# radius Published articles for radius. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective DevFeed: [The Implicit Bias of Hyperbolic Representation Learning for Multiclass Data: A Busemann Risk Perspective]() Original publisher: [Read original article]() Author: Xingrun Li, Sho Kuno, Yusuke Mukuta, Xin Yang, Tatsuya Harada Published: 2026-11-04T05:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Representation learning](), [Machine learning](), [clustering]() Tags: [bias](), [boundary](), [classification](), [clustering](), [critical](), [cs-lg](), [data](), [entropy](), [flow](), [learning](), [margin](), [perm](), [permutation](), [points](), [prototype](), [prototypes](), [radius](), [results](), [return](), [risk](), [sign]() ### AI overview The study analyzes implicit bias in hyperbolic multiclass classification with fixed prototypes under Riemannian gradient flow, covering permutation invariant relative margin (PERM) losses such as cross entropy. At large radius, prototype distances separate into a radial term and a direction dependent Busemann term. The sign of drift coefficient μ determines the radial behavior: persistent positive drift gives r(t)=½ log t+O(1), while persistent negative drift returns the trajectory to the large-radius threshold in finite time. Meanwhile, directions can approach critical points of Busemann risk on the ideal boundary, including during radial return. The authors use these results to characterize boundary saturation and near-boundary clustering. ### Source excerpt arXiv:2610.07131v2 Announce Type: replace Abstract: We study the implicit bias of Riemannian gradient flow for hyperbolic multiclass classification with fixed class prototypes in hyperbolic space $\mathbb H^n$. Our framework accommodates general permutation invariant relative margin (PERM) losses, a class that includes cross entropy and other standard multiclass losses. Our analysis is based on a decomposition: at large radius, the distance to each prototype splits into a radial term and a direction dependent term described by the Busemann function. This yields two main results. First, we prove a radial dichotomy: the sign of a drift coefficient $\mu$ determines whether the radius is pushed toward the ideal boundary or back toward the interior; if the positive drift persists, then $r(t)=\tfrac12\log t+O(1)$, while persistent negative drift returns the trajectory to the large radius threshold in finite time. Second, we show that large-radius directions can approach critical points of the Busemann risk on $\partial\mathbb H^n$, even during radial return. These results provide a rigorous large-radius perspective on two phenomena we refer to as boundary saturation and near-boundary clustering in hyperbolic representation learning. ## The Information Limits of Neural Controlled Differential Equations Under Sparse Observations DevFeed: [The Information Limits of Neural Controlled Differential Equations Under Sparse Observations]() Original publisher: [Read original article]() Author: Rostislav Gusev, Evgenia Romanenkova, Alexey Zaytsev Published: 2026-11-04T05:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Artificial Intelligence](), [Deep neural networks]() Tags: [acceleration](), [adaptive](), [approximation](), [bounded](), [certificate](), [continuous](), [cs-lg](), [drivers](), [experiments](), [hidden](), [input](), [measurements](), [neural](), [number](), [prediction](), [projection](), [radius](), [reduce](), [sampling](), [scalar](), [set]() ### AI overview Sparse observations do not uniquely determine a Neural CDE's terminal state: continuous input paths consistent with the same measurements can yield different outcomes. For planar drivers with bounded speed, the paper approximates the compatible terminal-state set using feasible signed areas and transported Lie brackets, then projects it onto a scalar prediction to produce a computable, target-specific ambiguity certificate. For nondegenerate planar CDEs, the optimal worst-case uncertainty radius under deterministic adaptive sampling scales as N⁻¹ with bounded speed and N⁻² when both speed and acceleration are bounded. Synthetic experiments assess the certificate using admissible path completions and examine path regularity. ### Source excerpt arXiv:2611.03887v1 Announce Type: new Abstract: Neural controlled differential equations (Neural CDEs) evolve hidden states along continuous paths constructed by interpolating discrete observations. Sparse measurements leave the input between observation times undetermined, and admissible continuous paths consistent with the same data can produce different terminal states. We characterize this ambiguity for planar drivers with bounded speed. The set of compatible terminal states admits a leading-order zonotopic approximation determined by feasible signed areas and transported Lie brackets. Its projection onto a scalar prediction yields a computable, target-specific ambiguity certificate. We also study the number of measurements needed to reduce the remaining uncertainty. For nondegenerate planar CDEs, the optimal worst-case radius over deterministic adaptive sampling policies scales as $N^{-1}$ when speed is bounded and $N^{-2}$ when both speed and acceleration are bounded, where $N$ is the number of observation intervals. Synthetic experiments assess the certificate using admissible continuous completions and examine the role of path regularity. ## Low-rank corrections to a shared reference Jacobian for GPU-parallel AC $N\\!-\\!1$ contingency analysis DevFeed: [Low-rank corrections to a shared reference Jacobian for GPU-parallel AC $N\\!-\\!1$ contingency analysis]() Original publisher: [Read original article]() Author: Marc Hunkem\\"oller, Nico Westerbeck, Joost van Dijk, Lars Schewe, Dirk Witthaut Published: 2026-11-03T05:00:00Z Content type: article Language: en Sources: [arXiv: Distributed Computing]() Topics: [High-Performance Computing](), [GPU](), [GPU optimization](), [deterministic-simulation](), [Fortran]() Tags: [benchmarks](), [central-processing-unit](), [cs-dc](), [cs-na](), [cs-sy](), [eess-sy](), [gpu](), [iteration](), [math-na](), [newton](), [outages](), [parallel](), [radius](), [scale](), [sparsity](), [state](), [topology]() ### AI overview The method makes GPU-parallel AC N−1 contingency analysis feasible at transmission scale by reusing one inverted reference Jacobian across outages, avoiding a separate factorization for each topology. It represents topology changes with low-rank Woodbury corrections and handles remaining state-dependent changes through an inner iterative solve, using either a truncated Neumann series or the biconjugate gradient stabilized method. The authors report competitive per-topology solve times against an optimized 80-core CPU baseline on transmission-scale benchmarks; low-rank corrections account for about 1-2% of the workload. The excerpt says the reference Jacobian is an effective preconditioner, based on analysis of iteration-matrix spectral radius and condition number. ### Source excerpt arXiv:2611.03012v1 Announce Type: cross Abstract: Contingency analysis repeatedly solves the power-flow equations under many single-element outages, an increasingly demanding workload as operating margins tighten and renewable variability grows. Graphics processing units (GPUs) are attractive for this task, but a change in topology alters the sparsity pattern of the Jacobian, preventing the uniform batched factorization on which efficient GPU solvers rely. This paper presents a GPU-parallel Newton--Raphson solver for $N\!