Science & Mathematics

Quadrotor trajectory tracking under unmodeled disturbances often relies on online residual adaptation, but short out-domain residuals can corrupt the learned disturbance model when constant-step updates treat every residual gradient uniformly. We propose Dual Gradient Consensus (DGC), an adaptive-learning method for mixed in-domain/out-domain disturbances that retains the random Fourier feature model, offline BPTT policy, and least-squares adaptation of a prior domain-adaptive residual policy (DAPL) while modifying the online update step size. DGC compares each residual gradient with long- and short-term gradient memories, classifies the current adaptation regime, and uses a confidence map to suppress unreliable updates while recovering adaptation after persistent domain shifts. We evaluate DGC in numerical quadrotor trajectory tracking under four residuals that mix an in-domain component with short out-domain events. Compared with $L_1$-augmented MPC, RFF-based MPC, constant-step DAPL, and a frozen-parameter baseline, DGC achieves the lowest mean position RMSE in all four cases.

Autonomous agents have been observed acting beyond their assigned tasks, accessing unauthorized systems, and establishing communication channels to exchange information, yet the Web and network-level techniques they use to extend their capabilities and circumvent security restrictions remain poorly understood. We study these techniques through the ProWiki incident, in which agents restricted to outbound HTTP GET requests repurposed a public German-language wiki as a message board. We analyze 14,591 agent edits containing 79,541 URL postings and present corroborating evidence that the published URLs reflect the agents' operational activity. We find that 26,717 URL occurrences (33.6%) embed target URLs within one to five layers of third-party Web services. By recursively reconstructing these nested URLs, we identify 67 distinct intermediate services and classify their functionality. Most intermediate layers (73.8%) extend agents' capabilities by delegating content extraction and transformation to external Web services: Markdown and OCR services convert web content into machine-readable text, JSON filtering services extract selected fields, and archival services expose historical versions of pages. The remaining 26.2% facilitate circumvention of access restrictions and evasion of detection, including CORS and fetch proxies that retrieve content on agents' behalf, and link shorteners and redirectors that hide destination URLs from mechanisms inspecting literal URLs or outer hostnames. Agents also reach the same targets through multiple URL paths, consistent with attempts to evade rate limits or obscure request origins. Our results expose a gap between the capabilities granted to agents and those they can obtain by composing publicly available Web services: restricting an agent's local toolset or direct Internet access may be insufficient while third-party services remain reachable.

Two-dimensional metal-organic porous networks (2DMOPNs) on metal surfaces provide a versatile platform for exploring emergent electronic and magnetic phenomena in designed surface nanostructures. While the porous architecture is governed by coordination between molecular building blocks and metal centers, most 2DMOPNs utilize only one type of coordination site, leaving the impact of multiple coordination sites largely unexplored. We address this question by investigating the structural formation of a Co-coordinated 2DMOPN on Ag(111) with the linker molecule hexaazatriphenylene-hexacarbonitrile (HATCN), which has two chemically distinct nitrogen coordination sites at the peripheral nitrile groups and pyrazine-type core nitrogen atoms. Scanning tunneling microscopy (STM) reveals the transformation from a simple honeycomb HATCN structure to a Co-coordinated porous network with three structurally and electronically inequivalent molecules in a 6:3:1 ratio. The existence of two distinct coordination sites leads to selective Co coordination geometries for all three molecules, accompanied by site-specific charge transfer from Co into the former lowest unoccupied molecular orbital (LUMO), as revealed by momentum-resolved photoemission and density functional theory. Our results demonstrate that site-selective Co coordination not only controls the overall architecture of the porous network structure but also strongly influences the local electronic properties through site-specific metal-molecule interaction, providing a route to tailor the site-specific electronic structure of 2DMOPNs at the molecular level.

