Rotational Repulsion Mechanism

Multi-Unmanned Aerial Vehicle (UAV) disaster-response systems require coordinated task assignment and local trajectory control, yet the individual and combined contributions of these coordination layers to mission efficiency and operational safety remain insufficiently characterised under controlled experimental conditions. TriSAR is evaluated as a five-UAV coordination system operating in a physics-based Gazebo simulation of an earthquake-damaged urban environment. A 2 x 2 factorial design compares two task-allocation strategies (Genetic Algorithm and greedy fitness-based allocation) with reactive collision avoidance enabled or disabled. Each of the four configurations was evaluated over 30 stochastic episodes in a common scenario of five UAVs and eight targets. Under greedy allocation, enabling repulsion eliminated recorded collision-threshold violations, confirmed by a Mann-Whitney test (U = 885, p = 4.03 x 10^-12, rank-biserial r = 0.97). Under GA allocation, the same protective effect was confirmed (U = 675, p = 1.26 x 10^-5, rank-biserial r = 0.50). For mission-efficiency metrics, GA-based allocation showed no statistically detectable advantage over greedy allocation when repulsion was enabled, but a significant advantage in steps, path length, and energy when repulsion was disabled (Welch's t-tests, |g| between 0.92 and 1.76). These results show that reactive repulsion provides a substantial, allocation-dependent safety benefit, while the additional computational complexity of GA-based task allocation yields a detectable mission-efficiency benefit only when repulsion is disabled.

Vision-Language Models (VLMs) are highly effective in retrieving semantically relevant images. However, in practice, relevance alone is often insufficient. Systems must also achieve Result Diversification (RD) across composite attributes such as geography and time, a task for which precise control remains challenging. Current re-ranking methods, such as Multi-Source Determinantal Point Processes (MS-DPP), address this using manifold-based repulsion over similarity representations. Although this strategy is effective for broad exploration, it exposes a key limitation in manifold-based models: when subjected to diversity-decrease tasks on discrete metadata, they suffer substantial degradation in early-rank recall. To bridge this gap, we introduce MASCOT (Model-Aware Submodular Coverage for Composite-Attribute Text-to-Image Retrieval). Instead of relying on manifold repulsion, MASCOT formulates multi-attribute diversity as a resource allocation problem, projecting attributes into a soft-binning space weighted by query-driven importance. Averaged across the three PixelProse diversity-decrease tasks, MASCOT preserves an early-rank recall (R@10) of 88.58%, while MS-DPP retains 67.63%. The margin widens under composite constraints: on PP_geo_hour, where temporal and geographic diversity must be suppressed simultaneously, MS-DPP's recall collapses from 0.9737 to 0.4931 and its top-ranked result degrades to R@1 = 0.23, while MASCOT holds R@10 = 0.9410 and R@1 = 0.7202 at a diversity metric above the unconstrained baseline. We do not claim uniform superiority: on aggregate diversity-relevance scores our own simpler ablations attain higher harmonic means on all three decrease tasks, and MASCOT's advantage is specific to recall beyond rank 1 under composite constraints.

We introduce the distributional determinantal point process (dDPP) as a novel repulsive point process whose atoms are probability distributions rather than points in a real space. The dDPP is constructed via an L-ensemble with a sliced Wasserstein (SW) kernel between distributions. We show its validity as a well-defined point process. In the discrete setting, we derive concentration results for plug-in estimators of the L-ensemble, the correlation kernel, and their determinants given i.i.d. samples from the distributional atoms. Leveraging this framework, we propose a distribution-valued random partition model by way of a repulsive generalized Bayesian mixture model. The model places a dDPP prior over the atoms of the mixing measure and defines a generalized likelihood based on SW distance. To summarize posterior inference, we develop a decision-theoretic approach to report a point estimate of the mixing measure as a Bayes rule under a hierarchical optimal transport utility function. The latter is a natural choice given that the mixing measure is itself a distribution over distributions. We use the proposed framework for inference with single-cell gene expression data and human epilepsy data, producing interpretable and well-separated clusters that reflect meaningful structure in the data.

