Growing Critical: Self-Organized Criticality in a Developing Neural System

Experiments in various neural systems found avalanches: bursts of activity with characteristics typical for critical dynamics. A possible explanation for their occurrence is an underlying network that self-organizes into a critical state. We propose a simple spiking model for developing neural networks, showing how these may "grow into" criticality. Avalanches generated by our model correspond to clusters of widely applied Hawkes processes. We analytically derive the cluster size and duration distributions and find that they agree with those of experimentally observed neuronal avalanches.Comment: 6 pages, 4 figures, supplemental material: 10 pages, 7 figure

A generalized neural tangent kernel for surrogate gradient learning

State-of-the-art neural network training methods depend on the gradient of the network function. Therefore, they cannot be applied to networks whose activation functions do not have useful derivatives, such as binary and discrete-time spiking neural networks. To overcome this problem, the activation function's derivative is commonly substituted with a surrogate derivative, giving rise to surrogate gradient learning (SGL). This method works well in practice but lacks theoretical foundation. The neural tangent kernel (NTK) has proven successful in the analysis of gradient descent. Here, we provide a generalization of the NTK, which we call the surrogate gradient NTK, that enables the analysis of SGL. First, we study a naive extension of the NTK to activation functions with jumps, demonstrating that gradient descent for such activation functions is also ill-posed in the infinite-width limit. To address this problem, we generalize the NTK to gradient descent with surrogate derivatives, i.e., SGL. We carefully define this generalization and expand the existing key theorems on the NTK with mathematical rigor. Further, we illustrate our findings with numerical experiments. Finally, we numerically compare SGL in networks with sign activation function and finite width to kernel regression with the surrogate gradient NTK; the results confirm that the surrogate gradient NTK provides a good characterization of SGL.Comment: 52 pages, 3 figures + 2 supplementary figure

A Fokker-Planck formalism for diffusion with finite increments and absorbing boundaries

Gaussian white noise is frequently used to model fluctuations in physical systems. In Fokker-Planck theory, this leads to a vanishing probability density near the absorbing boundary of threshold models. Here we derive the boundary condition for the stationary density of a first-order stochastic differential equation for additive finite-grained Poisson noise and show that the response properties of threshold units are qualitatively altered. Applied to the integrate-and-fire neuron model, the response turns out to be instantaneous rather than exhibiting low-pass characteristics, highly non-linear, and asymmetric for excitation and inhibition. The novel mechanism is exhibited on the network level and is a generic property of pulse-coupled systems of threshold units.Comment: Consists of two parts: main article (3 figures) plus supplementary text (3 extra figures

Dual-Fiberoptic Microcantilever Proximity Sensor

Microcantilevers are key components of many Micro-Electro-Mechanical Systems (MEMS) and Micro-Optical-Electro-Mechanical Systems (MOEMS) because slight changes to them physically or chemically lead to changes in mechanical characteristics. An inexpensive dual-fiberoptic microcantilever proximity sensor and model to predict its performance are reported here. Motion of a magnetic-material-coated cantilever is the basis of a system under development for measuring magnetic fields. The dual fiber proximity sensor will be used to monitor the motion of the cantilever. The specific goal is to sense induction fields produced by a current carrying conductor. The proximity sensor consists of two fibers side by side with claddings in contact. The fiber core diameter, 50 microns, and cladding thickness, 10 microns, are as small as routinely available commercially with the exception of single mode fiber. Light is launched into one fiber from a light-emitting diode (LED). It emerges from that fiber and reflects from the cantilever into the adjacent receiving fiber connected to a detector. The sensing end is cast molded with a diameter of 3-mm over the last 20-mm, yielding a low profile sensor. This reflective triangulation approach is probably the oldest and simplest fiber proximity sensing approach, yet the novelty here is in demonstrating high sensitivity at low expense from a triangular microstructure with amorphous magnetic coatings of iron, cobalt, permalloy, etc. The signal intensity versus distance curve yields an approximate gaussian shape. For a typical configuration, the signal grows from 10% to 90% of maximum in traversing from 6 to 50 microns from a coated cantilever. With signal levels exceeding a volt, nanometer resolution should be readily achievable for periodic signals

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Teaching Psychology At Undergraduate Level: Rethinking What We Teach And How We Teach It

Traditionally undergraduate psychology has maintained an allegiance to a positivist scientist-practitioner model and has focussed on building a solid theoretical foundation. The development of skills and self-awareness has typically been the domain of postgraduate study. It is argued that in the process of trying to justify itself as a ‘science’, psychology has lost many of the aspects that first attracts people to its study: the desire for greater understanding of self, others and social phenomena. This article reflects on the experience of offering an undergraduate degree that integrates theory and a valuing of personal and vocational development. A less positivist-dominated formulation of the scientist-practitioner model may offer a constructive way in which to unite the ‘human’ and ‘scientific’ sides of psychology