Kernel techniques are among the most powerful methods in data science and statistics. One of the key properties of kernels contributing to their numerous successful applications is that the associated reproducing kernel Hilbert space is expressive enough to encode probability distributions without loss of information or to capture the joint independence of $M\ge 2$ random variables, under mild conditions. Computationally, these measures (i) rely on the so-called Gram matrix which contains the pairwise similarity of sample points, and (ii) converge at a rate $O \left(n^{-\frac{1}{2}}\right)$, where $n$ denotes the sample size. We focus on measuring the independence of latent position random graphs (LPRGs), a model widely-applied for instance in neuroscience, sociology, and epidemiology. In LPRGs a latent representation is associated to each node. The similarity of these representations (meant via a kernel) determines whether two nodes are connected, making the Gram matrices only implicitly observable and the estimation challenging. Despite the fundamental importance of quantifying the independence of $M$ LPRGs, very little is known about the solution of this problem; existing techniques are restricted to $M=2$ components and only guarantee consistency without rates. In this work, (i) we define an independence measure called graph Hilbert-Schmidt independence criterion (GHSIC) for $M\ge 2$ LPRGs, (ii) we prove that it can be estimated at a rate $\tilde{O}\left(n^{-\frac{1}{3}}\right)$ relying on spectral decomposition of adjacency matrices, (iii) without the need to choose kernels and their hyperparameters. Numerical experiments demonstrate the effectiveness of the proposed GHSIC estimator both on synthetic examples and in the analysis of brain functional connectivity subnetworks in natural language perception.

Visual-token compression is usually evaluated by clean accuracy and efficiency, but these averages do not reveal failures that compression introduces under an image shift where the uncompressed model stays correct. We introduce VTC-AUDIT, which estimates this incremental risk only on pairs where the full model is correct on both images and the compressed model is correct on the clean image. The four arms then cross two binary choices: which image selects the retained token positions, and which image supplies the visual features. We audit three open 8-9B vision-language models on four tasks and eight pre-specified shifts. We evaluate two training-free compressors---hard-pruning DivPrune and prune-and-merge ApET---at a matched 25% retained-position budget, producing 708,000 inference records. Reselecting positions on the shifted image, rather than reusing the clean-image positions, raises the failure rate in all six model-compressor settings. The increase is 3.04-9.60 percentage points for DivPrune and 2.05-4.20 percentage points for ApET, with every 95% interval above zero. Repeating the audit on a separately resampled second manifest reproduces all six increases. In a pooled monitor audit across the four benchmarks, support Jaccard instability fails the practical AUROC criterion of 0.65 in all six settings, whereas clean compressed-model uncertainty clears it. Thus, support turnover is a weak ranking signal under the audited benchmark mixture, while clean compressed-model uncertainty is substantially more informative. These results suggest that future visual-token compression evaluations should report conditional reliability alongside clean accuracy and efficiency.

What does a recursive definition mean when the logic is grounded, so a sentence is true only if a terminating process makes it so? Kripke's answer for the special case of truth was the least fixed point. This paper takes that answer as a rule. Reflective Grounded Arithmetic (RGA) already writes any recursive definition as one self-referential term, paradoxes included. Inductive Grounded Arithmetic (IGA) adds the elimination rule for every positive one, so that accessibility, the winning positions of a game, and grounded truth itself each come with their own induction principle. The rule is sound for the omega model and the system is consistent, both machine-checked in Isabelle/HOL. With the rule, IGA proves Goodstein's theorem outright, in a logic without implication at an undecided hypothesis, and the Kirby-Paris hydra game for primitive recursive strategies, both with every step of the arithmetic a grounded derivation. It proves the Cantor normal forms well-founded, from which the well-foundedness of the standard $\varepsilon_0$ notation system in HOL follows, and it certifies the Veblen notation as an ordinal below every $\varphi(n,0)$. It defines Kripke truth for RGA's own language as one fixed point that agrees with the omega model exactly. Two equivalences locate what the classical world has and the grounded one does not. IGA proves the whole Veblen notation well-founded exactly when it admits bivalence of accessibility for that order, and bivalence of accessibility for an order is sound exactly when the order is well-founded; so $Γ_0$ lies at most one instance of excluded middle away, at the accessibility predicate of the notation, and that instance, the well-foundedness sentence and one membership claim in a primitive-recursive form of Kleene's $\mathcal O$ are interderivable over IGA.

Language models for metal-organic frameworks (MOFs) rely on formats that separate atomic geometry from structural topology, forcing models to choose between unstructured coordinate lists and non-spatial string identifiers[1]. We present MOFjson, the first representation separating structural data into a raw atomic layer with explicit bond shift vectors and a derived layer exposing secondary building units (metal nodes and organic linkers) and network topology. Additionally, we introduce a benchmark with crystal-derived ground truth across four question categories. Across four models, MOFjson beats all three baselines in every category: 100% vs. 18-47% on reaching a block's nearest periodic copy, 96% vs. 71% on crystal system characterisation, and 60% vs. 48% on metal node and organic linker coordination. Ablating shift labels drops accuracy to 12.7%, proving models read the periodic graph rather than the surface format. MOFjson gives language models structure to read rather than reconstruct, establishing a foundation for agentic tool workflows and constrained MOF generation.

