arXiv subjects

Jana Lepšová

Publications and source records attributed to Jana Lepšová.

8 recordsLinked to original sources

arXiv2026

Stochastic Penalty-Barrier Method for Constrained Machine Learning

Constrained Machine Learning (CML) enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. In this work, we introduce the Stochastic Penalty-Barrier Method (SPBM) for CML problems. SPBM extends classical penalty and barrier methods by incorporating an exponential averaging of the dual variables, a stabilized penalty schedule, and the Moreau envelope to handle non-smoothness. We analyze the bias that mini-batching introduces in the barrier function and show that the feasible set of the resulting transformed problem is contained within the original one. We compare SPBM with CML baselines across multiple fairness and physics informed neural networks experiments. We find that SPBM is competitive with state-of-the-art methods. We also observe, on our fairness-based computational benchmark, that the per-epoch runtime of CML methods is largely independent of the number of constraints, and within $1.3\times$ of the per-epoch runtime of regularized Adam, for a number of constraints ranging from $90$ to $9900$.

cs.LG↗

arXiv2026

Deep Learning as the Disciplined Construction of Tame Objects

One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of tame geometry (also known as o-minimality), optimization theory, and deep learning theory and practice. To do so, we gradually introduce the concepts and tools used to build convergence guarantees for stochastic gradient descent in a general nonsmooth nonconvex, but tame, setting. This illustrates some ways in which tame geometry is a natural mathematical framework for the study of AI systems, especially within Deep Learning.

math.OC↗

arXiv2026

Benchmarking Stochastic Approximation Algorithms for Fairness-Constrained Training of Deep Neural Networks

The ability to train Deep Neural Networks (DNNs) with constraints is instrumental in improving the fairness of modern machine-learning models. Many algorithms have been analysed in recent years, and yet there is no standard, widely accepted method for the constrained training of DNNs. In this paper, we provide a challenging benchmark of real-world large-scale fairness-constrained learning tasks, built on top of the US Census (Folktables). We point out the theoretical challenges of such tasks and review the main approaches in stochastic approximation algorithms. Finally, we demonstrate the use of the benchmark by implementing and comparing three recently proposed, but as-of-yet unimplemented, algorithms both in terms of optimization performance, and fairness improvement. We release the code of the benchmark as a Python package at https://github.com/humancompatible/train.

cs.LG↗

arXiv2025

humancompatible.train: Implementing Optimization Algorithms for Stochastically-Constrained Stochastic Optimization Problems

There has been a considerable interest in constrained training of deep neural networks (DNNs) recently for applications such as fairness and safety. Several toolkits have been proposed for this task, yet there is still no industry standard. We present humancompatible.train (https://github.com/humancompatible/train), an easily-extendable PyTorch-based Python package for training DNNs with stochastic constraints. We implement multiple previously unimplemented algorithms for stochastically constrained stochastic optimization. We demonstrate the toolkit use by comparing two algorithms on a deep learning task with fairness constraints.

cs.LG↗

arXiv2024

Dumont-Thomas complement numeration systems for $\mathbb{Z}$

We extend the well-known Dumont--Thomas numeration systems to $\mathbb{Z}$ using an approach inspired by the two's complement numeration system. Integers in $\mathbb{Z}$ are canonically represented by a finite word (starting with $\mathtt{0}$ when nonnegative and with $\mathtt{1}$ when negative). The systems are based on two-sided periodic points of substitutions as opposed to the right-sided fixed points. For every periodic point of a substitution, we construct an automaton which returns the letter at position $n\in\mathbb{Z}$ of the periodic point when fed with the representation of $n$ in the corresponding numeration system. The numeration system naturally extends to $\mathbb{Z}^d$. We give an equivalent characterization of the numeration system in terms of a total order on a regular language. Lastly, using particular periodic points, we recover the well-known two's complement numeration system and the Fibonacci analogue of the two's complement numeration system.

math.CO↗

arXiv2023

A Fibonacci analogue of the two's complement numeration system

Using the classic two's complement notation of signed integers, the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers. We introduce a Fibonacci-equivalent of the two's complement notation and we show that addition in this numeration system can be performed by a deterministic finite-state transducer. The result is based on the Berstel adder, which performs addition of the usual Fibonacci representations of nonnegative integers and for which we provide a new constructive proof. Moreover, we characterize the Fibonacci-equivalent of the two's complement notation as an increasing bijection between $\mathbb{Z}$ and a particular language.

cs.FL↗

arXiv2023

On a faithful representation of Sturmian morphisms

The set of morphisms mapping any Sturmian sequence to a Sturmian sequence forms together with composition the so-called monoid of Sturm. For this monoid, we defne a faithful representation by $(3\times 3)$-matrices with integer entries. We find three convex cones in $\mathbb{R}^3$ and show that a matrix $R \in Sl(\mathbb{Z},3)$ is a matrix representing a Sturmian morphism if the three cones are invariant under multiplication by $R$ or $R^{-1}$. This property offers a new tool to study Sturmian sequences. We provide alternative proofs of four known results on Sturmian sequences fixed by a primitive morphism and a new result concerning the square root of a Sturmian sequence.

math.CO↗

arXiv2021

A Numeration System for Fibonacci-like Wang Shifts

Motivated by the study of Fibonacci-like Wang shifts, we define a numeration system for $\mathbb{Z}$ and $\mathbb{Z}^2$ based on the binary alphabet $\{0,1\}$. We introduce a set of 16 Wang tiles that admits a valid tiling of the plane described by a deterministic finite automaton taking as input the representation of a position $(m,n)\in\mathbb{Z}^2$ and outputting a Wang tile.

math.CO↗