Quantifying

Autoraters, also referred to as LLM-as-judges, are increasingly used for evaluation and automated content moderation. However, there is limited statistical analysis of how modifications in a rubric presented to both humans and autoraters affect their score agreement. Rubrics that ask for an overall or \emph{holistic} judgment - for example, rating the quality'' of an essay - may be inconsistently interpreted due to the complexity or subjectivity of the criteria. Conversely, rubrics can ask for \emph{analytic} judgments, which decompose assessment criteria - for example, quality'' into fluency'' and organization''. While these rubrics can be edited to improve the individual accuracy of both human and automated scoring, this approach may result in disagreement between the two scores, or with the associated holistic judgment. Designing and deploying reliable autoraters requires understanding not just the relationship between human and autorater annotations but how that relationship changes as holistic or analytic judgments are elicited. The results indicate that rubric edits providing representative examples and additional context, and reducing positional bias in the rubric increased human-autorater agreement, while higher rubric complexity and conservative aggregation methods tended to decrease it. The findings from the automatic essay scoring and instruction-following evaluation domains suggest that practitioners should carefully analyze domain- and rubric-specific performance to move towards higher human-autorater agreement.

We propose a continuous measure of tonal ambiguity that extends the established concept of uniqueness. While uniqueness is widely regarded as necessary for tonality, it cannot (i) discriminate among sets that possess it, (ii) capture hierarchical organization in modes of limited transposition, or (iii) account for temporal unfolding. To address these limitations, we introduce a companion measure, grounded in information theory, that quantifies tonal ambiguity on a continuous scale. The measure applies across pitch-class sets and tuning systems, expanding analytic coverage of tonal relationships and offering a practical tool for theory and analysis.

The visual environment is a fundamental yet unquantified determinant of mental health. While the concept of the environmental exposome is well established, current methods rely on coarse geospatial proxies or biased self reports, failing to capture the first person visual context of daily life. We addressed this gap by coupling ecological momentary assessment with vision language models (VLMs) to quantify the semantic richness of human visual experience. Across 2674 participant generated photographs, VLM derived estimates of greenness robustly predicted momentary affect and chronic stress, consistent with established benchmarks. We then developed a semi autonomous large language model (LLM) based pipeline that mined over seven million scientific publications to extract nearly 1000 environmental features empirically linked to mental health. When applied to real world imagery, up to 33 percent of VLM extracted context ratings significantly correlated with affect and stress. These findings establish a scalable objective paradigm for visual exposomics, enabling high throughput decoding of how the visible world is associated with mental health.

This discussion paper reflects on how quantitative approaches to historical linguistics interact with dataset properties. Drawing on two worked examples, we examine English data using quad-based concept modelling of Early Modern English discourse in EEBO-TCP (c. 1470s-1690s; 765M words) alongside SynFlow analysis of scientific writing in Royal Society Corpus 6.0.4 (1750-1799; drawn from a 78.6M-token open corpus). Through parallel comparison, the paper explores how each approach operationalises concepts, the data assumptions they entail, and the diachronic interpretations they support. We argue that comparative methodological reflection clarifies the limits of purely lexical, frequency-based approaches and highlights how dataset structure shapes the kinds of semantic change that quantitative methods can reliably detect.

It is increasingly recognized that human annotators do not always agree, and such disagreement is inherent in many annotation tasks. However, not all instances in a given task elicit the same degree of opinion divergence. In this paper, we investigate annotation variation patterns in graded human ratings for inappropriate languages, including offensive language, hate speech, and toxic language perception. We examine whether the degree of annotation disagreement can be predicted from textual features. We further propose the Opposition Index, a metric that quantifies perspective opposition among annotators on a given item, and investigate the predictability of instances with potentially opposing human opinions. Our results show a moderate positive correlation between estimated and observed annotation variance. We find that two approaches achieve comparable performance in variance prediction: directly predicting the variance value and estimating it from predicted annotation distributions. Our results on opposition perspective prediction show that items with high opposition index values are more difficult to predict and are often underestimated by models.

