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01.
arXiv (math.PR) 2026-06-18

Cramér-Type Moderate Deviations for Engel's Series via a Martingale Approach

arXiv:2606.18866v1 Announce Type: new Abstract: Let $x$ be uniformly distributed on $(0,1)$, and let $(q_n)_{n\geq1}$ be the digits of its Engel series expansion. We establish a Cramér-type moderate deviation expansion for $(\log q_n-n)/\sqrt n$. The proof is based on a martingale decomposition and asymptotic results for martingales. As consequences, we obtain a moderate deviation principle over the full range of scales between the central limit theorem and the law of large numbers, without the additional lower rate restriction required in several earlier works. We also derive a uniform Berry–Esseen bound of order $(\log n)/\sqrt n$.

02.
arXiv (CS.CL) 2026-06-11

Unifying Learning Dynamics and Generalization in Transformers Scaling Law

Authors:

The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly understood. This work formalizes the learning dynamics of transformer-based language models as an ordinary differential equation (ODE) system, then approximates this process to kernel behaviors. Departing from prior toy-model analyses, we rigorously analyze stochastic gradient descent (SGD) training for multi-layer transformers on sequence-to-sequence data with arbitrary data distribution, closely mirroring real-world conditions. Our analysis characterizes the convergence of generalization error to the irreducible risk as computational resources scale with data, especially during the optimization process. We establish matching upper and lower bounds on the excess risk, characterized by a distinct phase transition. In the initial optimization phase, the excess risk decays exponentially relative to the computational cost ${\sf C}$. However, once a specific resource allocation threshold is crossed, the system enters a statistical phase, where the generalization error follows a power-law decay of $\Theta(\mathsf{C}^{-1/7})$. These rates are certified by complementary lower bounds – statistical, via an information-theoretic two-point reduction, and optimization-side, via a first-order oracle argument – rendering the two-stage law tight up to constants, logarithmic factors, and a condition-number gap. Beyond this unified framework, our theory derives isolated scaling laws for model size, training time, and dataset size, elucidating how each variable independently governs the bounds of generalization.

03.
arXiv (CS.LG) 2026-06-18

Unreduced Persistence Diagrams for Topological Machine Learning

arXiv:2507.07156v2 Announce Type: replace-cross Abstract: Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the most computationally demanding step in such a pipeline, however. To explore this dynamic, we introduce several methods to generate topological feature vectors from unreduced boundary matrices and investigate their theoretical and computational properties. We compared the performance of pipelines trained on vectorizations of unreduced PDs to vectorizations of fully-reduced PDs across several data and task types. Our results indicate that models trained on PDs built from unreduced diagrams can perform on par and even outperform those trained on fully-reduced diagrams on some tasks. We also benchmarked the computational performance of an algorithm for computing unreduced diagrams, which was implemented as a heavily modified version of Ripser. These computations are parallelizable and required an order of magnitude less memory on average compared to computing full persistence diagrams. Our results suggest that machine learning pipelines which incorporate topology-based features may benefit in terms of computational cost and performance by utilizing information contained in unreduced boundary matrices.

04.
arXiv (CS.LG) 2026-06-17

QueryMarket: Cost-Aware Online Active Learning in Data Markets

arXiv:2606.17805v1 Announce Type: new Abstract: Data acquisition is a major bottleneck for learning in real-time streams: analysts must decide on the fly which labels to purchase while respecting a rolling budget. However, existing online active learning rarely unifies pricing, information gain, and rolling budget constraints under concept drift. We introduce QueryMarket, a market-inspired framework that queries each incoming data point based on its estimated utility to the model and its price. Within this framework, we propose OVBAL (online variance-based active learning), which integrates data pricing with information-driven selection by estimating each sample's marginal utility via a D-optimality criterion with exponential forgetting and executing cost-aware purchases under rolling budget constraints. OVBAL yields a simple, fully online decision rule that adapts to nonstationary streams and heterogeneous label costs. Experiments on synthetic data and a real-world solar power generation forecasting task show that OVBAL is particularly effective under seller-centric pricing and yields a more favorable long-run error-cost trade-off in the real-world task under both pricing schemes.

