Spatial Transformations in the Parietal Cortex Using Basis Functions

Mixed selectivity: Cellular computations for complexity

The property of mixed selectivity has been discussed at a computational level and offers a strategy to maximize computational power by adding versatility to the functional role of each neuron. Here, we offer a biologically grounded implementational-level mechanistic explanation for mixed selectivity in neural circuits. We define pure, linear, and nonlinear mixed selectivity and discuss how these response properties can be obtained in simple neural circuits. Neurons that respond to multiple, statistically independent variables display mixed selectivity. If their activity can be expressed as a weighted sum, then they exhibit linear mixed selectivity; otherwise, they exhibit nonlinear mixed selectivity. Neural representations based on diverse nonlinear mixed selectivity are high dimensional; hence, they confer enormous flexibility to a simple downstream readout neural circuit. However, a simple neural circuit cannot possibly encode all possible mixtures of variables simultaneously, as this would require a combinatorially large number of mixed selectivity neurons. Gating mechanisms like oscillations and neuromodulation can solve this problem by dynamically selecting which variables are mixed and transmitted to the readout.

Two what, two where, visual cortical streams in humans

ROLLS, E. T. Two What, Two Where, Visual Cortical Streams in Humans. NEUROSCI BIOBEHAV REV 2024. Recent cortical connectivity investigations lead to new concepts about 'What' and 'Where' visual cortical streams in humans, and how they connect to other cortical systems. A ventrolateral 'What' visual stream leads to the inferior temporal visual cortex for object and face identity, and provides 'What' information to the hippocampal episodic memory system, the anterior temporal lobe semantic system, and the orbitofrontal cortex emotion system. A superior temporal sulcus (STS) 'What' visual stream utilising connectivity from the temporal and parietal visual cortex responds to moving objects and faces, and face expression, and connects to the orbitofrontal cortex for emotion and social behaviour. A ventromedial 'Where' visual stream builds feature combinations for scenes, and provides 'Where' inputs via the parahippocampal scene area to the hippocampal episodic memory system that are also useful for landmark-based navigation. The dorsal 'Where' visual pathway to the parietal cortex provides for actions in space, but also provides coordinate transforms to provide inputs to the parahippocampal scene area for self-motion update of locations in scenes in the dark or when the view is obscured.

Neural dynamic foundations of a theory of higher cognition: the case of grounding nested phrases

Because cognitive competences emerge in evolution and development from the sensory-motor domain, we seek a neural process account for higher cognition in which all representations are necessarily grounded in perception and action. The challenge is to understand how hallmarks of higher cognition, productivity, systematicity, and compositionality, may emerge from such a bottom-up approach. To address this challenge, we present key ideas from Dynamic Field Theory which postulates that neural populations are organized by recurrent connectivity to create stable localist representations. Dynamic instabilities enable the autonomous generation of sequences of mental states. The capacity to apply neural circuitry across broad sets of inputs that emulates the function call postulated in symbolic computation emerges through coordinate transforms implemented in neural gain fields. We show how binding localist neural representations through a shared index dimension enables conceptual structure, in which the interdependence among components of a representation is flexibly expressed. We demonstrate these principles in a neural dynamic architecture that represents and perceptually grounds nested relational and action phrases. Sequences of neural processing steps are generated autonomously to attentionally select the referenced objects and events in a manner that is sensitive to their interdependencies. This solves the problem of 2 and the massive binding problem in expressions such as "the small tree that is to the left of the lake which is to the left of the large tree". We extend earlier work by incorporating new types of grammatical constructions and a larger vocabulary. We discuss the DFT framework relative to other neural process accounts of higher cognition and assess the scope and challenges of such neural theories.

Mice require proprioception to establish long-term visuospatial memory

Because the retina moves constantly, the retinotopic representation of the visual world is spatially inaccurate and the brain must transform this spatially inaccurate retinal signal to a spatially accurate signal usable for perception and action. One of the salient discoveries of modern neuroscience is the role of the hippocampus in establishing gaze-independent, long-term visuospatial memories. The rat hippocampus has neurons which report the animal's position in space regardless of its angle of gaze. Rats with hippocampal lesions are unable to find the location of an escape platform hidden in a pool of opaque fluid, the Morris Water Maze (MWM) based on the visual aspects of their surrounding environment. Here we show that the representation of proprioception in the dysgranular zone of primary somatosensory cortex is equivalently necessary for mice to learn the location of the hidden platform, presumably because without it they cannot create a long-term gaze-independent visuospatial representation of their environment from the retinal signal. They have no trouble finding the platform when it is marked by a flag, and they have no motor or vestibular deficits.

A large-scale neurocomputational model of spatial cognition integrating memory with vision

We introduce a large-scale neurocomputational model of spatial cognition called 'Spacecog', which integrates recent findings from mechanistic models of visual and spatial perception. As a high-level cognitive ability, spatial cognition requires the processing of behaviourally relevant features in complex environments and, importantly, the updating of this information during processes of eye and body movement. The Spacecog model achieves this by interfacing spatial memory and imagery with mechanisms of object localisation, saccade execution, and attention through coordinate transformations in parietal areas of the brain. We evaluate the model in a realistic virtual environment where our neurocognitive model steers an agent to perform complex visuospatial tasks. Our modelling approach opens up new possibilities in the assessment of neuropsychological data and human spatial cognition.

Gated transformations from egocentric to allocentric reference frames involving retrosplenial cortex, entorhinal cortex, and hippocampus

This paper reviews the recent experimental finding that neurons in behaving rodents show egocentric coding of the environment in a number of structures associated with the hippocampus. Many animals generating behavior on the basis of sensory input must deal with the transformation of coordinates from the egocentric position of sensory input relative to the animal, into an allocentric framework concerning the position of multiple goals and objects relative to each other in the environment. Neurons in retrosplenial cortex show egocentric coding of the position of boundaries in relation to an animal. These neuronal responses are discussed in relation to existing models of the transformation from egocentric to allocentric coordinates using gain fields and a new model proposing transformations of phase coding that differ from current models. The same type of transformations could allow hierarchical representations of complex scenes. The responses in rodents are also discussed in comparison to work on coordinate transformations in humans and non-human primates.

Rethinking retrosplenial cortex: Perspectives and predictions

The last decade has produced exciting new ideas about retrosplenial cortex (RSC) and its role in integrating diverse inputs. Here, we review the diversity in forms of spatial and directional tuning of RSC activity, temporal organization of RSC activity, and features of RSC interconnectivity with other brain structures. We find that RSC anatomy and dynamics are more consistent with roles in multiple sensorimotor and cognitive processes than with any isolated function. However, two more generalized categories of function may best characterize roles for RSC in complex cognitive processes: (1) shifting and relating perspectives for spatial cognition and (2) prediction and error correction for current sensory states with internal representations of the environment. Both functions likely take advantage of RSC's capacity to encode conjunctions among sensory, motor, and spatial mapping information streams. Together, these functions provide the scaffold for intelligent actions, such as navigation, perspective taking, interaction with others, and error detection.

