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At this work we introduce horizontally symmetric convolutional kernels for CNNs which make the network output invariant to horizontal flips of the image. We also study other types of symmetric kernels which lead to vertical flip invariance,…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
We introduce a nonparametric algorithm to learn interaction kernels of mean-field equations for 1st-order systems of interacting particles. The data consist of discrete space-time observations of the solution. By least squares with…
I provide a convolution metric which takes neural membrane potential recordings as arguments and compares their subthreshold features along with the timing and number of spikes within them--summarizing differences in these with a single…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Kernel approximation methods create explicit, low-dimensional kernel feature maps to deal with the high computational and memory complexity of standard techniques. This work studies a supervised kernel learning methodology to optimize such…
How to aggregate spatial information plays an essential role in learning-based image restoration. Most existing CNN-based networks adopt static convolutional kernels to encode spatial information, which cannot aggregate spatial information…
System identification techniques -- projection pursuit regression models (PPRs) and convolutional neural networks (CNNs) -- provide state-of-the-art performance in predicting visual cortical neurons' responses to arbitrary input stimuli.…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
Both biological and artificial neural networks inherently balance their performance with their operational cost, which balances their computational abilities. Typically, an efficient neuromorphic neural network is one that learns…
We study transmission in a system consisting of a curved graphene surface as an arc (ripple) of circle connected to two flat graphene sheets on the left and right sides. We introduce a mass term in the curved part and study the effect of a…
An important inference from Neural Tangent Kernel (NTK) theory is the existence of spectral bias (SB), that is, low frequency components of the target function of a fully connected Artificial Neural Network (ANN) being learnt significantly…
Convolutional Neural Networks (CNNs) are known to be significantly over-parametrized, and difficult to interpret, train and adapt. In this paper, we introduce a structural regularization across convolutional kernels in a CNN. In our…
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…
Deformable medical image registration is an essential task in computer-assisted interventions. This problem is particularly relevant to oncological treatments, where precise image alignment is necessary for tracking tumor growth, assessing…
Precision experiments, such as the search for electric dipole moments of charged particles using storage rings, demand for an understanding of the spin dynamics with unprecedented accuracy. The ultimate aim is to measure the electric dipole…
Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and…
Wide neural networks are biased towards learning certain functions, influencing both the rate of convergence of gradient descent (GD) and the functions that are reachable with GD in finite training time. As such, there is a great need for…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…