Search

We present a unified framework for computing CVA sensitivities, hedging the CVA, and assessing CVA risk, using probabilistic machine learning meant as refined regression tools on simulated data, validatable by low-cost companion Monte Carlo procedures. Various notions of sensitivities are introduced and benchmarked numerically. We identify the sensitivities representing the best practical trade-offs in downstream tasks including CVA hedging and risk assessment., Comment: This is the long, preprint version of the eponymous paper forthcoming in Risk Magazine

Motivated by the equations of cross valuation adjustments (XVAs) in the realistic case where capital is deemed fungible as a source of funding for variation margin, we introduce a simulation/regression scheme for a class of anticipated BSDEs, where the coefficient entails a conditional expected shortfall of the martingale part of the solution. The scheme is explicit in time and uses neural network least-squares and quantile regressions for the embedded conditional expectations and expected shortfall computations. An a posteriori Monte Carlo validation procedure allows assessing the regression error of the scheme at each time step. The superiority of this scheme with respect to Picard iterations is illustrated in a high-dimensional and hybrid market/default risks XVA use-case.

Scintillating fibre detectors combine sub-mm resolution particle tracking, precise measurements of the particle stopping power and sub-ns time resolution. Typically, fibres are read out with silicon photomultipliers (SiPM). Hence, if fibres with a few hundred $\mu$m diameter are used, either they are grouped together and coupled with a single SiPM, losing spatial resolution, or a very large number of electronic channels is required. In this article we propose and provide a first demonstration of a novel configuration which allows each individual scintillating fibre to be read out regardless of the size of its diameter, by imaging them with Single-Photon Avalanche Diode (SPAD) array sensors. Differently from SiPMs, SPAD array sensors provide single-photon detection with single-pixel spatial resolution. In addition, O(us) or faster coincidence of detected photons allows to obtain noise-free images. Such a concept can be particularly advantageous if adopted as a neutrino active target, where scintillating fibres alternated along orthogonal directions can provide isotropic, high-resolution tracking in a dense material and reconstruct the kinematics of low-momentum protons (down to 150 MeV/c), crucial for an accurate characterisation of the neutrino nucleus cross section. In this work the tracking capabilities of a bundle of scintillating fibres coupled to SwissSPAD2 is demonstrated. The impact of such detector configuration in GeV-neutrino experiments is studied with simulations and reported. Finally, future plans, including the development of a new SPAD array sensor optimised for neutrino detection, are discussed.

Characterizing and understanding the dynamics of stochastic gradient descent (SGD) around saddle points remains an open problem. We first show that saddle points in neural networks can be divided into two types, among which the Type-II saddles are especially difficult to escape from because the gradient noise vanishes at the saddle. The dynamics of SGD around these saddles are thus to leading order described by a random matrix product process, and it is thus natural to study the dynamics of SGD around these saddles using the notion of probabilistic stability and the related Lyapunov exponent. Theoretically, we link the study of SGD dynamics to well-known concepts in ergodic theory, which we leverage to show that saddle points can be either attractive or repulsive for SGD, and its dynamics can be classified into four different phases, depending on the signal-to-noise ratio in the gradient close to the saddle., Comment: preprint

We discuss historic pressure computations for the hard-disk model performed since 1953, and compare them to results that we obtain with a powerful event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like other simple models in the sciences, such as the Drosophila model of biology, the hard-disk model has needed monumental effort to be understood. In particular, we argue that the difficulty of estimating the pressure has not been fully realized in the decades-long controversy over the hard-disk phase-transition scenario. We present the physics of the hard-disk model, the definition of the pressure and its unbiased estimators, several of which are new. We further treat different sampling algorithms and crucial criteria for bounding mixing times in the absence of analytical predictions. Our definite results for the pressure, for up to one million disks, may serve as benchmarks for future sampling algorithms. A synopsis of hard-disk pressure data as well as different versions of the sampling algorithms and pressure estimators are made available in an open-source repository., Comment: 21 pages, 13 figures, open-source repository

