Papers

Europe is warming faster than the global mean, yet the spatial organisation of this acceleration remains incompletely understood. Using ERA5 reanalysis for 1950–2024 across 28 IPCC AR6 European sub-regions, we identify two connected empirical results. First, the DFA1 Hurst exponent of interannual temperature residuals is strongly and negatively associated with the 1996–2024 warming rate ($r=-0.792$, $p=5.1\times10^{-7}$). High-persistence, mainly Atlantic-proximal regions warm more slowly, whereas low-persistence continental regions warm faster. This relationship is robust to five residualisation schemes, three memory estimators, leave-one-region-out analysis, and five null-test families, including spatial block permutation. It also persists across warming windows ($r=-0.550$ for 1981–2024, $-0.792$ for 1996–2024, and $-0.875$ for 2000–2024), but vanishes under DFA2, indicating that the signal lies in low-frequency interannual-to-decadal persistence rather than trend curvature. The pattern is consistent with, but does not prove, North Atlantic cold-blob and thermohaline influence on European land temperatures. Second, under a strict 2006–2024 holdout, contemporaneous Mediterranean SST reduces mean annual temperature RMSE by 43% (from $0.787$ to $0.449,^{\circ}\mathrm{C}$). A causal lag-weight predictor based on prior-year Mediterranean and Atlantic SST also outperforms AR(2) ($0.578$ versus $0.695,^{\circ}\mathrm{C}$) and remains informative after removing NAO, AO, and PNA effects. Similar skill from five-year moving-average and exponentially weighted predictors shows that short Mediterranean SST persistence at 1–5-year lags is the key predictive ingredient. Together, the results support a two-regime interpretation: Atlantic-proximal regions exhibit stronger memory and oceanic buffering, while continental interiors show faster warming and weaker interannual persistence.

Understanding how computational effort is allocated across individual chain-of-thought (CoT) reasoning steps remains an open challenge: existing interpretability methods rely on output-level signals or collapse processing depth into a single trajectory-level scalar, leaving step-wise effort opaque. We propose Step-Aware Reasoning Energy (SARE), a geometric framework that quantifies effort at the granularity of individual CoT steps via Centered Kernel Alignment (CKA) between Gram matrices of token hidden states across adjacent transformer layers, capturing inter-token relational structure without requiring eigenvector alignment or cluster correspondence. SARE further contextualizes this energy within reasoning's semantic progression by modeling CoT trajectories as transitions among latent semantic states. Across six reasoning benchmarks and three open-weight LLMs, we find that reasoning energy is highly non-uniform across step types, exhibiting phase-like transitions invisible to trajectory-level metrics; incorrect trajectories show systematically lower energy at critical reasoning junctions; and SARE-based features match or outperform output-based confidence baselines in most settings, indicating that internal geometric dynamics encode predictive information beyond surface-level signals.

Neural networks increasingly combine data across populations, time periods, and operating conditions to improve generalization. This raises a reliability question: whether a model refitted on pooled data preserves an action ordering supported by both sources. Case-Based Decision Theory (CBDT) formalizes this requirement through its composition axiom, which requires source-supported preferences to survive their union. We study when this property holds for fixed-representation neural networks with ordinary least squares (OLS) output heads. First, we show that pooled refitting recomputes the inverse-Gram geometry used to weight source evidence, which can reverse shared preferences, and derive exact and approximate preservation conditions. Next, we introduce a scale-invariant Gram mismatch measure for prioritizing candidate pools and geometry-oriented regularization for shaping source geometry during training. Finally, we develop a three-stage audit that traces strict pairwise reversals through decision changes to task-defined utility loss. Experiments spanning a load-based bidding proxy and medical and financial decision proxies reveal stable and reversal-prone pooling regimes: the load audit identifies a measurable nonzero class of source-consensus-relative harmful decisions under the proxy utility, while cross-domain audits show that comparable mismatch can correspond to sharply different preservation rates. Geometry-oriented objectives occupy distinct descriptive accuracy-consistency-geometry-harm operating points. Together, the framework makes compositional reliability measurable and operational through screening, analytic certification, geometry-oriented training, and decision-consequence auditing.