-\!1$ contingency analysis that separates the change in operating state from the change in topology. A single reference Jacobian is inverted once and reused across all contingencies. Each topology change is expressed as a low-rank Woodbury correction, while the residual state-dependent perturbation is handled by an inner iterative solve, a truncated Neumann series or the biconjugate gradient stabilized method. We analyze the spectral radius and condition number of the resulting iteration matrices and show that the reference Jacobian is an effective preconditioner. On transmission-scale benchmarks, the method attains per-topology solve times competitive with an optimized 80-core central processing unit baseline, with the low-rank correction accounting for approximately 1--2\% of the workload. This makes GPU-parallel $N\!-\!1$ contingency analysis feasible at transmission scale without per-topology refactorization. ## Probabilistic Meshless Methods on Manifolds DevFeed: [Probabilistic Meshless Methods on Manifolds]() Original publisher: [Read original article]() Author: Federico Pavesi, No\\'emie Jaquier, Antonio Candelieri Published: 2026-10-30T04:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Machine learning](), [Finite Element Method (FEM)]() Tags: [bayesian](), [consistency](), [convergence](), [cs-lg](), [error](), [experiments](), [fewer](), [flat](), [gaussian](), [matrix](), [partial-differential-equations](), [probabilistic](), [radius](), [real-world](), [scheme](), [sphere](), [stat-ml](), [torus](), [vertex]() ### AI overview The paper extends probabilistic meshless PDE methods to compact manifolds and provides convergence analysis in two settings. When Laplace-Beltrami eigenpairs are known, it evaluates the Gaussian process prior exactly and approximates the PDE operator with generalized finite differences on a sampled point cloud; consistency at cloud points is governed by fill distance. For implicit manifolds known only through a point cloud, it approximates both prior and operator and introduces a finite-difference scheme with a tunable stencil radius that controls coefficient growth while preserving consistency. Error bounds for the posterior mean separate collocation error from approximation errors. Experiments on the circle, sphere and flat torus support the theory. On cortical thickness data, the method reportedly matches established discretizations' accuracy using fewer than one tenth as many observations and provides a credible interval at each vertex. ### Source excerpt arXiv:2610.39855v1 Announce Type: cross Abstract: Probabilistic meshless methods solve partial differential equations (PDEs) by placing a Gaussian process prior on the solution and conditioning it on the PDE at a finite set of collocation nodes. The posterior provides both an approximation of the solution and a Bayesian quantification of its error. While these methods are well established on Euclidean domains, their extension to manifolds lacks, to our knowledge, any convergence analysis. We extend them to compact manifolds and study their convergence in two settings. First, for known manifolds whose Laplace-Beltrami eigenpairs are available, the prior can be evaluated exactly, but the PDE operator generally cannot be applied to it in closed form. We replace this operator by a standard generalized finite difference discretization on a point cloud sampled from the manifold, and show that the resulting method is consistent at the points of the cloud, at a rate governed by their fill distance. Second, for implicit manifolds, known only through a point cloud, both the prior and the operator must be approximated. We propose a new generalized finite difference scheme with a free stencil radius, and show that it retains the consistency of the standard construction while controlling the growth of its coefficients, and that an appropriate radius yields uniform convergence of the discrete Gram matrix. In both settings, we derive error bounds for the posterior mean which separate the collocation error intrinsic to the method from the error due to approximating the operator and, for implicit manifolds, the prior. Experiments on the circle, the sphere and the flat torus confirm our theoretical claims. On real-world cortical thickness data, our approach attains the accuracy of established discretizations, while conditioning on fewer than a tenth of the observations and providing a credible interval at every vertex. ## Learning Where It Matters: Geometric Anchoring for Robust Preference Alignment DevFeed: [Learning Where It Matters: Geometric Anchoring for Robust Preference Alignment]() Original publisher: [Read original article]() Author: Youngjae Cho, Jongsuk Kim, Ji-Hoon Kim Published: 2026-10-30T04:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [dpo](), [ai alignment](), [LLM Techniques](), [Large Language Model](), [llm-reasoning]() Tags: [adaptive](), [adversarial](), [align](), [alignment](), [anchor](), [benchmarks](), [cs-lg](), [dpo](), [language-models](), [learning](), [llm](), [local](), [margin](), [noise](), [optimization](), [optimizing](), [pair](), [performance](), [policy](), [radius](), [robust]() ### AI overview GAPO replaces DPO's fixed reference policy with a small, adversarial local perturbation of the current policy as a pessimistic anchor. It uses the reward difference between policy and anchor--the Anchor Gap--to reweight preference pairs by local sensitivity, reducing the influence of geometrically brittle examples and emphasizing robust signals. Under smoothness conditions, the gap approximates worst-case local margin degradation. The abstract reports improved robustness across diverse noise settings while matching or improving performance on standard LLM alignment and reasoning benchmarks; it does not provide quantitative results or benchmark details. ### Source excerpt arXiv:2602.04909v5 Announce Type: replace Abstract: Direct Preference Optimization (DPO) and related methods align large language models from pairwise preferences by regularizing updates against a fixed reference policy. As the policy drifts, a static reference, however, can become increasingly miscalibrated, leading to distributional mismatch and amplifying spurious preference signals under noisy supervision. Conversely, reference-free variants avoid mismatch but often suffer from unconstrained reward drift. We propose Geometric Anchor Preference Optimization (GAPO), which replaces the fixed