An Efficient Coding Theory for a Dynamic Trajectory Predicts non-Uniform Allocation of Grid Cells to Modules in the Entorhinal Cortex

Grid cells in the entorhinal cortex encode the position of an animal in its environment using spatially periodic tuning curves of varying periodicity. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal's motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trends seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder of the spikes. This readout scheme requires persistence over varying timescales, ranging from ~1ms to ~1s, depending on the grid cell module. Our results suggest that the brain employs an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory coding.Comment: 23 pages, 5 figures. Supplemental Information available from the authors on request. A previous version of this work appeared in abstract form (Program No. 727.02. 2015 Neuroscience Meeting Planner. Chicago, IL: Society for Neuroscience, 2015. Online.

Representations of ongoing experience within the rodent hippocampal subfield CA1

The hippocampus is critical for the encoding and retrieval of episodic memories. During ongoing experience, the hippocampus exhibits activity patterns related to the current spatiotemporal context. How hippocampal firing patterns relate to the representation of mental maps important for behavioral and cognitive processes is still an open question. Here a series of experiments aimed to test how the hippocampus represents the spatiotemporal context of ongoing experience. Extracellular recordings from the dorsal CA1 region of the hippocampus were collected from rats engaged in a blocked serial reversal object-association task. Behaviorally, rats did not utilize the temporal segregation between task blocks as a way to correctly match object valence and rather treated each block of trials as separate episodes. This lack of an alternating context was further uncovered in the neural coding of the rat’s hippocampal firing patterns. Furthermore, gradual drift in the hippocampal ensemble representation of experience was discovered, correlating with the temporal duration of the task and not the blocked organization of the behavioral paradigm. In the next two experiments, extracellular recordings from dorsal CA1 were collected from rats traversing a linear track environment, with different environmental manipulations. During variable starting location recording sessions, it was found that positional coding by the hippocampal population was relative to starting location and that place field allocation was biased towards the reference frame at the start of the journey, demonstrating that hippocampal place fields are not uniformly distributed and express compressed activity patterns referenced to the beginning point of trajectories. During blocked manipulation of lighting condition, individual units showed preference to specific lighting conditions and the hippocampal population rapidly remapped between lights ‘ON’ and lights ‘OFF’ blocks of trials, suggesting that hippocampal maps of space are not solely governed by internal dynamics and that alterations in sensory input can modify hippocampal motifs of ongoing experience. Overall, the findings of the three experiments further our understanding of how the hippocampus represents ongoing experience, highlighting the role of temporal drift as well as demonstrating how both external and internal stimuli and frames of reference coalesce into a comprehensive cognitive map of experience

Neural coding of representations of self-location

Grid cells in the hippocampal formation fire when the animal visits nodes of a triangular grid covering its environment. Their activity may represent the animal’s spatial location for use in memory and navigation. I used simulations to investigate grid cells’ encoding of self-location, showing that some properties of in-vivo firing patterns are adaptive for fidelity. In a related project, I found evidence suggesting medial entorhinal cortex cells may participate in non-local representations of remembered, planned or imagined routes, foreshadowing more recent work. First, I simulated firing patterns in modular grid cell systems with different parameters (e.g. grid scales, orientations), and assessed how well they encode self-location under different conditions (e.g. spatial uncertainty, environment size). I demonstrated that grid cell system parameters affect precision (within the smallest grid scale) and accuracy (including mis-localisation to the wrong repeating unit of a grid) differently. I showed that grid scale expansion partially mitigates the effect of spatial uncertainty on accuracy, supporting the hypothesis that the temporary expansion experimentally observed in rats exploring novel environments may be an adaptive response to uncertainty. In an environment with anisotropic spatial information, I showed that aligning the grid-patterns with the axis in which more information is available improves performance, matching collaborators’ findings that grid-patterns in humans virtually navigating such environments are aligned that way. I showed how self-localisation error in larger environments is influenced by the relation between the modules’ scales. In the presence of spatial uncertainty, absolute predictions of capacity break down, and accuracy varies sharply and irregularly with the ratio between modules’ scales. This, and the observed biological variability of the ratio, make some theoretical predictions of optimised values for the ratio implausible. In sum, I have demonstrated how biologically-inspired simulations can help interpret grid cell firing patterns and explore the adaptiveness of neural coding schemes

