Graph Element Networks: adaptive, structured computation and memory

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational process defined on the graph to model the relationship between an initial function defined over a space and a resulting function in the same space. We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned input-output relationship to generalize over the size of the underlying space and run the same model at different levels of precision, trading computation for accuracy. We demonstrate this method on a traditional PDE problem, a physical prediction problem from robotics, and learning to predict scene images from novel viewpoints.Comment: Accepted to ICML 201

Computational analyses of the role of hippocampal oscillations in familiar and novel environments.

The hippocampal formation is known to support several different types of spatial representation, and to play an important role in detecting environmental novelty. A striking aspect of hippocampal physiology is the theta rhythm, recorded in the electroencephalogram (EEG). This thesis investigates the role of the theta rhythm as an organising principle of the hippocampal formation, and in particular its role in the detection of novelty. In the first experimental chapter, the behavioural correlates of principal cells across several regions of the hippocampal formation - head direction and conjunctive place by direction cells in the presubiculum, place cells in CA1 and grid cells in the MEC - are studied, with an emphasis on the contribution of running speed. Subpopulations of cells, both positively and a minority which are negatively modulated by speed are found in each region. The second experimental chapter investigates the predictions of a recent model of entorhinal cortical grid cells. The model, based on the interference between somatic and dendritic oscillators, predicts that intrinsic firing frequency should exceed EEG theta frequency by a greater amount for small grids than for large grids and by a greater amount during fast running compared to slow. These relationships are confirmed in electrophysiological recordings in freely-moving rats. The third experimental chapter reports the results of a detailed examination of the rodent EEG under conditions of novelty and familiarity. The oscillatory interference model predicts a reduction in the theta frequency in a novel environmental context. This is substantiated by the data and reveals a new mechanism for signalling novelty in the brain. The fourth experimental chapter probes the specific roles played by the subiculum and CA1. There is debate as to whether the subiculum is an input as well as, traditionally considered, an output of the HF. I propose that subiculum is capable of informing CA1 and data is presented to show that subicular firing occurs earlier in the theta cycle and anticipates position further ahead than firing in CA1 does, and that this difference is modulated by familiarity with the environment

Novelty and anxiolytic drugs dissociate two components of hippocampal theta in behaving rats

Hippocampal processing is strongly implicated in both spatial cognition and anxiety and is temporally organized by the theta rhythm. However, there has been little attempt to understand how each type of processing relates to the other in behaving animals, despite their common substrate. In freely moving rats, there is a broadly linear relationship between hippocampal theta frequency and running speed over the normal range of speeds used during foraging. A recent model predicts that spatial-translation-related and arousal/anxiety-related mechanisms of hippocampal theta generation underlie dissociable aspects of the theta frequency–running speed relationship (the slope and intercept, respectively). Here we provide the first confirmatory evidence: environmental novelty decreases slope, whereas anxiolytic drugs reduce intercept. Variation in slope predicted changes in spatial representation by CA1 place cells and novelty-responsive behavior. Variation in intercept predicted anxiety-like behavior. Our findings isolate and doubly dissociate two components of theta generation that operate in parallel in behaving animals and link them to anxiolytic drug action, novelty, and the metric for self-motion

Spatial cell firing during virtual navigation of open arenas by head-restrained mice

We present a mouse virtual reality (VR) system which restrains head-movements to horizontal rotations, compatible with multi-photon imaging. This system allows expression of the spatial navigation and neuronal firing patterns characteristic of real open arenas (R). Comparing VR to R: place and grid, but not head-direction, cell firing had broader spatial tuning; place, but not grid, cell firing was more directional; theta frequency increased less with running speed; whereas increases in firing rates with running speed and place and grid cells' theta phase precession were similar. These results suggest that the omni-directional place cell firing in R may require local-cues unavailable in VR, and that the scale of grid and place cell firing patterns, and theta frequency, reflect translational motion inferred from both virtual (visual and proprioceptive) and real (vestibular translation and extra-maze) cues. By contrast, firing rates and theta phase precession appear to reflect visual and proprioceptive cues alone

Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network.

