Computer Science (arXiv)

Dimension reduction for dynamical systems is standard practice, and the standard route is spectral: model the transfer (Koopman) operator by its leading modes. We show that on systems assembled from several weakly interacting components --- a structure common in physical and biological settings --- this may either require an exponential number of modes, or drop an entire component: the component is absent from the model rather than modeled coarsely, and no function of it can be predicted at any accuracy. We call this linear masking. The cause is that a rank-based model pays one coordinate per mode. We propose to score instead the $σ$-algebra the coordinates generate, so that products and powers come free and a component's cost is governed only by its generators rather than by all its interactions. The criterion is a $χ^2$-divergence between the embedded present and future, and it carries a budget guarantee: twice the intrinsic dimension of the dynamics is enough coordinates for an embedding whose algebra carries the operator's entire spectrum, with its full infinite rank. In variational form the criterion admits off-the-shelf estimators, and restricting its critic to the bilinear class returns the VAMP score on the span, so rank-based methods are one end of the same family. We demonstrate the proposed objective on a composite of published benchmark systems. We exhibit examples where the rank-based methods completely miss the masked components at all ranks $k<100$, while ten algebra coordinates recover all of them. In addition, the resulting algebra representation supports predicting the masked components from few labels, while direct regression from the high-dimensional observation or from the VAMP features fail.

We investigate the structure of central extensions for algebras in a congruence modular variety. We use a multisorted algebraic object called a clonoid to understand the term clone of such a central extension. We develop the difference clonoid of such a central extension and use it to show that the number of $2$-step nilpotent algebras on a fixed finite set is finite if and only if the set is of squarefree order. The subpower membership problem for a finite algebraic structure $\mathbb{A}$ is the problem of deciding on input $a_1,\dots,a_k, b \in A^n$, whether $b$ is in the subalgebra of $\mathbb{A}^n$ generated by $a_1, \dots, a_k$. We show that for a large class of nilpotent Mal'cev algebras the subpower membership problem is solvable in polynomial time, in particular for $2$-step nilpotent Mal'cev algebras of squarefree order.

Hardware shifts, color variations, and changing patient characteristics between development and deployment routinely break trained medical image classifiers. Existing remedies fall short: standard color jittering provides insufficient diversity, while deep generative style transfer algorithms hallucinate features, destroy clinically relevant structures, and waste massive compute resources. To address this, we revisit classical statistical color matching and repurpose it as Colorist, a highly efficient data augmentation strategy that applies global mean-standard deviation matching directly in the RGB color space. We demonstrate that this training-free, fully interpretable approach safely generates structurally intact domain variations, outperforming deep generative models in structural fidelity and color alignment. Across out-of-distribution histopathology, peripheral blood, dermatology, and retinal datasets, it improves balanced accuracy by up to +9% over state-of-the-art domain generalization regularizers and by +13% over an unaugmented baseline. Moreover, by avoiding neural networks in the augmentation loop, Colorist preserves anatomical structure, minimizes carbon footprint, and integrates seamlessly into standard dataloaders. Together, these findings establish statistical matching as a safe, interpretable, yet overlooked alternative to deep architectures for clinical robustness. Source code is available at https://github.com/sdoerrich97/colorist.

We introduce the CDSP (context-conditional deliberation signal pipeline), converting an investment committee's meeting transcripts into structured predictive features. CDSP segments the meeting transcripts into topical chunks, assigns asset-class context labels using a large language model (LLM), maps financial keywords to a pre-determined taxonomy of labels, and constructs complementary features: sentiment polarity and mention frequency. This feature engineering framework is applied to a dataset spanning 48 monthly committee meetings to predict if global equities will perform better or worse than global bonds in the following month. In experiments with engineered features, raw transcript text, sentence embeddings, and combined representations, the prediction accuracy ranges from 62% to 73%, compared to always choosing stocks, which outperforms bonds 60.4% of the time. The best (73% accurate) model combines sentence embeddings with engineered CDSP features, achieving a 0.73 F1 score (although this is not statistically significant compared to always choosing stocks). Sentiment carries a stronger signal than mention frequency for several taxonomy categories. These findings suggest that experts' deliberations may contain forward-looking information that context-aware NLP can extract.