Four-Dimensional Consciousness

Conscious experience is the direct observation of conscious events. Human conscious experience is four-dimensional. Conscious events are linked (associated) by spacetime intervals to produce a coherent conscious experience. This explains why conscious experience appears to us the way it does. Conscious experience is an orientation in space and time, an understanding of the position of the observer in space and time. Causality, past-future relations, learning, memory, cognitive processing, and goal-directed actions all evolve from four-dimensional conscious experience. A neural correlate for four-dimensional conscious experience can be found in the human brain and is modelled by Einstein's special theory of relativity. The relativistic concept of spacetime interval is central for understanding conscious experience and cognition

A Neural Signal Processor for Low-Latency Spike Inference

This thesis describes the development of a system that can assign identities to a population of single-units, in multi-electrode recordings, at single-spike resolution with low-latency. The system has two parts. The first is a Field-Programmable Gate Array (FPGA)-based Neural Signal Processor (NSP) that receives raw input and generates labelled spikes as output, a process referred to as real-time spike inference. The second is a piece of software (Spiketag) that runs on a PC, communicates with the NSP, and generates a spike-sorted model to guide the real-time spike inference. The NSP provides clocks and control signals to five 32-channel INTAN RHD2132 chips to manage the acquisition of 160 channels of raw neural data. In parallel, the NSP further filters, detects and extracts extracellular spike waveforms from the raw neural data recorded by tetrodes or silicon probes and assigns single-unit identity to each detected spike. A set of Python application programming interfaces (APIs) was developed in Spiketag to enable the communication between the NSP and the PC. These APIs allow the NSP to obtain a model from the PC, which holds parameters such as reference channels, spike detection thresholds, spike feature transformation matrix and vector quantized clusters generated by spike sorting a short recording session. Using the spike-sorted model, the NSP performs data acquisition and real-time spike inference simultaneously. Algorithmic modules were implemented in the FPGA and pipelined to compute during 40 ms acquisition intervals. At the output end of the FPGA NSP, the real-time assigned single-unit identity (spike-id) is packaged with the timestamp, the electrode group, and the spike features as a spike-id packet. Spike-id packets are asynchronously transmitted through a low-latency Peripheral Component Interconnect Express (PCIe) interface to the PC, producing the real-time spike trains. The real-time spike trains can be used for further processing, such as real-time decoding. Several types of ground-truth data, including intracellular/extracellular paired recordings, synthesized tetrode extracellular waveforms with ground-truth spike timing and high-channel-count silicon probe recordings with ground-truth animal positions during navigation were used to validate the low-latency (1 ms) and high-accuracy (as high as state-of-the-art offline sorting and decoding algorithms) of the NSP’s real-time spike inference and the NSP-based real-time population decoding performance

Hippocampal predictive maps of an uncertain world

Humans and other animals can solve a wide variety of decision-making problems with remarkable flexibility. This flexibility is thought to derive from an internal model of the world, or ‘cognitive map’, used to predict the future and plan actions accordingly. A recent theoretical proposal suggests that the hippocampus houses a representation of long-run state expectancies. These “successor representations” (SRs) occupy a middle ground between model-free and model-based reinforcement learning strategies. However, it is not clear whether SRs can explain hippocampal contributions to spatial and model-based behaviour, nor how a putative hippocampal SR might interface with striatal learning mechanisms. More generally, it is not clear how the predictive map should encode uncertainty, and how an uncertainty-augmented predictive map modifies our experimental predictions for animal behaviour. In the first part of this thesis, I investigated whether viewing the hippocampus as an SR can explain experiments contrasting hippocampal and dorsolateral striatal contributions to behaviour in spatial and non-spatial tasks. To do this, I modelled the hippocampus as an SR and DLS as model-free reinforcement learning, combining their outputs via their relative reliability as a proxy for uncertainty. Current SR models do not formally address uncertainty. Therefore I extended the learning of SRs by temporal differences to include managing uncertainty in new observations versus existing knowledge. I generalise this approach to a multi-task setting using a Bayesian nonparametric switching Kalman Filter, allowing the model to learn and maintain multiple task-specific SR maps and infer which one to use at any moment based on the observations. I show that this Bayesian SR model captures animal behaviour in tasks which require contextual memory and generalisation. In conclusion, I consider how the hippocampal contribution to behaviour can be considered as a predictive map when adapted to take account of uncertainty and combined with other behavioural controllers