Detecting task-relevant spatiotemporal modules and their relation to motor adaptation

How does the central nervous system (CNS) control our bodies, including hundreds of degrees of freedom (DoFs)? A hypothesis to reduce the number of DoFs posits that the CNS controls groups of joints or muscles (i.e., modules) rather than each joint or muscle independently. Another hypothesis posits that the CNS primarily controls motion components relevant to task achievements (i.e., task-relevant components). Although the two hypotheses are examined intensively, the relationship between the two concepts remains unknown, e.g., unimportant modules may possess task-relevant information. Here, we propose a framework of task-relevant modules, i.e., modules relevant to task achievements, while combining the two concepts mentioned above in a data-driven manner. To examine the possible role of the task-relevant modules, we examined the modulation of the task-relevant modules in a motor adaptation paradigm in which trial-to-trial modifications of motor output are observable. The task-relevant modules, rather than conventional modules, showed adaptation-dependent modulations, indicating the relevance of task-relevant modules to trial-to-trial updates of motor output. Our method provides insight into motor control and adaptation via an integrated framework of modules and task-relevant components.

The role of temporal cortex in the control of attention

Attention is an indispensable component of active vision. Contrary to the widely accepted notion that temporal cortex processing primarily focusses on passive object recognition, a series of very recent studies emphasize the role of temporal cortex structures, specifically the superior temporal sulcus (STS) and inferotemporal (IT) cortex, in guiding attention and implementing cognitive programs relevant for behavioral tasks. The goal of this theoretical paper is to advance the hypothesis that the temporal cortex attention network (TAN) entails necessary components to actively participate in attentional control in a flexible task-dependent manner. First, we will briefly discuss the general architecture of the temporal cortex with a focus on the STS and IT cortex of monkeys and their modulation with attention. Then we will review evidence from behavioral and neurophysiological studies that support their guidance of attention in the presence of cognitive control signals. Next, we propose a mechanistic framework for executive control of attention in the temporal cortex. Finally, we summarize the role of temporal cortex in implementing cognitive programs and discuss how they contribute to the dynamic nature of visual attention to ensure flexible behavior.

Integrating Philosophy of Understanding With the Cognitive Sciences

We provide two programmatic frameworks for integrating philosophical research on understanding with complementary work in computer science, psychology, and neuroscience. First, philosophical theories of understanding have consequences about how agents should reason if they are to understand that can then be evaluated empirically by their concordance with findings in scientific studies of reasoning. Second, these studies use a multitude of explanations, and a philosophical theory of understanding is well suited to integrating these explanations in illuminating ways.

Geometry of sequence working memory in macaque prefrontal cortex

How the brain stores a sequence in memory remains largely unknown. We investigated the neural code underlying sequence working memory using two-photon calcium imaging to record thousands of neurons in the prefrontal cortex of macaque monkeys memorizing and then reproducing a sequence of locations after a delay. We discovered a regular geometrical organization: The high-dimensional neural state space during the delay could be decomposed into a sum of low-dimensional subspaces, each storing the spatial location at a given ordinal rank, which could be generalized to novel sequences and explain monkey behavior. The rank subspaces were distributed across large overlapping neural groups, and the integration of ordinal and spatial information occurred at the collective level rather than within single neurons. Thus, a simple representational geometry underlies sequence working memory.

Motor memories of object dynamics are categorically organized

The ability to predict the dynamics of objects, linking applied force to motion, underlies our capacity to perform many of the tasks we carry out on a daily basis. Thus, a fundamental question is how the dynamics of the myriad objects we interact with are organized in memory. Using a custom-built three-dimensional robotic interface that allowed us to simulate objects of varying appearance and weight, we examined how participants learned the weights of sets of objects that they repeatedly lifted. We find strong support for the novel hypothesis that motor memories of object dynamics are organized categorically, in terms of families, based on covariation in their visual and mechanical properties. A striking prediction of this hypothesis, supported by our findings and not predicted by standard associative map models, is that outlier objects with weights that deviate from the family-predicted weight will never be learned despite causing repeated lifting errors.

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.

A Neural Dynamic Model of the Perceptual Grounding of Spatial and Movement Relations

How does the human brain link relational concepts to perceptual experience? For example, a speaker may say "the cup to the left of the computer" to direct the listener's attention to one of two cups on a desk. We provide a neural dynamic account for both perceptual grounding, in which relational concepts enable the attentional selection of objects in the visual array, and for the generation of descriptions of the visual array using relational concepts. In the model, activation in neural populations evolves dynamically under the influence of both inputs and strong interaction as formalized in dynamic field theory. Relational concepts are modeled as patterns of connectivity to perceptual representations. These generalize across the visual array through active coordinate transforms that center the representation of target objects in potential reference objects. How the model perceptually grounds or generates relational descriptions is probed in 104 simulations that systematically vary the spatial and movement relations employed, the number of feature dimensions used, and the number of matching and nonmatching objects. We explain how sequences of decisions emerge from the time- and state-continuous neural dynamics, how relational hypotheses are generated and either accepted or rejected, followed by the selection of new objects or the generation of new relational hypotheses. Its neural realism distinguishes the model from information processing accounts, its capacity to autonomously generate sequences of processing steps distinguishes it from deep neural network accounts. The model points toward a neural dynamic theory of higher cognition.

Learning Invariant Object and Spatial View Representations in the Brain Using Slow Unsupervised Learning

First, neurophysiological evidence for the learning of invariant representations in the inferior temporal visual cortex is described. This includes object and face representations with invariance for position, size, lighting, view and morphological transforms in the temporal lobe visual cortex; global object motion in the cortex in the superior temporal sulcus; and spatial view representations in the hippocampus that are invariant with respect to eye position, head direction, and place. Second, computational mechanisms that enable the brain to learn these invariant representations are proposed. For the ventral visual system, one key adaptation is the use of information available in the statistics of the environment in slow unsupervised learning to learn transform-invariant representations of objects. This contrasts with deep supervised learning in artificial neural networks, which uses training with thousands of exemplars forced into different categories by neuronal teachers. Similar slow learning principles apply to the learning of global object motion in the dorsal visual system leading to the cortex in the superior temporal sulcus. The learning rule that has been explored in VisNet is an associative rule with a short-term memory trace. The feed-forward architecture has four stages, with convergence from stage to stage. This type of slow learning is implemented in the brain in hierarchically organized competitive neuronal networks with convergence from stage to stage, with only 4-5 stages in the hierarchy. Slow learning is also shown to help the learning of coordinate transforms using gain modulation in the dorsal visual system extending into the parietal cortex and retrosplenial cortex. Representations are learned that are in allocentric spatial view coordinates of locations in the world and that are independent of eye position, head direction, and the place where the individual is located. This enables hippocampal spatial view cells to use idiothetic, self-motion, signals for navigation when the view details are obscured for short periods.