Massive robot swarms can explore unknown environments quickly, but adding robots eventually stops helping. Doorways and dense traffic create congestion, increasing inter-robot contacts and reducing the value of each additional robot. We study this safety-efficiency tradeoff for ground swarms of tens to hundreds of robots. We present SPACE, Swarm Pheromone Fields for Adaptive Collision-Aware Exploration. Inspired by ant foraging, SPACE maintains a shared environmental field with an attractive frontier pheromone, a repellent explore pheromone, and a fast robot-density field. Coordination is decentralized and mediated through this field. We evaluate SPACE on real building floorplans, namely sixteen home layouts from the HouseExpo dataset and eight campus floors from the KTH dataset, with swarms of up to two hundred and fifty-six robots. SPACE lies on the empirical Pareto frontier. It attains the lowest inter-robot contact rate at every congested swarm size, four to seventeen times fewer than a greedy nearest-frontier planner, while keeping coverage time within about two percent of that near time-optimal planner. The results indicate that, at this scale, coordination mainly improves safety rather than coverage time.

Diffusion models are typically sampled independently, even when the downstream objective is to obtain a diverse set of candidates. We introduce a variance-weighted batch distribution that favours collections of samples with large empirical spread after a prescribed linear feature map. The target is specified explicitly, and the sampler is derived as the corresponding Doob $h$-transform of independent diffusion dynamics. The resulting correction has a compact form: an interaction term that repels posterior denoised means, together with a curvature term that moves particles to the region of higher feature variance. This yields an interacting-particle sampler with a transparent probabilistic target rather than a heuristic repulsive drift.

Variable-order Markov models preserve local symbolic syntax by adapting context length, but long continuations can enter recurring high-order "tunnels": repeated suffixes, locally periodic passages, or copied fragments longer than the formal Markov order. This paper introduces signed pattern control for variable-order Markov generation with BP-Regular sampling. A weighted recurrence automaton computes an activation R for a chosen family of target patterns, and belief propagation samples exactly from P_beta(x) proportional to P_0(x) exp(beta R(x)). Negative coupling makes the target patterns costly during sampling; positive coupling rewards the same patterns and turns them into controlled attractors. The target family may be mined online from overactive generated material, supplied by a score or style vocabulary, or designed as an experimental probe. The main experiments use the online homeostatic case, choosing patterns that become overactive in the sampling history. On six duration-bearing monophonic sources, including Bach and Telemann material, the negative branch reduces generated 8-gram self-reuse, increases the effective number of generated 8-grams, and increases coverage of training-supported 4-gram contexts while preserving substantial lower-order support. A pitch-sequence replication on five Weimar Jazz Database solos gives the same anti-reuse signature outside Baroque material. The same signed mechanism also provides a positive branch for probing attractor basins, phase transitions, and hysteresis in the underlying variable-order model.

People are increasingly using AI for creative tasks such as writing. While adoption continues to grow, this form of use risks undermining individual creativity locally and reducing the heterogeneity of creative output at scale. In response, we introduce the Semantic Repulsion Technique (SRT) and evaluate it both computationally and through a study with 16 participants who regularly use AI for creative tasks. Our computational assessment reveals that SRT increases semantic diversity by 85--167% while reducing consensus phrases by 43--95% across task modes. In the user study, SRT outputs received higher usefulness ($p = .019$, $W = .208$) and coherence ratings ( $p = .006$, $W = .260$); 68.8% of participants were willing to use SRT-Strong for multiple tasks versus 18.8% for baselines. Originality and coherence ratings were positively correlated across all systems ($ρ= +.40$ to $+.67$), suggesting that divergence need not compromise readability. Taken together, these preliminary findings can inform the design of AI systems that aim to support everyday creativity without contributing to homogenization.

Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space. An increasingly popular algorithm is Uniform Manifold Learning and Projection (UMAP), which uses algebraic topology to map distances between the two spaces. While it works well on many types of data sets, UMAP has trouble adding out-of-sample points to a pre-existing mapping. In particular, UMAP often places new points on the periphery of the found clusters, rather than in their interiors with their correlated neighbors. Here, we overcome this ``repulsion effect'' by optimizing pairwise interactions within the original k-nearest-neighbor graph. Moreover, we show that parameterizing UMAP obtains better embeddings than non-parametric algorithms, particularly as the data gets more complex (e.g., medical images). We also show that the repulsion effect is naturally mitigated when a parameterized UMAP is employed to embed the data. We characterize different UMAP approaches using trustworthiness, nearest neighbor classifiers, and by analyzing attractive and repulsive forces in the embeddings.