Hard combinatorial optimization problems, many of which are NP-hard, present fundamental algorithmic challenges. Average-case analysis on random instances has emerged as a powerful framework for understanding typical algorithmic performance beyond worst-case guarantees. A substantial body of work has established negative results: for sufficiently hard instances (often controlled by the underlying graph connectivity/constraints density), no known polynomial-time algorithm can significantly outperform naive heuristics in the double asymptotic limit where both problem size and constraints density tend to infinity. We revisit this picture by studying the finite-size behavior of some optimization algorithms across easy, intermediate, and hard regimes. Through rigorous analysis of large-graph asymptotics combined with numerical experiments on canonical problems (maximum independent set and maximum $K$-SAT), we demonstrate that while algorithms do eventually converge to theoretically predicted bounds, this convergence can be remarkably slow. In the intermediate regime where instances are already highly constrained, local algorithms achieve solutions substantially better than their predicted performance in the high-constraint-density limit. This gap between finite-regime and asymptotic behavior has important practical implications: sophisticated algorithmic design remains crucial even when asymptotic theory predicts inevitable failure.

In the context of urban planning, architects are normally instructed with creating presentation images that visualize proposed buildings within their urban context. This work aims to develop a GenAI model for automatically generating architectural presentation images in urban scenes, with emphasis on model optimization. To achieve this, we developed Mask-based Weighted Conditional Flow Matching (MWCFM), which extends Flow Matching by introducing contextual masks for precise feature focusing. This enables targeted training on critical spatial elements relevant to urban planning. Our trained model learns from urban street-view data while adhering to specific style-guidelines, which are integrated into training through the loss function. Furthermore, the model's performance is evaluated using application related metrics, derived from presentation image style guidelines.

Small-scale image classification is often limited by the scarcity of training data. Generative data augmentation (GDA) based on pretrained generative models has emerged as an effective solution. However, existing methods rely on task-agnostic augmentation strategies that overlook downstream model needs. Although recent dynamic GDA methods incorporate model feedback to guide augmentation, they still struggle to reliably determine sample-specific augmentation strengths and adapt augmentation strategies to different image regions while balancing image diversity and class semantics. To address these issues, we propose learning-state-aware dynamic generative data augmentation (LSADA). Specifically, LSADA constructs a learning state for each sample based on its current loss and loss-decrease rate, which is then mapped to a sample-specific augmentation strength. Furthermore, LSADA introduces a decoupled data augmentation and diffusion fusion strategy that applies strength-controlled transformations to class-relevant regions and generates diverse class-irrelevant regions, progressively fusing them to improve image diversity while preserving class semantics. Experiments on nine public datasets show that LSADA outperforms the existing SOTA dynamic GDA method by an average of 4.5% on six natural image datasets and 2.5% on three medical image datasets.

Additive codes over finite fields generalize linear codes, and additive MDS codes provide a natural extension of linear MDS codes. In this article, we study additive twisted Reed--Solomon (TRS) codes and obtain new constructions of additive MDS codes. First, for additive TRS codes with twist $t=2$ and an arbitrary hook, we establish necessary and sufficient conditions for the codes to be additive MDS, thereby generalizing the results in Section 3 of [Jiayu Ma et al., New families of additive non-Reed-Solomon MDS codes]. In particular, we show that the existence of an additive MDS TRS code with $t=2$ and hook $h=0$ yields codes of larger lengths than those obtained for $t=2$ and $h=k-1$ in [Jiayu Ma et al., New families of additive non-Reed-Solomon MDS codes]. Next, we consider additive TRS codes with twist vector $\mathbf{t}=(1,2)$ and hook vector $\mathbf{h}=(0,0)$, and derive necessary and sufficient conditions for them to be additive MDS. We further establish the existence of such codes. Using the Schur square technique, we obtain mild conditions under which the constructed families are inequivalent to additive Reed--Solomon (RS) codes. Finally, we determine parity-check matrices for both families of additive MDS codes considered in this article.

This work evaluates surrogate-assisted optimization of a seven-parameter current-excited coil--core benchmark subject to geometric, manufacturing, and separate core and copper mass constraints. A Python--MPh--COMSOL workflow couples a two-dimensional axisymmetric finite-element method (FEM) model to a Matern 5/2 Gaussian-process (GP) probabilistic surrogate. Here, physics-constrained denotes a design problem evaluated by a governing-equation FEM model and restricted by explicit physical, geometric, manufacturing, and material-allocation constraints; it does not denote a physics-informed GP architecture. Sequential Bayesian optimization (BO) ranks candidates using expected improvement (EI), and every reported incumbent is verified by FEM. Five paired runs show that optimizer ranking depends on the available FEM-evaluation budget: EI--BO improves rapidly at small continuation budgets, COBYLA is stronger at the earliest checkpoint, and BOBYQA attains the highest mean terminal response. A retrospective finite-pool study further finds no robust endpoint advantage of EI over posterior-mean ranking on this smooth response surface. The broader result is that early progress, terminal response, information use, and wall-clock cost can favor different methods in simulation-driven design. A selected-design check at a common total current preserves the observed BOBYQA--COBYLA--EI-BO ordering. The conclusions nevertheless remain conditional on this axisymmetric benchmark and do not establish a fixed-current optimum, fixed-power performance, or electrical-efficiency superiority.

