There is mounting experimental evidence that brain-state specific neural mechanisms supported by connectomic architectures serve to combine past and contextual knowledge with current, incoming flow of evidence (e.g. from sensory systems). Such mechanisms are distributed across multiple spatial and temporal scales and require dedicated support at the levels of individual neurons and synapses. A prominent feature in the neocortex is the structure of large, deep pyramidal neurons which show a peculiar separation between an apical dendritic compartment and a basal dentritic/peri-somatic compartment, with distinctive patterns of incoming connections and brain-state specific activation mechanisms, namely apical-amplification, -isolation and -drive associated to the wakefulness, deeper NREM sleep stages and REM sleep. The cognitive roles of apical mechanisms have been demonstrated in behaving animals. In contrast, classical models of learning spiking networks are based on single compartment neurons that miss the description of mechanisms to combine apical and basal/somatic information. This work aims to provide the computational community with a two-compartment spiking neuron model which includes features that are essential for supporting brain-state specific learning and with a piece-wise linear transfer function (ThetaPlanes) at highest abstraction level to be used in large scale bio-inspired artificial intelligence systems. A machine learning algorithm, constrained by a set of fitness functions, selected the parameters defining neurons expressing the desired apical mechanisms.
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We develop a Bayesian modeling framework to address a pressing real-life problem faced by the police in tackling insurgent gangs. Unlike criminals associated with common crimes such as robbery, theft or street crime, insurgent gangs are trained in sophisticated arms and strategise against the government to weaken its resolve. They are constantly on the move, operating over large areas causing damage to national properties and terrorizing ordinary citizens. Different from the more commonly addressed problem of modeling crime-events, our context requires that an approach be formulated to model the movement of insurgent gangs, which is more valuable to the police forces in preempting their activities and nabbing them. This paper evolved as a collaborative work with the Indian police to help augment their tactics with a systematic method, by integrating past data on observed gang-locations with the expert knowledge of the police officers. A methodological challenge in modeling the movement of insurgent gangs is that the data on their locations is incomplete, since they are observable only at some irregularly separated time-points. Based on a weighted kernel density formulation for temporal data, we analytically derive the closed form of the likelihood, conditional on incomplete past observed data. Building on the current tactics used by the police, we device an approach for constructing an expert-prior on gang-locations, along with a sequential Bayesian procedure for estimation and prediction. We also propose a new metric for predictive assessment that complements another known metric used in similar problems.
Semantic segmentation techniques for extracting building footprints from high-resolution remote sensing images have been widely used in many fields such as urban planning. However, large-scale building extraction demands higher diversity in training samples. In this paper, we construct a Global Building Semantic Segmentation (GBSS) dataset (The dataset will be released), which comprises 116.9k pairs of samples (about 742k buildings) from six continents. There are significant variations of building samples in terms of size and style, so the dataset can be a more challenging benchmark for evaluating the generalization and robustness of building semantic segmentation models. We validated through quantitative and qualitative comparisons between different datasets, and further confirmed the potential application in the field of transfer learning by conducting experiments on subsets.
Physics-informed neural networks (PINNs) and their variants have recently emerged as alternatives to traditional partial differential equation (PDE) solvers, but little literature has focused on devising accurate numerical integration methods for neural networks (NNs), which is essential for getting accurate solutions. In this work, we propose adaptive quadratures for the accurate integration of neural networks and apply them to loss functions appearing in low-dimensional PDE discretisations. We show that at opposite ends of the spectrum, continuous piecewise linear (CPWL) activation functions enable one to bound the integration error, while smooth activations ease the convergence of the optimisation problem. We strike a balance by considering a CPWL approximation of a smooth activation function. The CPWL activation is used to obtain an adaptive decomposition of the domain into regions where the network is almost linear, and we derive an adaptive global quadrature from this mesh. The loss function is then obtained by evaluating the smooth network (together with other quantities, e.g., the forcing term) at the quadrature points. We propose a method to approximate a class of smooth activations by CPWL functions and show that it has a quadratic convergence rate. We then derive an upper bound for the overall integration error of our proposed adaptive quadrature. The benefits of our quadrature are evaluated on a strong and weak formulation of the Poisson equation in dimensions one and two. Our numerical experiments suggest that compared to Monte-Carlo integration, our adaptive quadrature makes the convergence of NNs quicker and more robust to parameter initialisation while needing significantly fewer integration points and keeping similar training times.
By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.
Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of n-simplices or n-cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call indexed. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively in its unary and binary variants. We exploit this correspondence to develop an original uniform indexed definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.
Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, financial crises, and engineering reliability. To this end, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in the low-dimensional manifold. Then three effective warning signals (Onsager-Machlup Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are derived through the latent coordinates and the latent stochastic dynamical systems. To validate our framework, we apply this methodology to authentic electroencephalogram (EEG) data. We find that our early warning indicators are capable of detecting the tipping point during state transition. This framework not only bridges the latent dynamics with real-world data but also shows the potential ability for automatic labeling on complex high-dimensional time series.
This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The performance of this novel scheme is compared with that of the recursive least-squares algorithm in simulation.
In this paper we consider a nonlinear poroelasticity model that describes the quasi-static mechanical behaviour of a fluid-saturated porous medium whose permeability depends on the divergence of the displacement. Such nonlinear models are typically used to study biological structures like tissues, organs, cartilage and bones, which are known for a nonlinear dependence of their permeability/hydraulic conductivity on solid dilation. We formulate (extend to the present situation) one of the most popular splitting schemes, namely the fixed-stress split method for the iterative solution of the coupled problem. The method is proven to converge linearly for sufficiently small time steps under standard assumptions. The error contraction factor then is strictly less than one, independent of the Lam\'{e} parameters, Biot and storage coefficients if the hydraulic conductivity is a strictly positive, bounded and Lipschitz-continuous function.
Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations, blocking communication requests are avoided, which makes it hard to isolate and handle any global vector. While some termination protocols were proposed for asynchronous iterations, only very few of them are based on global residual computation and guarantee effective convergence. But the most effective and efficient existing solutions feature two reduction operations, which constitutes an important factor of termination delay. In this paper, we present new, non-intrusive, protocols to compute a residual error under asynchronous iterations, requiring only one reduction operation. Various communication models show that some heuristics can even be introduced and formally evaluated. Extensive experiments with up to 5600 processor cores confirm the practical effectiveness and efficiency of our approach.
We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.
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