In this paper, we present empirical and theoretical evidence against a central but largely implicit assumption in circuit and sheaf discovery (CSD), which we term the Functional Anisotropy Hypothesis: the idea that functions in large language models (LLMs) are localised to a unique or near-unique internal mechanism. We show that a single LLM task can instead be supported by multiple, structurally distinct circuits or sheaves that are simultaneously faithful, sparse, and complete. To systematically uncover such competing mechanisms, we introduce Overlap-Aware Sheaf Repulsion, a method that augments the CSD objective with an explicit penalty on structural overlap across multiple discovery runs, enabling the discovery of circuits or sheaves with strong task performance but minimal shared structure across a plethora of common CSD benchmarks. We find that this phenomenon becomes increasingly pronounced as the number of discovered sheaves grows and persists robustly across major CSD methods. We further identify an ultra-sparse three-edge sheaf and show that none of its edges is individually indispensable, undermining even weakened notions of canonical or essential components. To explain these findings, we propose a Distributive Dense Circuit Hypothesis and provide a theoretical analysis demonstrating that non-unique, low-overlap circuit explanations arise naturally from high-dimensional superposition under mild assumptions. Together, our results suggest that mechanistic explanations in LLMs are inherently non-canonical and call for a rethinking of how CSD results should be interpreted and evaluated.

Diffusion models generate realistic visual content, yet often fail to produce rare but plausible compositions. When prompted with combinations that are valid but underrepresented in training data, such as a snowy beach or a rainbow at night, the generation process frequently collapses toward more common alternatives. We identify this failure mode as default completion bias, where denoising trajectories are implicitly attracted toward high-frequency semantic configurations. Existing guidance mechanisms do not explicitly model this competing tendency and therefore struggle to prevent such collapse. We introduce Default Completion Repulsion (DCR), a training-free framework that explicitly models and suppresses default completion behavior. DCR constructs a counterfactual attractor by relaxing the rare compositional factor while preserving surrounding semantics, inducing an alternative denoising trajectory reflecting the model's preferred completion. We define the discrepancy between target and attractor trajectories as a counterfactual drift, and propose a projection-based repulsion mechanism that removes guidance components aligned with this drift direction. This suppresses undesired frequent completions while preserving other semantic components. DCR operates entirely within the standard diffusion sampling process without retraining or architectural modification. Experiments on rare compositional prompts show that DCR improves compositional fidelity while maintaining visual quality. Our analysis further shows that the framework exposes and counteracts intrinsic model biases, offering a new perspective on controllable generation beyond explicit constraint enforcement.

Tian (2025) proves a repulsion theorem (Theorem 6) for the matrix $B = (\widetilde{F}^\top \widetilde{F} + ηI)^{-1}$ during the interactive feature-learning stage of grokking: similar features have negative off-diagonal entries $B_{j\ell}$, producing an effective repulsive force that drives them apart. However, the theorem does not specify when this mechanism becomes empirically observable, nor whether it leaves a measurable spectral signature in the parameter updates. We test this directly on Tian's modular addition setup ($M = 71$, $K = 2048$, MSE loss) and observe a clear structure-mechanism dissociation. The predicted sign rule holds robustly on the top-200 most-similar feature pairs across activations (empirical sign-match rising from 0.865 to 0.985 on $σ= x^2$ across 5 seeds, and saturating at 1.000 on $σ= \operatorname{ReLU}$). However, the spectral signature in the parameter updates is strongly activation-dependent. With $σ= x^2$, a simple slope detector on the rolling eigengap $σ_2 / σ_3$ of $ΔW$ fires in 15/15 grokking seeds at epoch 174 (IQR [173,174]) and in 0/15 non-grokking controls, with 229$\times$ late-stage magnitude separation; the spectrum is rank-2. In contrast, with $σ= \operatorname{ReLU}$, the detector never fires and the spectrum remains effectively rank-1. This dissociation aligns with Tian's Theorem 5 distinction between focused (power-law) and spreading (ReLU) memorization: while the sign structure of $B$ depends only on $\widetilde{F}^\top \widetilde{F}$, how feature repulsion translates into weight updates critically depends on the activation derivative $σ'$.

