Dispersion

We study connectivity-preserving finite-jump dispersion of anonymous, identical, and oblivious agents under an idealized range-only sensing model. Each agent measures only the distances to its visible neighbors, without bearings, identifiers, communication, memory, or a shared coordinate system. We derive the largest isotropic displacement certifiable as safe from these measurements alone. The resulting rule requires only the distance to the farthest visible neighbor: each agent selects a random direction and moves by half of its remaining visibility margin. The rule preserves every existing visibility edge under synchronous finite motion and therefore preserves connectivity. For two agents, we prove positive conditional drift in squared distance, almost-sure convergence to the visibility boundary, and finite expected time to reach any fixed neighborhood of that boundary. A one-million-run Monte Carlo experiment agrees with the exact first-round moments and estimates approximately 9.5 rounds to reach distance 0.97V from coincident initial positions; an independent Bellman-equation computation gives the same estimate. For general swarms, 1,000 runs across five initial-topology classes reproduce the deterministic safety guarantee at implementation level and reveal a consistent topology-dependent ordering of attainable diameter under the tested protocol. These results provide a theoretical foundation for connectivity-preserving multi-robot dispersion under minimal sensing, while isolating the guarantees achievable from anonymous range measurements alone.

The sound speed profile in the deep Arctic Ocean causes the surface layer to form a normal mode waveguide. When the depth of the sound source or receiver is near a node of the eigenfunction, the source cannot excite the mode, or the receiver cannot detect it, resulting in the modal amplitude at the receiver being approximately zero. This manifests as a dispersion interruption in the dispersion structure, which can be observed through time-frequency analysis of the received acoustic signal. Based on the interruption frequency identified from the received signal, combined with the relationship between node depth and modal frequency calculated from the ocean sound speed profile, the source depth can be estimated if the receiver depth is known. The phenomenon of dispersion interruption and the method of estimating source depth have been validated through simulations and experiments.

Personality-conditioned LLM agents (PC-Agents) are increasingly used in emotional support, social simulation, and role-playing, motivating the development of lifelong agents that remain coherent over extended interactions. A key component of such coherence is personality evolution: agents should undergo plausible, psychology-grounded changes as they experience life events in different contexts. Although prior work shows that LLM personalities can shift under contextual perturbations, how these shifts vary across traits, events, personas, and models remains poorly understood. We study event-induced personality change after 11 major life events, using the Big Five traits as a psychometric anchor and interpreting the resulting trajectories against longitudinal evidence from human personality psychology. Across four diagnostic axes, PC-Agents exhibit measurable trait shifts at similar rates for event-trait pairs with and without documented human change directions. Even when shifts follow the expected direction, their magnitudes usually fall below human effect-size ranges. Gender and cultural-region prompts show little moderating effect, while persona-level dispersion is compressed three- to four-fold relative to human samples. To enable systematic comparison, we introduce BFI-Adapt, a reusable benchmark for scoring the directional fidelity of event-induced personality change, and use it to rank 14 models. A validation suite shows that the measured shifts exceed no-event retest noise, remain stable under independently paraphrased prompts, exhibit limited and model-dependent convergence with scenario-based behavioral choices, and persist across intervening unrelated dialogue. Together, these checks establish the measured trajectories as robust event-conditioned response patterns. Our results suggest that current PC-Agents simulate the mean of human personality dynamics, but not its shape.