Transformer-based surrogate models are increasingly used to replace expensive first-principles simulation in engineering design. But conventional transformer architectures are often over parameterized for the small, low-dimensional datasets typical of engineering design spaces, where large simulation data is expensive to generate. Under these conditions, excess parameter capacity leads to overfitting rather than improved accuracy, while also incurring unnecessary memory and compute overhead. This motivates a shift towards architectures that focus on additional compute rather than additional learnable parameters. This paper presents a hardware-aware evaluation of three recursive transformer paradigms for surrogate thermo-mechanical analysis of advanced packages: a)Tiny Recursive Model, b) our proposed Depth Recursive transformer, c) and a simple recursive transformer. We systematically compare their predictive performance (Recall, Mean Reciprocal Rank), parameter count, computational complexity (FLOPs), providing practical design guidelines for selecting recursive transformer architectures under resource-constrained scenarios. We validate this principle on two low-dimensional engineering prediction tasks: 1) thermo-mechanical reliability analysis of advanced semiconductor packages, where stress and warpage from thermal cycling must be evaluated repeatedly across a design-of-experiments sweep under costly finite element analysis (FEA). 2) Laplace PDE iterative numerical solver for capacitance field. Overall, recursive weight-sharing transformers provide an effective and generalizable trade-off between prediction accuracy, parameter efficiency, and computational cost for small data engineering surrogate modeling.

While large language models excel in reasoning, these generalists often lack knowledge for specialized scientific domains. Conversely, domain models~(specialists), while knowledgeable, suffer from specialization side-effects including diminished logic and reduced robustness.To address this dilemma, we introduce Divergence Decoding, a training-free framework for capability fusion. It reconstructs the "draft-and-verify" skeleton of speculative decoding into an adaptive routing mechanism. The core is using Jensen-Shannon divergence to monitor the distributional disagreement between the two models at each token. When the specialist exhibits significant divergence, our method identifies it as a potential reasoning risk and instantaneously routes control to the generalist. This allows the dynamic injection of general reasoning while preserving domain expertise, achieving inference-time policy composition of the generalist and the specialist.We evaluate Divergence Decoding across diverse model families (Qwen and Llama series) on challenging scientific benchmarks (GPQA, ChemBench, and ChemCoTBench). Experimental results demonstrate that Divergence Decoding outperforms both the domain-specialized and general-purpose models, effectively surpassing the performance of most single-model baseline. This suggests that Divergence Decoding provides a general, training-free paradigm for fusing diverse LLM capabilities through adaptive inference-time collaboration.

Modeling and forecasting nonlinear dynamics under distribution shifts is essential for robust decision-making in real-world systems. In this work, we propose MetaKoopman, a Bayesian meta-learning framework for modeling nonlinear dynamics through linear latent representations. MetaKoopman learns a Matrix Normal-Inverse Wishart (MNIW) prior over the Koopman operator, enabling closed-form Bayesian updates conditioned on recent trajectory segments. Moreover, it provides a closed-form posterior predictive distribution over future state trajectories, capturing both epistemic and aleatoric uncertainty in the learned dynamics. We evaluate MetaKoopman on a full-scale autonomous truck and trailer system across a wide range of adverse winter scenarios, including snow, ice, and mixed-friction conditions, as well as in simulated control tasks with diverse distribution shifts. MetaKoopman consistently outperforms prior approaches in multi-step prediction accuracy, uncertainty calibration, and robustness to distributional shifts. Field experiments further demonstrate its effectiveness in dynamically feasible motion planning, particularly during evasive maneuvers and operation at the limits of traction. Project website: https://mahmoud-selim.github.io/MetaKoopman/

A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit. It cannot do otherwise: message passing is exactly permutation equivariant, so any automorphism of the input leaves every attribution invariant. Yet the standard report, the top-k edges, names one of the two, and which one is settled by the order of an array. We show this is a structural obstruction rather than an implementation slip. When no minimal valid explanation is fixed by the input's automorphism group, no rule can be single-valued, minimal and symmetry-respecting at once. For the exact-k reports used in practice we give a parameter-free criterion, mechanised in Lean 4 with no axiom dependencies, that decides from the graph alone whether every score-optimal report of that size must split an orbit. Across 21298 instance-budget decisions the criterion agrees with a mechanical model-equivalence check without exception, and no severing case we found admitted a neutral alternative. The obstruction is common. Nontrivial automorphisms occur in 93.4% of Mutagenicity, the dataset the seminal explainability papers use, so the measure-zero dismissal of symmetric inputs, sound on the continuous domains it was made for, collapses here. At the sparsity budget those papers report, 24.0% of molecules with two interchangeable nitro groups (6 of 25) surface exactly one of them, every one arbitrary under mechanical verification. A model's blindness also manufactures symmetry: every MUTAG molecule contains atoms chemistry separates and the network provably cannot, and a matched control shows the resolution is set by what the model reads rather than how it is parameterised. Reporting orbits removes the arbitrariness at 0.11 ms and 0.43 extra edges per graph.

