arXiv subjects

Manuela Geiß

Publications and source records attributed to Manuela Geiß.

At least 19 recordsLinked to original sources

arXiv2026

Kernel Affine Hull Machines as Compute-Efficient Encoders for Frozen Semantic Spaces

Transformer-based semantic encoders are effective for retrieval, but in many deployments the recurring bottleneck is online query encoding rather than offline corpus indexing. This paper studies whether, once a strong teacher representation space and corpus index are fixed, repeated neural query encoding can be replaced by a substantially lighter and analytically explicit estimator. We formulate fixed-teacher lexical-to-semantic encoding as a conditional-mean estimation problem in which the target semantic vector is represented as a noisy mixture of semantic prototypes weighted by posterior cluster probabilities. Kernel Affine Hull Machine (KAHM) geometry is used to estimate these posterior weights from inexpensive lexical features in an explicitly identified RKHS hypothesis space, and the semantic prototypes are refined by normalized least-mean-squares updates from noisy teacher embeddings. This yields a backpropagation-free query-side encoder together with an end-to-end error decomposition into posterior-approximation, finite-sample/generalization, and teacher-noise terms. We instantiate the approach on a controlled Austrian-law retrieval benchmark with 5,000 test queries, 84 candidate laws, and 10,762 aligned retrieval units, using law-specific encoders into a frozen Mixedbread embedding space. Among evaluation-matched learned adapters, KAHM achieves the strongest teacher-space reconstruction and the best rank-sensitive retrieval performance at all evaluated cutoffs. At k=20, it obtains MRR@20 = 0.504, Hit@20 = 0.694, and Top-1 Accuracy = 0.411, while reducing online per-query time by 8.53 relative to direct transformer query encoding in the reported CPU setting. The results support KAHMs as compute-efficient encoders for supervised fixed-representation deployment regimes.

cs.LG↗

arXiv2025

Operator-Theoretic Framework for Gradient-Free Federated Learning

Federated learning must address heterogeneity, strict communication and computation limits, and privacy while ensuring performance. We propose an operator-theoretic framework that maps the $L^2$-optimal solution into a reproducing kernel Hilbert space (RKHS) via a forward operator, approximates it using available data, and maps back with the inverse operator, yielding a gradient-free scheme. Finite-sample bounds are derived using concentration inequalities over operator norms, and the framework identifies a data-dependent hypothesis space with guarantees on risk, error, robustness, and approximation. Within this space we design efficient kernel machines leveraging the space folding property of Kernel Affine Hull Machines. Clients transfer knowledge via a scalar space folding measure, reducing communication and enabling a simple differentially private protocol: summaries are computed from noise-perturbed data matrices in one step, avoiding per-round clipping and privacy accounting. The induced global rule requires only integer minimum and equality-comparison operations per test point, making it compatible with fully homomorphic encryption (FHE). Across four benchmarks, the gradient-free FL method with fixed encoder embeddings matches or outperforms strong gradient-based fine-tuning, with gains up to 23.7 points. In differentially private experiments, kernel smoothing mitigates accuracy loss in high-privacy regimes. The global rule admits an FHE realization using $Q \times C$ encrypted minimum and $C$ equality-comparison operations per test point, with operation-level benchmarks showing practical latencies. Overall, the framework provides provable guarantees with low communication, supports private knowledge transfer via scalar summaries, and yields an FHE-compatible prediction rule offering a mathematically grounded alternative to gradient-based federated learning under heterogeneity.

cs.LG↗

arXiv2023

Explainable AI by BAPC -- Before and After correction Parameter Comparison

A local surrogate for an AI-model correcting a simpler 'base' model is introduced representing an analytical method to yield explanations of AI-predictions. The approach is studied here in the context of the base model being linear regression. The AI-model approximates the residual error of the linear model and the explanations are formulated in terms of the change of the interpretable base model's parameters. Criteria are formulated for the precise relation between lost accuracy of the surrogate, the accuracy of the AI-model, and the surrogate fidelity. It is shown that, assuming a certain maximal amount of noise in the observed data, these criteria induce neighborhoods of the instances to be explained which have an ideal size in terms of maximal accuracy and fidelity.