reference with a dynamic, geometry-aware anchor: an adversarial local perturbation of the current policy within a small radius that serves as a pessimistic baseline. This anchor enables an adaptive reweighting mechanism, modulating the importance of each preference pair based on its local sensitivity. We further introduce the Anchor Gap, the reward discrepancy between the policy and its anchor, and show under smoothness conditions that it approximates worst-case local margin degradation. Optimizing a logistic objective weighted by this gap downweights geometrically brittle instances while emphasizing robust preference signals. Across diverse noise settings, GAPO consistently improves robustness while matching or improving performance on standard LLM alignment and reasoning benchmarks. ## The Batch Size Can Be One: Test-Time Adaptation from Classifier Geometry DevFeed: [The Batch Size Can Be One: Test-Time Adaptation from Classifier Geometry]() Original publisher: [Read original article]() Author: Jaeho Hwang, Yujin Oh, Juhyeon Shin, Juhye Lee, Sungroh Yoon, Uiwon Hwang Published: 2026-10-28T04:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Machine learning](), [model-deployment]() Tags: [batch](), [class](), [classes](), [confidence](), [cs-lg](), [distribution](), [feature](), [features](), [input](), [limit](), [memory](), [model](), [point](), [predictions](), [protocols](), [prototype](), [radius](), [regions](), [sample](), [source](), [test]() ### AI overview OriTTA adapts a model on one unlabeled test sample at a time by using fixed geometric targets derived from the source classifier, rather than relying on stream-wide statistics or confidence alone. It recenters class prototypes to spread their directions, then aligns selected features with the predicted class axis while penalizing excessive radius. A memory retaining one input per predicted class helps limit changes for classes missing from the stream, and the model resets if reclassifying that memory reveals collapse. The abstract reports the highest mean batch-size-one accuracy across all 16 tested combinations of four backbones, two protocols and two stream orders on CIFAR-10-C, CIFAR-100-C and ImageNet-C, without per-setting tuning. On ImageNet-C fog, it reports that recent methods collapsed in as many as two thirds of 100 runs, while OriTTA did not collapse. ### Source excerpt arXiv:2610.36628v1 Announce Type: new Abstract: Test-time adaptation updates a deployed model on an unlabeled test stream. In practice this stream often arrives one sample at a time, with the classes in no particular order. A single sample then provides limited information for estimating distribution-level statistics, and selecting samples by confidence can admit predictions that are wrong yet confident. A corruption, however, shifts the features while leaving the decision regions of the frozen classifier unchanged. We therefore propose Origin-recentered Test-Time Adaptation (OriTTA), which constructs fixed geometric targets from the source model and adapts selected features toward them. Seen from the origin of the feature space, the classes lean toward a common direction. We choose a new origin to bring class scores closer together while keeping it near the mean feature of one synthetic prototype per class. From this origin, prototype directions spread more evenly, and each class obtains an axis and an ideal point before any test data arrives. During adaptation, OriTTA aligns selected features with their predicted class axis and penalizes excessive radius, keeps one input per predicted class in memory to limit feature changes for classes absent from the stream, and resets the model when re-classifying this memory reveals collapse. Without tuning for each setting, OriTTA achieves the highest mean accuracy at batch size 1 on CIFAR-10-C, CIFAR-100-C and ImageNet-C in all sixteen combinations of four backbones, two protocols and two stream orders. On ImageNet-C fog, recent methods collapse in up to two thirds of one hundred runs, while OriTTA never does. ## Maximum-Likelihood Decoding of Gabidulin Codes Is NP-Hard Even in Dimension One DevFeed: [Maximum-Likelihood Decoding of Gabidulin Codes Is NP-Hard Even in Dimension One]() Original publisher: [Read original article]() Author: Philippe Gaborit Published: 2026-10-27T04:00:00Z Content type: article Language: en Sources: [arXiv: Cryptography and Security]() Topics: [Decoding](), [communications]() Tags: [complete](), [cs-cr](), [cs-it](), [cubic](), [decoding](), [hamming](), [linear](), [linear-codes](), [map](), [math-it](), [np-hard](), [planes](), [radius](), [rank](), [reduction](), [scalar](), [search](), [solution](), [square](), [support](), [systems]() ### AI overview The abstract proves that maximum-likelihood decoding for one-dimensional Gabidulin codes is NP-hard: deciding whether a received word lies within rank distance n−2 is NP-complete. Unlike the cited Hamming-metric result, this hardness holds at dimension k=1. The reduction is deterministic and yields deterministic polynomial reductions establishing NP-completeness of Rank Syndrome Decoding and Rank Minimum Distance for F_{q^m}-linear codes, improving on a previously randomized reduction. The proof encodes quadratic systems into Twisted Square Membership, then into Gabidulin decoding. It interprets the received word as an F_q-linear map and uses a scalar-acting plane to encode the membership relation. The constructions are explicit and polynomial, with the stated parameters N=O(qd²), n) Original publisher: [Read original article]() Author: Anthony Gatti, Anoosha Fayyaz, Prashant Krishnamurthy, Kaushik P. Seshadreesan, Amy Babay Published: 2026-10-27T04:00:00Z Content type: article Language: en Sources: [arXiv: Networking]() Topics: [distributed algorithm](), [IP routing]() Tags: [algorithm](), [availability](), [cs-ni](), [distributed](), [entanglement](), [exploits](), [link-state](), [local](), [metric](), [network](), [node](), [online](), [overhead](), [planning](), [protocol](), [quality](), [quant-ph](), [quantum](), [quantum-network](), [radius](), [resource](), [routing]() ### AI overview Q-GUARD aims to meet each request's end-to-end Bell-pair fidelity threshold without a centralized controller: nodes share link-state information only within k hops. Each slot, it builds purification cost tables from realized pairs, assigns per-hop fidelity targets using a Werner-state equal-split rule, then chooses path segments by expected goodput, accounting for swap success, purification overhead, and available resources. Q-GUARD-WS uses hardware quality estimates to distribute purification effort unevenly across hops. In synthetic 100-node tests with heterogeneous links and stochastic BBPSSW purification, Q-GUARD raised qualified success on 4-hop paths from under 20% to over 85% and nearly doubled qualified service radius versus throughput-only and naive-purification baselines; Q-GUARD-WS added throughput gains under high hardware heterogeneity. ### Source excerpt