Collective intelligence research treats disagreement as evidence of epistemic diversity: if agents express different views, the group should retain capacity to revise. In LLM collectives this proxy can break: agents can produce diverse-looking arguments while preserving the same conclusion. We operationalize dispersion-revision coupling: the degree to which an intervention that verifiably increases the dispersion of a collective's outputs in embedding space is accompanied by genuine revision of its epistemic stance rather than premise-preserving reformulation. The diagnostic is black-box: it operates on generated text alone and makes no claims about the internal representations of the generating models. Two channels are measured independently: an output channel, the Coherence Index (CI), verifies that the intervention changed output dispersion; an epistemic channel, per-turn stance annotation, measures whether the collective revised. We propose CI with the Meta-Predictive Clarity System (MPCS), which inserts a Re-Differentiation Protocol (RDP) when outputs over-converge, as a reusable method for estimating this coupling regime. We evaluate five-agent collectives from two configurations (gpt-4o-mini and gemini-2.5-flash; 310 paired episodes per condition). On gpt-4o-mini, conditional dissent improves false-premise recovery by +17.7 points (p<1e-6) while static persona diversity harms recovery (-8.1, p=.007). On gemini-2.5-flash, the same intervention at a comparable budget yields no gain (26.1% vs 27.1%, p=.84) despite a verified dispersion drop; the two treatment effects differ from each other (z=3.79, p<.001). Mechanism tagging shows Gemini preserves the false premise via intra-framework dissent: 94% of tagged post-RDP responses reformulate rather than concede (vs 24% on GPT). We recommend reporting per-intervention stance shift and premise-preservation rate alongside accuracy.

Sixteen language models drawn from ten families produced, on average, the semantic diversity of 1.69 distinct formulations of a psychotherapeutic case, against a single-model baseline of 1.43 from one model's own runs. Ensembles place more than one reading before a decision-maker on the premise that several models supply several perspectives. Dispersion over their outputs is measured both as diversity and as uncertainty, and both traditions validate it against a correctness criterion that this task does not admit. Measuring diversity is a solved problem: the Vendi Score, the exponential of the von Neumann entropy of a similarity matrix, is an effective number of distinct elements. What a single aggregate does not say is where the diversity comes from. We define a per-model dissent contribution, the complement of a model's mean similarity to the other members of its ensemble: a magnitude from the same matrix, not a decomposition of the spectral index, whose maximum identifies the most divergent voice. Crossing model and case, we test as a preregistered hypothesis whether model identity accounts for a non-zero share of the variance in dissent, and characterise the structure that test detects. The panel formulated fifteen stratified vignettes, yielding 7,082 formulations for analysis. Model identity was a detectable structuring factor of the dissent that remained, but the usual categories recovered it only partly: scale differences pointed in opposite directions across pairs, family grouped models on only five two-member lines, and the most divergent voice changed with panel composition, so that the surfaced outlier describes the ensemble rather than the model. Dissent did not track the interpretive openness for which the case bank was stratified; it was organised by clinical content instead, leaving the dispersion an ensemble produces a property to measure rather than assume.

Within-class variance in language-model representations is commonly read as incomplete neural collapse. We argue it is allocated information storage, and that the allocation obeys a law. A one-line centering identity voids a family of simplex equiangular-tight-frame claims, including our own earlier ones; in dimensionless variance shares across 14 models, macro-category structure carries only 4-12% of representational variance and within-token context carries 79-91%, stable across a 100x parameter range. On the theory side, token-level weight decay penalizes a category in proportion to its type count, not its occurrence mass, reducing next-token prediction to an imbalanced K-class problem whose optimum orders category norms by type count. A converse floor, proved for binary categories, forces within-category dispersion to be at least proportional to the conditional mutual information I(token; context | category). The law holds: identity dispersion, not total variance, tracks this information across every tested model and partition, under a model-free estimate and even across models, where one model's information predicts another's dispersion; and over pretraining the category share overshoots, decays, and partially recovers, because the information it must carry never left.

Noisy evolution strategies under fixed evaluation budgets face a depth-fidelity trade-off: spending evaluations to denoise intra-generation rankings reduces the number of distribution updates the optimizer can execute. We argue for depth over fidelity and propose probabilistic elite membership (PEM), which replaces hard rank-based weights in evolution strategies with conditional expected rank weights that integrate over ranking uncertainty. PEM preserves the conditional mean update while reducing conditional update dispersion, a Rao-Blackwellization of the noisy rank-based step. We instantiate PEM via residual bootstrapping (RB-PEM) with capped per-generation overhead, complemented by an adaptive probe-and-switch mechanism for low-noise regimes. Across the COCO bbob-noisy suite and external tasks including RL policy search and hyperparameter optimization, RB-PEM achieves consistent gains in high-misranking, budget-constrained settings.