stat.ML↗

arXiv2022

Automatic Bounding Box Annotation with Small Training Data Sets for Industrial Manufacturing

In the past few years, object detection has attracted a lot of attention in the context of human-robot collaboration and Industry 5.0 due to enormous quality improvements in deep learning technologies. In many applications, object detection models have to be able to quickly adapt to a changing environment, i.e., to learn new objects. A crucial but challenging prerequisite for this is the automatic generation of new training data which currently still limits the broad application of object detection methods in industrial manufacturing. In this work, we discuss how to adapt state-of-the-art object detection methods for the task of automatic bounding box annotation for the use case where the background is homogeneous and the object's label is provided by a human. We compare an adapted version of Faster R-CNN and the Scaled Yolov4-p5 architecture and show that both can be trained to distinguish unknown objects from a complex but homogeneous background using only a small amount of training data.

cs.CV↗

arXiv2022

Fast and Automatic Object Registration for Human-Robot Collaboration in Industrial Manufacturing

We present an end-to-end framework for fast retraining of object detection models in human-robot-collaboration. Our Faster R-CNN based setup covers the whole workflow of automatic image generation and labeling, model retraining on-site as well as inference on a FPGA edge device. The intervention of a human operator reduces to providing the new object together with its label and starting the training process. Moreover, we present a new loss, the intraspread-objectosphere loss, to tackle the problem of open world recognition. Though it fails to completely solve the problem, it significantly reduces the number of false positive detections of unknown objects.

cs.CV↗

arXiv2021

Arc-Completion of 2-Colored Best Match Graphs to Binary-Explainable Best Match Graphs

Best match graphs (BMGs) are vertex-colored digraphs that naturally arise in mathematical phylogenetics to formalize the notion of evolutionary closest genes w.r.t. an a priori unknown phylogenetic tree. BMGs are explained by unique least resolved trees. We prove that the property of a rooted, leaf-colored tree to be least resolved for some BMG is preserved by the contraction of inner edges. For the special case of two-colored BMGs, this leads to a characterization of the least resolved trees (LRTs) of binary-explainable trees and a simple, polynomial-time algorithm for the minimum cardinality completion of the arc set of a BMG to reach a BMG that can be explained by a binary tree.

cs.DS↗

arXiv2021

Heuristic Algorithms for Best Match Graph Editing

Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding graph editing problem can be used as a means of error correction. Since the arc set modification problems for BMGs are NP-complete, efficient heuristics are needed if BMGs are to be used for the practical analysis of biological sequence data. Since BMGs have a characterization in terms of consistency of a certain set of rooted triples, we consider heuristics that operate on triple sets. As an alternative, we show that there is a close connection to a set partitioning problem that leads to a class of top-down recursive algorithms that are similar to Aho's supertree algorithm and give rise to BMG editing algorithms that are consistent in the sense that they leave BMGs invariant. Extensive benchmarking shows that community detection algorithms for the partitioning steps perform best for BMG editing.

math.CO↗

arXiv2021

Best Match Graphs with Binary Trees

Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree. We provide a near-cubic algorithm to determine whether a BMG is binary-explainable, i.e., whether it can be explained by a fully resolved gene tree and, if so, to construct such a tree. Moreover, we show that all such binary trees are refinements of the unique binary-resolvable tree (BRT), which in general is a substantial refinement of the also unique least resolved tree of a BMG. Finally, we show that the problem of editing an arbitrary vertex-colored graph to a binary-explainable BMG is NP-complete and provide an integer linear program formulation for this task.

cs.DS↗

arXiv2021

Least resolved trees for two-colored best match graphs

2-colored best match graphs (2-BMGs) form a subclass of sink-free bi-transitive graphs that appears in phylogenetic combinatorics. There, 2-BMGs describe evolutionarily most closely related genes between a pair of species. They are explained by a unique least resolved tree (LRT). Introducing the concept of support vertices we derive an $O(|V|+|E|\log^2|V|)$-time algorithm to recognize 2-BMGs and to construct its LRT. The approach can be extended to also recognize binary-explainable 2-BMGs with the same complexity. An empirical comparison emphasizes the efficiency of the new algorithm.