arXiv:2605.00246v2 Announce Type: replace Abstract: Many quantum-network applications require end-to-end Bell pairs whose fidelity exceeds a request-specific threshold, but existing entanglement routing algorithms either optimize only throughput without regard for fidelity or enforce fidelity guarantees using centralized controllers with global link-state knowledge. We present Q-GUARD, an online entanglement routing algorithm that enforces per-request fidelity thresholds within a distributed protocol model in which nodes exchange link-state information only with their $k$-hop neighbors. After link outcomes are realized in each slot, Q-GUARD builds per-link purification cost tables from realized Bell pairs, allocates per-hop fidelity targets using a Werner-state equal-split rule, and selects between candidate path segments using a segment-local expected-goodput (EXG) metric that jointly accounts for swap success, purification overhead, and resource availability. We also introduce Q-GUARD-WS, an extension that exploits per-link hardware quality estimates to allocate purification effort non-uniformly across hops. On synthetic 100-node topologies with heterogeneous link fidelity and stochastic BBPSSW purification, Q-GUARD raises the qualified success rate from under 20\% to over 85\% on 4-hop paths and nearly doubles the qualified service radius in Euclidean distance relative to throughput-only and naive-purification baselines, while Q-GUARD-WS provides additional throughput gains under high hardware heterogeneity. ## How to Test Location-Aware APIs with FastAPI and PostGIS DevFeed: [How to Test Location-Aware APIs with FastAPI and PostGIS]() Original publisher: [Read original article]() Author: SitePoint Team Published: 2026-10-23T17:55:19Z Content type: tutorial Language: en Sources: [SitePoint]() Topics: [FastAPI](), [Test automation](), [test data](), [database-optimization]() Tags: [api](), [apis](), [bugs](), [ci](), [database](), [databases](), [explain](), [fastapi](), [geography](), [location](), [postgis](), [pytest](), [python](), [radius](), [spatial](), [test]() ### AI overview Test location APIs by checking spatial truth against a real PostGIS database, since a successful HTTP response and valid JSON can still hide large coordinate or distance errors. The example uses a `geography(Point, 4326)` column, a GiST index, and `ST_DWithin`/`ST_Distance` to filter and order results in meters. Seed deterministic fixtures with `ST_Project` at known distances, then verify radius inclusion, inclusive boundary behavior, coordinate validation, and GeoJSON's longitude-first order. Keep request-validation tests fast and run integration tests against PostGIS to catch database behavior that mocks miss. Inspect `EXPLAIN` plans for spatial-index use; exact plans depend on data and PostgreSQL version. ### Source excerpt Test location-aware APIs built with FastAPI and PostGIS: seed spatial data, run radius and distance queries, and assert results with pytest. Continue reading How to Test Location-Aware APIs with FastAPI and PostGIS on SitePoint. ## Metric Conformal Prediction via the Conditional Expected Local Radius DevFeed: [Metric Conformal Prediction via the Conditional Expected Local Radius]() Original publisher: [Read original article]() Author: Rui Qiu, Fang Yao, Zhou Yu Published: 2026-10-23T04:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Machine learning]() Tags: [conditional](), [conditional-probability](), [conformal-prediction](), [consistency](), [coverage](), [cs-lg](), [distribution](), [local](), [metric](), [multimodality](), [radius](), [responses](), [spaces](), [stat-ml](), [transport](), [uncertainty-quantification](), [vector]() ### AI overview The paper introduces conditional expected local radius (CELR), a conformal prediction method for responses in general metric spaces. CELR measures local conditional probability concentration, so prediction sets can reflect heterogeneity and multimodality without requiring densities or vector-space structure. Its conditional distribution provides nonconformity scores comparable across covariate values and avoids transport comparisons between distance profiles. A metric distributional random forest handles multivariate covariates and nonlinear interactions; one forest fit supplies the score components, avoiding repeated local fitting. The authors report uniform estimator consistency, asymptotic conditional validity under suitable regularity conditions, and finite-sample marginal coverage under exchangeability. Numerical studies report effective uncertainty quantification across metric spaces and computational savings over the conditional profile score method. ### Source excerpt arXiv:2610.31336v1 Announce Type: cross Abstract: We introduce the conditional expected local radius (CELR) and develop a new conformal prediction method for non-Euclidean responses in general metric spaces. CELR measures local conditional probability concentration, allowing prediction sets to accommodate heterogeneity and multimodality without requiring densities or a vector space structure. Its conditional distribution yields a nonconformity score that is comparable across covariate values and avoids costly transport comparisons between distance profiles. We further adapt a metric distributional random forest that handles multivariate covariates and nonlinear interactions, while a single forest fit supplies all score components, reducing computation by eliminating repeated local fitting. We establish uniform consistency of the estimators and asymptotic conditional validity under suitable regularity conditions, together with finite-sample marginal coverage under exchangeability. Numerical studies demonstrate effective uncertainty quantification across different metric spaces and substantial computational savings over the conditional profile score method. ## Hearing the shape of an arena with spectral swarm robotics DevFeed: [Hearing the shape of an arena with spectral swarm robotics]() Original publisher: [Read original article]() Author: Leo Cazenille, Nicolas Lobato-Dauzier, Alessia Loi, Loona Macabre, Mika Ito, Olivier Marchal, Soo-Hyeon Kim, Nathanael Aubert-Kato, Nicolas Bredeche, Anthony J. Genot Published: 2026-10-23T04:00:00Z Content type: article Language: en Sources: [arXiv: Artificial Intelligence]() Topics: [Robotics]() Tags: [arena](), [classification](), [connectivity](), [cs-ai](), [cs-cg](), [cs-ro](), [diffusion](), [embedded](), [environment](), [environments](), [global](), [hardware](), [interaction](), [invariants](), [law](), [local](), [noise](), [parameter](), [platforms](), [proof-of-concept](), [radius](), [robotics](), [swarm]() ### AI overview Spectral swarm robotics lets robots infer arena shape through local interactions: they emulate diffusion to estimate Laplacian spectral invariants that ordinarily require centralized computation. In this proof of concept, a swarm estimated the second Laplacian eigenvalue and used it to classify arenas from a predefined set with