Tensor Networks are a relatively new machine learning approach. The architectures proposed initially are inspired by approaches from quantum many-body physics simulations. One common layout is the matrix product state (MPS) also known as a tensor train optimized with gradient descent techniques. We introduce a global normalization condition, so that the MPS represents a quantum state. We investigate two optimization methods that find the locally optimal tensors and compare them regarding their effectiveness. One is based on gradient descent and the other on an adaptation of DMRG.

As AI systems are increasingly deployed in safety-critical application domains (e.g., autonomous driving), associated risks increase too. Deep learning models underlying modern AI systems, therefore, must undergo thorough testing to ensure their correct behaviour. A single robustness test involves thousands of inferences to empirically verify if a model's outputs remain stable under a bounded perturbation of its inputs. However, existing testing frameworks lack the means to systematically explore and summarise robustness across a combinatorial space of perturbations. We propose TestifAI, a deep learning testing framework for efficient and accurate estimation of robustness against combinations of perturbations. TestifAI enables users to specify operational conditions as structured spaces of semantic input perturbations (e.g., image blur, brightness and zoom) and discrete severity levels (e.g., low, medium and high). Users can query model robustness for any combination (e.g., "low blur, high brightness, and medium zoom"). To achieve efficiency and accuracy, TestifAI introduces partial model tomography, a novel approach to reconstructing model behaviour in a multi-perturbation space from tests that apply only a small number of perturbations (lower-order projections). To estimate robustness against at least three perturbations, TestifAI trains an auxiliary model on the results of tests involving up to two perturbations only, avoiding execution of an exponential number of tests. Our experiments on five image and language classification tasks show that TestifAI can predict higher-order (3 and 4 perturbations) test outcomes from low-order (1 and 2 perturbations) observations with an aggregate robustness estimation error of less than 7%, while reducing the number of inferences by 60-80%.

Class expression learning often produces complex OWL class expressions that are difficult to interpret and reason over. However, by following theoretically grounded simplification principles, this complexity can be reduced. In this paper, we propose Class Expression Simplifier (CES), a novel algorithm for the syntactic simplification of class expressions in Description Logics (DL). CES aims to preserve formal semantics while reducing representational complexity. It systematically applies rewriting rules to eliminate redundancies and identify simpler yet equivalent expressions, thereby producing more compact and human-readable representations without altering logical entailments. We evaluate the effectiveness of CES on class expressions learned from two medium-sized ontologies, demonstrating measurable improvements in reasoning efficiency and reductions in verbosity. This work contributes to the broader goal of making ontology-driven applications more accessible, maintainable, and scalable, with direct implications for knowledge graph construction, semantic search, and Web-scale reasoning. CES is implemented within the open-source Python framework OWLAPY and is publicly available.

Multimodal knowledge graphs typically treat multimedia documents as opaque, external entities. This content-agnostic approach constrains retrieval and analysis by isolating media from the graph's core structure, hindering the ability to capture and query complex relationships across media types. To address this, we introduce the MediaGraph Data Model and its prototypical implementation MeGraS, the MediaGraph Store, a novel approach that integrates multimedia content as graph nodes. This paradigm shift enables the query engine to directly access and process a document's intrinsic content, allowing for native operations such as feature-based similarity search, dynamic segmentation, and the inference of non-materialized relations. By extending the SPARQL query language, MeGraS provides a cohesive platform for the storage, management, and expressive querying of multimodal data. MeGraS is open-source software that establishes a new framework, moving the field toward content-aware multimodal knowledge graphs.