For constructing text embeddings, mean pooling, which averages token embeddings, is the standard approach. This paper examines whether mean pooling actually works well in real models. First, we note that mean pooling can collapse information beyond the first-order statistics of the token embeddings, such as second-order statistics that capture their spatial structure, potentially mapping distinct token embedding distributions to similar text embeddings. Motivated by this concern, we propose a simple metric to quantify such a collapse induced by mean pooling. Then, using this metric, we empirically measure how often this collapse occurs in actual models and texts, and find that modern text encoders are robust to this collapse. In particular, contrastive fine-tuned text encoders tend to be less prone to the collapse than their pretrained backbone models. We also find that the robustness of these text encoders lies in the concentration of token embeddings within each text. In addition, we find that robustness to the collapse, as quantified by our proposed metric, correlates with downstream task performance. Overall, our findings offer a new perspective on why modern text encoders remain effective despite relying on seemingly coarse mean pooling.

Dynamic quantization emerged as a practical approach to increase the utilization and efficiency of the machine learning serving flow. Unlike static quantization, which applies quantization offline, dynamic quantization operates on tensors at run-time, adapting its parameters to the actual input data. Today's mainstream machine learning frameworks, including ML compilers and inference engines, frequently recommend dynamic quantization as an initial step for optimizing model serving. This is because dynamic quantization can significantly reduce memory usage and computational load, leading to faster token generation and improved model serving efficiency without substantial loss in model accuracy. In this paper, we reveal a critical vulnerability in dynamic quantization: an adversary can exploit such quantization strategy to steal sensitive user data placed in the same batch as the adversary's input. Our analysis demonstrates that dynamic quantization, when improperly implemented or configured, can create side channels that expose information about other inputs within the same batch. We call this phenomenon Quantamination, describing contamination from quantization. Specifically, we show that at least 4 of the most popular ML frameworks in use today either default to or can use configurations that leak data across the batch boundary. This data leakage, in theory, allows attackers to partially or even fully recover other users' batched input data, representing a serious privacy risk for existing ML serving frameworks.

Patient-specific occlusal positioning splints can be regarded as physical realisations of planned mandibular transformations. However, the achieved mandibular pose may differ from the planned one because of acquisition, registration, fabrication, and positioning errors. This study presents a transformation-based biomedical engineering framework for quantifying mandibular positioning accuracy and propagating the resulting error to a simulated temporomandibular joint configuration. Multimodal 3D data, including CBCT, facial motion acquisition, and dental scans, were integrated in a common coordinate system. Positioning splints corresponding to selected mandibular poses were designed and fabricated, and their realised positions were evaluated using repeated scans of plaster models. Discrepancies between planned and achieved positions were represented as rigid-body error transformations and analysed in SE(3), together with surface-distance metrics. The estimated transformations were propagated to CBCT-derived TMJ structures to quantify changes in condyle-fossa distance maps. The results demonstrate a systematic translational component and anisotropic variability of mandibular positioning error, with measurable propagation to simulated TMJ-space changes. The proposed framework provides an objective method for documenting planned and achieved mandibular configurations and for analysing positioning uncertainty in patient-specific splint workflows.

We present CRC-SAM, a unified framework for colorectal cancer segmentation across colonoscopy, CT, and histopathology images. Unlike prior single-modality methods, CRC-SAM provides consistent, modality-agnostic segmentation throughout the clinical workflow. Built on MedSAM, it incorporates low-rank adaptation (LoRA) layers into a frozen encoder, enabling efficient domain transfer to underrepresented modalities with minimal trainable parameters. Experiments on MSD-Colon, CVC-ClinicDB, and EBHI-Seg demonstrate superior performance across modalities, outperforming state-of-the-art baselines and highlighting the effectiveness of lightweight LoRA adaptation for foundation-model-based colorectal cancer analysis.

LLM-as-a-Judge has become a dominant approach in automated evaluation systems, playing critical roles in model alignment, leaderboard construction, quality control, and so on. However, the scalability and trustworthiness of this approach can be substantially distorted by Self-Preference Bias (SPB), which is a directional evaluative deviation in which LLMs systematically favor or disfavor their own generated outputs during evaluation. Existing measurements rely on costly human annotations and conflate generative capability with evaluative stance, and thus are impractical for large-scale deployment in real-world systems. To address this issue, we introduce a fully automated framework to quantifying and mitigating SPB, which constructs equal-quality pairs of responses with negligible quality differences, enabling statistical disentanglement of discriminability from bias propensity without human gold standards. Empirical analysis across 20 mainstream LLMs reveals that advanced capabilities are often uncorrelated, or even negatively correlated, with low SPB. To mitigate this bias, we propose a structured multi-dimensional evaluation strategy grounded in cognitive load decomposition, which reduces SPB by 31.5% on average.