Mixture of Experts (MoE) architectures have become key to large language models; however, their typical round-robin (RR) scheduling introduces significant bottlenecks. In this paper, we demonstrate that RR causes a previously-undiscovered exponential incast phenomenon with MoE traffic. We propose an alternative proactive fair scheduling framework tailored for MoE workloads, which effectively prevents fabric oversubscription. We also outline how it can be implemented in NICs. Finally, through extensive simulations with real and synthetic workloads, we demonstrate that this framework consistently eliminates incast, maintains a near-100% link utilization, and reduces Collective Completion Time (CCT).

Retrieval-Augmented Generation (RAG) systems ground large language models (LLMs) in external corpora, but this reliance exposes them to corpus poisoning: maliciously injected passages that manipulate retrieved evidence. We introduce RAGuard, a layered defense against factual corpus-poisoning attacks on RAG pipelines. The first layer adversarially fine-tunes a dense retriever on synthetic poisoned documents (fabricated facts, contradictions, and reasoning traps), teaching it to downrank malicious passages before generation. The second layer, the Zero-Knowledge Inference Patch ZKIP, is a label-free, black-box filter: for each retrieved document, it performs a leave-one-out decode and scores the document by the semantic shift and output-entropy change that its removal induces. ZKIP requires no poison labels, no ground-truth answers, and no access to model internals; it compares the model's own answers under counterfactual contexts. On poisoned Natural Questions at 5–30% poison ratios, adversarial retriever training alone reduces but does not eliminate attack success, while ZKIP drives the measured attack success rate to 0.000 in every defended configuration, keeping Recall@5 within 0.03 of the clean-corpus baseline. Supervised analyses on both Natural Questions and BEIR (NFCorpus) confirm that the counterfactual signals ZKIP relies on carry learnable poison structure. The defense costs $k{+}1$ generator passes per query ($6\times$ for $k{=}5$); we analyze batching and early-stopping approximations that reduce this overhead. We also show that keyword-preserving poisons leave lexical retrievers such as BM25 essentially unaffected, an observation that delineates the boundary of the threat model. Code, datasets, and evaluation harnesses are released for reproducibility.

In model-based reinforcement learning, world models exist as internal simulators, but their training often conflates statistical correlations with causal mechanisms. This problem is exacerbated in multi-agent systems where physical transitions are intertwined with strategic agent intents, causing world models to fail under distribution shift. We introduce Implicit Causal World Models to recover environmental dynamics from offline demonstrations without requiring pre-defined causal graphs. By incorporating policy variance, we render world models discoverable via the sequential backdoor condition. Evaluations across coordination tasks (Two-Door, Navigation, and Giveway) demonstrate that these models provide interpretable causal representations under both full and partial observability, with model accuracy scaling directly with interventional strength.

Chest X-ray (CXR) machine learning relies heavily on automated evaluation using reference standards that aim to approximate clinical judgment. However, commonly used report-derived labels for pathology classification or generic image quality metrics for reconstruction may not reliably reflect clinical judgment. We systematically investigate how evaluation-reference choices affect model performance and ranking in both pathology classification and image quality assessment (IQA). To enable controlled comparison across evaluation references, we collected paired expert image- and report-derived labels for thoracic findings from a clinical cohort at Cambridge University Hospitals (CUH) and curated a subset of the public MIMIC-CXR dataset, along with expert ratings of diagnostic image quality. We show that for supervised image classifiers (ResNet, DenseNet), several zero-shot and fine-tuned vision-language models (e.g., MedKLIP, GLoRIA, and ConVIRT), changing the label source leads to substantial differences not only in performance estimates but also in model rankings. In parallel, alignment of IQA measures with expert judgment depends heavily on the choice of measure, and commonly used IQA metrics such as SSIM and PSNR often fail to align with expert assessments of diagnostic usability. Our results demonstrate that evaluation choices are crucial: they can determine which models and methods appear best and are therefore selected for further development or deployment. The selection of evaluation references should therefore be treated as a central component of clinical validity in CXR machine learning, and justified with respect to the pathology, imaging task, and intended downstream clinical use.