Foundation models provide powerful representations for unstructured data, such as text and images, and parameter-efficient fine-tuning (PEFT) makes their adaptation to downstream tasks increasingly practical. For neural estimators that lack a tractable sampling distribution, resampling-based procedures offer a flexible route to statistical inference, but they often require hundreds of model fits, making them computationally prohibitive at foundation-model scale. We introduce HIFI, a two-stage fine-tuning framework for statistical inference on parameters such as conditional means. Stage 1 adapts a foundation model once on a larger sample, capturing the complex structure of the data and controlling estimation bias through a single fit. Stage 2 applies a resampling inference procedure to a smaller independent sample, concurrently fitting multiple lightweight PEFT estimators to the residual to quantify estimation variability without relearning the full task. HIFI accommodates a broad class of resampling procedures, including ensemble subsampling and the nonparametric bootstrap. Across vision and text experiments, HIFI scales to pretrained models ranging from tens of millions to more than ten billion parameters while providing accurate point estimates and well-calibrated confidence intervals across diverse architectures, and reduces training compute by up to 91.9% relative to direct resampling. An application to gene-expression inference illustrates the practical value of the framework for uncertainty-aware scientific inference.

Machine learning interatomic potentials enable atomistic simulations with near \textit{ab initio} accuracy over large length and time scales. Foundation models extend this capability across the periodic table but inherit the thermodynamic description of the electronic structure methods used to generate their training data. Small errors in relative phase stability can therefore produce large errors in transformation temperatures. We introduce an additive thermodynamic correction layer that shifts phase free energies towards an assessed reference without retraining or modifying the base potential. A first order thermodynamic construction converts the required phase free energy shifts directly into configuration energy targets, which are fitted using a linear atomic cluster expansion and refined iteratively from measured free energies. We apply the method to melting and solid to solid transformations across elements with different crystal structures using a foundation GRACE model. After the correction, all transformation temperatures lie within the prescribed tolerance of the assessed values, including Ca, Ti, and Zr, where a solid to solid transition and melting are corrected together. Static energy curves, bulk moduli, and liquid structure remain close to those of the base model. Vacancy formation energies, thermal expansion, and liquid density depend on the corrected phase balance and change where the correction is large. The method requires neither retraining, differentiable dynamics, nor access to the parameters of the base potential. It provides a modular route for combining transferable atomistic models with assessed phase thermodynamics.

How efficiently can transformers store factual knowledge? The answer to this question has implications for both model design and understanding the limits of transformer-based systems. Prior studies observe a linear relationship between the number of facts memorized and the number of model parameters required, substantially worse than what theoretical analyses predict is achievable. We re-examine empirical scaling: through rigorous and systematic experiments, including extensive hyperparameter search via Bayesian optimization, we determine the smallest model that can perfectly memorize a given set of facts, and measure how this minimum size scales with the number of facts. On synthetic datasets of random, independent (subject, relation, object) triples---e.g., (Paris, capital_of, France) ---drawn at random with no exploitable structure, we find that memorization capacity, the size of the largest dataset that a model memorizes completely, grows exponentially with the transformer dimension. Equivalently, the minimum transformer dimension $d_{\min}$ required to memorize $N$ facts grows logarithmically in $N$. Across 11 dataset sizes spanning $N = 45$ to $49{,}920$, a lack-of-fit F-test does not reject the logarithmic fit (with an offset), but it does reject all other tested alternatives including power-law. Along the depth axis, however, at fixed width, the maximum memorizable dataset size grows sublinearly with the number of layers over the measured range. We further extend our exploration to structured data containing symmetric relations or two-hop composition. In this setting, we find that transformers exploit these regularities to further improve capacity. All code to reproduce our results is available at https://github.com/Magronox/transformer_information_capacity.