Standard approaches to forecasting the weekly number of earthquakes on a spatial grid rely on the Poisson distribution with a single global dispersion assumption. We show that this assumption is systematically violated in seismic data from Central Asia (2010-2024), where a likelihood-ratio test with boundary correction strongly rejects the Poisson hypothesis (p < 10^{-179}). The main contribution of this work is the EarthquakeNet architecture, which provides an endogenous per-cell estimate of the overdispersion parameter alpha via a neural network (spatial embeddings + MLP), without explicit spatial covariance specification. In contrast to existing negative binomial regression approaches in seismological forecasting, which typically assume a single global alpha, the proposed per-cell formulation allows the model to identify spatial heterogeneity in seismic clustering and to construct probabilistic risk-aware alerts via quantiles of the predicted distribution. A walk-forward evaluation (2018-2023) over four systems shows an 8.6 percent reduction in mean pinball deviation (MPD) relative to a negative binomial GLM baseline. The strongest improvements are observed in the tail regime (Y >= 5), where the continuous ranked probability score (CRPS) of the proposed model is 12.5 percent lower than that of the baseline, indicating improved calibration in extreme-event forecasting.

We developed a tool for detecting domain shifts, namely subtle differences in the probability distributions of datasets. We identify these shifts using an algorithm designed to detect localised density anomalies in high-dimensional feature spaces. If an anomaly is present, we then identify the feature subspace in which the anomaly is most pronounced. This allows us to trace the domain shift to a small set of features, making the shift interpretable. Moreover, we provide a protocol for compensating domain shifts by extracting, from two unlabelled datasets, subsets of samples with no detectable residual distributional difference. We validate the framework on controlled 20-dimensional benchmarks with known ground truth, recovering both broad and localized shifts together with their supporting feature subspaces. We then apply it to healthy electrocardiogram (ECG) recordings represented by 782 features. In age- and sex-matched cohort comparisons differing in measurement-device composition, the method detects device-induced shifts, extracts representative subsets enriched in the imbalanced device components, and identifies ECG features associated with the acquisition contrast. These results suggest that density-shift detection and subspace attribution provide a practical framework for uncovering hidden cohort biases before downstream modelling.

Accurate medical image segmentation is fundamental to precision medicine, yet robust delineation remains challenging under heterogeneous appearances, ambiguous boundaries, and large anatomical variability. Similar intensity and texture patterns between targets and surrounding tissues often lead to blurred activations and unreliable separation. We attribute these failures to representation collapse during encoding and insufficient fine grained multi scale decoding. To address these issues, we propose Med DisSeg, a dispersion driven medical image segmentation framework that jointly improves representation learning and anatomical delineation. Med DisSeg combines a lightweight Dispersive Loss with adaptive attention for fine grained structure segmentation. The Dispersive Loss enlarges inter sample margins by treating in batch hidden representations as negative pairs, producing well dispersed and boundary aware embeddings with negligible overhead. Based on these enhanced representations, the encoder strengthens structure sensitive responses, while the decoder performs adaptive multi scale calibration to preserve complementary local texture and global shape information. Extensive experiments on five datasets spanning three imaging modalities demonstrate consistent state of the art performance. Moreover, Med DisSeg achieves competitive results on multi organ CT segmentation, supporting its robustness and cross task applicability.