This work finds the analytical expression of the global minima of a deep linear network with weight decay and stochastic neurons, a fundamental model for understanding the landscape of neural networks. Our result implies that the origin is a special point in deep neural network loss landscape where highly nonlinear phenomenon emerges. We show that weight decay strongly interacts with the model architecture and can create bad minima at zero in a network with more than $1$ hidden layer, qualitatively different from a network with only $1$ hidden layer. Practically, our result implies that common deep learning initialization methods are insufficient to ease the optimization of neural networks in general., Comment: NeurIPS 2022

We propose locally stable sparse hard-disk packings, as introduced by B\"or\"oczky, as a model for the analysis and benchmarking of Markov-chain Monte Carlo (MCMC) algorithms. We first generate such packings in a square box with periodic boundary conditions and analyze their properties. We then study how local MCMC algorithms, namely the Metropolis algorithm and several versions of event-chain Monte Carlo (ECMC), escape from configurations that are obtained by slightly reducing all disk radii by a relaxation parameter. A scaling analysis is confirmed by simulation results. We obtain two classes of ECMC, one in which the escape time varies algebraically with the relaxation parameter (as for the local Metropolis algorithm) and another in which the escape time scales as the logarithm of the relaxation parameter. We discuss the connectivity of the hard-disk sample space, the ergodicity of local MCMC algorithms, as well as the meaning of packings in the context of the NPT ensemble. Our work is accompanied by open-source, arbitrary-precision software for B\"or\"oczky packings (in Python) and for straight, reflective, forward, and Newtonian ECMC (in Go)., Comment: 24 pages, 6 figures, 1 table

Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit many strange and potentially undesirable behaviors. Specifically, we construct landscapes and data distributions such that (1) SGD converges to local maxima, (2) SGD escapes saddle points arbitrarily slowly, (3) SGD prefers sharp minima over flat ones, and (4) AMSGrad converges to local maxima. We also realize results in a minimal neural network-like example. Our results highlight the importance of simultaneously analyzing the minibatch sampling, discrete-time updates rules, and realistic landscapes to understand the role of SGD in deep learning., Comment: Fixed typos

We present a multithreaded event-chain Monte Carlo algorithm (ECMC) for hard spheres. Threads synchronize at infrequent breakpoints and otherwise scan for local horizon violations. Using a mapping onto absorbing Markov chains, we rigorously prove the correctness of a sequential-consistency implementation for small test suites. On x86 and ARM processors, a C++ (OpenMP) implementation that uses compare-and-swap primitives for data access achieves considerable speed-up with respect to single-threaded code. The generalized birthday problem suggests that for the number of threads scaling as the square root of the number of spheres, the horizon-violation probability remains small for a fixed simulation time. We provide C++ and Python open-source code that reproduces all our results., Comment: 24 pages, 7 figures

Hemispherical power asymmetry has emerged as a new challenge to cosmology in early universe. While the cosmic microwave background (CMB) measurements indicated the asymmetry amplitude $A \simeq 0.07$ at the CMB scale $k_{\rm CMB}\simeq 0.0045\,{\rm Mpc}^{-1}$, the high-redshift quasar observations found no significant deviation from statistical isotropy. This conflict can be reconciled in some scale-dependent asymmetry models. We put forward a new parameterization of scale-dependent asymmetric power spectrum, inspired by a multi-speed inflation model. The 21-cm power spectrum from the epoch of reionization can be used to constrain the scale-dependent hemispherical asymmetry. We demonstrate that an optimum, multi-frequency observation by the Square Kilometre Array (SKA) Phase 2 can impose a constraint on the amplitude of the power asymmetry anomaly at the level of $\Delta A \simeq 0.2$ at $0.056 \lesssim k_{\rm 21cm} \lesssim 0.15 \,{\rm Mpc}^{-1}$. This limit may be further improved by an order of magnitude as $\Delta A \simeq 0.01$ with a cosmic variance limited experiment such as the Omniscope., Comment: Accepted for publication in MNRAS