Portamento in string performance has been studied primarily as a binary presence-or-absence phenomenon, with existing research measuring frequency of occurrence and, less commonly, duration in milliseconds. This paper introduces a third quantitative descriptor; the spectrographic gradient of the portamento slide, measured in Hz/second, and demonstrates its measurement using a protocol combining Sonic Visualizer's melodic spectrogram layer, GIMP pixel analysis, and metric calibration against the spectrogram's known frequency axis. The gradient captures what duration alone cannot: the steepness of the pitch trajectory, which encodes the expressive character of the slide independently of its length. Applied to the opening measures of. Specifically because their monophonic texture permits reliable spectrographic pitch tracking. The method yields gradient values ranging from approximately 600Hz/s in late-period recordings to over 4,000Hz/s in early twentieth-century performances. The paper further documents a gain-recovery protocol that extends the analysable corpus to analogue recordings from the 1930s where portamento traces are faint in digital transfer. Applying the method to a corpus of 22 recordings spanning 1930--2012, the paper tests the hypothesis that gradient steepness correlates negatively with tempo: that slower performances produce steeper, longer slides while faster performances produce shallower slides or none at all. The results support this hypothesis, suggesting that the widely documented decline of portamento across the twentieth century is not a binary transition from presence to absence but a continuou

Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely unexamined. In this paper, we present a stability evaluation framework that probes parametric projections with Gaussian perturbations around selected anchor points and assesses how neighborhoods deform in the 2D embedding. Our approach combines quantitative measures of mean displacement, bias, and nearest-anchor assignment error with per-anchor visualizations of displacement vectors, local PCA ellipsoids, and Voronoi misassignment for detailed inspection. We demonstrate the framework's effectiveness on UMAP- and t-SNE-based neural projectors of varying network sizes and study the effect of Jacobian regularization as a gradient-based robustness strategy. We apply our framework to the MNIST and Fashion-MNIST datasets. The results show that our framework identifies unstable projection regions invisible to reconstruction error or neighborhood-preservation metrics.

Since software performance requirements are documented in natural language, quantifying them into mathematical forms is essential for software engineering. Yet, the vagueness in performance requirements and uncertainty of human cognition have caused highly uncertain ambiguity in the interpretations, rendering their automated quantification an unaddressed and challenging problem. In this paper, we formalize the problem and propose IRAP, an approach that quantifies performance requirements into mathematical functions via interactive retrieval-augmented preference elicitation. IRAP differs from the others in that it explicitly derives from problem-specific knowledge to retrieve and reason the preferences, which also guides the progressive interaction with stakeholders, while reducing the cognitive overhead. Experiment results against 10 state-of-the-art methods on four real-world datasets demonstrate the superiority of IRAP on all cases with up to 40x improvements under as few as five rounds of interactions.

Model distillation is a primary driver behind the rapid progress of LLM agents, yet it often leads to behavioral homogenization. Many emerging agents share nearly identical reasoning steps and failure modes, suggesting they may be distilled echoes of a few dominant teachers. Existing metrics, however, fail to distinguish mandatory behaviors required for task success from non-mandatory patterns that reflect a model's autonomous preferences. We propose two complementary metrics to isolate non-mandatory behavioral patterns: \textbf{Response Pattern Similarity (RPS)} for verbal alignment and \textbf{Action Graph Similarity (AGS)} for tool-use habits modeled as directed graphs. Evaluating 18 models from 8 providers on $τ$-Bench and $τ^2$-Bench against Claude Sonnet 4.5 (thinking), we find that within-family model pairs score 5.9 pp higher in AGS than cross-family pairs, and that Kimi-K2 (thinking) reaches 82.6% $S_{\text{node}}$ and 94.7% $S_{\text{dep}}$, exceeding Anthropic's own Opus 4.1. A controlled distillation experiment further confirms that AGS distinguishes teacher-specific convergence from general improvement. RPS and AGS capture distinct behavioral dimensions (Pearson $r$ = 0.491), providing complementary diagnostic signals for behavioral convergence in the agent ecosystem. Our code is available at https://github.com/Syuchin/AgentEcho.

