While Moores law has driven exponential computing power expectations, its nearing end calls for new avenues for improving the overall system performance. One of these avenues is the exploration of new alternative brain-inspired computing architecture
s that promise to achieve the flexibility and computational efficiency of biological neural processing systems. Within this context, neuromorphic intelligence represents a paradigm shift in computing based on the implementation of spiking neural network architectures tightly co-locating processing and memory. In this paper, we provide a comprehensive overview of the field, highlighting the different levels of granularity present in existing silicon implementations, comparing approaches that aim at replicating natural intelligence (bottom-up) versus those that aim at solving practical artificial intelligence applications (top-down), and assessing the benefits of the different circuit design styles used to achieve these goals. First, we present the analog, mixed-signal and digital circuit design styles, identifying the boundary between processing and memory through time multiplexing, in-memory computation and novel devices. Next, we highlight the key tradeoffs for each of the bottom-up and top-down approaches, survey their silicon implementations, and carry out detailed comparative analyses to extract design guidelines. Finally, we identify both necessary synergies and missing elements required to achieve a competitive advantage for neuromorphic edge computing over conventional machine-learning accelerators, and outline the key elements for a framework toward neuromorphic intelligence.
We consider Gaussian measures $mu, tilde{mu}$ on a separable Hilbert space, with fractional-order covariance operators $A^{-2beta}$ resp. $tilde{A}^{-2tilde{beta}}$, and derive necessary and sufficient conditions on $A, tilde{A}$ and $beta, tilde{bet
a} > 0$ for I. equivalence of the measures $mu$ and $tilde{mu}$, and II. uniform asymptotic optimality of linear predictions for $mu$ based on the misspecified measure $tilde{mu}$. These results hold, e.g., for Gaussian processes on compact metric spaces. As an important special case, we consider the class of generalized Whittle-Matern Gaussian random fields, where $A$ and $tilde{A}$ are elliptic second-order differential operators, formulated on a bounded Euclidean domain $mathcal{D}subsetmathbb{R}^d$ and augmented with homogeneous Dirichlet boundary conditions. Our outcomes explain why the predictive performances of stationary and non-stationary models in spatial statistics often are comparable, and provide a crucial first step in deriving consistency results for parameter estimation of generalized Whittle-Matern fields.
Optimal linear prediction (also known as kriging) of a random field ${Z(x)}_{xinmathcal{X}}$ indexed by a compact metric space $(mathcal{X},d_{mathcal{X}})$ can be obtained if the mean value function $mcolonmathcal{X}tomathbb{R}$ and the covariance f
unction $varrhocolonmathcal{X}timesmathcal{X}tomathbb{R}$ of $Z$ are known. We consider the problem of predicting the value of $Z(x^*)$ at some location $x^*inmathcal{X}$ based on observations at locations ${x_j}_{j=1}^n$ which accumulate at $x^*$ as $ntoinfty$ (or, more generally, predicting $varphi(Z)$ based on ${varphi_j(Z)}_{j=1}^n$ for linear functionals $varphi, varphi_1, ldots, varphi_n$). Our main result characterizes the asymptotic performance of linear predictors (as $n$ increases) based on an incorrect second order structure $(tilde{m},tilde{varrho})$, without any restrictive assumptions on $varrho, tilde{varrho}$ such as stationarity. We, for the first time, provide necessary and sufficient conditions on $(tilde{m},tilde{varrho})$ for asymptotic optimality of the corresponding linear predictor holding uniformly with respect to $varphi$. These general results are illustrated by weakly stationary random fields on $mathcal{X}subsetmathbb{R}^d$ with Matern or periodic covariance functions, and on the sphere $mathcal{X}=mathbb{S}^2$ for the case of two isotropic covariance functions.
We have studied the anomalous Hall effect (AHE) in strained thin films of the frustrated antiferromagnet Mn$_{3}$NiN. The AHE does not follow the conventional relationships with magnetization or longitudinal conductivity and is enhanced relative to t
hat expected from the magnetization in the antiferromagnetic state below $T_{mathrm{N}} = 260$,K. This enhancement is consistent with origins from the non-collinear antiferromagnetic structure, as the latter is closely related to that found in Mn$_{3}$Ir and Mn$_{3}$Pt where a large AHE is induced by the Berry curvature. As the Berry phase induced AHE should scale with spin-orbit coupling, yet larger AHE may be found in other members of the chemically flexible Mn$_{3}A$N structure.
We have studied the barocaloric effect (BCE) in the geometrically frustrated antiferromagnet Mn$_{3}$NiN across the N{e}el transition temperature. Experimentally we find a larger barocaloric entropy change by a factor of 1.6 than that recently discov
ered in the isostructural antiperovskite Mn$_{3}$GaN despite greater magnetovolume coupling in the latter. By fitting experimental data to theory we show that the larger BCE of Mn$_{3}$NiN originates from multi-site exchange interactions amongst the local Mn magnetic moments and their coupling with itinerant electron spins. Using this framework, we discuss the route to maximise the BCE in the wider Mn$_{3}$AN family.
The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order elliptic
differential operator. The solution is approximated by means of a finite element discretization in space and a quadrature approximation of an integral representation of the fractional inverse from the Dunford-Taylor calculus. For the resulting approximation, a concise analysis of the weak error is performed. Specifically, for the class of twice continuously Frechet differentiable functionals with second derivatives of polynomial growth, an explicit rate of weak convergence is derived, and it is shown that the component of the convergence rate stemming from the stochasticity is doubled compared to the corresponding strong rate. Numerical experiments for different functionals validate the theoretical results.
The numerical approximation of solutions to stochastic partial differential equations with additive spatial white noise on bounded domains in $mathbb{R}^d$ is considered. The differential operator is given by the fractional power $L^beta$, $betain(0,
1)$, of an integer order elliptic differential operator $L$ and is therefore non-local. Its inverse $L^{-beta}$ is represented by a Bochner integral from the Dunford-Taylor functional calculus. By applying a quadrature formula to this integral representation, the inverse fractional power operator $L^{-beta}$ is approximated by a weighted sum of non-fractional resolvents $(I + t_j^2 L)^{-1}$ at certain quadrature nodes $t_j>0$. The resolvents are then discretized in space by a standard finite element method. This approach is combined with an approximation of the white noise, which is based only on the mass matrix of the finite element discretization. In this way, an efficient numerical algorithm for computing samples of the approximate solution is obtained. For the resulting approximation, the strong mean-square error is analyzed and an explicit rate of convergence is derived. Numerical experiments for $L=kappa^2-Delta$, $kappa > 0$, with homogeneous Dirichlet boundary conditions on the unit cube $(0,1)^d$ in $d=1,2,3$ spatial dimensions for varying $betain(0,1)$ attest the theoretical results.