The rapid advancement of Natural Language Generation (NLG) has made the reliable evaluation of generated text increasingly critical, as these systems, such as large language models (LLMs), are now widely deployed in real-world applications. However, traditional automatic metrics fail to capture the multifaceted nature of perceived quality. In this paper, we introduce TextQ-German, a novel dataset suite for human-centered evaluation of German NLG from a Quality of Experience (QoE) perspective, covering automatic text summarization and machine translation. Through crowdsourcing studies with German speakers, we collect human quality ratings and identify relevant perceptual quality dimensions for each task. We develop automatic QoE prediction models, including transformer-based, linguistic feature-based, and hybrid approaches. Hybrid models outperform pure transformer baselines in almost all experimental settings, while linguistic features alone can approach the performance of fine-tuned language models. The dataset is extended with LLM-generated outputs annotated with overall QoE scores. Final validation on held-out sets indicates generalization to unseen data. Our work contributes a publicly accessible resource for NLG evaluation and baselines for automatic QoE prediction, providing a foundation for developing NLG systems that better align with human quality perception.

The epileptogenic zone (EZ) is the brain region that generates seizures in an individual, and is the target of epilepsy surgery. Localizing the EZ from stereo-EEG (sEEG) recordings supports surgical planning, but manual interpretation is time-consuming and focuses on seizure recordings. Graphical learning models of resting-state functional connectivity among the recorded brain regions are an attractive alternative, but depend crucially on the network topology chosen for the model. We present a controlled study of graph-based models to explore how graph topology affects EZ localization from resting-state sEEG in 40 patients. Using the same simple learnable model and leave-one-patient-out evaluation, we compare dense graphs, anatomy- and geometry-informed priors, budgeted sparsification methods, and learned sparsification, including the proposed Region-Bridge-$c$ topology. To compare graph constructions fairly, we control the number of incoming edges per node and vary graph sparsity. At $\approx 30\%$ edge retention, Region-Bridge-$c$ achieves the highest observed mean PR-AUC ($0.371\pm0.015$; ROC-AUC $0.743\pm0.010$) while using $\approx 69\%$ fewer edges than Dense (PR-AUC $0.349\pm0.014$). Spatial-$k$ is competitive, whereas random pruning requires near-dense retention. Learned sparsification benefits from anatomical node metadata but, on average, does not surpass the best fixed prior. Across all topologies, the best choice varies by patient. These results suggest that graph construction should be evaluated explicitly rather than treated as fixed preprocessing.

Reinforcement-learning training of reasoning LLMs (e.g., GRPO) is expensive and requires a controllable environment, committing every contribution to a full training pipeline. We present EvoResearcher, a training-free, inference-time protocol that adds cost-bounded self-reflection to a single frozen LLM backbone. The protocol iterates generate -> self-critique -> revise until a maximum depth D is reached or the critique returns the CONFIRMED sentinel, an implicit early stop that lets the backbone self-verify its answer under a strict compute budget. Four self-reflective meta-reward components (correctness, efficiency, reflection depth, tool-call diversity) act as design principles instantiated as prompt-level mechanisms, so their benefits accrue with zero gradient updates. We validate the protocol on Big-Bench Hard (100 questions) and establish cross-domain behavior on GSM8K (500) and MATH (500) on the same frozen backbone, with cross-model replication on Qwen2.5-72B. All experiments use pure-reasoning benchmarks; the tool-call diversity component is validated in prompt-level form, and the environment-level and multi-agent extensions are design blueprints left to future work. On clean BBH the protocol does not raise accuracy beyond the 95% Wilson interval; its value is cost-bounded self-verification, with the CONFIRMED early stop terminating 82-88% of items at equal accuracy (about 2.1 generations per question).

Autoregressive perception models trained to localize visual entities under the open-vocabulary setting are mostly trained using Supervised fine-tuning (SFT) with maximum likelihood, yet it optimizes a proxy objective (per-token cross-entropy) that is fundamentally misaligned with perception metrics such as precision and recall. In this paper, we explore post-training reinforcement learning (RL), specifically GRPO, to directly align these models with their evaluation metrics. Building up on the recently introduced Falcon Perception, we design an RL framework that addresses perception-specific challenges: reward design for set-structured outputs and multi-head sampling control. We discover multiple benefits from RL for perception: first, RL unlocks state-of-the-art performance in very dense scenes (up to 500 objects per scene), a regime where most existing systems degrade sharply or collapse; furthermore it fixes common issues in autoregressive perception models like mask repetitions and removes almost entirely the need for NMS and coordinate deduplication, which improve both performance and efficiency and remove the need for hyperparameters tuning; overall, we notice improvements on all levels of difficulties in referring expression segmentation (on PBench and SACO-Gold), and we find an elegant way to preserve the knowledge of whether an object exists or not (as evaluated by MCC) without training on negative samples. We show that a simple reward that penalizes false negatives and positives is sufficient. We develop two hybrid self-annotation pipelines, respectively tailored for difficult referring expressions and very dense scenes, and show their benefits on RL-training. Model weights are released as a Falcon Perception revision~\footnote{https://huggingface.co/tiiuae/Falcon-Perception}. Datasets will be published.