05.
arXiv (CS.LG) 2026-06-19

Calibrating Generative Models to Feature Distributions with MMD Finetuning

arXiv:2606.19496v1 Announce Type: new Abstract: Generative models can produce individually plausible samples while deviating substantially from a target set in the distribution of key features. For example, a model pretrained on broad drug-like chemical space may generate molecules whose molecular features differ from those of a therapeutic class of interest, such as known antibiotics. Correcting such distributional miscalibration is challenging: direct finetuning on the target set can overfit and does not control which features are matched. To fill this gap, we introduce kernel Calibrating Generative Models (kCGM). kCGM minimizes a maximum mean discrepancy (MMD) between generated and target feature distributions using an unbiased score-function estimator, with KL regularization to remain close to the pretrained model. On a target set of 174 antibiotics, direct finetuning sacrifices chemical validity for feature-distribution matching, whereas kCGM improves target feature matching while increasing validity. We further demonstrate kCGM in protein and DNA generation tasks, showing it can adapt autoregressive, continuous-space diffusion, and discrete diffusion models using only feature-level supervision. Code is available at https://github.com/smithhenryd/cgm.

06.
arXiv (CS.LG) 2026-06-16

Using Reinforcement Learning to Optimize the Global and Local Crossing Number

arXiv:2509.06108v2 Announce Type: replace-cross Abstract: Graph drawing concerns the algorithmic visualization of graphs. A good drawing of a graph is easy to read and facilitates solving tasks on the graph. Several properties have been identified to occur in good drawings of graphs. Such properties include a low number of crossings, large angles between edges, short edges, and depicting symmetries. Many of these properties are explicitly measurable metrics. This brings us to the insight that graph drawing can be seen as a game. In this paper, we study a single-player optimization game in which the player iteratively moves vertices of a straight-line graph drawing to reduce edge crossings. This game arose naturally from the automatic track of the Graph Drawing Challenge, where solutions are obtained by repeatedly performing local vertex movements. We formalize this process as a game with full information and investigate whether reinforcement learning can discover effective strategies for playing it. Our reinforcement-learning agent observes the local geometric and structural context of a vertex and selects a movement direction with the goal of reducing either the global or the local crossing number, that is, the total number of crossings or the maximum number of crossings per edge. We compare the resulting strategies to existing methods and established crossing-minimization heuristics on standard benchmark graphs. While our approach does not out-compete state-of-the-art methods for minimizing the global crossing number, it is competitive and often superior for minimizing the local crossing number.

07.
arXiv (CS.LG) 2026-06-17

HeteRo-Select: Informativeness as the Participation Driver in Heterogeneous Federated Learning

arXiv:2508.06692v2 Announce Type: replace Abstract: Federated learning systems typically allocate gradient compression by link speed. This is sensible when bandwidth and data informativeness align. However, under non-IID data, these signals often decorrelate or invert. A bandwidth-driven allocator then risks compressing the most informative gradients hardest. We propose HeteRo-Select, a framework that replaces bandwidth with a per-client informativeness score as the primary driver of compression. The score jointly governs three decisions per round: client selection, compression ratio, and server aggregation weight, with bandwidth retained only as a hard ceiling. Score-proportional selection provably reduces the effective heterogeneity of the chosen subset; score-proportional compression provably lowers aggregate top-$k$ error at fixed traffic. Under the exact FedCG simulation protocol, HeteRo-Select delivers a $1.78\times$ speedup and an $18.2\%$ reduction in traffic on CIFAR-10. The same configuration, unchanged, scales from a $7{,}850$-parameter logistic regression to an $11.27$M-parameter ResNet-18, hitting the accuracy target on three of four benchmarks. When bandwidth and informativeness are deliberately anti-correlated, the method still achieves the target accuracy with less traffic than the normal-bandwidth run.

08.
arXiv (CS.CL) 2026-06-17

Priors Persist Through Suppression: A Stroop Paradigm for Lexical Override

Authors:

Glossaries, technical specifications, and system prompts routinely ask language models to use familiar words in unfamiliar ways. When this works, the local rule does not install the new meaning on top of the old one; the pretrained prior keeps operating underneath, and its strength still shows through. We test this with a Stroop-style paradigm: a remapping rule (doctor means forest) pitted against the query word's lexical-prior distractor (hospital), with matched neutral controls. Across 11 open-weight models spanning four families and 1B-9B parameters, lexical-prior strength predicts interference even after item-level controls for answer prior, frequency, tokenization, and prompt wording. Activation patching on five aligned models locates a source-position triplet (definition subject, definition target, query word) that nearly fully recovers the conflict effect (aggregate $R \in [0.92, 1.06]$); a definition-target swap shows the triplet performs binding rather than identity matching. Dissociation experiments isolate target preservation as the binding-specific signature: distractor suppression occurs under matched, swap, and item-mismatched conditions alike, whereas target logit collapse occurs only when the definition-target position is corrupted. Behavior and mechanism converge on the same channel: the prior's strength both predicts which overrides fail and marks where the causal repair lands.