Public procurement is vulnerable to error, fraud, and corruption, particularly as high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payment monitoring remains underexplored. Since labelled datasets are rare and methods like Benford's Law face restrictive assumptions, there is a need for interpretable, unsupervised frameworks for high-volume procurement oversight and decision support. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples, and its payment-specific instantiation, the Payment Heterogeneity Index (PHI), characterising payment structure and latent regimes. It incorporates Gaussian Mixture Model (GMM) parameters alongside non-parametric statistics, integrating four interpretable components: modality, asymmetry, tail behaviour, and structural dispersion. Uniquely, the tail-behaviour component captures both distributional heaviness and extreme-value concentration, while structural-dispersion combines the variability, prevalence, and separation of latent payment regimes. Applied to UK municipal procurement data, PHI identifies a financially significant cohort (0.6% of suppliers; 10.1% of high-volume vendors) with structurally distinct payment patterns. Statistical testing further supports these differences, and targeted human verification confirms the plausibility of prioritised cases. Comparative analysis shows PHI reveals regime separation obscured by the Coefficient of Variation ($ρ= 0.310$). PHI provides a transparent, decomposable, and computationally lightweight framework for procurement integrity oversight and targeted audit prioritisation.

Mode separation, namely how sharply a distribution fragments into barrier-separated clusters, is a fundamental geometric property of densities, difficult to quantify in high dimensions. It is structurally distinct from dispersion, yet existing tools fall short: differential entropy rises with spread regardless of fragmentation, PCA orders directions by variance regardless of barriers, and mutual information requires a mixture decomposition one usually does not have. We measure mode separation through a single stochastic process intrinsic to the density: a unique reversible diffusion with $f$ as its stationary distribution and constant scalar diffusion coefficient. We extract two readouts from its autocovariance matrix: SSA (Sum of Squared Autocorrelations), a scalar barrier-sensitive measure; and DA (Dominant Autocorrelation directions), linear projections ordered by metastability rather than variance. Under an isotropic-Gaussian null, we derive a closed-form spectrum for the empirical autocovariance that generalizes Marchenko--Pastur, with an analytic upper edge that selects the lag at which DA is read off. Both readouts use only samples and a score function, scaling to high dimensions through pretrained score-based generative models via Tweedie's identity. We apply our framework to three settings: (i) synthetic Gaussian mixtures, where SSA tracks mutual information; (ii) SDXL text-to-image generations, where SSA and DA capture structure that entropy and PCA miss; and (iii) molecular dynamics of alanine dipeptide, where DA recovers the known slow backbone dihedrals from static samples alone.

Measuring the breadth of a word's meaning, or its spread across contexts, has become feasible with contextualized token embeddings. A word type can be represented as a cloud of token vectors, with dispersion-based statistics serving as proxies for contextual diversity (Nagata and Tanaka-Ishii, ACL2025). These measurements are useful for deciding appropriate sense distinctions when constructing thesauri and domain-specific dictionaries. However, when comparing the breadth of two word types, naive hypothesis testing on dispersion can be misleading: differences in semantic direction can masquerade as dispersion differences, inflating Type-I error and yielding "statistically significant" outcomes even when there is no true breadth difference. This is problematic because significance testing should distinguish genuine effects from incidental fluctuations in small-difference regimes. We propose a Householder-aligned permutation test to isolate dispersion differences from directional differences. Our method applies a single Householder reflection to align the mean directions of the two word types and then performs a permutation test on the aligned token clouds, yielding calibrated, non-parametric p-values. For practicality, we introduce a GPU-oriented implementation that batches permutations and linear algebra operations. Empirically, our alignment reduced Type-I error by 32.5% while preserving sensitivity to genuine breadth differences, and achieved a 23x speedup over the CPU baseline.

Empirical causal claims depend on many analyst decisions, from selecting covariates to choosing estimators. Existing robustness tools summarize how results vary across these choices, but, to the best of our knowledge, do not answer: \textbf{How many analyst decisions must change to reach a specification, which is a set of choices, whose confidence interval (CI) contains zero?} We introduce \emph{Minimum Specification Perturbation (MSP)}, the smallest number of changes. MSP is small under the null, grows with effect strength and captures distance-to-falsification information that dispersion-based summaries cannot report; when making decisions under weak effects, an MSP-based rule yields lower false-positive rates than dispersion-based rules. We show that Fragility Index and MSP measure orthogonal vulnerabilities: fragility to influential observations need not imply fragility to specification choices. On the LaLonde benchmark, MSP = 1 implies that one decision change makes the CI contain zero. We further provide exact permutation calibration under randomization and characterize computation, showing tractable cases under additive structure and NP-hardness in general.

