction (intersaccades). When during intersaccades the gaze direction is kept relatively constant, the apparent motion contains information about the distance of the animal to environmental objects, and thus, in an egocentric reference frame. Alternatively, when the gaze direction rotates around a fixed point in space, the animal perceives the depth structure relative to this pivot point, i.e., in an allocentric reference frame. If the pivot point is at the nest-hole, the information is nest-centric. Here, we investigate in which reference frames bumblebees perceive depth information during their learning flights. By precisely tracking the head orientation, we found that half of the time, the head appears to pivot actively. However, only few of the corresponding pivot points are close to the nest entrance. Our results indicate that bumblebees perceive visual information in several reference frames when they learn about the surroundings of a behaviorally relevant location.

Path integration error and adaptable search behaviors in a mantis shrimp

Mantis shrimp of the species Neogonodactylus oerstedii occupy small burrows in shallow waters throughout the Caribbean. These animals use path integration, a vector-based navigation strategy, to return to their homes while foraging. Here, we report that path integration in N. oerstedii is prone to error accumulated during outward foraging paths and we describe the search behavior that N. oerstedii employs after it fails to locate its home following the route provided by its path integrator. This search behavior forms continuously expanding, non-oriented loops that are centered near the point of search initiation. The radius of this search is scaled to the animal's positional uncertainty during path integration, improving the effectiveness of the search. The search behaviors exhibited by N. oerstedii bear a striking resemblance to search behaviors in other animals, offering potential avenues for the comparative examination of search behaviors and how they are optimized in disparate taxa.

Principles of Insect Path Integration

Continuously monitoring its position in space relative to a goal is one of the most essential tasks for an animal that moves through its environment. Species as diverse as rats, bees, and crabs achieve this by integrating all changes of direction with the distance covered during their foraging trips, a process called path integration. They generate an estimate of their current position relative to a starting point, enabling a straight-line return, following what is known as a home vector. While in theory path integration always leads the animal precisely back home, in the real world noise limits the usefulness of this strategy when operating in isolation. Noise results from stochastic processes in the nervous system and from unreliable sensory information, particularly when obtaining heading estimates. Path integration, during which angular self-motion provides the sole input for encoding heading (idiothetic path integration), results in accumulating errors that render this strategy useless over long distances. In contrast, when using an external compass this limitation is avoided (allothetic path integration). Many navigating insects indeed rely on external compass cues for estimating body orientation, whereas they obtain distance information by integration of steps or optic-flow-based speed signals. In the insect brain, a region called the central complex plays a key role for path integration. Not only does the central complex house a ring-attractor network that encodes head directions, neurons responding to optic flow also converge with this circuit. A neural substrate for integrating direction and distance into a memorized home vector has therefore been proposed in the central complex. We discuss how behavioral data and the theoretical framework of path integration can be aligned with these neural data.

From skylight input to behavioural output: A computational model of the insect polarised light compass

Many insects navigate by integrating the distances and directions travelled on an outward path, allowing direct return to the starting point. Fundamental to the reliability of this process is the use of a neural compass based on external celestial cues. Here we examine how such compass information could be reliably computed by the insect brain, given realistic constraints on the sky polarisation pattern and the insect eye sensor array. By processing the degree of polarisation in different directions for different parts of the sky, our model can directly estimate the solar azimuth and also infer the confidence of the estimate. We introduce a method to correct for tilting of the sensor array, as might be caused by travel over uneven terrain. We also show that the confidence can be used to approximate the change in sun position over time, allowing the compass to remain fixed with respect to 'true north' during long excursions. We demonstrate that the compass is robust to disturbances and can be effectively used as input to an existing neural model of insect path integration. We discuss the plausibility of our model to be mapped to known neural circuits, and to be implemented for robot navigation.

Stellate Cells in the Medial Entorhinal Cortex Are Required for Spatial Learning

Spatial learning requires estimates of location that may be obtained by path integration or from positional cues. Grid and other spatial firing patterns of neurons in the superficial medial entorhinal cortex (MEC) suggest roles in behavioral estimation of location. However, distinguishing the contributions of path integration and cue-based signals to spatial behaviors is challenging, and the roles of identified MEC neurons are unclear. We use virtual reality to dissociate linear path integration from other strategies for behavioral estimation of location. We find that mice learn to path integrate using motor-related self-motion signals, with accuracy that decreases steeply as a function of distance. We show that inactivation of stellate cells in superficial MEC impairs spatial learning in virtual reality and in a real world object location recognition task. Our results quantify contributions of path integration to behavior and corroborate key predictions of models in which stellate cells contribute to location estimation.