09.
arXiv (CS.CL) 2026-06-16

CoCoGEC: Counterfactual Generation for Robust Grammatical Error Correction

Grammatical error correction (GEC) systems are usually trained and evaluated on GEC benchmarks, but their performance often drops sharply once the surrounding context is slightly perturbed or extended. This indicates that the existing GEC models usually fail to understand the error patterns in the varying contexts. In this paper, we thoroughly investigate the counterfactuals for GEC tasks, where the subtle changes to the contexts could lead to the label flipping issue. We propose CoCoGEC, a counterfactual generation framework that creates copies of training instances with error-irrelevant contexts altered. Our framework systematically generates counterfactuals by (1) generating intra- and inter-sentence counterfactuals that maintain the error patterns as well as syntax of the original instances by altering the word-level and sentence-level contexts; (2) revising the generated counterfactuals by selecting the instances with flipped labels and high GEC Mutual Information (MI) coefficient. Extensive experiments show that our method substantially improves the stability of GEC models, outperforming a set of data augmentation baselines. Particularly, it could achieve absolute F0.5 gains of +9.9, +11.3, and +20.8 points on the perturbed BEA-19*,CoNLL-14*, and TEM-8* data set.Our code is released at https://github.com/Quinnok/CoCoGEC

10.
arXiv (CS.CL) 2026-06-24

MMed-Bench-IR: A Heterogeneous Benchmark for Multilingual Medical Information Retrieval

Retrieval-augmented generation (RAG) in clinical settings increasingly requires multilingual retrieval against predominantly English evidence corpora. Multilingual medical retrieval demands three capabilities: cross-lingual alignment, concept discrimination, and evidence retrieval. However, existing benchmarks evaluate these only in isolation, leaving the interaction between biomedical expertise and multilingual coverage unmeasured. We introduce MMed-Bench-IR, a benchmark designed to disentangle these axes across 6 languages and three structurally heterogeneous tasks: (1) cross-lingual medical QA retrieval with 6,127 queries grounded in the Unified Medical Language System (UMLS), (2) concept discrimination over 4,975 confusion sets at three difficulty tiers, and (3) multilingual evidence retrieval for RAG with 2,040 quality-assured queries. The three tasks share zero concept and query overlap by design, ensuring that aggregate scores reflect genuine capability breadth. Evaluation of ten systems across six paradigm families reveals severe cross-lingual failure: biomedical encoders that score 0.818 nDCG@10 in English drop to 0.056 in Japanese, a gap that English-only benchmarks cannot detect.

11.
arXiv (quant-ph) 2026-06-16

Single-Image Entanglement Verification with Spatially Encoded Measurement Contexts

arXiv:2606.15382v1 Announce Type: new Abstract: Entangled photon pairs produced by spontaneous parametric down-conversion exhibit rich spatial entanglement structure that is often difficult to probe with conventional measurements. Here, we show that spin-orbit optical elements can convert this spatial structure into directly observable quantum interference patterns. Using a $q$-plate, we demonstrate that the relative wavefront curvature of biphoton states generated by a pair of nonlinear crystals can be retrieved from the spatial modulation of coincidence images. Building on this principle, we introduce a liquid-crystal metasurface that performs spatially multiplexed Bell measurements across the transverse profile of the photon field. The device, which we call a Clauser-Horne-Shimony-Holt (CHSH) plate, assigns different polarization projections to different azimuthal sectors of the beam, allowing the sixteen joint measurements required for a CHSH test to be realized simultaneously in a single acquisition. In this architecture, the spatial coordinate acts as a classical register selecting the measurement context, while photon pairs sample these contexts according to their emission directions. We further demonstrate that the same measurement concept can be implemented using a programmable spatial light modulator, providing a dynamically reconfigurable realization of the scheme. Our results show that spatially structured optical elements can transform Bell tests into parallel measurements distributed across the transverse plane, enabling rapid characterization of spatially varying entanglement. This approach opens new possibilities for structured-light quantum measurements, Bell-inequality-based imaging, and the study of spatially engineered entangled photon sources.