Oral diseases affect billions of people worldwide, underscoring a pressing need for accurate and reliable dental assessment that integrates heterogeneous evidence from domain knowledge, radiographs, intraoral photographs, and 3D dental data. Most existing dental AI systems remain modality- or task-specific. Although recent vision-language models support flexible dental question answering, directly generated response leaves evidence implicit and untraceable. To address these limitations, we introduce DentAgent, an evidence-centric multi-agent framework, in which the Orchestrator coordinate five specialized agents spanning various modalities. Each specialist utilizes domain tools to convert observations into structured evidence records. The Evidence Blackboard manages these records as a shared evidence state, tracking coverage, gaps, and conflicts before response generation. This standardized evidence representation integrates isolated dental capabilities into a unified agentic workflow. Across four benchmarks, DentAgent demonstrates leading performance, even surpassing the senior specialists by 17.3 percentage points on multi-label diagnosis, which supports its value for broadly applicable and traceable multimodal dental reasoning, and highlights its potential as a technical foundation for population oral health assessment and management.

Static Application Security Testing (SAST) tools are widely used in both industry and academia. Such tools often make design choices that sacrifice detection to achieve higher performance, i.e., increased precision, decreased runtime, or increased scalability. These design choices rely on certain assumptions regarding the target code or the analysis technique itself. Hence, the assumptions directly impact the detection outcome through the design choices they influence. This motivates a key question: do the sacrifices in the detection capabilities actually help tools achieve the expected performance gains? That is, are the underlying assumptions valid? This paper seeks to address this question by relying on a key observation that the assumptions made by these tools are generally of a causal nature. We propose CAUSEC, a causal analysis framework that makes SAST assumptions testable and explains why the performance changes given certain assumptions, beyond simple correlations. CAUSEC formalizes the assumptions of the SAST tool into the abstraction of a security assumption and combines assumption-driven causal modeling with effect estimation and validation to test its validity and investigate the factors affecting it. To understand what security assumptions generally entail, we perform a systematic literature review of SASTs that detect crypto-API misuse, leading to the discovery and qualitative analysis of 57 assumptions. We then demonstrate the utility and robustness of CAUSEC by testing a popular assumption in four highly relevant tools, using a manually labeled ground truth dataset consisting of 57,038 alerts. Our analysis leads to several key findings that represent insights regarding assumptions and causal effects, which we distill into 3 takeaways for future work.

For $p \ge 1$, the $p$-Wasserstein distance measures the minimum cost of transporting probability mass between distributions, where moving unit mass between two points costs the $p$th power of their distance. For discrete distributions in one dimension, full transport is especially simple: after sorting, mass is matched in order along the line. By contrast, partial and unbalanced transport on the line remains much less understood. Recently, Chapel and Tavenard [ICLR'25] showed that, for $p=1$, all optimal partial transport plans between distributions supported on $n$ points, with uniform mass at each point, can be computed in $O(n\log n)$ time by exploiting the metric structure of the cost. For $p>1$, this structure no longer applies, and existing approaches require $Ω(n^2)$ time. Our main contribution is an FFT-based data structure for balanced-interval transport queries, which bypasses this quadratic bottleneck and yields an $O(p\,n\log^2 n)$-time algorithm for computing all optimal partial transports on the line for every finite $p\ge 1$. We also provide an open-source C++ implementation that outperforms the state-of-the-art baseline on a range of synthetic instances. Finally, we establish a conditional lower bound for $p=\infty$: any subquadratic-time algorithm for computing all optimal partial transport plan costs on the line would violate the $(\min,+)$-Convolution Hypothesis. This separates the problem from full optimal transport, which is solvable in $O(n\log n)$.

