Synaptic balancing: A biologically plausible local learning rule that provably increases neural network noise robustness without sacrificing task performance.

We introduce a novel, biologically plausible local learning rule that provably increases the robustness of neural dynamics to noise in nonlinear recurrent neural networks with homogeneous nonlinearities. Our learning rule achieves higher noise robustness without sacrificing performance on the task and without requiring any knowledge of the particular task. The plasticity dynamics-an integrable dynamical system operating on the weights of the network-maintains a multiplicity of conserved quantities, most notably the network's entire temporal map of input to output trajectories. The outcome of our learning rule is a synaptic balancing between the incoming and outgoing synapses of every neuron. This synaptic balancing rule is consistent with many known aspects of experimentally observed heterosynaptic plasticity, and moreover makes new experimentally testable predictions relating plasticity at the incoming and outgoing synapses of individual neurons. Overall, this work provides a novel, practical local learning rule that exactly preserves overall network function and, in doing so, provides new conceptual bridges between the disparate worlds of the neurobiology of heterosynaptic plasticity, the engineering of regularized noise-robust networks, and the mathematics of integrable Lax dynamical systems.

Morphogenesis of termite mounds.

Several species of millimetric-sized termites across Africa, Asia, Australia, and South America collectively construct large, meter-sized, porous mound structures that serve to regulate mound temperature, humidity, and gas concentrations. These mounds display varied yet distinctive morphologies that range widely in size and shape. To explain this morphological diversity, we introduce a mathematical model that couples environmental physics to insect behavior: The advection and diffusion of heat and pheromones through a porous medium are modified by the mound geometry and, in turn, modify that geometry through a minimal characterization of termite behavior. Our model captures the range of naturally observed mound shapes in terms of a minimal set of dimensionless parameters and makes testable hypotheses for the response of mound morphology to external temperature oscillations and internal odors. Our approach also suggests mechanisms by which evolutionary changes in odor production rate and construction behavior coupled to simple physical laws can alter the characteristic mound morphology of termites.

Emergent elasticity in the neural code for space.

Upon encountering a novel environment, an animal must construct a consistent environmental map, as well as an internal estimate of its position within that map, by combining information from two distinct sources: self-motion cues and sensory landmark cues. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to accomplish this feat? Here we show analytically how a neural attractor model that combines path integration of self-motion cues with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network. Moreover, our model makes several experimentally testable predictions, including (i) systematic path-dependent shifts in the firing fields of grid cells toward the most recently encountered landmark, even in a fully learned environment; (ii) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers; and (iii) the creation of topological defects in grid cell firing patterns through specific environmental manipulations. Taken together, our results conceptually link known aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

Solar-powered ventilation of African termite mounds.

How termite mounds function to facilitate climate control is still only partially understood. Recent experimental evidence in the mounds of a single species, the south Asian termite Odontotermes obesus, suggests that the daily oscillations of radiant heating associated with diurnal insolation patterns drive convective flow within them. How general this mechanism is remains unknown. To probe this, we consider the mounds of the African termite Macrotermes michaelseni, which thrives in a very different environment. By directly measuring air velocities and temperatures within the mound, we see that the overall mechanisms and patterns involved are similar to that in the south Asian species. However, there are also some notable differences between the physiology of these mounds associated with the temporal variations in radiant heating patterns and CO2 dynamics. Because of the difference between direct radiant heating driven by the position of the sun in African conditions, and the more shaded south Asian environments, we see changes in the convective flows in the two types of mounds. Furthermore, we also see that the south Asian mounds show a significant overturning of stratified gases, once a day, while the African mounds have a relatively uniform concentration of CO2 Overall, our observations show that despite these differences, termite architectures can harness periodic solar heating to drive ventilation inside them in very different environments, functioning as an external lung, with clear implications for human engineering.

Feedback-induced phase transitions in active heterogeneous conductors.

An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm's law or Darcy's law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that characterize the way in which addition or removal of matter follows a simple local (or nonlocal) feedback rule corresponding to either flow-seeking or flow-avoiding behavior. Using numerical simulations and a continuum mean field theory, we show that flow-avoiding feedback causes an initially uniform system to become strongly heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feedback leads to an immuring (wall-building) phase separation. Our results provide a qualitative explanation for the patterning of active conducting media in natural systems, while suggesting ways to realize complex architectures using simple rules in engineered systems.

A unified theory for the computational and mechanistic origins of grid cells.

The discovery of entorhinal grid cells has generated considerable interest in how and why hexagonal firing fields might emerge in a generic manner from neural circuits, and what their computational significance might be. Here, we forge a link between the problem of path integration and the existence of hexagonal grids, by demonstrating that such grids arise in neural networks trained to path integrate under simple biologically plausible constraints. Moreover, we develop a unifying theory for why hexagonal grids are ubiquitous in path-integrator circuits. Such trained networks also yield powerful mechanistic hypotheses, exhibiting realistic levels of biological variability not captured by hand-designed models. We furthermore develop methods to analyze the connectome and activity maps of our networks to elucidate fundamental mechanisms underlying path integration. These methods provide a road map to go from connectomic and physiological measurements to conceptual understanding in a manner that could generalize to other settings.