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Mice learn to estimate location by path integration and cue-based strategies

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Motor-related self-motion signals are used for path integration

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Accuracy of path integration decreases with distance

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Stellate cells in medial entorhinal cortex are required for spatial learning

The Central Complex as a Potential Substrate for Vector Based Navigation

Insects use path integration (PI) to maintain a home vector, but can also store and recall vector-memories that take them from home to a food location, and even allow them to take novel shortcuts between food locations. The neural circuit of the Central Complex (a brain area that receives compass and optic flow information) forms a plausible substrate for these behaviors. A recent model, grounded in neurophysiological and neuroanatomical data, can account for PI during outbound exploratory routes and the control of steering to return home. Here, we show that minor, hypothetical but neurally plausible, extensions of this model can additionally explain how insects could store and recall PI vectors to follow food-ward paths, take shortcuts, search at the feeder and re-calibrate their vector-memories with experience. In addition, a simple assumption about how one of multiple vector-memories might be chosen at any point in time can produce the development and maintenance of efficient routes between multiple locations, as observed in bees. The central complex circuitry is therefore well-suited to allow for a rich vector-based navigational repertoire.

Optimal multiguidance integration in insect navigation

In the last decades, desert ants have become model organisms for the study of insect navigation. In finding their way, they use two major navigational routines: path integration using a celestial compass and landmark guidance based on sets of panoramic views of the terrestrial environment. It has been claimed that this information would enable the insect to acquire and use a centralized cognitive map of its foraging terrain. Here, we present a decentralized architecture, in which the concurrently operating path integration and landmark guidance routines contribute optimally to the directions to be steered, with "optimal" meaning maximizing the certainty (reliability) of the combined information. At any one time during its journey, the animal computes a path integration (global) vector and landmark guidance (local) vector, in which the length of each vector is proportional to the certainty of the individual estimates. Hence, these vectors represent the limited knowledge that the navigator has at any one place about the direction of the goal. The sum of the global and local vectors indicates the navigator's optimal directional estimate. Wherever applied, this decentralized model architecture is sufficient to simulate the results of quite a number of diverse cue-conflict experiments, which have recently been performed in various behavioral contexts by different authors in both desert ants and honeybees. They include even those experiments that have deliberately been designed by former authors to strengthen the evidence for a metric cognitive map in bees.

An Anatomically Constrained Model for Path Integration in the Bee Brain

Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task-a celestial-cue-based visual compass and an optic-flow-based visual odometer-but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light-based compass neurons and optic-flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy, we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically identified neurons suggested for each processing step. The resulting model circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e., a ground velocity that is not precisely aligned with body orientation) typical of bee flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings-suggesting a more basic function for central complex connectivity, from which path integration may have evolved.

Finding Home: Landmark Ambiguity in Human Navigation

Memories of places often include landmark cues, i.e., information provided by the spatial arrangement of distinct objects with respect to the target location. To study how humans combine landmark information for navigation, we conducted two experiments: To this end, participants were either provided with auditory landmarks while walking in a large sports hall or with visual landmarks while walking on a virtual-reality treadmill setup. We found that participants cannot reliably locate their home position due to ambiguities in the spatial arrangement when only one or two uniform landmarks provide cues with respect to the target. With three visual landmarks that look alike, the task is solved without ambiguity, while audio landmarks need to play three unique sounds for a similar performance. This reduction in ambiguity through integration of landmark information from 1, 2, and 3 landmarks is well modeled using a probabilistic approach based on maximum likelihood estimation. Unlike any deterministic model of human navigation (based e.g., on distance or angle information), this probabilistic model predicted both the precision and accuracy of the human homing performance. To further examine how landmark cues are integrated we introduced systematic conflicts in the visual landmark configuration between training of the home position and tests of the homing performance. The participants integrated the spatial information from each landmark near-optimally to reduce spatial variability. When the conflict becomes big, this integration breaks down and precision is sacrificed for accuracy. That is, participants return again closer to the home position, because they start ignoring the deviant third landmark. Relying on two instead of three landmarks, however, goes along with responses that are scattered over a larger area, thus leading to higher variability. To model the breakdown of integration with increasing conflict, the probabilistic model based on a simple Gaussian distribution used for Experiment 1 needed a slide extension in from of a mixture of Gaussians. All parameters for the Mixture Model were fixed based on the homing performance in the baseline condition which contained a single landmark. from the 1-Landmark Condition. This way we found that the Mixture Model could predict the integration performance and its breakdown with no additional free parameters. Overall these data suggest that humans use similar optimal probabilistic strategies in visual and auditory navigation, integrating landmark information to improve homing precision and balance homing precision with homing accuracy.