distinct spectral signatures. The authors report that this single value enabled one-shot classification, and identify a scaling law relating swarm size to interaction radius for robust estimation. Experiments on Kilobots and Pogobots achieved reliable classification despite realistic noise and sparse connectivity. The evidence described is limited to selected confined environments; broader uses are discussed as a possibility. ### Source excerpt arXiv:2403.17147v2 Announce Type: replace-cross Abstract: Swarm robotics relies on robots with minimal sensing and computation that achieve self-organization at the level of the collective to address a variety of tasks. Yet swarm robotics still struggles with global tasks that require understanding the broader spatial context in which robots operate, such as identifying the shape of the arena in which they are embedded. Here, we introduce spectral swarm robotics, a framework in which robots recover global spectral descriptors of the swarm's geometric structure through strictly local interactions. To do so, robots emulate diffusion to locally estimate Laplacian spectral invariants, quantities normally obtained only through centralized computation. These spectral values serve as compact descriptors of the environment. In the present proof of concept, robots estimated the second Laplacian eigenvalue and used it to classify arenas from a predefined set of shapes with distinct spectral signatures. We show that estimating a single eigenvalue is sufficient for one-shot classification among selected confined environments with distinct spectral signatures. We uncovered a scaling law linking swarm size (a global parameter) and interaction radius (a local parameter) that ensures robust estimation. We validated the approach experimentally on two distinct hardware platforms, Kilobots and Pogobots, achieving reliable classification of arena shapes under realistic noise and sparse-connectivity conditions. Last, we discuss how locally recovering Laplacian spectral invariants opens avenues for swarm robotics in settings where producing efficient collective behaviors strongly depends on the global structure of the swarm. ## Looped GNNs Beyond Fixed Depth: Graph Size Generalization and Parameter-Efficient Adaptation DevFeed: [Looped GNNs Beyond Fixed Depth: Graph Size Generalization and Parameter-Efficient Adaptation]() Original publisher: [Read original article]() Author: Zhiyang Wang, Zhishang Luo, Yusu Wang Published: 2026-10-21T04:00:00Z Content type: article Language: en Sources: [arXiv: Machine Learning]() Topics: [Machine learning](), [Neural Network](), [peft]() Tags: [analysis](), [application](), [cs-lg](), [effects](), [experiments](), [fine-tuning](), [gnn](), [graph](), [information](), [pretraining](), [processor](), [radius](), [reuse](), [sample](), [size](), [small](), [sufficient]() ### AI overview Looped GNNs extend information reach to larger graphs by repeatedly applying a GNN processor pretrained on smaller graphs, without retraining. The paper studies tasks with a shared local iterative computation whose effective dependency radius grows with graph size, and categorizes six schemes to distinguish depth extension, fine-tuning, and freeze-and-steer adaptation. Its analysis gives fixed-depth information limits and conditions for accurate iterative reuse. For adaptation, Loop-Freeze-Steer (LFS) freezes the pretrained processor and trains a small controller to guide repeated application, using fewer trainable parameters than full fine-tuning. Finite-sample analysis provides conditions under which adaptation can improve larger-graph performance. Experiments on synthetic tasks and chip placement evaluate these approaches and their accuracy-trainable-parameter trade-off. ### Source excerpt arXiv:2610.24112v1 Announce Type: new Abstract: Generalizing from small graphs to larger ones can require computation beyond the depth of a neural model used during training. We study target tasks that admit a common local iterative computation and whose effective dependency radius grows with graph size. The central idea is to learn a local update rule through GNN pretraining, then repeatedly apply the same learned processor beyond the training depth to extend information reach on larger graphs without retraining. Calling such parameter-shared architecture a \emph{looped GNN}, we categorize six schemes for looped GNNs to separate the effects of depth extension, fine-tuning, and freeze-and-steer adaptation. Our analysis establishes fixed-depth information limits and sufficient conditions under which accurate iterative reuse overcomes them. To improve beyond unadapted reuse, we introduce \emph{Loop-Freeze-Steer} (LFS), which freezes the pretrained processor and learns a small controller to steer its repeated application, using much fewer trainable parameters than full fine-tuning. Our finite-sample analysis gives sufficient conditions for adaptation to improve performance on larger graphs. Experiments on synthetic tasks and chip placement evaluate depth extension and adaptation, highlighting LFS's accuracy--trainable-parameter trade-off for size generalization. ## Zella Stack Micro Data Center Ships by Courier, Stacks From 24RU to 48RU, and Cools Up to 124kW DevFeed: [Zella Stack Micro Data Center Ships by Courier, Stacks From 24RU to 48RU, and Cools Up to 124kW]() Original publisher: [Read original article]() Author: Harold Fritts Published: 2026-09-30T17:56:43Z Content type: news Language: en Sources: [StorageReview.com]() Topics: [Software-Defined Data Center](), [AI Infrastructure](), [infrastructure monitoring](), [observability]() Tags: [api](), [authentication](), [cooling](), [data-center](), [enterprise](), [infrastructure](), [modbus](), [radius](), [server-rack](), [servers](), [snmp]() ### AI overview Zella DC introduced Zella Stack, a modular indoor micro data center designed for sites where conventional cabinets are difficult to install. It ships in blocks and scales from 24RU to 48RU. The article notes that the published cabinet weights do not support the company's claim that Stack is about one-quarter the weight of its Zella Pro, and that the 124kW figure applies to cooling options rather than the fully loaded cabinet's power draw. Stack includes monitoring, automation, security sensors, and network management integrations. ### Source excerpt Zella DC used Yotta 2026 in Las Vegas to introduce Zella Stack, an indoor micro data center that ships by standard courier and is assembled on site from stackable blocks. A base block carries the supporting infrastructure, IT blocks go on top of it, and the cabinet starts at 24RU and grows in 12RU increments The post Zella Stack Micro Data Center Ships by Courier, Stacks From 24RU to 48RU, and Cools Up to 124kW appeared first on StorageReview.com. ## CodeSOD: Quite a Distance from the Right Solution DevFeed: [CodeSOD: Quite a Distance from the Right Solution]() Original publisher: [Read original article]() Author: Remy Porter Published: 