Thinking LLMs produce reasoning traces before answering. Prior activation steering work mainly targets on shaping these traces. It remains less understood how answer tokens actually read and integrate the reasoning to produce reliable outcomes. Focusing on quantitative reasoning, we analyze the answer-to-reasoning attention and observe a benign self-reading pattern aligned with correctness, characterized by a forward drift of the reading focus along the reasoning trace and a persistent concentration on key semantic anchors, whereas incorrect solutions exhibit diffuse and irregular attention pattern. We interpret this as internal certainty during answer decoding, where the model commits to a viable solution branch and integrates key evidence. Following this, we propose a training-free steering method driven by Self-Reading Quality (SRQ) scores combining geometric metrics for process control with semantic metrics for content monitoring. SRQ selects data to build steering vectors that guide inference toward benign self-reading and away from uncertain and disorganized reading. Experiments show that our method yields consistent accuracy gains.

Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular self-reflection, yet how much of this deliberation is actually necessary has never been measured at scale or explained from first principles. This paper closes both gaps. We formalise reasoning redundancy directly in terms of the reasoning model itself: the redundancy of a correct trace is the largest fraction of its trailing segmented steps that can be truncated while $π$, forced to terminate thinking and emit a final answer, still produces the correct answer. A large-scale quantification across four frontier reasoning models and two mathematical benchmarks shows that step-level redundancy is consistently high -- between 61% and 93% across the 8 (model, benchmark) conditions we study, with the median critical prefix equal to a single segmented step in six of the eight conditions -- that the finding is robust to the choice of judge family, and that although $ρ$ decreases with problem difficulty on MATH-500, all four models remain substantially redundant ($ρ\in [46\%, 85\%]$) even on the hardest Level-5 problems. We then prove that this redundancy is a structural consequence of length-agnostic outcome rewards, not a model-specific artefact: under any such reward, no finite expected stopping time is optimal. The result holds regardless of RL algorithm, base model, data distribution, or whether the policy is obtained via RL or distillation; over-thinking is therefore not a bug to be patched in individual models but a structural property of how current reasoning models are trained. Code: https://github.com/zhiyuanZhai20/how-much-thinking-is-enough

Large language models frequently produce mutually inconsistent answers when reasoning over multiple related queries. We study case-file logical consistency: maintaining a globally satisfiable belief state across interdependent queries. We introduce a benchmark of 390 multi-query reasoning instances with entailment/contradiction/unknown labels and propose set-level metrics including Case Satisfiability Rate, Contradiction Density and Revision Cost. Our solver-augmented approach extracts commitments, verifies global satisfiability and performs counterexample-guided repair. Across four reasoning domains, our method substantially reduces cross-query contradictions (SetCons: 0.56 to 0.94) while preserving per-query accuracy, demonstrating that global coherence is critical for robust multi-query reasoning.

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.

Parton Distribution Functions (PDFs) play a central role in describing experimental data at colliders and provide insight into the structure of nucleons. As the LHC enters an era of high-precision measurements, a robust PDF determination with a reliable uncertainty quantification has become mandatory in order to match the experimental precision. The NNPDF collaboration has pioneered the use of Machine Learning (ML) techniques for PDF determinations, using Neural Networks (NNs) to parametrise the unknown PDFs in a flexible and unbiased way. The NNs are then trained on experimental data by means of stochastic gradient descent algorithms. The statistical robustness of the results is validated by extensive closure tests using synthetic data. In this work, we develop a theoretical framework based on the Neural Tangent Kernel (NTK) to analyse the training dynamics of neural networks. This approach allows us to derive, under precise assumptions, an analytical description of the neural network evolution during training, enabling a quantitative understanding of the training process. Having an analytical handle on the training dynamics allows us to clarify the role of the NN architecture and the impact of the experimental data in a transparent way. Similarly, we are able to describe the evolution of the covariance of the NN output during training, providing a quantitative description of how uncertainties are propagated from the data to the fitted function. While our results are not a substitute for PDF fitting, they do provide a powerful diagnostic tool to assess the robustness of current fitting methodologies. Beyond its relevance for particle physics phenomenology, our analysis of PDF determinations provides a testbed to apply theoretical ideas about the learning process developed in the ML community.