Grid cells fire in sequences that represent rapid trajectories in space. During locomotion, theta sequences encode sweeps in position starting slightly behind the animal and ending ahead of it. During quiescence and slow wave sleep, bouts of synchronized activity represent long trajectories called replays, which are well-established in place cells and have been recently reported in grid cells. Theta sequences and replay are hypothesized to facilitate many cognitive functions, but their underlying mechanisms are unknown. One mechanism proposed for grid cell formation is the continuous attractor network. We demonstrate that this established architecture naturally produces theta sequences and replay as distinct consequences of modulating external input. Driving inhibitory interneurons at the theta frequency causes attractor bumps to oscillate in speed and size, which gives rise to theta sequences and phase precession, respectively. Decreasing input drive to all neurons produces traveling wavefronts of activity that are decoded as replays

Developmental underpinnings of differences in rodent novelty‐seeking and emotional reactivity

Innate differences in human temperament strongly influence how individuals cope with stress and also predispose towards specific types of psychopathology. The present study examines the developing brain in an animal model of temperamental differences to examine how altered neurodevelopment may engender differences in emotional reactivity that are stable throughout the animal’s life. We utilize selectively‐bred High Responder (bHR) and Low Responder (bLR) rats that exhibit dramatic emotional behavior differences, with bHRs exhibiting exaggerated novelty‐exploration, aggression, impulsivity and drug self‐administration, and bLRs showing marked behavioral inhibition and exaggerated anxiety‐like and depressive‐like behavior. Using Affymetrix microarrays, we assessed bLR and bHR gene expression in the developing brain on postnatal days (P)7, 14 and 21, focusing on the hippocampus and nucleus accumbens, two regions related to emotionality and known to differ in adult bLR and bHR rats. We found dramatic gene expression differences between bLR and bHR in the P7 and P14 hippocampus, with minimal differences in the nucleus accumbens. Some of the most profound differences involved genes critical for neurodevelopment and synaptogenesis. Stereological studies evaluated hippocampal structure in developing bHR and bLR pups, revealing enhanced hippocampal volume and cell proliferation in bLR animals. Finally, behavioral studies showed that the characteristic bHR and bLR behavioral phenotypes emerge very early in life, with exploratory differences apparent at P16 and anxiety differences present by P25. Together these data point to specific brain regions and critical periods when the bHR and bLR phenotypes begin to diverge, which may eventually allow us to test possible therapeutic interventions to normalize extreme phenotypes (e.g. the anxiety‐prone nature of bLRs or drug addiction proclivity of bHRs).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87155/1/j.1460-9568.2011.07811.x.pd

Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ3/(4πσ)2 seconds where µ is the mean period of an oscillator in seconds and σ2 its variance in seconds2. We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed

From synaptic plasticity to spatial maps and sequence learning

The entorhinal-hippocampal circuit is crucial for several forms of learning and memory, especially sequence learning, including spatial navigation. The challenge is to understand the underlying mechanisms. Pioneering discoveries of spatial selectivity in this circuit, i.e. place cells and grid cells, provided a major step forward in tackling this challenge. Considerable research has also shown that sequence learning relies on synaptic plasticity, especially the Hebbian or the NMDAR-dependent synaptic plasticity. This raises several questions: Are spatial maps plastic? If so, what is the contribution of Hebbian plasticity to spatial map plasticity? How does the spatial map plasticity contribute to sequence learning? A combination of computational and experimental studies has shown that NMDAR-mediated plasticity and theta rhythm can have specific effects on the formation and experiential modification of spatial maps to facilitate predictive coding. Advances in transgenic techniques have provided further support for these mechanisms. Although many exciting challenges remain, these findings have brought us closer to solving the puzzle of how the hippocampal system contributes to spatial memory, and point to a way forward