q-bio.PE↗

arXiv2020

Complete Characterization of Incorrect Orthology Assignments in Best Match Graphs

Genome-scale orthology assignments are usually based on reciprocal best matches. In the absence of horizontal gene transfer (HGT), every pair of orthologs forms a reciprocal best match. Incorrect orthology assignments therefore are always false positives in the reciprocal best match graph. We consider duplication/loss scenarios and characterize unambiguous false-positive (u-fp) orthology assignments, that is, edges in the best match graphs (BMGs) that cannot correspond to orthologs for any gene tree that explains the BMG. Moreover, we provide a polynomial-time algorithm to identify all u-fp orthology assignments in a BMG. Simulations show that at least $75\%$ of all incorrect orthology assignments can be detected in this manner. All results rely only on the structure of the BMGs and not on any a priori knowledge about underlying gene or species trees.

q-bio.PE↗

arXiv2020

Best Match Graphs

THIS IS A CORRECTED VERSION INCLUDING AN APPENDED CORRIGENDUM. Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let $T$ be a phylogenetic (gene) tree $T$ and $σ$ an assignment of leaves of $T$ to species. The best match graph $(G,σ)$ is a digraph that contains an arc from $x$ to $y$ if the genes $x$ and $y$ reside in different species and $y$ is one of possibly many (evolutionary) closest relatives of $x$ compared to all other genes contained in the species $σ(y)$. Here, we characterize best match graphs and show that it can be decided in cubic time and quadratic space whether $(G,σ)$ derived from a tree in this manner. If the answer is affirmative, there is a unique least resolved tree that explains $(G,σ)$, which can also be constructed in cubic time.

math.CO↗

arXiv2020

Hierarchical and Modularly-Minimal Vertex Colorings

Cographs are exactly the hereditarily well-colored graphs, i.e., the graphs for which a greedy vertex coloring of every induced subgraph uses only the minimally necessary number of colors $χ(G)$. We show that greedy colorings are a special case of the more general hierarchical vertex colorings, which recently were introduced in phylogenetic combinatorics. Replacing cotrees by modular decomposition trees generalizes the concept of hierarchical colorings to arbitrary graphs. We show that every graph has a modularly-minimal coloring $σ$ satisfying $|σ(M)|=χ(M)$ for every strong module $M$ of $G$. This, in particular, shows that modularly-minimal colorings provide a useful device to design efficient coloring algorithms for certain hereditary graph classes. For cographs, the hierarchical colorings coincide with the modularly-minimal coloring. As a by-product, we obtain a simple linear-time algorithm to compute a modularly-minimal coloring of $P_4$-sparse graphs.

math.CO↗

arXiv2020

From Best Hits to Best Matches

Many of the commonly used methods for orthology detection start from mutually most similar pairs of genes (reciprocal best hits) as an approximation for evolutionary most closely related pairs of genes (reciprocal best matches). This approximation of best matches by best hits becomes exact for ultrametric dissimilarities, i.e., under the Molecular Clock Hypothesis. It fails, however, whenever there are large lineage specific rate variations among paralogous genes. In practice, this introduces a high level of noise into the input data for best-hit-based orthology detection methods. If additive distances between genes are known, then evolutionary most closely related pairs can be identified by considering certain quartets of genes provided that in each quartet the outgroup relative to the remaining three genes is known. \emph{A priori} knowledge of underlying species phylogeny greatly facilitates the identification of the required outgroup. Although the workflow remains a heuristic since the correct outgroup cannot be determined reliably in all cases, simulations with lineage specific biases and rate asymmetries show that nearly perfect results can be achieved. In a realistic setting, where distances data have to be estimated from sequence data and hence are noisy, it is still possible to obtain highly accurate sets of best matches. Improvements of tree-free orthology assessment methods can be expected from a combination of the accurate inference of best matches reported here and recent mathematical advances in the understanding of (reciprocal) best match graphs and orthology relations.