A Neurocomputational Model of Goal-Directed Navigation in Insect-Inspired Artificial Agents

Despite their small size, insect brains are able to produce robust and efficient navigation in complex environments. Specifically in social insects, such as ants and bees, these navigational capabilities are guided by orientation directing vectors generated by a process called path integration. During this process, they integrate compass and odometric cues to estimate their current location as a vector, called the home vector for guiding them back home on a straight path. They further acquire and retrieve path integration-based vector memories globally to the nest or based on visual landmarks. Although existing computational models reproduced similar behaviors, a neurocomputational model of vector navigation including the acquisition of vector representations has not been described before. Here we present a model of neural mechanisms in a modular closed-loop control—enabling vector navigation in artificial agents. The model consists of a path integration mechanism, reward-modulated global learning, random search, and action selection. The path integration mechanism integrates compass and odometric cues to compute a vectorial representation of the agent's current location as neural activity patterns in circular arrays. A reward-modulated learning rule enables the acquisition of vector memories by associating the local food reward with the path integration state. A motor output is computed based on the combination of vector memories and random exploration. In simulation, we show that the neural mechanisms enable robust homing and localization, even in the presence of external sensory noise. The proposed learning rules lead to goal-directed navigation and route formation performed under realistic conditions. Consequently, we provide a novel approach for vector learning and navigation in a simulated, situated agent linking behavioral observations to their possible underlying neural substrates.

Learning New Sensorimotor Contingencies: Effects of Long-Term Use of Sensory Augmentation on the Brain and Conscious Perception

Theories of embodied cognition propose that perception is shaped by sensory stimuli and by the actions of the organism. Following sensorimotor contingency theory, the mastery of lawful relations between own behavior and resulting changes in sensory signals, called sensorimotor contingencies, is constitutive of conscious perception. Sensorimotor contingency theory predicts that, after training, knowledge relating to new sensorimotor contingencies develops, leading to changes in the activation of sensorimotor systems, and concomitant changes in perception. In the present study, we spell out this hypothesis in detail and investigate whether it is possible to learn new sensorimotor contingencies by sensory augmentation. Specifically, we designed an fMRI compatible sensory augmentation device, the feelSpace belt, which gives orientation information about the direction of magnetic north via vibrotactile stimulation on the waist of participants. In a longitudinal study, participants trained with this belt for seven weeks in natural environment. Our EEG results indicate that training with the belt leads to changes in sleep architecture early in the training phase, compatible with the consolidation of procedural learning as well as increased sensorimotor processing and motor programming. The fMRI results suggest that training entails activity in sensory as well as higher motor centers and brain areas known to be involved in navigation. These neural changes are accompanied with changes in how space and the belt signal are perceived, as well as with increased trust in navigational ability. Thus, our data on physiological processes and subjective experiences are compatible with the hypothesis that new sensorimotor contingencies can be acquired using sensory augmentation.

Neural mechanisms of insect navigation

We know more about the ethology of insect navigation than the neural substrates. Few studies have shown direct effects of brain manipulation on navigational behaviour; or measure brain responses that clearly relate to the animal's current location or spatial target, independently of specific sensory cues. This is partly due to the methodological problems of obtaining neural data in a naturally behaving animal. However, substantial indirect evidence, such as comparative anatomy and knowledge of the neural circuits that provide relevant sensory inputs provide converging arguments for the role of some specific brain areas: the mushroom bodies; and the central complex. Finally, modelling can help bridge the gap by relating the computational requirements of a given navigational task to the type of computation offered by different brain areas.

Early ant trajectories: spatial behaviour before behaviourism

In the beginning of the twentieth century, when Jacques Loeb's and John Watson's mechanistic view of life started to dominate animal physiology and behavioural biology, several scientists with different academic backgrounds got engaged in studying the wayfinding behaviour of ants. Largely unaffected by the scientific spirit of the time, they worked independently of each other in different countries: in Algeria, Tunisia, Spain, Switzerland and the United States of America. In the current literature on spatial cognition these early ant researchers--Victor Cornetz, Felix Santschi, Charles Turner and Rudolf Brun--are barely mentioned. Moreover, it is virtually unknown that the great neuroanatomist Santiago Ramón y Cajal had also worked on spatial orientation in ants. This general neglect is certainly due to the fact that nearly all these ant researchers were scientific loners, who did their idiosyncratic investigations outside the realm of comparative physiology, neurobiology and the behavioural sciences of the time, and published their results in French, German, and Spanish at rather inaccessible places. Even though one might argue that much of their work resulted in mainly anecdotal evidence, the conceptual approaches of these early ant researchers preempt much of the present-day discussions on spatial representation in animals.

