Meta-Learning the Inductive Biases of Simple Neural Circuits

Animals receive noisy and incomplete information, from which we must learn how to react in novel situations. A fundamental problem is that training data is always finite, making it unclear how to generalise to unseen data. But, animals do react appropriately to unseen data, wielding Occam's razor to select a parsimonious explanation of the observations. How they do this is called their inductive bias, and it is implicitly built into the operation of animals' neural circuits. This relationship between an observed circuit and its inductive bias is a useful explanatory window for neuroscience, allowing design choices to be understood normatively. However, it is generally very difficult to map circuit structure to inductive bias. In this work we present a neural network tool to bridge this gap. The tool allows us to meta-learn the inductive bias of neural circuits by learning functions that a neural circuit finds easy to generalise, since easy-to-generalise functions are exactly those the circuit chooses to explain incomplete data. We show that in systems where the inductive bias is known analytically, i.e. linear and kernel regression, our tool recovers it. Then, we show it is able to flexibly extract inductive biases from differentiable circuits, including spiking neural networks, and use it to interpret recent connectomic data through their effect on generalisation. This illustrates the intended use of our tool: understanding the role of otherwise opaque pieces of neural functionality through the inductive bias they induce.Comment: 15 pages, 11 figure

A differential Hebbian framework for biologically-plausible motor control

In the realm of motor control, artificial agents cannot match the performance of their biological counterparts. We thus explore a neural control architecture that is both biologically plausible, and capable of fully autonomous learning. The architecture consists of feedback controllers that learn to achieve a desired state by selecting the errors that should drive them. This selection happens through a family of differential Hebbian learning rules that, through interaction with the environment, can learn to control systems where the error responds monotonically to the control signal. We next show that in a more general case, neural reinforcement learning can be coupled with a feedback controller to reduce errors that arise non-monotonically from the control signal. The use of feedback control reduces the complexity of the reinforcement learning problem, because only a desired value must be learned, with the controller handling the details of how it is reached. This makes the function to be learned simpler, potentially allowing to learn more complex actions. We discuss how this approach could be extended to hierarchical architectures.Comment: 35 pages, 10 figures. Appendix: 9 pages, 2 figure

Actionable Neural Representations: Grid Cells from Minimal Constraints

To afford flexible behaviour, the brain must build internal representations that mirror the structure of variables in the external world. For example, 2D space obeys rules: the same set of actions combine in the same way everywhere (step north, then south, and you won't have moved, wherever you start). We suggest the brain must represent this consistent meaning of actions across space, as it allows you to find new short-cuts and navigate in unfamiliar settings. We term this representation an `actionable representation'. We formulate actionable representations using group and representation theory, and show that, when combined with biological and functional constraints - non-negative firing, bounded neural activity, and precise coding - multiple modules of hexagonal grid cells are the optimal representation of 2D space. We support this claim with intuition, analytic justification, and simulations. Our analytic results normatively explain a set of surprising grid cell phenomena, and make testable predictions for future experiments. Lastly, we highlight the generality of our approach beyond just understanding 2D space. Our work characterises a new principle for understanding and designing flexible internal representations: they should be actionable, allowing animals and machines to predict the consequences of their actions, rather than just encode

Dynamics and deposition of sediment-bearing multi-pulsed flows and geological implication

Previous studies on dilute, multi-pulsed, subaqueous saline flows have demonstrated that pulses will inevitably advect forwards to merge with the flow front. On the assumption that pulse merging occurs in natural-scale turbidity currents, it was suggested that multi-pulsed turbidites that display vertical cycles of coarsening and fining would transition laterally to single-pulsed, normally graded turbidites beyond the point of pulse merging. In this study, experiments of dilute, single- and multi-pulsed sediment-bearing flows (turbidity currents) are conducted to test the linkages between downstream flow evolution and associated deposit structure. Experimental data confirm that pulse merging occurs in laboratory-scale turbidity currents. However, only a weak correspondence was seen between longitudinal variations in the internal flow dynamics and the vertical structure of deposits; multi-pulsed deposits were documented, but transitioned to single-pulsed deposits before the pulse merging point. This early transition is attributed to rapid sedimentation-related depletion of the coarser-grained suspended fraction in the laboratory setting, whose absence may have prevented the distal development of multi-pulsed deposits; this factor complicates estimation of the transition point in natural-scale turbidite systems