An egocentric straight-ahead bias in primate's vision

As we plan to reach or manipulate objects, we generally orient our body so as to face them. Other objects occupying the same portion of space will likely represent potential obstacles for the intended action. Thus, either as targets or as obstacles, the objects located straight in front of us are often endowed with a special behavioral status. Here, we review a set of recent electrophysiological, imaging and behavioral studies bringing converging evidence that the objects which lie straight-ahead are subject to privileged visual processing. More precisely, these works collectively demonstrate that when gaze steers central vision away from the straight-ahead direction, the latter is still prioritized in peripheral vision. Straight-ahead objects evoke (1) stronger neuronal responses in macaque peripheral V1 neurons, (2) stronger EEG and fMRI activations across the human visual cortex and (3) faster reactive hand and eye movements. Here, we discuss the functional implications and underlying mechanisms behind this phenomenon. Notably, we propose that it can be considered as a new type of visuospatial attentional mechanism, distinct from the previously documented classes of endogenous and exogenous attention.

Deep Predictive Learning in Neocortex and Pulvinar

How do humans learn from raw sensory experience? Throughout life, but most obviously in infancy, we learn without explicit instruction. We propose a detailed biological mechanism for the widely embraced idea that learning is driven by the differences between predictions and actual outcomes (i.e., predictive error-driven learning). Specifically, numerous weak projections into the pulvinar nucleus of the thalamus generate top-down predictions, and sparse driver inputs from lower areas supply the actual outcome, originating in Layer 5 intrinsic bursting neurons. Thus, the outcome representation is only briefly activated, roughly every 100 msec (i.e., 10 Hz, alpha), resulting in a temporal difference error signal, which drives local synaptic changes throughout the neocortex. This results in a biologically plausible form of error backpropagation learning. We implemented these mechanisms in a large-scale model of the visual system and found that the simulated inferotemporal pathway learns to systematically categorize 3-D objects according to invariant shape properties, based solely on predictive learning from raw visual inputs. These categories match human judgments on the same stimuli and are consistent with neural representations in inferotemporal cortex in primates.

Compensating for a shifting world: evolving reference frames of visual and auditory signals across three multimodal brain areas

Stimulus locations are detected differently by different sensory systems, but ultimately they yield similar percepts and behavioral responses. How the brain transcends initial differences to compute similar codes is unclear. We quantitatively compared the reference frames of two sensory modalities, vision and audition, across three interconnected brain areas involved in generating saccades, namely the frontal eye fields (FEF), lateral and medial parietal cortex (M/LIP), and superior colliculus (SC). We recorded from single neurons in head-restrained monkeys performing auditory- and visually guided saccades from variable initial fixation locations and evaluated whether their receptive fields were better described as eye-centered, head-centered, or hybrid (i.e. not anchored uniquely to head- or eye-orientation). We found a progression of reference frames across areas and across time, with considerable hybrid-ness and persistent differences between modalities during most epochs/brain regions. For both modalities, the SC was more eye-centered than the FEF, which in turn was more eye-centered than the predominantly hybrid M/LIP. In all three areas and temporal epochs from stimulus onset to movement, visual signals were more eye-centered than auditory signals. In the SC and FEF, auditory signals became more eye-centered at the time of the saccade than they were initially after stimulus onset, but only in the SC at the time of the saccade did the auditory signals become "predominantly" eye-centered. The results indicate that visual and auditory signals both undergo transformations, ultimately reaching the same final reference frame but via different dynamics across brain regions and time.NEW & NOTEWORTHY Models for visual-auditory integration posit that visual signals are eye-centered throughout the brain, whereas auditory signals are converted from head-centered to eye-centered coordinates. We show instead that both modalities largely employ hybrid reference frames: neither fully head- nor eye-centered. Across three hubs of the oculomotor network (intraparietal cortex, frontal eye field, and superior colliculus) visual and auditory signals evolve from hybrid to a common eye-centered format via different dynamics across brain areas and time.

Low-Level Visual Information Is Maintained across Saccades, Allowing for a Postsaccadic Handoff between Visual Areas

Experience seems continuous and detailed despite saccadic eye movements changing retinal input several times per second. There is debate whether neural signals related to updating across saccades contain information about stimulus features, or only location pointers without visual details. We investigated the time course of low-level visual information processing across saccades by decoding the spatial frequency of a stationary stimulus that changed from one visual hemifield to the other because of a horizontal saccadic eye movement. We recorded magnetoencephalography while human subjects (both sexes) monitored the orientation of a grating stimulus, making spatial frequency task irrelevant. Separate trials, in which subjects maintained fixation, were used to train a classifier, whose performance was then tested on saccade trials. Decoding performance showed that spatial frequency information of the presaccadic stimulus remained present for ∼200 ms after the saccade, transcending retinotopic specificity. Postsaccadic information ramped up rapidly after saccade offset. There was an overlap of over 100 ms during which decoding was significant from both presaccadic and postsaccadic processing areas. This suggests that the apparent richness of perception across saccades may be supported by the continuous availability of low-level information with a "soft handoff" of information during the initial processing sweep of the new fixation.SIGNIFICANCE STATEMENT Saccades create frequent discontinuities in visual input, yet perception appears stable and continuous. How is this discontinuous input processed resulting in visual stability? Previous studies have focused on presaccadic remapping. Here we examined the time course of processing of low-level visual information (spatial frequency) across saccades with magnetoencephalography. The results suggest that spatial frequency information is not predictively remapped but also is not discarded. Instead, they suggest a soft handoff over time between different visual areas, making this information continuously available across the saccade. Information about the presaccadic stimulus remains available, while the information about the postsaccadic stimulus has also become available. The simultaneous availability of both the presaccadic and postsaccadic information could enable rich and continuous perception across saccades.