q-bio.PE↗

arXiv2019

Best Match Graphs and Reconciliation of Gene Trees with Species Trees

A wide variety of problems in computational biology, most notably the assessment of orthology, are solved with the help of reciprocal best matches. Using an evolutionary definition of best matches that captures the intuition behind the concept we clarify rigorously the relationships between reciprocal best matches, orthology, and evolutionary events under the assumption of duplication/loss scenarios. We show that the orthology graph is a subgraph of the reciprocal best match graph (RBMG). We furthermore give conditions under which an RBMG that is a cograph identifies the correct orthlogy relation. Using computer simulations we find that most false positive orthology assignments can be identified as so-called good quartets -- and thus corrected -- in the absence of horizontal transfer. Horizontal transfer, however, may introduce also false-negative orthology assignments.

q-bio.PE↗

arXiv2019

Reciprocal Best Match Graphs

Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical structure. Here, we investigate the structure of reciprocal best match graphs (RBMGs). In order to abstract from the details of measuring distances, we define reciprocal best matches here as pairwise most closely related leaves in a gene tree, arguing that conceptually this is the notion that is pragmatically approximated by distance- or similarity-based heuristics. We start by showing that a graph $G$ is an RBMG if and only if its quotient graph w.r.t.\ a certain thinness relation is an RBMG. Furthermore, it is necessary and sufficient that all connected components of $G$ are RBMGs. The main result of this contribution is a complete characterization of RBMGs with 3 colors/species that can be checked in polynomial time. For 3 colors, there are three distinct classes of trees that are related to the structure of the phylogenetic trees explaining them. We derive an approach to recognize RBMGs with an arbitrary number of colors; it remains open however, whether a polynomial-time for RBMG recognition exists. In addition, we show that RBMGs that at the same time are cographs (co-RBMGs) can be recognized in polynomial time. Co-RBMGs are characterized in terms of hierarchically colored cographs, a particular class of vertex colored cographs that is introduced here. The (least resolved) trees that explain co-RBMGs can be constructed in polynomial time.

q-bio.PE↗

arXiv2019

Complexity of Modification Problems for Reciprocal Best Match Graphs

Reciprocal best match graphs (RBMGs) are vertex colored graphs whose vertices represent genes and the colors the species where the genes reside. Edges identify pairs of genes that are most closely related with respect to an underlying evolutionary tree. In practical applications this tree is unknown and the edges of the RBMGs are inferred by quantifying sequence similarity. Due to noise in the data, these empirically determined graphs in general violate the condition of being a ``biologically feasible'' RBMG. Therefore, it is of practical interest in computational biology to correct the initial estimate. Here we consider deletion (remove at most $k$ edges) and editing (add or delete at most $k$ edges) problems. We show that the decision version of the deletion and editing problem to obtain RBMGs from vertex colored graphs is NP-hard. Using known results for the so-called bicluster editing, we show that the RBMG editing problem for $2$-colored graphs is fixed-parameter tractable. A restricted class of RBMGs appears in the context of orthology detection. These are cographs with a specific type of vertex coloring known as hierarchical coloring. We show that the decision problem of modifying a vertex-colored graph (either by edge-deletion or editing) into an RBMG with cograph structure or, equivalently, to an hierarchically colored cograph is NP-complete.

cs.CC↗

arXiv2018

Reconstructing Gene Trees From Fitch's Xenology Relation

Two genes are xenologs in the sense of Fitch if they are separated by at least one horizontal gene transfer event. Horizonal gene transfer is asymmetric in the sense that the transferred copy is distinguished from the one that remains within the ancestral lineage. Hence xenology is more precisely thought of as a non-symmetric relation: $y$ is xenologous to $x$ if $y$ has been horizontally transferred at least once since it diverged from the least common ancestor of $x$ and $y$. We show that xenology relations are characterized by a small set of forbidden induced subgraphs on three vertices. Furthermore, each xenology relation can be derived from a unique least-resolved edge-labeled phylogenetic tree. We provide a linear-time algorithm for the recognition of xenology relations and for the construction of its least-resolved edge-labeled phylogenetic tree. The fact that being a xenology relation is a heritable graph property, finally has far-reaching consequences on approximation problems associated with xenology relations.

cs.DM↗

arXiv2017

A Short Note on Undirected Fitch Graphs

The symmetric version of Fitch's xenology relation coincides with class of complete multipartite graph and thus cannot convey any non-trivial phylogenetic information.

cs.DM↗