We present CRADIPOR, a numerical dispersion prediction tool for automotive crash simulations. Finite Element (FE) crash models are widely used throughout vehicle development, but their predictions are not strictly repeatable because of parallel computation and model complexity. As a result, performance criteria evaluated during post-processing may exhibit significant numerical dispersion, which complicates engineering decision-making. Although dispersion can be estimated by repeating the same simulation, this approach is generally impractical because of its high computational cost. This work therefore investigates a prediction tool that can be applied during routine crash-simulation post-processing without repeating the computation. The proposed approach relies on a Rank Reduction Autoencoder (RRAE) combined with supervised classification in order to identify regions sensitive to numerical dispersion. The comparative analysis suggests that the RRAE-based framework is more effective than the Random Forest baseline on the studied dataset. Among the tested signal representations, wavelet-based and slope-based inputs appear to be the most promising, with slope variations providing the best classification performance. These results support the use of structured latent representations for improving numerical-dispersion detection in automotive crash post-processing.

Neural networks exhibit a remarkable degree of representational convergence across diverse architectures, training objectives, and even data modalities. This convergence is predictive of alignment with brain representation. A recent hypothesis suggests this arises from learning the underlying structure in the environment in similar ways. However, it is unclear how individual stimuli elicit convergent representations across networks. An image can be perceived in multiple ways and expressed differently using words. Here, we introduce a methodology based on the Generalized Procrustes Algorithm to measure intra-modal representational convergence at the single-stimulus level. We applied this to vision models with distinct training objectives, selecting stimuli based on their degree of alignment (intra-modal dispersion). Crucially, we found that this intra-modal dispersion strongly modulates alignment between vision and language models (cross-modal convergence). Specifically, stimuli with low intra-modal dispersion (high agreement among vision models) elicited significantly higher cross-modal alignment than those with high dispersion, by up to a factor of two (e.g., in pairings of DINOv2 with language models). This effect was robust to stimulus selection criteria and generalized across different pairings of vision and language models. Measuring convergence at the single-stimulus level provides a path toward understanding the sources of convergence and divergence across modalities, and between neural networks and human neural representations.

Uncertainty estimation is a promising approach to detect hallucinations in large language models (LLMs). Recent approaches commonly depend on model internal states to estimate uncertainty. However, they suffer from strict assumptions on how hidden states should evolve across layers, and from information loss by solely focusing on last or mean tokens. To address these issues, we present Sequential Internal Variance Representation (SIVR), a supervised hallucination detection framework that leverages token-wise, layer-wise features derived from hidden states. SIVR adopts a more basic assumption that uncertainty manifests in the degree of dispersion or variance of internal representations across layers, rather than relying on specific assumptions, which makes the method model and task agnostic. It additionally aggregates the full sequence of per-token variance features, learning temporal patterns indicative of factual errors and thereby preventing information loss. Experimental results demonstrate SIVR consistently outperforms strong baselines. Most importantly, SIVR enjoys stronger generalisation and avoids relying on large training sets, highlighting the potential for practical deployment. Our code repository is available online at https://github.com/ponhvoan/internal-variance.

Hallucinations in large ASR models present a critical safety risk. In this work, we propose the \textit{Spectral Sensitivity Theorem}, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an attractor regime (rank-1 collapse) governed by layer-wise gain and alignment. We validate this theory by analyzing the eigenspectra of activation graphs in Whisper models (Tiny to Large-v3-Turbo) under adversarial stress. Our results confirm the theoretical prediction: intermediate models exhibit \textit{Structural Disintegration} (Regime I), characterized by a $13.4\%$ collapse in Cross-Attention rank. Conversely, large models enter a \textit{Compression-Seeking Attractor} state (Regime II), where Self-Attention actively compresses rank ($-2.34\%$) and hardens the spectral slope, decoupling the model from acoustic evidence.