We built and evaluated a self-serve entity resolution (ER) system on six benchmarks spanning 864 to 5M records, and three lessons emerged that are absent from existing ER literature. (1) No single matching algorithm wins everywhere - a self-serve pipeline cannot predict its next dataset, so we recommend training several algorithm families per dataset and letting an automatic bake-off pick the winner. (2) Precision and recall need separate fixes, not a shared threshold - precision needs hard rule-based vetoes, recall needs more diverse candidate retrieval. (3) One false-positive link can silently merge unrelated entities - assuming "A matches B" and "B matches C" implies "A matches C" lets a single bad link chain hundreds of records together, so every cross-group merge must be actively re-verified. We hope these lessons save practitioners the months of dead-end experiments that led us to them.

Two central challenges in diffusion-based sampling are the theoretical one of understanding their remarkable effectiveness even in high-dimensional settings, and the practical one of designing algorithms with certified performance guarantees. We show that these questions are intimately connected via the denoising growth complexity ($\mathsf{DGC}$). It is a geometric measure defined by a log-time weighted integral of the derivative of the denoising mean-squared error along the Gaussian heat flow. We show how the $\mathsf{DGC}$ increments lead to a simple and explicit bound on the KL error of an Euler scheme applied to the stochastic innovations representation. The bound is local along the path: each step is controlled by the corresponding $\mathsf{DGC}$ increment and its relative stepsize. This structure allows us to derive KL sampling guarantees for optimized stepsize schedules, both in a simpler single-block setting and in a more refined $K$-block setting. The $\mathsf{DGC}$ function has a natural martingale structure, which we exploit to develop fully data-certified versions of these algorithms. It also admits information-theoretic upper bounds in terms of covariance, rate distortion, metric entropy, and the Poincar'e constant, thereby recovering and sharpening a range of existing diffusion-sampling guarantees, as well as giving new results. In log heat-time, the fine partition limit is governed by an integral involving the square root of the $\mathsf{DGC}$ density, whereas a single-block schedule depends on its ordinary integral. This comparison precisely characterizes when adaptation to data geometry yields substantial computational gains, including logarithmic-to-constant separations for simple Gaussian mixture models.

It is common for two-dimensional embeddings of high-dimensional data to be read far beyond what they can support. Distances in and between clusters, the meaning behind empty spaces, and the amount of structure hidden at each point are generally invisible in the output of methods such as t-SNE and UMAP. This is because the information that could support the meaning of these properties is discarded during the optimisation process. Here, we present FloDR, a dimensionality reduction method that embeds data through an invertible normalising flow. While FloDR only uses the first two output coordinates to create a two-dimensional embedding, it retains the remaining coordinates rather than discarding them. In addition to the embedding, an exact inverse and an exact density are properties of a trained mapping, which enable diagnostic visualisations that are computed from the exact inverse of the model that drew the layout rather than from an approximate one. Specifically, we draw two fields, the conditional spread, which measures how much of the original data remains undetermined at each embedding position in input units, and the hidden contrast, which measures how much information about a labelled contrast the two plotted coordinates discard. Both fields are rendered with a prespecified test against a held out portion of the input data and a bootstrap confidence. A field that fails the test is reported as refused.

We consider a stochastic multi-objective bandit problem where, at each round, the agent selects a slate of $k$ arms and observes their $d$-dimensional reward vectors under semi-bandit feedback. We do not aim at identifying a single optimal arm; instead, we consider the problem of maintaining a small set of actions that jointly approximate the Pareto frontier. We formalize this objective through the dominated hypervolume induced by the selected subset of arms, and define an $\alpha$-approximate hypervolume regret with respect to the best size-$k$ subset achievable in hindsight, where $\alpha = 1 - 1/e$ reflects the approximation guarantee of greedy maximization for monotone submodular functions. To address this problem, we introduce THV-UCB, an optimistic algorithm that selects arms greedily based on optimistic estimates of their marginal hypervolume contributions. We establish a gap-free regret bound $\tilde{O}(d\sqrt{nkT})$ that holds on every instance, together with a gap-dependent bound $\tilde{O}(nk^{2.5}/\Delta_{\min})$ that becomes polylogarithmic in $T$ once the arms are sufficiently well separated. Our results provide theoretical support for using small subsets to approximate Pareto fronts in various multi-objective applications.