A levelset free but a hybrid image segmentation approach based on a modified version of the piece wise constant shape gradient of an Mumford Shah shape functional and a repulsive function is considered. The segmentation is performed a non-local shape based through an evolution of discrete curves driven by a non local shape based energy to segment images containing disjoint regions and multiple boundaries. This formulation has a novel additional component as a multivariable function dependent on a few sampled points of the curves that handles the occurrence of self intersection during boundary curves evolution. The method is applied to a few gray scale and color images, including images with nested structures and astronomical objects. The results indicate effective segmentation in complex scenarios with absolute control on the topology of the segments and self-intersections of the boundaries

The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fdω$ relies on independent samples from $ω$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to $f$ and $ω$. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of $\mathcal{O}(N^{-(1+1/d)})$ for smooth $f$, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order $1/N$, like Monte Carlo, but its DPP is tailored to $f$. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.

This paper presents a decentralized, collision-free framework for path following guidance of multiple uncrewed aerial vehicles (UAVs), while maintaining uniform spacing along a reference path. A vector field-based guidance law is employed to drive each UAV toward the reference path. A rotational repulsion mechanism, utilizing relative distance and bearing between UAVs, is proposed to avoid collisions during convergence to the path, and an inter-UAV spacing error-based velocity control law is presented to achieve uniform separation along the path. Analytical guarantees are established for collision avoidance and convergence of the inter-UAV spacing errors to zero, ensuring uniform separation along the path. Numerical simulations demonstrate the efficacy of the proposed method.

Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconstruction of turbulent flow fields from sparse data. However, most existing PINN formulations are deterministic and do not provide reliable quantification of epistemic uncertainty, which is critical for ill-posed problems such as data-driven Reynolds-averaged Navier-Stokes (RANS) modeling. In this work, we develop and systematically evaluate a set of probabilistic extensions of PINNs for uncertainty quantification in turbulence modeling. The proposed framework combines (i) Bayesian PINNs with Hamiltonian Monte Carlo sampling and a tempered multi-component likelihood, (ii) Monte Carlo dropout, and (iii) repulsive deep ensembles that enforce diversity in function space. Particular emphasis is placed on the role of ensemble diversity and likelihood tempering in improving uncertainty calibration for PDE-constrained inverse problems. The methods are assessed on a hierarchy of test cases, including the Van der Pol oscillator and turbulent flow past a circular cylinder at Reynolds numbers Re=3,900 (direct numerical simulation data) and Re = 10,000 (experimental particle image velocimetry data). The results demonstrate that Bayesian PINNs provide the most consistent uncertainty estimates across all inferred quantities, while function-space repulsive ensembles offer a computationally efficient approximation with competitive accuracy for primary flow variables. These findings provide quantitative insight into the trade-offs between accuracy, computational cost, and uncertainty calibration in physics-informed learning, and offer practical guidance for uncertainty quantification in data-driven turbulence modeling.

Combinatorial black-box optimization in high-dimensional settings demands a careful trade-off between exploiting promising regions of the search space and preserving sufficient exploration to identify multiple optima. Although Estimation-of-Distribution Algorithms (EDAs) provide a powerful model-based framework, they often concentrate on a single region of interest, which may result in premature convergence when facing complex or multimodal objective landscapes. In this work, we incorporate the Stein operator to introduce a repulsive mechanism among particles in the parameter space, thereby encouraging the population to disperse and jointly explore several modes of the fitness landscape. Empirical evaluations across diverse benchmark problems show that the proposed method achieves performance competitive with, and in several cases superior to, leading state-of-the-art approaches, particularly on large-scale instances. These findings highlight the potential of Stein variational gradient descent as a promising direction for addressing large, computationally expensive, discrete black-box optimization problems.

A central problem in self-supervised learning is preventing representation collapse. Most methods avoid it through global mechanisms, such as contrastive expansion, variance constraints, decorrelating dimensions, or enforcing certain output distributions. In this work, we study a different design: short-range repulsion. We introduce Hypersolid, a self-supervised objective that combines view alignment with local collision avoidance. Our method induces a latent geometry of compact, semantically aligned neighborhoods with low anisotropy. This geometry is especially effective for unsupervised clustering and fine-grained separation, although it comes at the cost of weaker transferability.