Visual and Vestibular Selectivity for Self-Motion in Macaque Posterior Parietal Area 7a

We examined the responses of neurons in posterior parietal area 7a to passive rotational and translational self-motion stimuli, while systematically varying the speed of visually simulated (optic flow cues) or actual (vestibular cues) self-motion. Contrary to a general belief that responses in area 7a are predominantly visual, we found evidence for a vestibular dominance in self-motion processing. Only a small fraction of neurons showed multisensory convergence of visual/vestibular and linear/angular self-motion cues. These findings suggest possibly independent neuronal population codes for visual versus vestibular and linear versus angular self-motion. Neural responses scaled with self-motion magnitude (i.e., speed) but temporal dynamics were diverse across the population. Analyses of laminar recordings showed a strong distance-dependent decrease for correlations in stimulus-induced (signal correlation) and stimulus-independent (noise correlation) components of spike-count variability, supporting the notion that neurons are spatially clustered with respect to their sensory representation of motion. Single-unit and multiunit response patterns were also correlated, but no other systematic dependencies on cortical layers or columns were observed. These findings describe a likely independent multimodal neural code for linear and angular self-motion in a posterior parietal area of the macaque brain that is connected to the hippocampal formation.

Neuronal vector coding in spatial cognition

Several types of neurons involved in spatial navigation and memory encode the distance and direction (that is, the vector) between an agent and items in its environment. Such vectorial information provides a powerful basis for spatial cognition by representing the geometric relationships between the self and the external world. Here, we review the explicit encoding of vectorial information by neurons in and around the hippocampal formation, far from the sensory periphery. The parahippocampal, retrosplenial and parietal cortices, as well as the hippocampal formation and striatum, provide a plethora of examples of vector coding at the single neuron level. We provide a functional taxonomy of cells with vectorial receptive fields as reported in experiments and proposed in theoretical work. The responses of these neurons may provide the fundamental neural basis for the (bottom-up) representation of environmental layout and (top-down) memory-guided generation of visuospatial imagery and navigational planning.

Spiking neurons with spatiotemporal dynamics and gain modulation for monolithically integrated memristive neural networks

As a key building block of biological cortex, neurons are powerful information processing units and can achieve highly complex nonlinear computations even in individual cells. Hardware implementation of artificial neurons with similar capability is of great significance for the construction of intelligent, neuromorphic systems. Here, we demonstrate an artificial neuron based on NbO_x volatile memristor that not only realizes traditional all-or-nothing, threshold-driven spiking and spatiotemporal integration, but also enables dynamic logic including XOR function that is not linearly separable and multiplicative gain modulation among different dendritic inputs, therefore surpassing neuronal functions described by a simple point neuron model. A monolithically integrated 4 × 4 fully memristive neural network consisting of volatile NbO_x memristor based neurons and nonvolatile TaO_x memristor based synapses in a single crossbar array is experimentally demonstrated, showing capability in pattern recognition through online learning using a simplified δ-rule and coincidence detection, which paves the way for bio-inspired intelligent systems.

Designing energy efficient and scalable artificial networks for neuromorphic computing remains a challenge. Here, the authors demonstrate online learning in a monolithically integrated 4 × 4 fully memristive neural network consisting of volatile NbOx memristor neurons and nonvolatile TaOx memristor synapses.

Egocentric boundary vector tuning of the retrosplenial cortex

The retrosplenial cortex is reciprocally connected with multiple structures implicated in spatial cognition, and damage to the region itself produces numerous spatial impairments. Here, we sought to characterize spatial correlates of neurons within the region during free exploration in two-dimensional environments. We report that a large percentage of retrosplenial cortex neurons have spatial receptive fields that are active when environmental boundaries are positioned at a specific orientation and distance relative to the animal itself. We demonstrate that this vector-based location signal is encoded in egocentric coordinates, is localized to the dysgranular retrosplenial subregion, is independent of self-motion, and is context invariant. Further, we identify a subpopulation of neurons with this response property that are synchronized with the hippocampal theta oscillation. Accordingly, the current work identifies a robust egocentric spatial code in retrosplenial cortex that can facilitate spatial coordinate system transformations and support the anchoring, generation, and utilization of allocentric representations.

Eye position signals in the dorsal pulvinar during fixation and goal-directed saccades

Sensorimotor cortical areas contain eye position information thought to ensure perceptual stability across saccades and underlie spatial transformations supporting goal-directed actions. One pathway by which eye position signals could be relayed to and across cortical areas is via the dorsal pulvinar. Several studies have demonstrated saccade-related activity in the dorsal pulvinar, and we have recently shown that many neurons exhibit postsaccadic spatial preference. In addition, dorsal pulvinar lesions lead to gaze-holding deficits expressed as nystagmus or ipsilesional gaze bias, prompting us to investigate the effects of eye position. We tested three starting eye positions (−15°, 0°, 15°) in monkeys performing a visually cued memory saccade task. We found two main types of gaze dependence. First, ~50% of neurons showed dependence on static gaze direction during initial and postsaccadic fixation, and might be signaling the position of the eyes in the orbit or coding foveal targets in a head/body/world-centered reference frame. The population-derived eye position signal lagged behind the saccade. Second, many neurons showed a combination of eye-centered and gaze-dependent modulation of visual, memory, and saccadic responses to a peripheral target. A small subset showed effects consistent with eye position-dependent gain modulation. Analysis of reference frames across task epochs from visual cue to postsaccadic fixation indicated a transition from predominantly eye-centered encoding to representation of final gaze or foveated locations in nonretinocentric coordinates. These results show that dorsal pulvinar neurons carry information about eye position, which could contribute to steady gaze during postural changes and to reference frame transformations for visually guided eye and limb movements.

NEW & NOTEWORTHY Work on the pulvinar focused on eye-centered visuospatial representations, but position of the eyes in the orbit is also an important factor that needs to be taken into account during spatial orienting and goal-directed reaching. We show that dorsal pulvinar neurons are influenced by eye position. Gaze direction modulated ongoing firing during stable fixation, as well as visual and saccade responses to peripheral targets, suggesting involvement of the dorsal pulvinar in spatial coordinate transformations.

Neurophysiological coding of space and time in the hippocampus, entorhinal cortex, and retrosplenial cortex

Neurophysiological recordings in behaving rodents demonstrate neuronal response properties that may code space and time for episodic memory and goal-directed behaviour. Here, we review recordings from hippocampus, entorhinal cortex, and retrosplenial cortex to address the problem of how neurons encode multiple overlapping spatiotemporal trajectories and disambiguate these for accurate memory-guided behaviour. The solution could involve neurons in the entorhinal cortex and hippocampus that show mixed selectivity, coding both time and location. Some grid cells and place cells that code space also respond selectively as time cells, allowing differentiation of time intervals when a rat runs in the same location during a delay period. Cells in these regions also develop new representations that differentially code the context of prior or future behaviour allowing disambiguation of overlapping trajectories. Spiking activity is also modulated by running speed and head direction, supporting the coding of episodic memory not as a series of snapshots but as a trajectory that can also be distinguished on the basis of speed and direction. Recent data also address the mechanisms by which sensory input could distinguish different spatial locations. Changes in firing rate reflect running speed on long but not short time intervals, and few cells code movement direction, arguing against path integration for coding location. Instead, new evidence for neural coding of environmental boundaries in egocentric coordinates fits with a modelling framework in which egocentric coding of barriers combined with head direction generates distinct allocentric coding of location. The egocentric input can be used both for coding the location of spatiotemporal trajectories and for retrieving specific viewpoints of the environment. Overall, these different patterns of neural activity can be used for encoding and disambiguation of prior episodic spatiotemporal trajectories or for planning of future goal-directed spatiotemporal trajectories.

