In clustering, strong dominance in the size of a particular cluster is often undesirable, motivating a measure of cluster size uniformity that can be used to filter such partitions. A basic requirement of such a measure is stability: partitions that differ only slightly in their point assignments should receive similar uniformity scores. A difficulty arises because cluster labels are not fixed objects; algorithms may produce different numbers of labels even when the underlying point distribution changes very little. Measures defined directly over labels can therefore become unstable under label-count perturbations. I introduce the Mass Agreement Score (MAS), a point-centric metric bounded in [0, 1] that evaluates the consistency of expected cluster size as measured from the perspective of points in each cluster. Its construction yields fragment robustness by design, assigning similar scores to partitions with similar bulk structure while remaining sensitive to genuine redistribution of cluster mass.

However, one might argue that this analysis might not allow for sufficient differentiation between tasks. To address this concern, we expanded our evaluation to the entire MMLU benchmark. This enabled a comparable assessment of task similarity, akin to our earlier experiments.

Definition 1.Let p (r) := P s,ap (r|s, a), p (rc|s, a) := P

Learning to accurately represent environmental uncertainty is crucial for adaptive and optimal behaviors in various cognitive tasks. However, it remains unclear how the human brain, constrained by finite cognitive resources, internalise the highly structured environmental uncertainty. In this study, we explore how these learned distributions deviate from the ground truth, resulting in observable inconsistency in a novel structured density estimation task. During each trial, human participants were asked to learn and report the latent probability distribution functions underlying sequentially presented independent observations. As the number of observations increased, the reported predictive density became closer to the ground truth. Nevertheless, we observed an intriguing inconsistency in human structure estimation, specifically a large error in the number of reported clusters.

However, DeepPurpose inherits several limitations from early MRL models.

Recent advances in center-based clustering continue to improve upon the drawbacksofLloyd'scelebrated k-meansalgorithmover 60yearsafteritsintroduction.

Analysis of learned representations has a blind spot: it focuses on $similarity$, measuring how closely embeddings align with external references, but similarity reveals only what is represented, not whether that structure is robust. We introduce $geometric$ $stability$, a distinct dimension that quantifies how reliably representational geometry holds under perturbation, and present $Shesha$, a framework for measuring it. Across 2,463 configurations in seven domains, we show that stability and similarity are empirically uncorrelated ($ρ\approx 0.01$) and mechanistically distinct: similarity metrics collapse after removing the top principal components, while stability retains sensitivity to fine-grained manifold structure. This distinction yields actionable insights: for safety monitoring, stability acts as a functional geometric canary, detecting structural drift nearly 2$\times$ more sensitively than CKA while filtering out the non-functional noise that triggers false alarms in rigid distance metrics; for controllability, supervised stability predicts linear steerability ($ρ= 0.89$-$0.96$); for model selection, stability dissociates from transferability, revealing a geometric tax that transfer optimization incurs. Beyond machine learning, stability predicts CRISPR perturbation coherence and neural-behavioral coupling. By quantifying $how$ $reliably$ systems maintain structure, geometric stability provides a necessary complement to similarity for auditing representations across biological and computational systems.

Narratives about artificial intelligence (AI) entangle autonomy, the capacity to self-govern, with sentience, the capacity to sense and feel. AI agents that perform tasks autonomously and companions that recognize and express emotions may activate mental models of autonomy and sentience, respectively, provoking distinct reactions. To examine this possibility, we conducted three pilot studies (N = 374) and four preregistered vignette experiments describing an AI as autonomous, sentient, both, or neither (N = 2,702). Activating a mental model of sentience increased general mind perception (cognition and emotion) and moral consideration more than autonomy, but autonomy increased perceived threat more than sentience. Sentience also increased perceived autonomy more than vice versa. Based on a within-paper meta-analysis, sentience changed reactions more than autonomy on average. By disentangling different mental models of AI, we can study human-AI interaction with more precision to better navigate the detailed design of anthropomorphized AI and prompting interfaces.