Reinforcement learning with verifiable rewards (RLVR) is bottlenecked by rollout generation, yet many sampled prompts produce saturated groups (all responses correct or all incorrect) whose zero reward variance yields no policy-gradient signal. Existing remedies either oversample a larger candidate pool and discard saturated prompts (dynamic sampling), paying heavy extra rollouts, or predict prompt difficulty before sampling, which is fragile under a shifting policy. We observe that a group's effectiveness is usually decided early, within the first few of its rollouts, so spending a full group on an already-decided prompt is wasteful. We cast per-step rollout collection as a budget-constrained sequential allocation (optimal stopping) problem and introduce SARA (Sequential Adaptive Rollout Allocation). SARA maintains a Beta posterior over each prompt's success rate, evaluates a closed-form predictor of group effectiveness, and applies a two-threshold, SPRT-style rule that commits effective groups, abandons saturated ones after a short probe, and reallocates the freed budget to fresh prompts, without any extra prediction rollouts. We prove abandonment reliability, expected rollout savings, fixed-budget yield dominance, and a link between effective-group yield and the GRPO gradient norm. On mathematical reasoning and planning with 1.5B/3B models on a single GPU, SARA matches DPS (both below the DS oracle) while using 22% fewer rollouts than DS; composing SARA with DPS yields the best accuracy, slightly above DS, at 67% fewer rollouts (near-uniform cost).

Low-rank adaptation (LoRA) fine-tunes large pretrained models at a fraction of the cost of full fine-tuning, but its performance depends strongly on how the adapters are initialized. Recent schemes initialize the adapters from the downstream loss gradient: some project the raw gradient onto its top directions, while others first whiten it with an estimate of the loss curvature. We show that these seemingly distinct methods are points on a single continuum: a two-parameter family of preconditioned gradient initializations, which we call Unified LoRA (ULoRA), governed by a spectral whitening exponent and an Adam-like diagonal exponent. Sweeping this family under a full learning-rate search, we find that no single fixed preconditioning strength dominates: the best operating point is task-dependent and frequently lies strictly inside the family, away from the published endpoints. Treated as an upper bound of this family, a tuned ULoRA configuration matches or exceeds full fine-tuning on all five GLUE tasks with RoBERTa-base and is competitive with the strongest baselines on GSM8K with LLaMA-2-7B. Our deployable, search-free variant, ULoRA-Auto, selects per-layer exponents from measured spectral statistics, approaches this upper bound at no additional search cost, and ranks at or near the top among deployable LoRA methods. Our results show that a principled design space for LoRA initialization and curvature preconditioning should be treated as a tunable dimension rather than a fixed design decision.

On-policy distillation (OPD), which aligns a student with the teacher's token-level distribution on the student's own rollouts, is an effective paradigm for transferring capabilities across LLMs. Prevailing approaches assume a teacher at least as capable as the student: they either distill a larger model into a smaller one, which fails at the frontier where no larger teacher exists, or consolidate multiple domain experts trained from a shared base, which requires costly training at the student's scale. We introduce Weak-to-Strong On-Policy Distillation (W2S-OPD), a simple yet effective OPD framework that improves the strong student by distilling from multiple weak models. W2S-OPD constructs a proxy teacher in logit space from a contrast pair of a positive and a negative model, both smaller than the student and cheap to obtain. Their logit difference isolates the capability direction, which is added to the student's own base model, yielding a proxy teacher that couples this direction while staying distributionally adjacent to the student. The student then distills it by minimizing the per-token reverse KL on its own rollouts. We instantiate the contrast pair as i) a post-RL expert against its pre-RL initialization, isolating the skill RL instills, ii) a larger against a smaller base model, isolating the capability from scale, and iii) a small base model with correct versus wrong hints, isolating the instance-level direction toward the solution. Across four math and three code benchmarks, W2S-OPD outperforms OPD, enables the student to surpass the domain teacher, and keeps improving the student even when every supervision source is weaker. Analysis shows different contrasts yield distinct signals: the post-RL and hint contrasts emphasize reasoning frameworks, while the scale contrast emphasizes the solving procedure. Our code will be available at https://github.com/Yu-Fangxu/W2S-OPD.