12.
arXiv (CS.CV) 2026-06-16

Improved Knowledge Distillation for Land-Use Image Classification

In the present article, an improved Knowledge Distillation (KD) framework has been proposed for efficient compression of deep convolutional neural networks for land-use image classification task. Motivated by the need to achieve competitive classification accuracy while reducing computational complexity, a teacher-student learning paradigm is adopted in which a VGG16 network transfers knowledge to a lightweight MobileNetV2 model. The proposed framework integrates hard supervision from ground truth labels with a soft supervision strategy that combines Kullback-Leibler divergence and Cosine Similarity losses. Experiments conducted on three land-use datasets show that the proposed KD-based method yields improved performance, and achieves an accuracy of 99.04%, outperforming both baseline student training and single-loss distillation approaches, while retaining substantial model compression.

13.
arXiv (CS.LG) 2026-06-19

An Information Theoretic Framework for Graph Novelty Generation via Latent Mixture Modeling

arXiv:2606.19770v1 Announce Type: new Abstract: We propose an information-theoretic framework for graph novelty generation, which aims to generate data that are distinct from existing patterns while preserving global structural consistency. Our approach embeds data into a latent space, models the latent distribution using finite mixture models, and generates novel samples by imposing explicit novelty and reliability conditions formulated in terms of description length. Specifically, novelty is enforced by requiring generated samples to be poorly explained by all existing mixture components, while reliability constrains their impact on the overall mixture structure under the Minimum Description Length (MDL) principle. We provide a theoretical analysis showing that, with appropriate threshold choices, the probabilities of misclassifying non-novel or unreliable samples converge to zero with explicit rates. Experiments on synthetic and benchmark graph datasets demonstrate that the proposed method enables principled novelty generation with quantifiable risk.

14.
arXiv (CS.AI) 2026-06-17

Understanding LLMs in Title-Abstract Screening: From Disagreements to Recommendations

arXiv:2606.17588v1 Announce Type: cross Abstract: Several studies have examined the use of large language models (LLMs) for title-abstract screening in systematic reviews (SRs), reporting mixed accuracy. However, questions of reliability remain largely unaddressed. In this study, we go beyond quantitative LLM-human agreement metrics and qualitatively investigate how and why LLMs fail. We also propose actionable recommendations. We analyzed disagreements between LLMs and researchers across six software engineering SRs and over 1,000 primary study papers. For each SR, papers were screened independently by human experts and LLMs in zero-shot mode, resulting in Kappa values ranging from 0.52 to 0.77. Qualitative analysis suggests that human-LLM disagreement results from recurring, identifiable causes, such as boundary ambiguity in key terms, keyword overemphasization, and incorrect topic inference. Based on these findings, we propose recommendations such as validating semantic understanding before deployment, running multiple LLMs, and focusing validation efforts on borderline cases. Future studies are needed to validate the impact of our recommendations, and community efforts are needed to develop normative guidelines on LLM usage in SRs.

15.
arXiv (CS.AI) 2026-06-18

Code-Augur: Agentic Vulnerability Detection via Specification Inference

arXiv:2606.18619v1 Announce Type: cross Abstract: The advent of agentic vulnerability detection is already becoming a watershed moment for software security. Audits conducted entirely by autonomous LLM agents are uncovering critical vulnerabilities in fundamental software underpinning digital society. Many of these vulnerabilities remained masked for years, surfacing only now with AI agents. Yet the reasoning behind these discoveries remains alarmingly opaque and unvalidated. What assumptions did the agent make about a function's inputs when it deemed that function to be secure? Failures in reasoning and incorrect assumptions can lead to missed vulnerabilities and reduce trust in agentic analysis. We propose a security-specification-first paradigm that (1) exposes the agent's tacit assumptions explicitly as security specifications and (2) continuously refines those specifications via runtime falsification. We realize our approach in Code-Augur, a novel harness for agentic vulnerability detection. Given a codebase, Code-Augur analyzes each component of the system for vulnerable code. When it deems a component to be secure, it commits the local invariants behind that judgment as in-source assertions. In parallel, Code-Augur leverages a guided fuzzer to attempt to falsify those assumptions. When the fuzzer triggers an assertion, this either reveals a genuine vulnerability or a flawed specification to refine. In both cases, this process grounds the agent's understanding, aligning its view of code intent with how the code actually behaves. On real-world subjects, Code-Augur effectively leverages security specifications to detect more vulnerabilities than other state-of-the-art agents. Additionally, Code-Augur found 22 new vulnerabilities in key open-source projects. Compared to curated specialized models like Claude Mythos, Code-Augur offers effective agentic vulnerability detection built on widely available LLMs like Sonnet and DeepSeek.