This paper studies integrated sensing and communications (ISAC) over a hybrid system that seamlessly combines legacy cellular base stations with distributed cell-free (CF) access points (APs). We propose a hierarchical ISAC architecture where a central base station (CBS) serves its near users and simultaneously operates as a monostatic radar for aerial target detection, while distributed APs---many idle under user-centric clustering---act as cost-free bistatic receivers. The CBS jointly handles communication processing and multi-static sensing fusion, reducing fronthaul overhead compared to conventional cell-free ISAC. To achieve this, a five-phase time-division duplexing workflow with precise ISAC role assignment is specified. Closed-form expressions for spectral efficiency and multi-static sensing signal-to-noise ratio analytically characterize the communications--sensing Pareto frontier. Numerical results confirm that the proposed hierarchical design simultaneously achieves higher sum throughput and superior sensing accuracy than conventional cell-free ISAC.

Hyperreduced nonlinear solid-mechanics components can be generated offline and reused as transferable building blocks across different assemblies, boundary conditions, meshes, material parameters, and constitutive models. We use proper orthogonal decomposition (POD) and energy conserving sampling and weighting (ECSW) on the component level and connect the substructures by mortar mesh tying. The POD modes and the ECSW weights and elements are computed offline from simulations of single components and the finite rigid body motions are treated by 12 additional rigid body modes per substructure. The numerical examples demonstrate errors below 1 \% for large quasi-static assemblies while evaluating less than 10 \% of the elements. The same component bases and ECSW elements are successfully reused for finite-strain viscoelastic dynamics, although they were trained only on elastic Neo-Hookean component simulations. These results indicate that component-wise hyperreduction can provide reusable reduced building blocks for modular nonlinear solid-mechanics simulations.

LiDAR scene flow estimates point-wise motion between two consecutive scans, referred to as the source and target. Leading self-supervised methods typically minimize the Chamfer loss, the nearest neighbor distance between the flow-compensated source and the target. However, nearest-neighbor search does not enforce motion rigidity, often leading to inconsistent flows within object instances. Existing approaches address this issue with additional regularization terms, but flow consistency among points remains limited, especially for large objects. We propose RVLoss, a self-supervised loss that incorporates motion rigidity by design through a runoff vote mechanism. Our key observation is that the point-wise motion, calculated from nearest neighbor search, can often be grouped into a small set of dominant flow candidates by voting (top-k voting). Furthermore, when compensating the source by these candidates, the flow that best represents the underlying rigid motion often yields the highest consensus after a second voting (top-1 voting). Based on this insight, we incorporate the two-stage runoff vote into loss design and create cluster-wise rigid flows and free-form flows as pseudo-labels for self-supervised learning. RVLoss can be seamlessly integrated into existing feedforward architectures. Experiments on the Argoverse2 2026 Challenge show that models trained with RVLoss achieve state-of-the-art performance among self-supervised approaches, outperforming baseline models trained with alternative loss designs by 20%. Moreover, cross-dataset evaluations demonstrate consistent performance improvements across four additional datasets. Code will be released upon acceptance.

We study Bayesian optimization in a time-varying environment where the unknown reward function evolves according to a Gaussian process drift model. Existing GP-UCB analyses in this setting typically require the exploration parameter to grow with the horizon to maintain uniform confidence bounds. Using per-round local confidence events, we show that GP-UCB can instead be run with a constant exploration parameter and obtain an expected-regret bound whose coefficient depends on the drift rate. We also derive a sharper time-varying maximum-information-gain bound. For the squared exponential kernel, it yields $\tildeγ_T/T=\widetilde{\mathcal O}(ε^{1/2})$ and expected average regret $\widetilde{\mathcal O}(ε^{1/4})$ in the persistent-drift regime. The same constant-exploration analysis also yields realized-regret guarantees. Simulations support the predicted logarithmic dependence of the bound-suggested exploration parameter on $1/ε$.

Confluence guarantees that diverging rewrite choices can always be rejoined. For finite terminating string- and term-rewriting systems, confluence is decidable by critical-pair analysis, and in polynomial time for length-reducing strings. For finite terminating (hyper)graph transformation systems, in contrast, confluence is undecidable. We show that undecidability already appears for words on a circle, that is, strings up to rotation. Confluence of finite cycle-rewriting systems over the fixed alphabet $\{0,1\}$ is undecidable, indeed $Π^0_1$-complete, even when every rule has a nonempty right-hand side and strictly reduces length. Under this restriction termination is syntactically evident, and derivations from a nonempty length-$n$ cycle have fewer than $n$ steps. The same holds over every fixed alphabet with at least two letters, while the one-letter case is decidable. Rotation alone separates cyclic from string rewriting. The proof compiles a deterministic verifier into a weighted cycle system with one controlled branch, then into a binary length-reducing system via a run-length code whose cleanup rules send every reducible malformed cycle to one error normal form.