The Word Problem has been a subject of intensive mathematical study for over a century, initially driving advances in combinatorial group theory and more recently emerging as a foundational hardness assumption in post-quantum cryptography (PQC). While generally undecidable, several families of infinite non-abelian groups exhibit solvable or algorithmically fast word problems, making them attractive platforms for cryptographic design. This paper introduces WPNet, a novel Graph Neural Network architecture capable of solving the Word Problem heuristically, which is demonstrated on the Baumslag-Solitar group $BS(1,2)$ and on an Artin group. By mapping unreduced words to dynamic graph structures, the model learns to cluster algebraically equivalent elements in a continuous embedding space, effectively identifying the geodesic representative of a word without executing discrete reduction steps. As an application, a model variant is developed that can predict the geodesic length of an unreduced word in both groups. To demonstrate the cryptographic severity of this structural leakage, WPNet is successfully deployed against the Wagner-Magyarik public-key cryptosystem.

We investigate lightweight raptor-species classification for real-time edge deployment in wind-turbine collision mitigation. Using DINOv2-L (304M parameters) as a teacher, we distilled three lightweight students (MobileNetV4, ViT-Small, and EfficientNet-B0). To reduce confusion between closely related species, we expanded the dataset to 12,519 images, including an increase in Steller's Sea Eagle images from 463 to 2,050 via video-frame extraction. Under a group split that separates samples at the video- and source-image level to mitigate source leakage at that granularity, the three-student ensemble achieved a macro recall of 0.935 +/- 0.004 over five distillation seeds (0.955 on a conventional image-level split, retaining 97.5% of the teacher's macro recall) with roughly one-eighth as many parameters. On a subset of 1,258 images disjoint from the former training images, White-tailed Eagle recall improved by up to 38.6 percentage points, while the rate at which it was misclassified as the Steller's Sea Eagle decreased from 61% to 15% of errors. TensorRT FP16 deployment of EfficientNet-B0 on an NVIDIA Jetson Orin Nano achieved 3.19 ms/image including host-device transfer (313 images/s), with 99.95% argmax agreement with FP32. In five-seed controlled comparisons, neither distillation (versus CE-only) nor the change from a DINOv2-L to a DINOv3-L teacher yielded a clear ensemble-level improvement; the primary gains stem from the dataset expansion and teacher re-fine-tuning.

Regression estimates from observational data can depend on specification under multicollinearity, while sequential sums of squares (SS) depend on term order. We introduce Retrospective Orthogonal Design (ROD), which reconstructs conditional mean surfaces on a probability-balanced lattice. ROD preserves observed cell means, completes unsupported cells, applies weighted tensor-product contrasts, and evaluates the reconstructed surface through piecewise-affine interpolation over Freudenthal polyhedra. Resolution and completion are selected jointly by validation among rank-admissible candidates, followed by refitting and evaluation on an untouched test set. For an admissible lattice, $\mathbf{X}^{\top}\mathbf{W}\mathbf{X}=c\mathbf{I}$, yielding specification-invariant contrast effects and unique, order-independent SS within the retained contrast space. Response-free projection calibration maps the fixed reconstruction onto a declared scientific basis and corrects finite-resolution recovery loss. Across 6,480 simulation conditions spanning nine data-generating processes, ROD matched or exceeded polynomial regression in five processes and performed strongest on threshold, sign-interaction, and localized surfaces. For the quadratic-interaction process, mean out-of-sample $R^2$ differed by only $0.0001$, while calibrated coefficient bias remained small across prespecified targets. A Rao-based information adjustment provides dependence-aware sample-size guidance for ROD planning. In a weighted Mincer application, ROD produced the highest out-of-sample $R^2$ point estimate, with substantial interval overlap with polynomial regression, and provided exhaustive SS allocations invariant to term-entry order.

The $k$-means++ algorithm is a standard and widely used seeding method for $k$-means clustering, but for a fixed number $k$ of centers its worst-case expected approximation ratio is $\Theta(\log k)$. We consider the same algorithm when an adversary first fixes the dataset and some $K$; the number of centers $k$ is then chosen uniformly from $\{K,\ldots,2K-1\}$. We prove that $k$-means++ is an $O(1)$-approximation with constant probability in this budget-smoothed setup.

