Related papers: Tensoring volatility calibration
Deep learning methods have become a widespread toolbox for pricing and calibration of financial models. While they often provide new directions and research results, their `black box' nature also results in a lack of interpretability. We…
Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…
Information loss in numerical physics simulations can arise from various sources when solving discretized partial differential equations. In particular, errors related to numerical precision ("sub-precision errors") can accumulate in the…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Dynamic neural networks are a recent technique that promises a remedy for the increasing size of modern deep learning models by dynamically adapting their computational cost to the difficulty of the inputs. In this way, the model can adjust…
We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p([0,1))$, which allows to identify a univariate function with…
This paper is concerned with convergence estimates for fully discrete tree tensor network approximations of high-dimensional functions from several model classes. For functions having standard or mixed Sobolev regularity, new estimates…
We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…
Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…
This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw…
In recent years, deep learning techniques have outperformed traditional models in many machine learning tasks. Deep neural networks have successfully been applied to address time series forecasting problems, which is a very important topic…
Evaluating financial products with early-termination clauses, in particular those with path-dependent structures, is challenging. This paper focuses on Asian options, look-back options, and callable certificates. We will compare regression…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…
The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that…
Deep Neural Networks (DNNs) are computationally and memory intensive, which makes their hardware implementation a challenging task especially for resource constrained devices such as IoT nodes. To address this challenge, this paper…
Traditional neural networks employ fixed weights during inference, limiting their ability to adapt to changing input conditions, unlike biological neurons that adjust signal strength dynamically based on stimuli. This discrepancy between…
Deep learning is finding its way into the embedded world with applications such as autonomous driving, smart sensors and aug- mented reality. However, the computation of deep neural networks is demanding in energy, compute power and memory.…
Forecasting severe weather conditions is still a very challenging and computationally expensive task due to the enormous amount of data and the complexity of the underlying physics. Machine learning approaches and especially deep learning…
The next-generation CMB experiments are expected to constrain the tensor-to-scalar ratio $r$ with high precision. Delensing is an important process as the observed CMB $B$-mode polarization that contains the primordial tensor perturbation…
Neural activity forecasting is central to understanding neural systems and enabling closed-loop control. While deep learning has recently advanced the state-of-the-art in the time series forecasting literature, its application to neural…