This paper presents a quantitative comparison between centralised and distributed multi-agent reinforcement learning (MARL) architectures for controlling a soft robotic arm modelled as a Cosserat rod in simulation. Using PyElastica and the OpenAI Gym interface, we train both a global Proximal Policy Optimisation (PPO) controller and a Multi-Agent PPO (MAPPO) under identical budgets. Both approaches are based on the arm having $n$ number of controlled sections. The study systematically varies $n$ and evaluates the performance of the arm to reach a fixed target in three scenarios: default baseline condition, recovery from external disturbance, and adaptation to actuator failure. Quantitative metrics used for the evaluation are mean action magnitude, mean final distance, mean episode length, and success rate. The results show that there are no significant benefits of the distributed policy when the number of controlled sections $n\le4$. In very simple systems, when $n\le2$, the centralised policy outperforms the distributed one. When $n$ increases to $4< n\le 12$, the distributed policy shows a high sample efficiency. In these systems, distributed policy promotes a stronger success rate, resilience, and robustness under local observability and yields faster convergence given the same sample size. However, centralised policies achieve much higher time efficiency during training as it takes much less time to train the same size of samples. These findings highlight the trade-offs between centralised and distributed policy in reinforcement learning-based control for soft robotic systems and provide actionable design guidance for future sim-to-real transfer in soft rod-like manipulators.

Biophysical diffusion MRI models like Neurite Exchange Imaging (NEXI) are essential for probing gray matter microstructure, estimating compartment diffusivities, neurite fraction, and exchange time. However, NEXI's multi-shell, multi-diffusion-time requirements cause prohibitively long acquisitions. Leveraging the Connectome 2.0 ultra-high gradient scanner, we developed a time-efficient protocol using an Explainable AI (XAI) framework. Combining XGBoost, SHAP, and Recursive Feature Elimination trained on synthetic signals, XAI identified an optimal 8-feature subset, cutting scan time from 27 to 14 minutes. Validated in vivo in seven healthy participants, the XAI protocol was benchmarked against the full 15-feature acquisition, a Cram'er-Rao Lower Bound (CRLB) theoretical optimum, and two heuristics ("Mid-Range" and "Corner"). It robustly reproduced parameter estimates and maintained test-retest reproducibility. Remarkably, the XAI selection converged to the CRLB optimum. This validates XAI's optimality while highlighting its main advantage: achieving gold-standard optimization without complex analytical Jacobians, making it easily adaptable to numerical models or complex noise where CRLB is intractable. Furthermore, XAI showed superior in vivo robustness over heuristics: "Mid-Range" sampling yielded biased exchange time estimates from insufficient temporal diversity, while "Corner" sampling gave unstable intra-neurite diffusivity estimates (5-fold higher CV) due to noise sensitivity. Ultimately, this robust 14-minute protocol accelerates exchange-sensitive microstructural mapping, establishing a model-agnostic optimization framework adaptable to future ultra-high gradient systems and existing clinical scanners.

It was recently observed that the representations of different models that process identical or semantically related inputs tend to align. We analyze this phenomenon using the Information Imbalance, an asymmetric rank-based measure that quantifies the capability of a representation to predict another, providing a proxy of the cross-entropy which can be computed efficiently in high-dimensional spaces. By measuring the Information Imbalance between representations generated by DeepSeek-V3 processing translations, we find that semantic information is spread across many tokens, and that semantic predictability is strongest in a set of central layers of the network, robust across six language pairs. We measure clear information asymmetries: English representations are systematically more predictive than those of other languages, and DeepSeek-V3 representations are more predictive of those in a smaller model such as Llama3-8b than the opposite. In the visual domain, we observe that semantic information concentrates in middle layers for autoregressive models and in final layers for encoder models, and these same layers yield the strongest cross-modal predictability with textual representations of image captions. Our results support the hypothesis of semantic convergence across languages, modalities, and architectures, while showing that directed predictability between representations varies strongly with layer-depth, model scale, and language.