2026-09-30T06:30:00Z Content type: article Language: en Sources: [The Daily WTF]() Topics: [Test-driven development]() Tags: [codesod](), [math](), [metric](), [radius]() ### AI overview The article examines a C# method that checks whether a point lies within a stated distance by iterating over integer coordinates in a square around a center. It explains that this tests a box-shaped region rather than a conventional radius and that direct bounds checks would be simpler if a box were intended. ### Source excerpt Fritz's team needed to see if one point was within a certain distance from a center point. You or I would likely try and answer this question using a simple distance calculation, since that's the question we're trying to answer. But what if you didn't understand distances at all? Then you could write this little piece of genius. private bool IsWithin(Point point, int radius) { for (int x = -radius; x < radius + 1; x++) { for (int y = -radius; y < radius + 1; y++) { if ((PositionX == point.X + x) && (PositionY == point.Y + y)) return true; } } return false; } This limits us to integer point values, which itself is fine. This iterates across every coordinate from (x-radius,y-radius) to (x+radius,y+radius) and checks if any of them are equal to our center point, (PositionX,PositionY). Notably, this means we're not checking a radius, at least not in a traditional metric, we're checking a box (or using the taxicab metric). Which if we wanted to check a box, we actually have even easier math than the distance equation- we could do that with pure bounds checking. I've never thought to try and brute force distance checking, and that feels like a failure of my own creativity. Fritz's team mate at least was able to WTF in a way I wouldn't have considered. [Advertisement] Keep the plebs out of prod. Restrict NuGet feed privileges with ProGet. Learn more. ## Made in Compose: Airbnb Month Picker Dial DevFeed: [Made in Compose: Airbnb Month Picker Dial]() Original publisher: [Read original article]() Author: sinasamaki Published: 2026-04-17T12:55:42Z Content type: tutorial Language: en Sources: [sinasamaki]() Topics: [Jetpack Compose](), [User interface design](), [UI/UX Design]() Tags: [3d](), [airbnb](), [app](), [arc](), [article](), [border](), [canvas](), [circle](), [clipping](), [compose](), [customization](), [dots](), [drawing](), [gradient](), [library](), [lower-bound](), [mapping](), [radius](), [range](), [render](), [ring]() ### AI overview The excerpt shows how ChromaDial can recreate Airbnb's 12-month picker in Jetpack Compose. It maps 12 segments across a 330° sweep with 30° intervals, starting at one month at 1 o'clock and ending at 12 months at 12 o'clock; the active section accounts for the omitted 30°, and interval wrapping makes the thumb glide between months. The described styling uses a shaded, bordered thumb and a canvas-drawn inactive track with dots placed around its circumference. For the active track, the excerpt says Compose's regular arc is insufficient for reusable clipping or stroking with independently rounded ends. ChromaDial's tube shape accepts separate corner radii for each cap, allowing a smaller starting cap and a rounded end near the thumb. The supplied text cuts off during this API description. ### Source excerpt How to create a gorgeous Dial in Jetpack Compose ## Kubernetes Scheduling And Secure Design DevFeed: [Kubernetes Scheduling And Secure Design]() Original publisher: [Read original article]() Published: 2024-01-22T23:00:00Z Content type: article Language: en Sources: [Doyensec]() Topics: [Cloud Architecture](), [enterprise data protection](), [trust]() Tags: [auditing](), [automation](), [blast-radius](), [business](), [compromise](), [context](), [critical](), [custom](), [deployment](), [design](), [doyensec](), [doyensecurity](), [exploit](), [hacking](), [infosec](), [isolation](), [kubernetes](), [lateral](), [node](), [offensive](), [pentest](), [pentester](), [pods](), [policies](), [radius](), [reduce](), [reverse-engineering](), [risk](), [scheduled](), [scheduler](), [scheduling](), [security](), [vulnerability]() ### AI overview Kubernetes scheduling can reduce the impact of a compromised pod by separating critical workloads from less trusted or higher-risk workloads on shared nodes. The text describes nodeSelector as simple but dependent on maintained labels; nodeName as overriding scheduler rules and requiring careful resource and node management; hard node or inter-pod affinity rules as enforceable isolation that may leave pods pending; and taints and tolerations as a way for nodes to repel workloads, with tolerations permitting but not guaranteeing placement. Topology spread constraints distribute pods across domains, while a custom scheduler can handle specialized risk requirements but is complex. The article recommends choosing isolation based on team trust, data sensitivity, network exposure, and pod privileges, with reserved nodes for critical workloads as a core pattern. It also warns that manipulated labels or pod specifications can attract workloads to critical nodes or block scheduling, and suggests NodeRestriction for protecting prefixed node labels. ### Source excerpt During testing activities, we usually analyze the design choices and context needs in order to suggest applicable remediations depending on the different Kubernetes deployment patterns. Scheduling is often overlooked in Kubernetes designs. Typically, various mechanisms take precedence, including, but not limited to, admission controllers, network policies, and RBAC configurations. Nevertheless, a compromised pod could allow attackers to move laterally to other tenants running on the same Kubernetes node. Pod-escaping techniques or shared storage systems could be exploitable to achieve cross-tenant access despite the other security measures. Having a security-oriented scheduling strategy can help to reduce the overall risk of workload compromise in a comprehensive security design. If critical workloads are separated at the scheduling decision, the blast radius of a compromised pod is reduced. By doing so, lateral movements related to the shared node, from low-risk tasks to business-critical workloads, are prevented. Attackers on a compromised pod with nothing around Kubernetes provides multiple mechanisms to achieve isolation-oriented designs like node tainting or affinity. Below, we describe the scheduling mechanisms offered by Kubernetes and highlight how they contribute to actionable risk reduction. The following methods to apply a scheduling strategy will be discussed: nodeSelector field matching against node labels; nodeName and namespace fields, basic and effective; Affinity and anti-affinity, constraints type expansion for inclusion and repulsion; Inter-pod affinity and anti-affinity, which focus labels matching on pods labels instead of nodes labels when dealing with inclusion and repulsion; Taints and Tolerations, allowing a node to repel or tolerate a pod being scheduled; pod topology spread constraints, based on regions, zones, nodes, and other user-defined topology domains; Design a Custom Scheduler, tailored to your security needs Mechanisms for Workload ## Are you using the right Mongo geospatial query? DevFeed: [Are you using the right Mongo geospatial query?]