Animal path integration: a model of positional uncertainty along tortuous paths

Exact closed form mathematical solutions are reported which quantify the dynamic uncertainty resulting from path integration (PI) along tortuous paths. Based on a correlated random walk model, the derived results quantify positional estimation error moments with and without a compass, in discrete and continuous time. Consistent with earlier studies on attempted straight-line navigation, using a compass significantly reduces the uncertainty during PI, making purely idiothetic PI biologically implausible except over short distances. Examples are used to illustrate the contributions of angular noise, linear noise and path tortuosity, under different conditions. Linear noise is shown to be relatively more important with a compass while angular noise is more important without. It is shown that increasing path tortuosity decreases positional uncertainty, true for long and short journeys, irrespective of whether a compass is used, or the level of noise. In contrast, reducing angular noise also reduces uncertainty, but only below some critical level of noise. Using canonical equations of PI, it is shown that polar PI using a compass accumulates uncertainty in a manner similar to Cartesian PI without a compass. Issues of data sampling bias and intermittent use of a compass are also considered for PI along tortuous paths.

Mapping the navigational knowledge of individually foraging ants, Myrmecia croslandi

Ants are efficient navigators, guided by path integration and visual landmarks. Path integration is the primary strategy in landmark-poor habitats, but landmarks are readily used when available. The landmark panorama provides reliable information about heading direction, routes and specific location. Visual memories for guidance are often acquired along routes or near to significant places. Over what area can such locally acquired memories provide information for reaching a place? This question is unusually approachable in the solitary foraging Australian jack jumper ant, since individual foragers typically travel to one or two nest-specific foraging trees. We find that within 10 m from the nest, ants both with and without home vector information available from path integration return directly to the nest from all compass directions, after briefly scanning the panorama. By reconstructing panoramic views within the successful homing range, we show that in the open woodland habitat of these ants, snapshot memories acquired close to the nest provide sufficient navigational information to determine nest-directed heading direction over a surprisingly large area, including areas that animals may have not visited previously.

Impact and sources of neuronal variability in the fly's motion vision pathway

Nervous systems encode information about dynamically changing sensory input by changes in neuronal activity. Neuronal activity changes, however, also arise from noise sources within and outside the nervous system or from changes of the animal's behavioral state. The resulting variability of neuronal responses in representing sensory stimuli limits the reliability with which animals can respond to stimuli and may thus even affect the chances for survival in certain situations. Relevant sources of noise arising at different stages along the motion vision pathway have been investigated from the sensory input to the initiation of behavioral reactions. Here, we concentrate on the reliability of processing visual motion information in flies. Flies rely on visual motion information to guide their locomotion. They are among the best established model systems for the processing of visual motion information allowing us to bridge the gap between behavioral performance and underlying neuronal computations. It has been possible to directly assess the consequences of noise at major stages of the fly's visual motion processing system on the reliability of neuronal signals. Responses of motion sensitive neurons and their variability have been related to optomotor movements as indicators for the overall performance of visual motion computation. We address whether and how noise already inherent in the stimulus, e.g. photon noise for the visual system, influences later processing stages and to what extent variability at the output level of the sensory system limits behavioral performance. Recent advances in circuit analysis and the progress in monitoring neuronal activity in behaving animals should now be applied to understand how the animal meets the requirements of fast and reliable manoeuvres in naturalistic situations.

Maintaining a cognitive map in darkness: the need to fuse boundary knowledge with path integration

Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's “cognitive map”, or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and – we conjecture – necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and elaborate on their implications and significance for the design, analysis and interpretation of experiments.