Spatial coordinate transforms linking the allocentric hippocampal and egocentric parietal primate brain systems for memory, action in space, and navigation

A theory and model of spatial coordinate transforms in the dorsal visual system through the parietal cortex that enable an interface via posterior cingulate and related retrosplenial cortex to allocentric spatial representations in the primate hippocampus is described. First, a new approach to coordinate transform learning in the brain is proposed, in which the traditional gain modulation is complemented by temporal trace rule competitive network learning. It is shown in a computational model that the new approach works much more precisely than gain modulation alone, by enabling neurons to represent the different combinations of signal and gain modulator more accurately. This understanding may have application to many brain areas where coordinate transforms are learned. Second, a set of coordinate transforms is proposed for the dorsal visual system/parietal areas that enables a representation to be formed in allocentric spatial view coordinates. The input stimulus is merely a stimulus at a given position in retinal space, and the gain modulation signals needed are eye position, head direction, and place, all of which are present in the primate brain. Neurons that encode the bearing to a landmark are involved in the coordinate transforms. Part of the importance here is that the coordinates of the allocentric view produced in this model are the same as those of spatial view cells that respond to allocentric view recorded in the primate hippocampus and parahippocampal cortex. The result is that information from the dorsal visual system can be used to update the spatial input to the hippocampus in the appropriate allocentric coordinate frame, including providing for idiothetic update to allow for self-motion. It is further shown how hippocampal spatial view cells could be useful for the transform from hippocampal allocentric coordinates to egocentric coordinates useful for actions in space and for navigation.

Categorical encoding of decision variables in orbitofrontal cortex

A fundamental and recurrent question in systems neuroscience is that of assessing what variables are encoded by a given population of neurons. Such assessments are often challenging because neurons in one brain area may encode multiple variables, and because neuronal representations might be categorical or non-categorical. These issues are particularly pertinent to the representation of decision variables in the orbitofrontal cortex (OFC)-an area implicated in economic choices. Here we present a new algorithm to assess whether a neuronal representation is categorical or non-categorical, and to identify the encoded variables if the representation is indeed categorical. The algorithm is based on two clustering procedures, one variable-independent and the other variable-based. The two partitions are then compared through adjusted mutual information. The present algorithm overcomes limitations of previous approaches and is widely applicable. We tested the algorithm on synthetic data and then used it to examine neuronal data recorded in the primate OFC during economic decisions. Confirming previous assessments, we found the neuronal representation in OFC to be categorical in nature. We also found that neurons in this area encode the value of individual offers, the binary choice outcome and the chosen value. In other words, during economic choice, neurons in the primate OFC encode decision variables in a categorical way.

Navigating with grid and place cells in cluttered environments

Hippocampal formation contains several classes of neurons thought to be involved in navigational processes, in particular place cells and grid cells. Place cells have been associated with a topological strategy for navigation, while grid cells have been suggested to support metric vector navigation. Grid cell‐based vector navigation can support novel shortcuts across unexplored territory by providing the direction toward the goal. However, this strategy is insufficient in natural environments cluttered with obstacles. Here, we show how navigation in complex environments can be supported by integrating a grid cell‐based vector navigation mechanism with local obstacle avoidance mediated by border cells and place cells whose interconnections form an experience‐dependent topological graph of the environment. When vector navigation and object avoidance fail (i.e., the agent gets stuck), place cell replay events set closer subgoals for vector navigation. We demonstrate that this combined navigation model can successfully traverse environments cluttered by obstacles and is particularly useful where the environment is underexplored. Finally, we show that the model enables the simulated agent to successfully navigate experimental maze environments from the animal literature on cognitive mapping. The proposed model is sufficiently flexible to support navigation in different environments, and may inform the design of experiments to relate different navigational abilities to place, grid, and border cell firing.

Neural Organization of Hierarchical Motor Sequence Representations in the Human Neocortex

Although it is widely accepted that the brain represents movement sequences hierarchically, the neural implementation of this organization is still poorly understood. To address this issue, we experimentally manipulated how participants represented sequences of finger presses at the levels of individual movements, chunks, and entire sequences. Using representational fMRI analyses, we then examined how this hierarchical structure was reflected in the fine-grained brain activity patterns of the participants while they performed the 8 trained sequences. We found clear evidence of each level of the movement hierarchy at the representational level. However, anatomically, chunk and sequence representations substantially overlapped in the premotor and parietal cortices, whereas individual movements were uniquely represented in the primary motor cortex. The findings challenge the common hypothesis of an orderly anatomical separation of different levels of an action hierarchy and argue for a special status of the distinction between individual movements and sequential context.

Humans Use Predictive Gaze Strategies to Target Waypoints for Steering

A major unresolved question in understanding visually guided locomotion in humans is whether actions are driven solely by the immediately available optical information (model-free online control mechanisms), or whether internal models have a role in anticipating the future path. We designed two experiments to investigate this issue, measuring spontaneous gaze behaviour while steering, and predictive gaze behaviour when future path information was withheld. In Experiment 1 participants (N = 15) steered along a winding path with rich optic flow: gaze patterns were consistent with tracking waypoints on the future path 1–3 s ahead. In Experiment 2, participants (N = 12) followed a path presented only in the form of visual waypoints located on an otherwise featureless ground plane. New waypoints appeared periodically every 0.75 s and predictably 2 s ahead, except in 25% of the cases the waypoint at the expected location was not displayed. In these cases, there were always other visible waypoints for the participant to fixate, yet participants continued to make saccades to the empty, but predictable, waypoint locations (in line with internal models of the future path guiding gaze fixations). This would not be expected based upon existing model-free online steering control models, and strongly points to a need for models of steering control to include mechanisms for predictive gaze control that support anticipatory path following behaviours.

Neural correlates of sparse coding and dimensionality reduction

Supported by recent computational studies, there is increasing evidence that a wide range of neuronal responses can be understood as an emergent property of nonnegative sparse coding (NSC), an efficient population coding scheme based on dimensionality reduction and sparsity constraints. We review evidence that NSC might be employed by sensory areas to efficiently encode external stimulus spaces, by some associative areas to conjunctively represent multiple behaviorally relevant variables, and possibly by the basal ganglia to coordinate movement. In addition, NSC might provide a useful theoretical framework under which to understand the often complex and nonintuitive response properties of neurons in other brain areas. Although NSC might not apply to all brain areas (for example, motor or executive function areas) the success of NSC-based models, especially in sensory areas, warrants further investigation for neural correlates in other regions.