() Original publisher: [Read original article]() Published: 2023-02-10T00:00:00Z Content type: article Language: en Sources: [Artsy]() Topics: [geospatial](), [Tool](), [Ruby on Rails](), [GeoJSON]() Tags: [api](), [application](), [best-practices](), [conversion](), [data](), [debugging](), [events](), [exhibition](), [exhibitions](), [gallery](), [geospatial](), [geospatial-data](), [gravity](), [json](), [mongo](), [mongodb](), [partner](), [point](), [queries](), [query](), [radius](), [rails](), [shows]() ### AI overview A Los Angeles gallery in Santa Monica was missing from listings despite appearing to be within the API's default 25 km radius. The investigation reproduced the MongoDB query, widened it to 50 km, and mapped results in Placemark against a geodesic 25 km circle. Spot checks suggested that points near the circle's top and bottom were evaluated correctly, while points near its left and right edges could be wrongly omitted. The excerpt explains that the query converts kilometers to degrees using approximately 111.32 km per degree, a conversion described as accurate enough at the equator. It ends before identifying the cause or showing a fix. ### Source excerpt We recently got a report from one of our galleries in the Los Angeles area that they weren't showing up on our Los Angeles exhibition listings. I fielded the report and right away confirmed: when we asked our core API for /shows?near=, sure enough this gallery partner didn't make the cut. Turns out they are based in Santa Monica, a separate and neighboring municipality. They must not be within the 25km radius that we use by default for these sorts of queries. Case closed. Or so I thought. After some back and forth with our partner I decided to investigate more thoroughly, this time using some tricks of the trade from my other life outside of Artsy. Casting a wider net If there was something wrong with our 25km radius query, I wanted to start by casting a wider net and visualizing the results. I consulted our Rails application code to find the query logic in question, and then issued the same query directly to MongoDB. Something like the following query (simplified for clarity): // a $geoWithin $center query db.events.find({ coordinates: { $geoWithin: { $center: [[-118.24, 34.05], 25 / 111.32], }, }, }) In the query above we are asking MongoDB to give us all events within a 25km radius around the point 34.05°N, 118.24°W which we have designated as a central point within Los Angeles. For our purposes in this post we can consider "events" ~= "exhibitions" ~= "shows." We are not asking for the 25km radius directly, but rather converting it into an equivalent amount of geographic degrees by using a conversion factor of 1° ~= 111.32 kilometers, a factor which is true at enough the equator. I modified the above query to cast a 50km net in order to see if there were some edges cases that needed scrutiny. Taking the resulting JSON response, I fired up Placemark, my favorite new tool for wrangling geospatial data. (Incidentally I recommend reading Tom Macwright's recent reflection on creating Placemark as a bootstrapped indie developer.) All shows within ## Conditional Border Radius In CSS DevFeed: [Conditional Border Radius In CSS]() Original publisher: [Read original article]() Author: Ahmad Shadeed Published: 2021-10-04T00:00:00Z Content type: tutorial Language: en Sources: [Ahmad Shadeed]() Topics: [CSS](), [function](), [Web Development]() Tags: [border](), [border-radius](), [conditional](), [css](), [functions](), [how-to](), [radius]() ### AI overview A tutorial explains how CSS comparison functions can conditionally remove a card's border radius when the card spans the full viewport width. It describes the underlying logic and how the technique is implemented in CSS. ### Source excerpt How to use CSS comparison functions to create a conditional border radius ## Custom Shape with Jetpack Compose DevFeed: [Custom Shape with Jetpack Compose]() Original publisher: [Read original article]() Author: Julien Salvi Published: 2021-04-26T14:33:26Z Content type: tutorial Language: en Sources: [Julien Salvi]() Topics: [Jetpack Compose](), [User interface design]() Tags: [android](), [android-development](), [androiddev](), [animations](), [api](), [background](), [border](), [canvas](), [chaining](), [clip](), [code](), [color](), [compose](), [custom](), [drawing](), [foundation](), [functions](), [google-developer-expert](), [image](), [jetpack](), [jetpack-compose](), [library](), [radius](), [size]() ### AI overview Jetpack Compose custom outlines can be built with `GenericShape` and a `Path`, or with a class implementing `Shape` and overriding `createOutline()`. The excerpt demonstrates a cinema ticket path made from arcs and lines, closed with `close()`, then applied through `graphicsLayer{}` and `background()`; `drawBehind{}` can reuse the path to draw a dashed inner border. Modifier order matters: the background follows `graphicsLayer{}`, and the border drawing follows both. For animation, the author describes using changing values to create a wave outline or a polygon with a changing number of sides. Because shapes are expected to be immutable and return the same outline for the same size, the animation value should be passed into a newly constructed `Shape`; state read inside the shape's outline lambda alone will not trigger animation. The excerpt recommends extending `Shape` for dynamic shapes. ### Source excerpt After exploring the Jetpack Compose Canvas in a previous article, this new post will explain how you can draw and use a custom Shape for your Composables to give them a specific outline. The Jetpack Compose foundation library already provides common shapes but we'll see how to take advantage of the Path API to build custom outlines. We will go even further by adding some animations to our brand new shapes. Introduction to Shape With Jetpack Compose, it is easy to add some rounded or cut corners to your Composable thanks to the foundation library which provides several shapes: RoundedCornerShape(): to have a rounded corner outline with a given radius CutCornerShape(): to have a cut corner outline with a given size GenericShape(): to build custom outlines with a given Path For example, a CutCornerShape with a corner size of 32dp applied to a Text Composable looks like the following image: CutCornerShape Shapes can be applied to your Composable thanks to by using several Modifier functions. Let's have a look at them: background(color, shape): it will define the new outline of the Composable with a given Color or Brush. graphicsLayer{}: set the shape attribute to define the new outline. Do not forget to set clip to true if you want that the shadow elevation matches the