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High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
Spiking neural networks (SNNs) offer inherent energy efficiency due to their event-driven computation model, making them promising for edge AI deployment. However, their practical adoption is limited by the computational overhead of deep…
In this paper, using the shrinkage-based approach for portfolio weights and modern results from random matrix theory we construct an effective procedure for testing the efficiency of the expected utility (EU) portfolio and discuss the…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
Acyclic join queries can be evaluated instance-optimally using Yannakakis' algorithm, which avoids needlessly large intermediate results through semi-join passes. Recent work proposes to address the significant hidden constant factors…
Spiking Neural Networks (SNNs) are bio-plausible models that hold great potential for realizing energy-efficient implementations of sequential tasks on resource-constrained edge devices. However, commercial edge platforms based on standard…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…
How does the choice of optimization algorithm shape a model's ability to learn features? To address this question for steepest descent methods --including sign descent, which is closely related to Adam --we introduce steepest mirror flows…
Stochastic computing (SC) has emerged as an efficient low-power alternative for deploying neural networks (NNs) in resource-limited scenarios, such as the Internet of Things (IoT). By encoding values as serial bitstreams, SC significantly…
With the recent proliferation of large-scale learning problems,there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However,…
In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…
Although deep learning models are highly effective for various learning tasks, their high computational costs prohibit the deployment to scenarios where either memory or computational resources are limited. In this paper, we focus on…
In this paper we propose a novel parallel stochastic coordinate descent (SCD) algorithm with convergence guarantees that exhibits strong scalability. We start by studying a state-of-the-art parallel implementation of SCD and identify…
The increasing scale and complexity of large language models (LLMs) pose significant inference latency challenges, primarily due to their autoregressive decoding paradigm characterized by the sequential nature of next-token prediction. By…
This paper proposes an approach, Spectral Dynamics Embedding Control (SDEC), to optimal control for nonlinear stochastic systems. This method reveals an infinite-dimensional feature representation induced by the system's nonlinear…
Image downscaling is a fundamental operation in image processing, crucial for adapting high-resolution content to various display and storage constraints. While classic methods often introduce blurring or aliasing, recent learning-based…
In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…
Spiking neural networks (SNNs) promise energy-efficient computation by mimicking biological neural dynamics, yet existing plasticity rules focus on isolated spike pairs and fail to leverage the synchronous activity patterns that drive…
The main result of this thesis is the development of a novel connectivity estimation method, called Total Spiking Probability Edges (TSPE). Based on cross-correlation and edge filtering at different time scales this method is proposed and…