Nonperturbative gadget for topological quantum codes.

Many-body entangled systems, in particular topologically ordered spin systems proposed as resources for quantum information processing tasks, often involve highly nonlocal interaction terms. While one may approximate such systems through two-body interactions perturbatively, these approaches have a number of drawbacks in practice. In this Letter, we propose a scheme to simulate many-body spin Hamiltonians with two-body Hamiltonians nonperturbatively. Unlike previous approaches, our Hamiltonians are not only exactly solvable with exact ground state degeneracy, but also support completely localized quasiparticle excitations, which are ideal for quantum information processing tasks. Our construction is limited to simulating the toric code and quantum double models, but generalizations to other nonlocal spin Hamiltonians may be possible.

Quantum codes give counterexamples to the unique preimage conjecture of the N-representability problem.

It is well known that the ground state energy of many-particle Hamiltonians involving only 2-body interactions can be obtained using constrained optimizations over density matrices which arise from reducing an N-particle state. While determining which 2-particle density matrices are "N-representable" is a computationally hard problem, all known extreme N-representable 2-particle reduced density matrices arise from a unique N-particle preimage, satisfying a conjecture established in 1972. We present explicit counterexamples to this conjecture through giving Hamiltonians with 2-body interactions which have degenerate ground states that cannot be distinguished by any 2-body operator. We relate the existence of such counterexamples to quantum error correction codes and topologically ordered spin systems.

Distance-tuned neurons drive specialized path integration calculations in medial entorhinal cortex.

During navigation, animals estimate their position using path integration and landmarks, engaging many brain areas. Whether these areas follow specialized or universal cue integration principles remains incompletely understood. We combine electrophysiology with virtual reality to quantify cue integration across thousands of neurons in three navigation-relevant areas: primary visual cortex (V1), retrosplenial cortex (RSC), and medial entorhinal cortex (MEC). Compared with V1 and RSC, path integration influences position estimates more in MEC, and conflicts between path integration and landmarks trigger remapping more readily. Whereas MEC codes position prospectively, V1 codes position retrospectively, and RSC is intermediate between the two. Lowered visual contrast increases the influence of path integration on position estimates only in MEC. These properties are most pronounced in a population of MEC neurons, overlapping with grid cells, tuned to distance run in darkness. These results demonstrate the specialized role that path integration plays in MEC compared with other navigation-relevant cortical areas.

Topography in the Bursting Dynamics of Entorhinal Neurons.

Medial entorhinal cortex contains neural substrates for representing space. These substrates include grid cells that fire in repeating locations and increase in scale progressively along the dorsal-to-ventral entorhinal axis, with the physical distance between grid firing nodes increasing from tens of centimeters to several meters in rodents. Whether the temporal scale of grid cell spiking dynamics shows a similar dorsal-to-ventral organization remains unknown. Here, we report the presence of a dorsal-to-ventral gradient in the temporal spiking dynamics of grid cells in behaving mice. This gradient in bursting supports the emergence of a dorsal grid cell population with a high signal-to-noise ratio. In vitro recordings combined with a computational model point to a role for gradients in non-inactivating sodium conductances in supporting the bursting gradient in vivo. Taken together, these results reveal a complementary organization in the temporal and intrinsic properties of entorhinal cells.

Principles governing the integration of landmark and self-motion cues in entorhinal cortical codes for navigation.

To guide navigation, the nervous system integrates multisensory self-motion and landmark information. We dissected how these inputs generate spatial representations by recording entorhinal grid, border and speed cells in mice navigating virtual environments. Manipulating the gain between the animal's locomotion and the visual scene revealed that border cells responded to landmark cues while grid and speed cells responded to combinations of locomotion, optic flow and landmark cues in a context-dependent manner, with optic flow becoming more influential when it was faster than expected. A network model explained these results by revealing a phase transition between two regimes in which grid cells remain coherent with or break away from the landmark reference frame. Moreover, during path-integration-based navigation, mice estimated their position following principles predicted by our recordings. Together, these results provide a theoretical framework for understanding how landmark and self-motion cues combine during navigation to generate spatial representations and guide behavior.

Collective thermoregulation in bee clusters.

Swarming is an essential part of honeybee behaviour, wherein thousands of bees cling onto each other to form a dense cluster that may be exposed to the environment for several days. This cluster has the ability to maintain its core temperature actively without a central controller. We suggest that the swarm cluster is akin to an active porous structure whose functional requirement is to adjust to outside conditions by varying its porosity to control its core temperature. Using a continuum model that takes the form of a set of advection-diffusion equations for heat transfer in a mobile porous medium, we show that the equalization of an effective 'behavioural pressure', which propagates information about the ambient temperature through variations in density, leads to effective thermoregulation. Our model extends and generalizes previous models by focusing the question of mechanism on the form and role of the behavioural pressure, and allows us to explain the vertical asymmetry of the cluster (as a consequence of buoyancy-driven flows), the ability of the cluster to overpack at low ambient temperatures without breaking up at high ambient temperatures, and the relative insensitivity to large variations in the ambient temperature. Our theory also makes testable hypotheses for the response of the cluster to external temperature inhomogeneities and suggests strategies for biomimetic thermoregulation.