17.
arXiv (quant-ph) 2026-06-16

Generalized Kerr-Cat Qubit Codes

arXiv:2606.14901v1 Announce Type: new Abstract: We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut–Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between $\mathfrak{su}(2)$, $\mathfrak{su}(1,1)$ coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.

18.
arXiv (CS.CV) 2026-06-17

Does the Data Processing Inequality Reflect Practice? On the Utility of Low-Level Tasks

The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations. In particular, it suggests that there is no benefit in enhancing the signal or encoding it before addressing a classification problem. This assertion can be proven to be true for the case of the optimal Bayes classifier. However, in practice, it is common to perform "low-level" tasks before "high-level" downstream tasks despite the overwhelming capabilities of modern deep neural networks. In this paper, we aim to understand when and why low-level processing can be beneficial for classification. We present a comprehensive theoretical study of a binary classification setup, where we consider a classifier that is tightly connected to the optimal Bayes classifier and converges to it as the number of training samples increases. We prove that for any finite number of training samples, there exists a pre-classification processing that improves the classification accuracy. We also explore the effect of class separation, training set size, and class balance on the relative gain from this procedure. We support our theory with an empirical investigation of the theoretical setup. Finally, we conduct an empirical study where we investigate the effect of denoising and encoding on the performance of practical deep classifiers on benchmark datasets. Specifically, we vary the size and class distribution of the training set, and the noise level, and demonstrate trends that are consistent with our theoretical results.

19.
arXiv (CS.AI) 2026-06-18

LivePI: More Realistic Benchmarking of Agents Against Indirect Prompt Injection

arXiv:2605.17986v3 Announce Type: replace-cross Abstract: AI agents such as OpenClaw are increasingly deployed in local workflows with access to external tools. This creates indirect prompt-injection (IPI) risk: an agent may execute harmful instructions embedded in untrusted inputs such as email, downloaded files, webpages, repositories, or group-chat messages. Existing evaluations are often small, purely simulated, or focused on a narrow set of channels. We introduce LivePI (Live Prompt Injection), a structured benchmark for IPI risk in a production-like but test-controlled environment. LivePI covers seven input surfaces, twelve attack/rendering families, and five malicious goals, including protected-information exfiltration, unauthorized security-control changes, unsafe code retrieval or execution, inbox-summary exfiltration, and cryptocurrency transfer. We run LivePI on a real virtual machine with live but test-controlled email, chat, web, local-file, repository, and wallet interfaces. Across GPT-5.3-Codex, Claude Opus 4.6, Gemini 3.1 Pro, Kimi K2.5, and GLM-5, total attack success rates range from 10.7% to 29.6%. Group-chat injection is uniformly successful across the evaluated backbones in our deployment, and repository-link attacks produce high-severity failures despite a small denominator. We also evaluate a two-layer defense consisting of prompt-level filtering and pre-execution tool-call authorization. In the GPT-5.3-Codex setting, the defense intercepts all tested malicious-goal completions in LivePI before execution while preserving benign utility on PinchBench-derived workloads.

20.
arXiv (CS.CV) 2026-06-16

Assessing Reliability of Symbol Detection in Concept Bottleneck Models

Concept Bottleneck Models (CBMs) are a relevant tool for explainable Artificial Intelligence because they make their predictions through human-interpretable symbols. However, high task accuracy does not guarantee that these symbols are detected faithfully: jointly trained CBMs may encode task-specific shortcuts in the bottleneck, making their explanations unreliable. In this paper, we study concept-detection reliability by swapping independently trained concept detectors and classification heads that share the same symbolic vocabulary. We use the resulting performance degradation, concept-level metrics, and symbol-wise uncertainty estimates to identify concepts that are especially prone to spurious firing. Finally, we propose a reliability-aware training strategy in which a shared concept detector is optimized with multiple classification heads and penalized for relying on globally or instance-wise unreliable symbols. On CUB-200-2011 with full concept supervision, detectors and heads are almost freely interchangeable (swap drop below one accuracy point, relative retention above $99\%$, and no concept detected below chance), whereas on a controlled synthetic task we show that, as the concept-supervision weight is reduced, models keep near-perfect task accuracy while swapped accuracy and agreement with the ground-truth concepts collapse to chance. Our reliability-aware training substantially mitigates this leakage, roughly doubling swap accuracy in the leaky regime.

