Learning to process with spikes and to localise pulses

In the last few decades, deep learning with artificial neural networks (ANNs) has emerged as one of the most widely used techniques in tasks such as classification and regression, achieving competitive results and in some cases even surpassing human-level performance. Nonetheless, as ANN architectures are optimised towards empirical results and departed from their biological precursors, how exactly human brains process information using these short electrical pulses called spikes remains a mystery. Hence, in this thesis, we explore the problem of learning to process with spikes and to localise pulses. We first consider spiking neural networks (SNNs), a type of ANN that more closely mimic biological neural networks in that neurons communicate with one another using spikes. This unique architecture allows us to look into the role of heterogeneity in learning. Since it is conjectured that the information is encoded by the timing of spikes, we are particularly interested in the heterogeneity of time constants of neurons. We then trained SNNs for classification tasks on a range of visual and auditory neuromorphic datasets, which contain streams of events (spike times) instead of the conventional frame-based data, and show that the overall performance is improved by allowing the neurons to have different time constants, especially on tasks with richer temporal structure. We also find that the learned time constants are distributed similarly to those experimentally observed in some mammalian cells. Besides, we demonstrate that learning with heterogeneity improves robustness against hyperparameter mistuning. These results suggest that heterogeneity may be more than the byproduct of noisy processes and perhaps serves a key role in learning in changing environments, yet heterogeneity has been overlooked in basic artificial models. While neuromorphic datasets, which are often captured by neuromorphic devices that closely model the corresponding biological systems, have enabled us to explore the more biologically plausible SNNs, there still exists a gap in understanding how spike times encode information in actual biological neural networks like human brains, as such data is difficult to acquire due to the trade-off between the timing precision and the number of cells simultaneously recorded electrically. Instead, what we usually obtain is the low-rate discrete samples of trains of filtered spikes. Hence, in the second part of the thesis, we focus on a different type of problem involving pulses, that is to retrieve the precise pulse locations from these low-rate samples. We make use of the finite rate of innovation (FRI) sampling theory, which states that perfect reconstruction is possible for classes of continuous non-bandlimited signals that have a small number of free parameters. However, existing FRI methods break down under very noisy conditions due to the so-called subspace swap event. Thus, we present two novel model-based learning architectures: Deep Unfolded Projected Wirtinger Gradient Descent (Deep Unfolded PWGD) and FRI Encoder-Decoder Network (FRIED-Net). The former is based on the existing iterative denoising algorithm for subspace-based methods, while the latter models directly the relationship between the samples and the locations of the pulses using an autoencoder-like network. Using a stream of K Diracs as an example, we show that both algorithms are able to overcome the breakdown inherent in the existing subspace-based methods. Moreover, we extend our FRIED-Net framework beyond conventional FRI methods by considering when the shape is unknown. We show that the pulse shape can be learned using backpropagation. This coincides with the application of spike detection from real-world calcium imaging data, where we achieve competitive results. Finally, we explore beyond canonical FRI signals and demonstrate that FRIED-Net is able to reconstruct streams of pulses with different shapes.Open Acces

Bayesian Field Theory: Nonparametric Approaches to Density Estimation, Regression, Classification, and Inverse Quantum Problems

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a likelihood model, providing a probabilistic description of the measurement process, and a prior model, providing the information necessary to generalize from training to non-training data. The particular likelihood models discussed in the paper are those of general density estimation, Gaussian regression, clustering, classification, and models specific for inverse quantum problems. Besides problem typical hard constraints, like normalization and positivity for probabilities, prior models have to implement all the specific, and often vague, "a priori" knowledge available for a specific task. Nonparametric prior models discussed in the paper are Gaussian processes, mixtures of Gaussian processes, and non-quadratic potentials. Prior models are made flexible by including hyperparameters. In particular, the adaption of mean functions and covariance operators of Gaussian process components is discussed in detail. Even if constructed using Gaussian process building blocks, Bayesian field theories are typically non-Gaussian and have thus to be solved numerically. According to increasing computational resources the class of non-Gaussian Bayesian field theories of practical interest which are numerically feasible is steadily growing. Models which turn out to be computationally too demanding can serve as starting point to construct easier to solve parametric approaches, using for example variational techniques.Comment: 200 pages, 99 figures, LateX; revised versio