Decomposing motion that changes over time into task-relevant and task-irrelevant components in a data-driven manner: application to motor adaptation in whole-body movements

Motor variability is inevitable in human body movements and has been addressed from various perspectives in motor neuroscience and biomechanics: it may originate from variability in neural activities, or it may reflect a large number of degrees of freedom inherent in our body movements. How to evaluate motor variability is thus a fundamental question. Previous methods have quantified (at least) two striking features of motor variability: smaller variability in the task-relevant dimension than in the task-irrelevant dimension and a low-dimensional structure often referred to as synergy or principal components. However, the previous methods cannot be used to quantify these features simultaneously and are applicable only under certain limited conditions (e.g., one method does not consider how the motion changes over time, and another does not consider how each motion is relevant to performance). Here, we propose a flexible and straightforward machine learning technique for quantifying task-relevant variability, task-irrelevant variability, and the relevance of each principal component to task performance while considering how the motion changes over time and its relevance to task performance in a data-driven manner. Our method reveals the following novel property: in motor adaptation, the modulation of these different aspects of motor variability differs depending on the perturbation schedule.

A Stable Visual World in Primate Primary Visual Cortex

Humans and other primates rely on eye movements to explore visual scenes and to track moving objects. As a result, the image that is projected onto the retina-and propagated throughout the visual cortical hierarchy-is almost constantly changing and makes little sense without taking into account the momentary direction of gaze. How is this achieved in the visual system? Here, we show that in primary visual cortex (V1), the earliest stage of cortical vision, neural representations carry an embedded "eye tracker" that signals the direction of gaze associated with each image. Using chronically implanted multi-electrode arrays, we recorded the activity of neurons in area V1 of macaque monkeys during tasks requiring fast (exploratory) and slow (pursuit) eye movements. Neurons were stimulated with flickering, full-field luminance noise at all times. As in previous studies, we observed neurons that were sensitive to gaze direction during fixation, despite comparable stimulation of their receptive fields. We trained a decoder to translate neural activity into metric estimates of gaze direction. This decoded signal tracked the eye accurately not only during fixation but also during fast and slow eye movements. After a fast eye movement, the eye-position signal arrived in V1 at approximately the same time at which the new visual information arrived from the retina. Using simulations, we show that this V1 eye-position signal could be used to take into account the sensory consequences of eye movements and map the fleeting positions of objects on the retina onto their stable position in the world.

Brain-Inspired Coding of Robot Body Schema Through Visuo-Motor Integration of Touched Events

Representing objects in space is difficult because sensorimotor events are anchored in different reference frames, which can be either eye-, arm-, or target-centered. In the brain, Gain-Field (GF) neurons in the parietal cortex are involved in computing the necessary spatial transformations for aligning the tactile, visual and proprioceptive signals. In reaching tasks, these GF neurons exploit a mechanism based on multiplicative interaction for binding simultaneously touched events from the hand with visual and proprioception information.By doing so, they can infer new reference frames to represent dynamically the location of the body parts in the visual space (i.e., the body schema) and nearby targets (i.e., its peripersonal space). In this line, we propose a neural model based on GF neurons for integrating tactile events with arm postures and visual locations for constructing hand- and target-centered receptive fields in the visual space. In robotic experiments using an artificial skin, we show how our neural architecture reproduces the behaviors of parietal neurons (1) for encoding dynamically the body schema of our robotic arm without any visual tags on it and (2) for estimating the relative orientation and distance of targets to it. We demonstrate how tactile information facilitates the integration of visual and proprioceptive signals in order to construct the body space.

Self-organising coordinate transformation with peaked and monotonic gain modulation in the primate dorsal visual pathway

We study a self-organising neural network model of how visual representations in the primate dorsal visual pathway are transformed from an eye-centred to head-centred frame of reference. The model has previously been shown to robustly develop head-centred output neurons with a standard trace learning rule, but only under limited conditions. Specifically it fails when incorporating visual input neurons with monotonic gain modulation by eye-position. Since eye-centred neurons with monotonic gain modulation are so common in the dorsal visual pathway, it is an important challenge to show how efferent synaptic connections from these neurons may self-organise to produce head-centred responses in a subpopulation of postsynaptic neurons. We show for the first time how a variety of modified, yet still biologically plausible, versions of the standard trace learning rule enable the model to perform a coordinate transformation from eye-centred to head-centred reference frames when the visual input neurons have monotonic gain modulation by eye-position.

Active dendritic integration and mixed neocortical network representations during an adaptive sensing behavior

Animals strategically scan the environment to form an accurate perception of their surroundings. Here we investigated the neuronal representations that mediate this behavior. Ca²⁺ imaging and selective optogenetic manipulation during an active sensing task reveals that layer 5 pyramidal neurons in the vibrissae cortex produce a diverse and distributed representation that is required for mice to adapt their whisking motor strategy to changing sensory cues. The optogenetic perturbation degraded single-neuron selectivity and network population encoding through a selective inhibition of active dendritic integration. Together the data indicate that active dendritic integration in pyramidal neurons produces a nonlinearly mixed network representation of joint sensorimotor parameters that is used to transform sensory information into motor commands during adaptive behavior. The prevalence of the layer 5 cortical circuit motif suggests that this is a general circuit computation.

A neural-level model of spatial memory and imagery

We present a model of how neural representations of egocentric spatial experiences in parietal cortex interface with viewpoint-independent representations in medial temporal areas, via retrosplenial cortex, to enable many key aspects of spatial cognition. This account shows how previously reported neural responses (place, head-direction and grid cells, allocentric boundary- and object-vector cells, gain-field neurons) can map onto higher cognitive function in a modular way, and predicts new cell types (egocentric and head-direction-modulated boundary- and object-vector cells). The model predicts how these neural populations should interact across multiple brain regions to support spatial memory, scene construction, novelty-detection, 'trace cells', and mental navigation. Simulated behavior and firing rate maps are compared to experimental data, for example showing how object-vector cells allow items to be remembered within a contextual representation based on environmental boundaries, and how grid cells could update the viewpoint in imagery during planning and short-cutting by driving sequential place cell activity.

Neural-like computing with populations of superparamagnetic basis functions

In neuroscience, population coding theory demonstrates that neural assemblies can achieve fault-tolerant information processing. Mapped to nanoelectronics, this strategy could allow for reliable computing with scaled-down, noisy, imperfect devices. Doing so requires that the population components form a set of basis functions in terms of their response functions to inputs, offering a physical substrate for computing. Such a population can be implemented with CMOS technology, but the corresponding circuits have high area or energy requirements. Here, we show that nanoscale magnetic tunnel junctions can instead be assembled to meet these requirements. We demonstrate experimentally that a population of nine junctions can implement a basis set of functions, providing the data to achieve, for example, the generation of cursive letters. We design hybrid magnetic-CMOS systems based on interlinked populations of junctions and show that they can learn to realize non-linear variability-resilient transformations with a low imprint area and low power.