21.
Nature (Science) 2026-06-10

A vast whale necropolis has been found

In the Indian Ocean, a deep-sea area roughly 1,200 kilometres long and 7 kilometres deep was found to harbour an ecological landmark site of whale remains. In the Indian Ocean, a deep-sea area roughly 1,200 kilometres long and 7 kilometres deep was found to harbour an ecological landmark site of whale remains.

22.
arXiv (CS.AI) 2026-06-17

AI Adoption Across a Multinational Workforce: Sociotechnical Conditions for GenAI Acceptance in Human Resources

arXiv:2606.17887v1 Announce Type: cross Abstract: Generative AI (GenAI) deployment in the workplace is accelerating rapidly. Nevertheless, questions of who adopts, who benefits, and who is left behind and why are still understudied. In this paper, we investigate these dynamics in the context of a multinational tech company transitioning from a legacy Human Resources (HR) search system to a GenAI-supported system, analyzing search log data, survey data (n=25), and ten semi-structured interviews. Our findings show that adoption depended on the fit between the GenAI system's design assumptions and employees' work positionalities (role, spoken language, tenure). Further, we find that employees' trust in GenAI answers was built through source-checking, comparison among systems, and seeking input from colleagues or HR when in doubt. Our contribution is twofold. First, we provide empirical evidence of workplace GenAI adoption during a live organizational transition, showing that adoption is influenced by factors such as situational fit, search literacy, and trust calibration. It is also further shaped by knowledge conditions such as the system's content quality, employee training, and guidance. Second, we translate these findings into design considerations for inclusive deployment and adoption in high-stakes environments such as HR. We argue that organizations should design systems considering the role and context-sensitive benefits they yield to different social groups. They also need to treat the organizational knowledge infrastructure as AI infrastructure to improve the accountability and usability of GenAI systems

23.
arXiv (CS.CL) 2026-06-11

Geometric Metrics and LLMs: What They Measure and When They Work

We present a systematic stress-test of geometric metrics for LLM evaluation. Rank-based geometric properties of internal representations have shown promise as reference-free quality signals, but the conditions under which they are reliable remain unclear. We evaluate eight commonly-used metrics: intrinsic-dimensionality estimators, spectral norms, and related quantities across six tester models (0.5-8B) and eight generators on contrasting tasks, separating genuine geometric signal from text-length effects and from what standard text statistics already capture. Three findings emerge. First, some metrics (notably Schatten Norm and MOM) mainly reflect output length, and their apparent discriminative power collapses once length is controlled. Second, geometric metrics add modest but real information beyond text statistics: combined with them, a classifier reaches 78% accuracy on 6-way generator identification versus 69% for text statistics alone. Third, rather than tracking a general notion of text quality, the metrics demonstrate only moderate association between the intrinsic-dimensionality and lexical diversity (RTTR). We give use-case-specific recommendations and identify failure detection as the most promising near-term application.

24.
arXiv (CS.LG) 2026-06-15

XRDiff: Crystal Structure Prediction from Powder X-Ray Diffraction Data Using Diffusion Models

arXiv:2606.14003v1 Announce Type: cross Abstract: Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.

25.
arXiv (CS.LG) 2026-06-24

The Degeneracy Distillery

arXiv:2606.23838v1 Announce Type: new Abstract: When two or more parameters or labels produce similar data, they are degenerate, or hard to distinguish. Degeneracies render both label prediction and inverse problems difficult, since both machine learning algorithms and probabilistic samplers rely on the distinguishability of data and its gradients with respect to parameters. However, identifying degeneracies in physical models or real-world datasets can be elucidating about the choice of model or the underlying process that produces the data. We present the degeneracy distillery, a method that (1) detects and (2) resolves degenerate parameter combinations (a) automatically and (b) symbolically, from parameter-data (or parameter-simulation) pairs alone, through estimation and flattening of the Fisher information matrix. By exploring the information geometry of the likelihood, we characterize degeneracies as an intrinsic property of the physical model, requiring no realised data observation. We demonstrate our approach on a range of synthetic and real-world problems, discovering symbolic coordinate transformations that identify the combinations of parameters of a model which yield independent effects on the data. The resulting coordinates flatten the Fisher information in expectation globally, in contrast to posterior-based methods that flatten only at a single point, and substantially reduce the simulation budget required for downstream neural posterior estimation. In test cases we require up to $10\times$ fewer simulations for posterior estimation at matched validation calibration whilst simultaneously gaining physical insight on the system.