Input-dependent controller coefficients are often treated as evidence of dynamic inference or computational savings. This interpretation conflates three properties: coefficient variation, dependence of a frozen model on how coefficients are assigned to inputs, and conditional execution. We focus on the second property and formulate a general principle of frozen-controller auditing. We provide one concrete implementation, Frozen-Controller Auditing (FCA), which caches the complete coefficient tensor along an unperturbed trajectory, disables the controller, and replays the frozen model with cross-input reassignment, token shuffling, and static profiles estimated from an independent calibration set. Because the coefficients are cached before any intervention, performance changes under replay measure assignment dependence without feedback from recomputing the controller on perturbed hidden states. Across seven independently trained 76M FeatureGate Transformers and three 504M models, static layerwise profiles retain 98.70% and 99.43% of the Correct-to-GlobalMean performance gap, respectively. Layer identity explains 87% to 96% of the coefficient variance. FeatureGate nevertheless executes every Transformer block, and its measured inference is 30.8% slower than Dense. On the public MUDDPythia-1.4B checkpoint, cross-input reassignment and token shuffling increase NLL by 1.9067 and 2.9637, respectively. These penalties show that the model depends strongly on content-conditioned cross-layer assignment. MUDDPythia also executes every Transformer block. The results show that dynamic parameterization alone does not establish dynamic inference and that functional dynamics do not establish computational savings. Claims about dynamic models should separately report coefficient variation, functional dependence of the frozen model, and actual execution.

Evaluation methodologies for language models increasingly combine multiple signals, from automated metrics and LLM-as-judge ratings to human assessments and benchmark suite results. When these signals are aggregated via averaging, evaluation confidence can then substantially exceed the reliability of the weakest signal: a phenomenon we call trust inflation in evaluation. We argue that evaluation scores should be treated as epistemic claims with three properties: formality (human evaluation provides stronger evidence than an automated metric), scope (a benchmark result applies to the tested distribution, not universally), and validity windows (benchmark results expire as contamination accumulates and distributions shift). Several converging research traditions (chain-of-thought analysis, possibilistic logic, and algebraic theory) establish weakest-link aggregation as the conservative endpoint of a parameterized operator family controlled by a single pessimism parameter. Drawing on those traditions, and on concrete lessons from building an evaluation harness for agentic AI, we propose that evaluation results carry explicit metadata (formality tier, scope declaration, and expiration date) to make their epistemic status transparent. We illustrate the cost of mean aggregation on the public HELM leaderboard: across 54 frontier models on ten scenarios, the top-five models ranked by mean score and by weakest-link are completely disjoint.

Alignment training, model organisms, and toy models are usually treated as separate research areas. But projects in all three frequently use supervised fine-tuning (SFT) to pursue the same underlying goals. When projects share a goal, we should test whether lessons learned from one area transfer to the other areas. We study three such transfers, each taking a lesson developed in one SFT setting and testing it in another. First, we port a lesson about behavior generalization from alignment training into toy models. Training on the reason for a behavior, as in Teaching Claude Why, can make the behavior generalize better than training on examples of the behavior alone. Second, we port a lesson about capability preservation from model organisms into the Model-Spec Midtraining alignment setting. SFT on outputs written by a model other than the student (off-model outputs) can damage capabilities when trained on. Mixing in benign on-model (and on-policy) data into our training can prevent most of this damage while still embedding the target behavior. Third, we port a lesson about robustness from model organisms into the same alignment setting. We find that follow-up benign SFT can erase the alignment behavior while preserving capabilities, showing that capability preservation alone does not ensure robustness to subsequent training. Our work illustrates how porting SFT lessons between different research fields can uplift them all, suggesting more researchers should borrow techniques from outside their own areas.

This study developed a hybrid computer vision method to quantify exposed skin from images for dermal exposure assessment. Using 170 indoor-painting images, Mask R-CNN first identified human subjects and removed background interference; a color-based algorithm then segmented exposed skin. The resulting exposed-skin-to-body pixel ratios showed approximately 80% agreement with human estimates. The approach demonstrates a scalable way to extract semi-quantitative exposure information from images, with future extensions to body-part recognition, PPE detection, and video-based exposure analysis.