Do animals need “cognitive maps“? One of the main difficulties in answering this question is finding a definitive scenario where having and not having a “cognitive map“ result in measurably different outcomes. Many key predictions made by models involving some sort of “cognitive map“ can also be replicated by models without a “cognitive map“. Here we consider published data on rodents navigating in darkness inside homogeneous arenas. The head direction system becomes unstable within three minutes in darkness, yet place and grid cells have been reported to fire in the same locations for thirty minutes or longer. We show firstly that it is theoretically implausible for path integration alone to maintain a stable positional representation beyond three minutes, given a drifting head direction system in darkness. Secondly, we prove that even assuming perfect boundary knowledge is insufficient to maintain a stable positional representation. Finally, we show in simulated and real arenas that a nearoptimal combination of path integration and boundary representation is sufficient to produce stable positional representations in darkness consistent with published data. The necessity for fusing path integration and landmark information for accurate localization in darkness is both consistent with, and motivates the existence of, “cognitive maps.“

The neuroscience of learning: beyond the Hebbian synapse

From the traditional perspective of associative learning theory, the hypothesis linking modifications of synaptic transmission to learning and memory is plausible. It is less so from an information-processing perspective, in which learning is mediated by computations that make implicit commitments to physical and mathematical principles governing the domains where domain-specific cognitive mechanisms operate. We compare the properties of associative learning and memory to the properties of long-term potentiation, concluding that the properties of the latter do not explain the fundamental properties of the former. We briefly review the neuroscience of reinforcement learning, emphasizing the representational implications of the neuroscientific findings. We then review more extensively findings that confirm the existence of complex computations in three information-processing domains: probabilistic inference, the representation of uncertainty, and the representation of space. We argue for a change in the conceptual framework within which neuroscientists approach the study of learning mechanisms in the brain.

Path integration mediated systematic search: a Bayesian model

The systematic search behaviour is a backup system that increases the chances of desert ants finding their nest entrance after foraging when the path integrator has failed to guide them home accurately enough. Here we present a mathematical model of the systematic search that is based on extensive behavioural studies in North African desert ants Cataglyphis fortis. First, a simple search heuristic utilising Bayesian inference and a probability density function is developed. This model, which optimises the short-term nest detection probability, is then compared to three simpler search heuristics and to recorded search patterns of Cataglyphis ants. To compare the different searches a method to quantify search efficiency is established as well as an estimate of the error rate in the ants' path integrator. We demonstrate that the Bayesian search heuristic is able to automatically adapt to increasing levels of positional uncertainty to produce broader search patterns, just as desert ants do, and that it outperforms the three other search heuristics tested. The searches produced by it are also arguably the most similar in appearance to the ant's searches.

No need for a cognitive map: decentralized memory for insect navigation

In many animals the ability to navigate over long distances is an important prerequisite for foraging. For example, it is widely accepted that desert ants and honey bees, but also mammals, use path integration for finding the way back to their home site. It is however a matter of a long standing debate whether animals in addition are able to acquire and use so called cognitive maps. Such a ‘map’, a global spatial representation of the foraging area, is generally assumed to allow the animal to find shortcuts between two sites although the direct connection has never been travelled before. Using the artificial neural network approach, here we develop an artificial memory system which is based on path integration and various landmark guidance mechanisms (a bank of individual and independent landmark-defined memory elements). Activation of the individual memory elements depends on a separate motivation network and an, in part, asymmetrical lateral inhibition network. The information concerning the absolute position of the agent is present, but resides in a separate memory that can only be used by the path integration subsystem to control the behaviour, but cannot be used for computational purposes with other memory elements of the system. Thus, in this simulation there is no neural basis of a cognitive map. Nevertheless, an agent controlled by this network is able to accomplish various navigational tasks known from ants and bees and often discussed as being dependent on a cognitive map. For example, map-like behaviour as observed in honey bees arises as an emergent property from a decentralized system. This behaviour thus can be explained without referring to the assumption that a cognitive map, a coherent representation of foraging space, must exist. We hypothesize that the proposed network essentially resides in the mushroom bodies of the insect brain.

When desert ants search for food, they often have to travel over long distances, more then ten thousand times their body lengths and then turn back to find the nest entrance. It is known from many experiments that these animals employ a skylight compass including the sun, a pedometer, and a mechanism called path integration. This means that during walking they continuously update the vector pointing from their actual position back to the nest site. In addition they use landmarks. However, based on observations of the behaviour of ants and honey bees several authors have argued that these animals finally employ a neural system that is able to represent frequently visited locations in the form of a map (a “cognitive map”). Having a map-like system available would allow the animal to find a shortcut between two separately learned locations without having learned this direct path between both locations beforehand. As such shortcuts have been observed, cognitive maps have been assumed to exist. Here we show in a simulation study based on artificial neural networks that shortcuts as observed in the experiments are also possible with a memory system using a completely decentralized architecture not including an explicit cognitive map.