On the Effectiveness of the z-Transform Method in Quadratic Optimization
Francis Bach (SIERRA)
Sep 2026
Machine Learning
Abstract
The z-transform of a sequence is a classical tool used within signal processing, control theory, computer science, and electrical engineering. It allows for studying sequences from their generating functions, with many operations that can be equivalently defined on the original sequence and its $z$-transform. In particular, the z-transform method focuses on asymptotic behaviors and allows the use of Taylor expansions. We present a sequence of results of increasing significance and difficulty for linear models and optimization algorithms, demonstrating the effectiveness and versatility of the z-transform method in deriving new asymptotic results. Starting from the simplest gradient descent iterations in an infinite-dimensional Hilbert space, we show how the spectral dimension characterizes the convergence behavior. We then extend the analysis to Nesterov acceleration, averaging techniques, and stochastic gradient descent.
The results indicate that software engineering work practices are chosen opportunistically, adapted and configured to provide value under the constrains imposed by the startup context.
Nicolò Paternoster, Carmine Giardino, M. Unterkalmsteiner et al.· Information and Software Tec...· 394 citations· ⚡54
The possibility of inferring high-dimensional data inference in a model that consists of a prior and an auxiliary differentiable constraint given some additional information is considered, thereby allowing a range of potential applications in adapting models to new domains and tasks.
Alexandros Graikos, Esmeralda S. Whitammer, N. Jojic et al.· Neural Information Processin...· 316 citations· ⚡15
It is proved that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution, and empirically demonstrate the benefits of the trajectories balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequences and large action spaces.
Esmeralda S. Whitammer, Moksh Jain, Emmanuel Bengio et al.· Neural Information Processin...· 302 citations· ⚡60
This state-of-practice investigation was performed using a literature review followed by a multiple-case study approach and presents how inconsistency between managerial strategies and execution can lead to failure by means of a behavioral framework.
Carmine Giardino, Xiaofeng Wang, P. Abrahamsson· International Conference on...· 175 citations· ⚡19
This work investigates the possibilities of using LLMs in a resume screening setting via a document retrieval framework that simulates job candidate selection and finds that the MTEs are biased, significantly favoring White-associated names in 85% of cases and female-associated names in only 11.1% of cases.
This study conducts a case survey study based on the secondary data of the major pivots happened in 49 software startups, and demonstrates that customer need pivot is the most common among all pivot types.
Sohaib Shahid Bajwa, Xiaofeng Wang, Anh Nguyen-Duc et al.· Empirical Software Engineeri...· 127 citations· ⚡15
A weeklong summer workshop brought higher education faculty to campus to explore how AI and machine learning materials can be adapted for their classrooms.
