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David Rosenthal

Publications and source records attributed to David Rosenthal.

12 recordsLinked to original sources
arXiv2025

Apertus: Democratizing Open and Compliant LLMs for Global Language Environments

We present Apertus, a fully open suite of large language models (LLMs) designed to address two systemic shortcomings in today's open model ecosystem: data compliance and multilingual representation. Unlike many prior models that release weights without reproducible data pipelines or regard for content-owner rights, Apertus models are pretrained exclusively on openly available data, retroactively respecting `robots.txt` exclusions and filtering for non-permissive, toxic, and personally identifiable content. To mitigate risks of memorization, we adopt the Goldfish objective during pretraining, strongly suppressing verbatim recall of data while retaining downstream task performance. The Apertus models also expand multilingual coverage, training on 15T tokens from over 1800 languages, with ~40% of pretraining data allocated to non-English content. Released at 8B and 70B scales, Apertus approaches state-of-the-art results among fully open models on multilingual benchmarks, rivalling or surpassing open-weight counterparts. Beyond model weights, we release all scientific artifacts from our development cycle with a permissive license, including data preparation scripts, checkpoints, evaluation suites, and training code, enabling transparent audit and extension.

cs.CL↗
arXiv2020

Finitely $\mathcal{F}$-amenable actions and Decomposition Complexity of Groups

In his work on the Farrell-Jones Conjecture, Arthur Bartels introduced the concept of a "finitely $\mathcal{F}$-amenable" group action, where $\mathcal{F}$ is a family of subgroups. We show how a finitely $\mathcal{F}$-amenable action of a countable group $G$ on a compact metric space, where the asymptotic dimensions of the elements of $\mathcal{F}$ are bounded from above, gives an upper bound for the asymptotic dimension of $G$ viewed as a metric space with a proper left invariant metric. We generalize this to families $\mathcal{F}$ whose elements are contained in a collection, $\mathfrak{C}$, of metric families that satisfies some basic permanence properties: If $G$ is a countable group and each element of $\mathcal{F}$ belongs to $\mathfrak{C}$ and there exists a finitely $\mathcal{F}$-amenable action of $G$ on a compact metrizable space, then $G$ is in $\mathfrak{C}$. Examples of such collections of metric families include: metric families with weak finite decomposition complexity, exact metric families, and metric families that coarsely embed into Hilbert space.

math.GT↗
arXiv2017

Regular Finite Decomposition Complexity

We introduce the notion of regular finite decomposition complexity of a metric family. This generalizes Gromov's finite asymptotic dimension and is motivated by the concept of finite decomposition complexity (FDC) due to Guentner, Tessera and Yu. Regular finite decomposition complexity implies FDC and has all the permanence properties that are known for FDC, as well as a new one called Finite Quotient Permanence. We show that for a collection containing all metric families with finite asymptotic dimension all other permanence properties follow from Fibering Permanence.

math.MG↗
arXiv2016

On the K-theory of groups with finite asymptotic dimension

It is proved that the assembly maps in algebraic K- and L-theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for the classifying space for proper actions. The result also applies to certain groups that admit only a finite dimensional model for this space. In particular, it applies to discrete subgroups of virtually connected Lie groups.

math.KT↗
arXiv2015

Hyperbolic Dimension and Decomposition Complexity

The aim of this paper is to provide some new tools to aid the study of decomposition complexity, a notion introduced by Guentner, Tessera and Yu. In this paper, three equivalent definitions for decomposition complexity are established. We prove that metric spaces with finite hyperbolic dimension have finite (weak) decomposition complexity, and we prove that the collection of metric families that are coarsely embeddable into Hilbert space is closed under decomposition. A method for showing that certain metric spaces do not have finite decomposition complexity is also discussed.

math.GT↗
arXiv2014

Metric dimensions of minor excluded graphs and minor exclusion in groups

An infinite graph G is minor excluded if there is a finite graph that is not a minor of G. We prove that minor excluded graphs have finite Assouad-Nagata dimension and study minor exclusion for Cayley graphs of finitely generated groups. Our main results and observations are: (1) minor exclusion is not a group property: it depends on the choice of generating set; (2) a group with one end has a generating set for which the Cayley graph is not minor excluded; (3) there are groups that are not minor excluded for any set of generators; (4) minor exclusion is preserved under free products; and (5) virtually free groups are minor excluded for any choice of finite generating set.

math.GR↗
arXiv2012

Coarse structures on groups

We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the group-compact coarse structure generalizing several familiar results for discrete groups. We show that the asymptotic dimension in our sense of the free topological group on a non-empty topological space that is homeomorphic to a closed subspace of a Cartesian product of metrizable spaces is 1.

math.GT↗
arXiv2003

Continuous Control and the Algebraic L-theory Assembly Map

In this work, the assembly map in L-theory for the family of finite subgroups is proven to be a split injection for a class of groups. Groups in this class, including virtually polycyclic groups, have universal spaces that satisfy certain geometric conditions. The proof follows the method developed by Carlsson-Pedersen to split the assembly map in the case of torsion free groups. Here, the continuously controlled techniques and results are extended to handle groups with torsion.

math.AT↗
arXiv2003

Split Injectivity of the Baum-Connes Assembly Map

In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the Baum-Connes map is a split injection for groups satisfying certain geometric conditions.

math.AT↗
arXiv2003

Splitting With Continuous Control in Algebraic K-theory

In this work, the continuously controlled assembly map in algebraic $K$-theory, as developed by Carlsson and Pedersen, is proved to be a split injection for groups $Γ$ that satisfy certain geometric conditions. The group $Γ$ is allowed to have torsion, generalizing a result of Carlsson and Pedersen. Combining this with a result of John Moody, $K_0(kΓ)$ is proved to be isomorphic to the colimit of $K_0(kH)$ over the finite subgroups $H$ of $Γ$, when $Γ$ is a virtually polycyclic group and $k$ is a field of characteristic zero.

math.AT↗