Review : Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy

Bifurcation Analysis of Large Networks of Neurons

The human brain contains on the order of a hundred billion neurons, each with several thousand synaptic connections. Computational neuroscience has successfully modeled both the individual neurons as various types of oscillators, in addition to the synaptic coupling between the neurons. However, employing the individual neuronal models as a large coupled network on the scale of the human brain would require massive computational and financial resources, and yet is the current undertaking of several research groups. Even if one were to successfully model such a complicated system of coupled differential equations, aside from brute force numerical simulations, little insight may be gained into how the human brain solves problems or performs tasks. Here, we introduce a tool that reduces large networks of coupled neurons to a much smaller set of differential equations that governs key statistics for the network as a whole, as opposed to tracking the individual dynamics of neurons and their connections. This approach is typically referred to as a mean-field system. As the mean-field system is derived from the original network of neurons, it is predictive for the behavior of the network as a whole and the parameters or distributions of parameters that appear in the mean-field system are identical to those of the original network. As such, bifurcation analysis is predictive for the behavior of the original network and predicts where in the parameter space the network transitions from one behavior to another. Additionally, here we show how networks of neurons can be constructed with a mean-field or macroscopic behavior that is prescribed. This occurs through an analytic extension of the Neural Engineering Framework (NEF). This can be thought of as an inverse mean-field approach, where the networks are constructed to obey prescribed dynamics as opposed to deriving the macroscopic dynamics from an underlying network. Thus, the work done here analyzes neuronal networks through both top-down and bottom-up approaches

A gradient optimization approach to adaptive multi-robot control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 181-190).This thesis proposes a unified approach for controlling a group of robots to reach a goal configuration in a decentralized fashion. As a motivating example, robots are controlled to spread out over an environment to provide sensor coverage. This example gives rise to a cost function that is shown to be of a surprisingly general nature. By changing a single free parameter, the cost function captures a variety of different multi-robot objectives which were previously seen as unrelated. Stable, distributed controllers are generated by taking the gradient of this cost function. Two fundamental classes of multi-robot behaviors are delineated based on the convexity of the underlying cost function. Convex cost functions lead to consensus (all robots move to the same position), while any other behavior requires a nonconvex cost function. The multi-robot controllers are then augmented with a stable on-line learning mechanism to adapt to unknown features in the environment. In a sensor coverage application, this allows robots to learn where in the environment they are most needed, and to aggregate in those areas. The learning mechanism uses communication between neighboring robots to enable distributed learning over the multi-robot system in a provably convergent way. Three multi-robot controllers are then implemented on three different robot platforms. Firstly, a controller for deploying robots in an environment to provide sensor coverage is implemented on a group of 16 mobile robots.(cont.) They learn to aggregate around a light source while covering the environment. Secondly, a controller is implemented for deploying a group of three flying robots with downward facing cameras to monitor an environment on the ground. Thirdly, the multi-robot model is used as a basis for modeling the behavior of a herd of cows using a system identification approach. The controllers in this thesis are distributed, theoretically proven, and implemented on multi-robot platforms.by Mac Schwager.Ph.D

Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications

The monograph investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress". Traditional asymptotics deal mainly with either n=1 or $n=\infty$, and the real world is in between, under of the "laws of the medium numbers" --which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: + The sample mean is rarely in line with the population mean, with effect on "naive empiricism", but can be sometimes be estimated via parametric methods. + The "empirical distribution" is rarely empirical. + Parameter uncertainty has compounding effects on statistical metrics. + Dimension reduction (principal components) fails. + Inequality estimators (GINI or quantile contributions) are not additive and produce wrong results. + Many "biases" found in psychology become entirely rational under more sophisticated probability distributions + Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles

Advances in Reinforcement Learning

Reinforcement Learning (RL) is a very dynamic area in terms of theory and application. This book brings together many different aspects of the current research on several fields associated to RL which has been growing rapidly, producing a wide variety of learning algorithms for different applications. Based on 24 Chapters, it covers a very broad variety of topics in RL and their application in autonomous systems. A set of chapters in this book provide a general overview of RL while other chapters focus mostly on the applications of RL paradigms: Game Theory, Multi-Agent Theory, Robotic, Networking Technologies, Vehicular Navigation, Medicine and Industrial Logistic