Automated molecular structure elucidation from infrared (IR) spectroscopy data has seen significant advancements in recent years, but its broad applicability is limited by a reliance on pre-determined chemical formulas provided as auxiliary model inputs. This limits model predictions to isomer identification rather than full molecular structure prediction. Although transformer models have been shown to identify molecular isomers with high accuracy, their reliability for unconstrained structure elucidation is comparatively low and poorly understood. In this work, we propose and evaluate key modifications to the traditional encoder-decoder transformer. To better address the vast chemical space of the unconstrained problem, we implement a novel Mixture-of-Experts (MoE) decoder module that utilizes non-additive aggregation via linear-order statistics and the Choquet integral. We further modify the transformer to utilize these non-additive operators when aggregating spectral representations as well. Together with an auxiliary contrastive alignment loss term, these enhancements improve Top-K prediction accuracy by over 10 percentage points compared to baseline IR-only models. Through sub-structure fragment analysis of molecular predictions, we further confirm that infrared spectra encode the vast majority of relevant chemical information, implying that the higher performance of isomer-ranking models is largely due to underrepresented or overlapping absorption bands for molecules in the explored chemical space. Ultimately, by demonstrating the efficacy of automated molecular structure elucidation from measured IR spectra, this work serves to significantly broaden the utility of AI in analytical chemistry.

An AI benchmark result rarely reaches a consequential claim in one step. Evaluators generalize it to further cases, interpret it as evidence of capability, extrapolate it to new tasks, transport it to another system or site, and combine it with assumptions about human review and downstream consequences. Validity-centred approaches require evidence for each claim. This paper makes explicit and operationalizes a problem those approaches leave to the analyst: warranted links don't automatically make a warranted chain. The target of one study may not be the source of the next; system, population, outcome, or conditions may change at the interface; and shared data or model lineage may make apparently independent support dependent. Projectibility concerns whether a bounded extension from observed to unobserved cases is warranted. Goodman supplies the problem of rival extensions; argument-based validity supplies an architecture for testing them. The contribution is an interface audit for distributed AI evidence: typed source and target descriptions, and a procedure separating endpoints that never meet from endpoints that meet while warrant fails to cross. A legal-research case shows how benchmark evidence and a deployment study can each be sound while remaining parallel. A known-truth demonstration shows why aggregate stability can erase distinctions a later projection requires. The resulting projectibility audit diagnoses unsupported joins in benchmark-to-use arguments.

Self-repair - returning a failed program to the model together with its test output and asking for a correction - is a standard component of code agents, and is almost always evaluated against a baseline that does not retry at all. We argue that this comparison confounds the value of the feedback with the value of the extra attempt. Using a placebo-controlled design on MBPP+ at three model scales (1.5B, 3B, 7B), we compare four matched-budget retry conditions: blind resampling, a content-free failure notice, genuine execution feedback, and feedback augmented with verbal self-reflection. Blind resampling is the strongest condition below 7B, and remains statistically tied with the best condition at 7B, while consuming 2.5-5.5x fewer tokens; conditioning on the model's own failed attempt costs 6.1 points at 1.5B (p=0.006), and the informational content of execution feedback adds nothing measurable over the placebo. We attribute this to anchoring: when shown its previous attempt, a model reproduces a near-identical program in 33-68% of retries, against 2-14% under blind resampling. Two further experiments delimit the effect. Retrieved solutions to other tasks change nothing (bounded to +/-3.5 points), which localizes the harm to self-conditioning rather than context length; and reflection, the only condition that measurably weakens the anchor, remains dominated on cost. Replication rules out two competing explanations: the penalty is unchanged at full precision, and it reproduces on an independent model family. Across six configurations spanning two families and two precisions, its magnitude is predicted by baseline quality alone (r=0.96) - the cost of anchoring is the cost of committing to a bad first attempt.

We introduce GPT-Red, an automated red-teaming agent that is trained to discover novel prompt injection attacks against frontier LLMs. The goal of this model is to evaluate and improve the robustness of our production systems. To this end, we use it to adversarially train GPT-5.6, our most robust model to prompt injections to date. To create GPT-Red, we design a scalable self-play algorithm where the model is tasked with attacking a diverse population of simultaneously-trained defender agents. We train the model on realistic red-teaming environments using compute on the same scale as some of our largest RL post-training runs, making it the single-largest LLM safety training run ever documented. GPT-Red excels at red-teaming: it reliably breaks our past models up to GPT-5.5, it finds more successful attacks than human red-teamers, and it generalizes to held-out environments, defender models, and harnesses. In the future, we expect that as we improve the robustness of each new GPT model, it will in turn will provide better learning signal for even stronger red-teamer agents, thus unlocking a self-improvement flywheel.