Ila Fiete

Accurate path integration in continuous attractor network models of grid cells

Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animals position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rats velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.

Spike-time-dependent plasticity and heterosynaptic competition organize networks to produce long scale-free sequences of neural activity.

Sequential neural activity patterns are as ubiquitous as the outputs they drive, which include motor gestures and sequential cognitive processes. Neural sequences are long, compared to the activation durations of participating neurons, and sequence coding is sparse. Numerous studies demonstrate that spike-time-dependent plasticity (STDP), the primary known mechanism for temporal order learning in neurons, cannot organize networks to generate long sequences, raising the question of how such networks are formed. We show that heterosynaptic competition within single neurons, when combined with STDP, organizes networks to generate long unary activity sequences even without sequential training inputs. The network produces a diversity of sequences with a power law length distribution and exponent -1, independent of cellular time constants. We show evidence for a similar distribution of sequence lengths in the recorded premotor song activity of songbirds. These results suggest that neural sequences may be shaped by synaptic constraints and network circuitry rather than cellular time constants.

What Grid Cells Convey about Rat Location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rats location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code.

Testing Odor Response Stereotypy in the Drosophila Mushroom Body

The mushroom body is an insect brain structure required for olfactory learning. Its principal neurons, the Kenyon cells (KCs), form a large cell population. The neuronal populations from which their olfactory input derives (olfactory sensory and projection neurons) can be identified individually by genetic, anatomical, and physiological criteria. We ask whether KCs are similarly identifiable individually, using genetic markers and whole-cell patch-clamp in vivo. We find that across-animal responses are as diverse within the genetically labeled subset as across all KCs in a larger sample. These results combined with those from a simple model, using projection neuron odor responses as inputs, suggest that the precise circuit specification seen at earlier stages of odor processing is likely absent among the mushroom body KCs.

Specific evidence of low-dimensional continuous attractor dynamics in grid cells

We examined simultaneously recorded spikes from multiple rat grid cells, to explain mechanisms underlying their activity. Among grid cells with similar spatial periods, the population activity was confined to lie close to a two-dimensional (2D) manifold: grid cells differed only along two dimensions of their responses and otherwise were nearly identical. Relationships between cell pairs were conserved despite extensive deformations of single-neuron responses. Results from novel environments suggest such structure is not inherited from hippocampal or external sensory inputs. Across conditions, cell-cell relationships are better conserved than responses of single cells. Finally, the system is continually subject to perturbations that, were the 2D manifold not attractive, would drive the system to inhabit a different region of state space than observed. These findings have strong implications for theories of grid-cell activity and substantiate the general hypothesis that the brain computes using low-dimensional continuous attractors.

Grid cells generate an analog error-correcting code for singularly precise neural computation.

Entorhinal grid cells in mammals fire as a function of animal location, with spatially periodic response patterns. This nonlocal periodic representation of location, a local variable, is unlike other neural codes. There is no theoretical explanation for why such a code should exist. We examined how accurately the grid code with noisy neurons allows an ideal observer to estimate location and found this code to be a previously unknown type of population code with unprecedented robustness to noise. In particular, the representational accuracy attained by grid cells over the coding range was in a qualitatively different class from what is possible with observed sensory and motor population codes. We found that a simple neural network can effectively correct the grid code. To the best of our knowledge, these results are the first demonstration that the brain contains, and may exploit, powerful error-correcting codes for analog variables.

Grid cells: The position code, neural network models of activity, and the problem of learning

We review progress on the modeling and theoretical fronts in the quest to unravel the computational properties of the grid cell code and to explain the mechanisms underlying grid cell dynamics. The goals of the review are to outline a coherent framework for understanding the dynamics of grid cells and their representation of space; to critically present and draw contrasts between recurrent network models of grid cells based on continuous attractor dynamics and independent‐neuron models based on temporal interference; and to suggest open questions for experiment and theory.

Fundamental limits on persistent activity in networks of noisy neurons

Neural noise limits the fidelity of representations in the brain. This limitation has been extensively analyzed for sensory coding. However, in short-term memory and integrator networks, where noise accumulates and can play an even more prominent role, much less is known about how neural noise interacts with neural and network parameters to determine the accuracy of the computation. Here we analytically derive how the stored memory in continuous attractor networks of probabilistically spiking neurons will degrade over time through diffusion. By combining statistical and dynamical approaches, we establish a fundamental limit on the network’s ability to maintain a persistent state: The noise-induced drift of the memory state over time within the network is strictly lower-bounded by the accuracy of estimation of the network’s instantaneous memory state by an ideal external observer. This result takes the form of an information-diffusion inequality. We derive some unexpected consequences: Despite the persistence time of short-term memory networks, it does not pay to accumulate spikes for longer than the cellular time-constant to read out their contents. For certain neural transfer functions, the conditions for optimal sensory coding coincide with those for optimal storage, implying that short-term memory may be co-localized with sensory representation.

A Model of Grid Cell Development through Spatial Exploration and Spike Time-Dependent Plasticity

Grid cell responses develop gradually after eye opening, but little is known about the rules that govern this process. We present a biologically plausible model for the formation of a grid cell network. An asymmetric spike time-dependent plasticity rule acts upon an initially unstructured network of spiking neurons that receive inputs encoding animal velocity and location. Neurons develop an organized recurrent architecture based on the similarity of their inputs, interacting through inhibitory interneurons. The mature network can convert velocity inputs into estimates of animal location, showing that spatially periodic responses and the capacity of path integration can arise through synaptic plasticity, acting on inputs that display neither. The model provides numerous predictions about the necessity of spatial exploration for grid cell development, network topography, the maturation of velocity tuning and neural correlations, the abrupt transition to stable patterned responses, and possible mechanisms to set grid period across grid modules.

Do We Understand the Emergent Dynamics of Grid Cell Activity

Single neurons in the dorsolateral band of the rat entorhinal cortex (dMEC) fire as a function of rat position whenever the rat is on any vertex of a regular triangular lattice, that tiles the entire plane ([Hafting et al., 2005][1]). Even in the dark, the pattern refreshes correctly with rat