Relating the Flow Processes and Bedforms of Steady-State and Waning Density Currents

© Copyright© 2020 de Cala, Ohata, Dorrell, Naruse, Patacci, Amy, Simmons, McLelland and McCaffrey. The interaction between turbidity currents and mobile substrates can lead to the development of different types of bedforms. Although much research has been conducted on bedform development beneath open channel flows, research into bedform development beneath waning gravity currents is relatively rare. Analysis of density current-related bedform development has therefore relied upon open channel flow phase diagrams. We report on an experimental study designed to assess the development of bedforms under steady and waning saline density currents. The experimental density currents developed stepped density profiles in which a higher-density basal zone was separated from the ambient fluid by a zone of intermediate density; any bedforms that developed were contained within the bottom layer of the current. Under different conditions ripples, dunes, downstream migrating antidunes and long wavelength antidunes were observed to form and could be distinguished based on their interactions and phase relationships with the upper surface of the lower denser layer of the current. Due to limited mixing between the upper and lower layer of the current and maintenance of current momentum, currents set with slowing discharge flow rates maintained a steady flow velocity in the lower layer of the flow. As a result, sustained bedform formative conditions were achieved within this lower layer, while waning current conditions effected the rest of the flow. Under waning currents, it was seen how pre-existing bed states can determine the subsequent evolution of bedforms. This illustrates the limitations of existing phase diagrams as they do not account for trajectory or rate of passage of flows through different bedform phase spaces. In order to establish a reliable quantitative association between the flow regime and the type of bedform development, it is critical to adopt an appropriate Froude number calculation method for stratified flow. The updated density current phase diagram indicates supercritical flow can be achieved at lower flow velocities than for open channel flows due to the effects of reduced gravity. Bedform depositional structures found in outcrop and on the modern sea floor provide data that helps to interpret the hydrodynamic and sedimentological character of the current that formed them. Therefore, understanding the processes involved in bedform development beneath density currents will enable more accurate estimation of the properties of flows

The inherent instability of leveed seafloor channels

New analytical models demonstrate that under 2 aggradational flow conditions seafloor channel-levee systems are inherently unstable; both channel area and stability necessarily decrease at long timescales. In time such systems must avulse purely through internal (autogenic) forcing. Although autogenic instabilities likely arise over long enough time for additional allogenic forcing to be expected, channel-levee sensitivity to variations in flow character depends on the prior degree of system evolution. Recalibrated modern Amazon Fan avulsion timings are consistent with this model, challenging accepted interpretations of avulsion triggering

Dynamics and Deposition of Sediment-Bearing Multi- Pulsed Flows and Geological Implication

Copyright © 2019, SEPM (Society for Sedimentary Geology) Previous studies on dilute, multi-pulsed, subaqueous saline flows have demonstrated that pulses will inevitably advect forwards to merge with the flow front. On the assumption that pulse merging occurs in natural-scale turbidity currents, it was suggested that multi-pulsed turbidites that display vertical cycles of coarsening and fining would transition laterally to single-pulsed, normally graded turbidites beyond the point of pulse merging. In this study, experiments of dilute, single- and multi-pulsed sediment-bearing flows (turbidity currents) are conducted to test the linkages between downstream flow evolution and associated deposit structure. Experimental data confirm that pulse merging occurs in laboratory-scale turbidity currents. However, only a weak correspondence was seen between longitudinal variations in the internal flow dynamics and the vertical structure of deposits; multi-pulsed deposits were documented, but transitioned to single-pulsed deposits before the pulse merging point. This early transition is attributed to rapid sedimentation-related depletion of the coarser-grained suspended fraction in the laboratory setting, whose absence may have prevented the distal development of multi-pulsed deposits; this factor complicates estimation of the transition point in natural-scale turbidite systems