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Rami Luisto

Publications and source records attributed to Rami Luisto.

15 recordsLinked to original sources
arXiv2026

Observing rurality of a geographical area from road graph geometry -- a qualitative study

In this paper we analyze the Finnish road network as a graph in order to measure whether the "rurality" or "urbanity" of an area correlates with local geometrical properties of the graph. Our primary motivation is the observation that the road systems in rural areas look similar to hyperbolic graphs, while in large cities they resemble more the Cayley graph of $\mathbb{Z}^2$. We do not aim for a comprehensive analysis, but rather wish to demonstrate that this observation can be measured and analyzed through looking at various "hyperbolicity measures" of randomly sampled geodesic triangles in the road graph.

physics.soc-ph↗
arXiv2026

Domain Fine-Tuning FinBERT on Finnish Histopathological Reports: Train-Time Signals and Downstream Correlations

In NLP classification tasks where little labeled data exists, domain fine-tuning of transformer models on unlabeled data is an established approach. In this paper we have two aims. (1) We describe our observations from fine-tuning the Finnish BERT model on Finnish medical text data. (2) We report on our attempts to predict the benefit of domain-specific pre-training of Finnish BERT from observing the geometry of embedding changes due to domain fine-tuning. Our driving motivation is the common\situation in healthcare AI where we might experience long delays in acquiring datasets, especially with respect to labels.

cs.CL↗
arXiv2026

A visual observation on the geometry of UMAP projections of the difference vectors of antonym and synonym word pair embeddings

Antonyms, or opposites, are sometimes defined as \emph{word pairs that have all of the same contextually relevant properties but one}. Seeing how transformer models seem to encode concepts as directions, this begs the question if one can detect ``antonymity'' in the geometry of the embedding vectors of word pairs, especially based on their difference vectors. Such geometrical studies are then naturally contrasted by comparing antonymic pairs to their opposites; synonyms. This paper started as an exploratory project on the complexity of the systems needed to detect the geometry of the embedding vectors of antonymic word pairs. What we now report is a curious ``swirl'' that appears across embedding models in a somewhat specific projection configuration.

cs.CL↗
arXiv2025

A short survey on almost orthogonal vectors in a few specific large dimensions

The concept of \emph{almost orthogonal vectors}, i.e.\ vectors whose cosine similarity is close to $0$, relates to topics both in pure mathematics and in coding theory under the guises of spherical packing and spherical codes. In recent years the rise of advanced language models in AI has created new interest in this concept as the models seem to store certain concepts as almost orthogonal directions in high-dimensional spaces. In this survey we represent some ideas regarding almost orthogonal vectors through three approaches: (1) the mathematical theory of almost orthogonality, (2) some observations from the embedding spaces of language models, and (3) generation of large sets of almost orthogonal vectors by simulations.

math.MG↗
arXiv2022

A non-Euclidean story or: how to persist when your geometry doesn't

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping $f \colon X \to Y$ between uniformly Ahlfors $q$-regular, complete and locally compact path-metric spaces $X$ and $Y$ is an $L$-bilipschitz map when $Y$ is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set; see e.g. [L17]. As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of the ideas in [L17] in a more general setting when the branch set is empty.

math.HO↗
arXiv2020

Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps

The image of the branch set of a PL branched cover between PL $n$-manifolds is a simplicial $(n-2)$-complex. We demonstrate that the reverse implication also holds: an open and discrete map $f \colon \mathbb{S}^n \to \mathbb{S}^n$ with the image of the branch set contained in a simplicial $(n-2)$-complex is equivalent up to homeomorphism to a PL branched cover.

math.CV↗
arXiv2020

On BLD-mappings with small distortion

We show that every $L$-BLD-mapping in a domain of $\mathbb{R}^n$ is a local homeomorphism if $L < \sqrt{2}$ or $K_I(f) < 2$. These bounds are sharp as shown by a winding map.

math.MG↗
arXiv2019

A Newman property for BLD-mappings

We define a Newman property for BLD-mappings and study its connections to the porosity of the branch set in the setting of generalized manifolds equipped with complete path metrics.

math.MG↗
arXiv2019

Weak regularity of the inverse under minimal assumptions

Let $Ω\subset\mathbb{R}^3$ be a domain and let $f\in BV_{\operatorname{loc}}(Ω,\mathbb{R}^3)$ be a homeomorphism such that its distributional adjugate is a finite Radon measure. We show that its inverse has bounded variation $f^{-1}\in BV_{\operatorname{loc}}$. The condition that the distributional adjugate is finite measure is not only sufficient but also necessary for the weak regularity of the inverse.

math.CA↗
arXiv2019

On proper branched coverings and a question of Vuorinen

We study global injectivity of proper branched coverings defined on the Euclidean $n$-ball in the case when the branch set is compact. In particular we show that such mappings are homeomorphisms when $n=3$ or when the branch set is empty. This proves the corresponding cases of a question of Vuorinen from [Vuo79].

math.CV↗
arXiv2019

Stoïlow's theorem revisited

Stoïlow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps $z\mapsto z^k$ and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps.

math.CV↗
arXiv2018

Mappings of finite distortion: compactness of the branch set

We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, has a branch set homeomorphic to $(n-2)$-dimensional torus and distortion arbitrarily close to the asymptotic bound.

math.CV↗
arXiv2015

Note on local-to-global properties of BLD-mappings

We give a proof, based on Lipschitz quotient mappings, for the fact that limits of BLD-mappings between manifolds of bounded geometry are BLD. Furthermore we show that such mappings share some properties of covering maps and especially have no asymptotic values.

math.MG↗
arXiv2014

Rigidity of extremal quasiregularly elliptic manifolds

We show that for a closed $n$-manifold $N$ admitting a quasiregular mapping from the Euclidean $n$-space the following are equivalent: (1) order of growth of $π_1(N)$ is $n$, (2) $N$ is aspherical, and (3) $π_1(N)$ is virtually $\mathbb{Z}^n$ and torsion free.

math.MG↗