Population coding, where populations of artificial neurons process information collectively can facilitate robust data processing, but require high circuit overheads. Here, the authors realize this approach with reduced circuit area and power consumption, by utilizing superparamagnetic tunnel junction based neurons.

Robust mixture modeling reveals category-free selectivity in reward region neuronal ensembles

Classification of neurons into clusters based on their response properties is an important tool for gaining insight into neural computations. However, it remains unclear to what extent neurons fall naturally into discrete functional categories. We developed a Bayesian method that models the tuning properties of neural populations as a mixture of multiple types of task-relevant response patterns. We applied this method to data from several cortical and striatal regions in economic choice tasks. In all cases, neurons fell into only two clusters: one multiple-selectivity cluster containing all cells driven by task variables of interest and another of no selectivity for those variables. The single cluster of task-sensitive cells argues against robust categorical tuning in these areas. The no-selectivity cluster was unanticipated and raises important questions about what distinguishes these neurons and what role they play. Moreover, the ability to formally identify these nonselective cells allows for more accurate measurement of ensemble effects by excluding or appropriately down-weighting them in analysis. Our findings provide a valuable tool for analysis of neural data, challenge simple categorization schemes previously proposed for these regions, and place useful constraints on neurocomputational models of economic choice and control. NEW & NOTEWORTHY We present a Bayesian method for formally detecting whether a population of neurons can be naturally classified into clusters based on their response tuning properties. We then examine several data sets of reward system neurons for variables and find in all cases that neurons can be classified into only two categories: a functional class and a non-task-driven class. These results provide important constraints for neural models of the reward system.

Beyond the labeled line: variation in visual reference frames from intraparietal cortex to frontal eye fields and the superior colliculus

We accurately perceive the visual scene despite moving our eyes ~3 times per second, an ability that requires incorporation of eye position and retinal information. In this study, we assessed how this neural computation unfolds across three interconnected structures: frontal eye fields (FEF), intraparietal cortex (LIP/MIP), and the superior colliculus (SC). Single-unit activity was assessed in head-restrained monkeys performing visually guided saccades from different initial fixations. As previously shown, the receptive fields of most LIP/MIP neurons shifted to novel positions on the retina for each eye position, and these locations were not clearly related to each other in either eye- or head-centered coordinates (defined as hybrid coordinates). In contrast, the receptive fields of most SC neurons were stable in eye-centered coordinates. In FEF, visual signals were intermediate between those patterns: around 60% were eye-centered, whereas the remainder showed changes in receptive field location, boundaries, or responsiveness that rendered the response patterns hybrid or occasionally head-centered. These results suggest that FEF may act as a transitional step in an evolution of coordinates between LIP/MIP and SC. The persistence across cortical areas of mixed representations that do not provide unequivocal location labels in a consistent reference frame has implications for how these representations must be read out. NEW & NOTEWORTHY How we perceive the world as stable using mobile retinas is poorly understood. We compared the stability of visual receptive fields across different fixation positions in three visuomotor regions. Irregular changes in receptive field position were ubiquitous in intraparietal cortex, evident but less common in the frontal eye fields, and negligible in the superior colliculus (SC), where receptive fields shifted reliably across fixations. Only the SC provides a stable labeled-line code for stimuli across saccades.

Role of Rostral Fastigial Neurons in Encoding a Body-Centered Representation of Translation in Three Dimensions

Many daily behaviors rely critically on estimates of our body motion. Such estimates must be computed by combining neck proprioceptive signals with vestibular signals that have been transformed from a head- to a body-centered reference frame. Recent studies showed that deep cerebellar neurons in the rostral fastigial nucleus (rFN) reflect these computations, but whether they explicitly encode estimates of body motion remains unclear. A key limitation in addressing this question is that, to date, cell tuning properties have only been characterized for a restricted set of motions across head-re-body orientations in the horizontal plane. Here we examined, for the first time, how 3D spatiotemporal tuning for translational motion varies with head-re-body orientation in both horizontal and vertical planes in the rFN of male macaques. While vestibular coding was profoundly influenced by head-re-body position in both planes, neurons typically reflected at most a partial transformation. However, their tuning shifts were not random but followed the specific spatial trajectories predicted for a 3D transformation. We show that these properties facilitate the linear decoding of fully body-centered motion representations in 3D with a broad range of temporal characteristics from small groups of 5-7 cells. These results demonstrate that the vestibular reference frame transformation required to compute body motion is indeed encoded by cerebellar neurons. We propose that maintaining partially transformed rFN responses with different spatiotemporal properties facilitates the creation of downstream body motion representations with a range of dynamic characteristics, consistent with the functional requirements for tasks such as postural control and reaching.SIGNIFICANCE STATEMENT Estimates of body motion are essential for many daily activities. Vestibular signals are important contributors to such estimates but must be transformed from a head- to a body-centered reference frame. Here, we provide the first direct demonstration that the cerebellum computes this transformation fully in 3D. We show that the output of these computations is reflected in the tuning properties of deep cerebellar rostral fastigial nucleus neurons in a specific distributed fashion that facilitates the efficient creation of body-centered translation estimates with a broad range of temporal properties (i.e., from acceleration to position). These findings support an important role for the rostral fastigial nucleus as a source of body translation estimates functionally relevant for behaviors ranging from postural control to perception.

Neural mechanisms of navigation involving interactions of cortical and subcortical structures

Animals must perform spatial navigation for a range of different behaviors, including selection of trajectories toward goal locations and foraging for food sources. To serve this function, a number of different brain regions play a role in coding different dimensions of sensory input important for spatial behavior, including the entorhinal cortex, the retrosplenial cortex, the hippocampus, and the medial septum. This article will review data concerning the coding of the spatial aspects of animal behavior, including location of the animal within an environment, the speed of movement, the trajectory of movement, the direction of the head in the environment, and the position of barriers and objects both relative to the animal's head direction (egocentric) and relative to the layout of the environment (allocentric). The mechanisms for coding these important spatial representations are not yet fully understood but could involve mechanisms including integration of self-motion information or coding of location based on the angle of sensory features in the environment. We will review available data and theories about the mechanisms for coding of spatial representations. The computation of different aspects of spatial representation from available sensory input requires complex cortical processing mechanisms for transformation from egocentric to allocentric coordinates that will only be understood through a combination of neurophysiological studies and computational modeling.

Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network

The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically.

Detecting the relevance to performance of whole-body movements

Goal-directed whole-body movements are fundamental in our daily life, sports, music, art, and other activities. Goal-directed movements have been intensively investigated by focusing on simplified movements (e.g., arm-reaching movements or eye movements); however, the nature of goal-directed whole-body movements has not been sufficiently investigated because of the high-dimensional nonlinear dynamics and redundancy inherent in whole-body motion. One open question is how to overcome high-dimensional nonlinear dynamics and redundancy to achieve the desired performance. It is possible to approach the question by quantifying how the motions of each body part at each time point contribute to movement performance. Nevertheless, it is difficult to identify an explicit relation between each motion element (the motion of each body part at each time point) and performance as a result of the high-dimensional nonlinear dynamics and redundancy inherent in whole-body motion. The current study proposes a data-driven approach to quantify the relevance of each motion element to the performance. The current findings indicate that linear regression may be used to quantify this relevance without considering the high-dimensional nonlinear dynamics of whole-body motion.

Diverse coordinate frames on sensorimotor areas in visuomotor transformation

The visuomotor transformation during a goal-directed movement may involve a coordinate transformation from visual 'extrinsic' to muscle-like 'intrinsic' coordinate frames, which might be processed via a multilayer network architecture composed of neural basis functions. This theory suggests that the postural change during a goal-directed movement task alters activity patterns of the neurons in the intermediate layer of the visuomotor transformation that recieves both visual and proprioceptive inputs, and thus influence the multi-voxel pattern of the blood oxygenation level dependent signal. Using a recently developed multi-voxel pattern decoding method, we found extrinsic, intrinsic and intermediate coordinate frames along the visuomotor cortical pathways during a visuomotor control task. The presented results support the hypothesis that, in human, the extrinsic coordinate frame was transformed to the muscle-like frame over the dorsal pathway from the posterior parietal cortex and the dorsal premotor cortex to the primary motor cortex.

Numerical Proportion Representation: A Neurocomputational Account

Proportion representation is an emerging subdomain in numerical cognition. However, its nature and its correlation with simple number representation remain elusive, especially at the theoretical level. To fill this gap, we propose a gain-field model of proportion representation to shed light on the neural and computational basis of proportion representation. The model is based on two well-supported neuroscientific findings. The first, gain modulation, is a general mechanism for information integration in the brain; the second relevant finding is how simple quantity is neurally represented. Based on these principles, the model accounts for recent relevant proportion representation data at both behavioral and neural levels. The model further addresses two key computational problems for the cognitive processing of proportions: invariance and generalization. Finally, the model provides pointers for future empirical testing.

Environmental Anchoring of Head Direction in a Computational Model of Retrosplenial Cortex

Allocentric (world-centered) spatial codes driven by path integration accumulate error unless reset by environmental sensory inputs that are necessarily egocentric (body-centered). Previous models of the head direction system avoided the necessary transformation between egocentric and allocentric reference frames by placing visual cues at infinity. Here we present a model of head direction coding that copes with exclusively proximal cues by making use of a conjunctive representation of head direction and location in retrosplenial cortex. Egocentric landmark bearing of proximal cues, which changes with location, is mapped onto this retrosplenial representation. The model avoids distortions due to parallax, which occur in simple models when a single proximal cue card is used, and can also accommodate multiple cues, suggesting how it can generalize to arbitrary sensory environments. It provides a functional account of the anatomical distribution of head direction cells along Papez' circuit, of place-by-direction coding in retrosplenial cortex, the anatomical connection from the anterior thalamic nuclei to retrosplenial cortex, and the involvement of retrosplenial cortex in navigation. In addition to parallax correction, the same mechanism allows for continuity of head direction coding between connected environments, and shows how a head direction representation can be stabilized by a single within arena cue. We also make predictions for drift during exploration of a new environment, the effects of hippocampal lesions on retrosplenial cells, and on head direction coding in differently shaped environments.

SIGNIFICANCE STATEMENT

The activity of head direction cells signals the direction of an animal's head relative to landmarks in the world. Although driven by internal estimates of head movements, head direction cells must be kept aligned to the external world by sensory inputs, which arrive in the reference frame of the sensory receptors. We present a computational model, which proposes that sensory inputs are correctly associated to head directions by virtue of a conjunctive representation of place and head directions in the retrosplenial cortex. The model allows for a stable head direction signal, even when the sensory input from nearby cues changes dramatically whenever the animal moves to a different location, and enables stable representations of head direction across connected environments.

Implementing a Bayes Filter in a Neural Circuit: The Case of Unknown Stimulus Dynamics

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli that caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the predictions of an internal model. The internal model of the Bayes filter is based on the true stimulus dynamics, and in this note, we present a method for training a theoretical neural circuit to approximately implement a Bayes filter when the stimulus dynamics are unknown. To do this we use the inferential properties of linear probabilistic population codes to compute Bayes' rule and train a neural network to compute approximate predictions by the method of maximum likelihood. In particular, we perform stochastic gradient descent on the negative log-likelihood of the neural network parameters with a novel approximation of the gradient. We demonstrate our methods on a finite-state, a linear, and a nonlinear filtering problem and show how the hidden layer of the neural network develops tuning curves consistent with findings in experimental neuroscience.

Hebbian learning of hand-centred representations in a hierarchical neural network model of the primate visual system

A subset of neurons in the posterior parietal and premotor areas of the primate brain respond to the locations of visual targets in a hand-centred frame of reference. Such hand-centred visual representations are thought to play an important role in visually-guided reaching to target locations in space. In this paper we show how a biologically plausible, Hebbian learning mechanism may account for the development of localized hand-centred representations in a hierarchical neural network model of the primate visual system, VisNet. The hand-centered neurons developed in the model use an invariance learning mechanism known as continuous transformation (CT) learning. In contrast to previous theoretical proposals for the development of hand-centered visual representations, CT learning does not need a memory trace of recent neuronal activity to be incorporated in the synaptic learning rule. Instead, CT learning relies solely on a Hebbian learning rule, which is able to exploit the spatial overlap that naturally occurs between successive images of a hand-object configuration as it is shifted across different retinal locations due to saccades. Our simulations show how individual neurons in the network model can learn to respond selectively to target objects in particular locations with respect to the hand, irrespective of where the hand-object configuration occurs on the retina. The response properties of these hand-centred neurons further generalise to localised receptive fields in the hand-centred space when tested on novel hand-object configurations that have not been explored during training. Indeed, even when the network is trained with target objects presented across a near continuum of locations around the hand during training, the model continues to develop hand-centred neurons with localised receptive fields in hand-centred space. With the help of principal component analysis, we provide the first theoretical framework that explains the behavior of Hebbian learning in VisNet.