outline. border(width, color, shape): for drawing a border around the composable with a given shape, width and color. drawBehind{}: accessing the DrawScope and the Canvas to draw the outline of the composable. We can combine multiple Modifier methods to get the shape you can see above. The order matters when chaining the Modifier functions! For example, be sure to always call background() after graphicsLayer{} to ensure that your Composable will be correctly painted with the right color. Here is the code snippet of the Composable. https://medium.com/media/0d9ccf4b24727e20c1e32cd80016b24d/href Now that we've had a glimpse at the capabilities of shapes and how to use them, let's see how we can build our own ## Introduction to Classes and Objects DevFeed: [Introduction to Classes and Objects]() Original publisher: [Read original article]() Author: author@typealias.com (Dave Leeds) Published: 2020-06-29T00:00:00Z Content type: article Language: en Sources: [Dave Leeds on Kotlin - typealias.com]() Topics: [Object-oriented programming (OOP)](), [class]() Tags: [area](), [circle](), [class](), [classes](), [constructor](), [function](), [functions](), [introduction](), [kotlin](), [learn-to-program](), [object](), [programming](), [property](), [radius](), [type](), [types](), [variable](), [variables](), [visibility-modifier]() ### AI overview The excerpt introduces Kotlin classes as a way to define new types by grouping related variables and functions. Using a circle as the example, it explains that keeping radius, circumference, and calculation functions separate becomes harder to manage as more properties, operations, and shapes are added. It begins building a Circle class step by step, starting with an empty class; the excerpt does not provide the later implementation details. ### Source excerpt In Chapter 1, we learned about a variety of types in Kotlin, such as Double, String, and Boolean. Get ready, because in this chapter, we're going to start creating our very own types! We'll put variables and functions together into a class. Let's get started! Putting Variables and Functions Together As you might recall, we started off this book by creating variables to hold things pertaining to a circle, such as its radius and circumference. ## Target FlashBuilds DevFeed: [Target FlashBuilds]() Original publisher: [Read original article]() Author: Target Brands, Inc Published: 2014-11-10T06:00:00Z Content type: article Language: en Sources: [Target]() Topics: [DevOps](), [Self-organizing Team](), [engineering-leadership]() Tags: [agile](), [challenge](), [delivery](), [devops](), [flashbuilds](), [fun](), [innovation](), [it](), [journey](), [organization](), [people](), [philosophies](), [principles](), [problems](), [process](), [questions](), [radius](), [scrum](), [service](), [stuff](), [target]() ### AI overview Target describes FlashBuilds as one-day sessions with two agile sprints, the needed participants, and a facilitator, aimed at tackling difficult business challenges while improving communication and relationships across teams. The approach is intended to reduce organizational and process barriers and give teams more control over how work gets done. Target says sessions can produce new products and faster problem solving, but not every session yields a finished, viable product; even unsuccessful sessions provide learnings and greater appreciation for partner teams. This overview is based on the supplied excerpt. ### Source excerpt At a couple of recent conferences around DevOps (MSP DevOps Days and DevOps Enterprise Summit), Heather Mickman and Ross Clanton from Target explained some high level concepts and actions we're taking to break our mold of working on complex problems. When presented with an opportunity to work differently and challenge our normal delivery of IT assets - from plan to decommission - what would that look like? First, we asked some questions: What can we do to address the barriers within our organization; can we remove that impact on our ability to get things done? What can we do to remove time spent moving from meeting to meeting, often recapping the same discussions that you had in your last meeting 2 weeks ago? What process barriers exist that can be included in the delivery and built as part of the 'service'? And then we asked ... What if we could alleviate all of these problems (and more) all at the same time, all while you build team morale and actually have fun (gasp!) building stuff? What if? Two simple words that can: spark amazing conversations; generate innovation and excitement; challenge the status quo; break through to show how DevOps philosophies break through - even with the big horses. A ton of this post is simply about getting stuff done (GSD) but also to get into some specifics around how we approached fixing a business problem in some new ways - at least for us. So let's embark on some early details around Target's journey to challenge the traditional approaches to get stuff done and take control of the 'how' ... to redefine our working philosophies, principles, and minimize the impact radius of our efforts while still going deep with the teams and persons engaged. Any endeavor such as this has to have a name ... We affectionately call this process FlashBuilds! What is a FlashBuild?! Glad you asked! FlashBuild: A one-day session that includes 2 agile sprints, all the smart people that you need to build stuff, a facilitator, and a whole lot of positive focus ## Beveled corners & negative border-radius with CSS3 gradients DevFeed: [Beveled corners & negative border-radius with CSS3 gradients]() Original publisher: [Read original article]() Author: Lea Verou Published: 2011-03-14T00:00:00Z Content type: tutorial Language: en Sources: [Lea Verou's blog]() Topics: [CSS](), [HTML](), [color](), [Image]() Tags: [blog](), [border](), [border-radius](), [css](), [css-gradients](), [css-images](), [css3](), [original](), [radius](), [tips]() ### AI overview The text describes using CSS gradients to create beveled corners and simulate a negative border-radius without images. It says the technique falls back to a solid-color background where gradients are unsupported and lists support for Firefox 3.6+, Chrome, Safari, Opera 11.10+, and IE10+. The actual code or gradient construction is not included in the supplied excerpt. ### Source excerpt Just found out how to do beveled corners and simulate negative border radius without images, by utilizing CSS gradients once again. It's amazing how many CSS problems can be solved with gradients alone. Read the text in the dabblet below to find out how (or just check the code): It also falls back to a solid color background if CSS gradients are not supported. It will work on Firefox 3.6+, Chrome, Safari, Opera 11.10+ and IE10+. PS: For my twitter friends, I had already written this when the robbers came and I was about to post it. I might have been really calm, but not as much as making CSS experiments the same day I was robbed and threatened by a gun :P