Artemis surface operations will depend on 3GPP cellular links, yet no public product shows where such links are physically possible across the lunar south pole. We present LunarRF, a GPU system for terrain-aware surface coverage, and the pole-wide atlas produced with it. A footprint engine casts 8192 radial profiles from one of 11,827 candidate masts enumerated by stated rules on the orbit-adjusted LOLA elevation model, takes the viewshed, and evaluates ITU-R P.1812 Delta-Bullington propagation on every profile, continuous through the radio horizon. An order-independent resolver merges the footprints per 20 m cell, making the run shardable and resumable. The atlas covers the disc south of 80°S at 20 m for four SFCG-recommended surface bands and the IM-2 demonstration band, 1.8 to 25.375 GHz, under a stated link budget, storing per cell the best-server power and identity, redundancy count, line of sight and coverability. The engine is validated against a parabolic-equation solver, ray tracing and analytic solutions. Swapping Deygout for Delta-Bullington, or adding terrain noise at the level of the published height-error map of the DEM, moves the coverable class on under 1% of a mast's disc in the mean. With every candidate active, 90.5% of the disc is coverable at 1.8 GHz, 59% at 5.855 GHz and 10% at 25.375 GHz, or 84, 43 and 5% after the measured 3-4 dB engine optimism. A mast covers about 90% of its visible area within its budget-set range, and no band is terrain-limited. The nine current Artemis regions are 85-99% coverable at 1.8 GHz and 22-85% at 5.855 GHz. The atlas and candidate table are released with a DOI.

Let $\mathcal O_K$ be the ring of integers of a number field $K$. A finite subset $\mathcal H=\{η_1,\ldots,η_k\}\subset\mathcal O_K$ is said to be \emph{admissible} if for every prime ideal $\mathfrak p$ in $\mathcal O_K$, the reductions of the $η_i$ modulo $\mathfrak p$ do not represent every residue class. The diameter of a finite subset $S$ of $\mathcal O_K$ is defined to be \[\mathrm{diam}(S):= \max_{η_i,η_j\in S:η_i\neqη_j}|\mathcal N(η_i-η_j)|\] where $\mathcal N$ denotes the norm down to the rational field. This paper computationally investigates admissible subsets of rings of integers in imaginary quadratic fields of class number 1 (such as the Gaussian integers or the Eisenstein integers) that are large relative to their diameter. The motivation is twofold. Firstly, there is the improvement of results analogous to the question of an upper bound for the least gap between large rational primes, which has been one of the great number theoretic successes of the twenty-first century. A second motivation is that there is the opportunity to disprove a variation of the second Hardy-Littlewood conjecture. The calculations in the paper provide new records on the smallest distance between primes in the fields in question, and explicit counter-examples to a generalisation of the second Hardy-Littlewood conjecture in all bar one of the fields.

Many-query applications such as design optimization, uncertainty quantification and digital twins call for repeated full-field predictions from expensive partial differential equation (PDE) simulations. Grassmannian reduced-order models interpolate parameter-dependent subspaces but commonly vectorize the spatial field, and the ambient dimension then grows with the product of the grid sizes. Tensor-based models preserve the multiway structure but often use shared mode-wise bases or a fixed core across parameters. We propose a Tucker-based surrogate that keeps the spatial directions and time as separate modes. The factor subspaces are interpolated on a product Grassmann manifold, Procrustes alignment places the Tucker cores in one coordinate system, and a truncated singular value decomposition models their variation. Across five PDE benchmarks in two and three spatial dimensions, including public computational fluid dynamics data, the interpolation size is reduced by factors of 13 to 482 and the stored model by factors of 13 to 464 relative to a single-subspace Grassmannian surrogate with the same local interpolation. Cached queries run 3.3 to 8.5 times faster, the mean errors over ten resampled splits differ by at most 0.22 percentage points (0.36 when every model choice is re-selected inside each split), and the prediction-error terms of the two methods differ by less than 0.1 percentage points. The remaining accuracy differences are consistent with the larger representation error of the Tucker format. In a three-dimensional grid study the interpolation-size ratio rises to 2,260 and the query speedup to 11.9 at 64^3.

Stateful cloud workloads require high-performance persistent storage when running on untrusted cloud infrastructure. Confidential Virtual Machines (CVMs) promise to protect these workloads through hardware-enforced memory encryption and isolation without requiring application changes. However, they protect only data in use; persistent storage lies outside the CVM trust boundary, exposing all stateful data to the cloud provider. Extending the trust boundary to persistent storage presents inherent challenges. High-bandwidth workloads require near-raw NVMe throughput, yet the default kernel CVM I/O stacks are inadequate, and userspace I/O libraries are not designed with CVM use cases in mind. Access patterns and storage semantics vary between workloads, necessitating access-pattern-aware security abstractions rather than uniform block-level encryption. In order to mitigate against rollback, freshness is needed, but CVMs lack hardware primitives for this purpose, requiring alternative solutions. We present CVM-Store, a storage system that co-designs a high-throughput userspace I/O engine with CIF (confidentiality, integrity, freshness) data protection. The key insight is that neither authenticated encryption nor I/O is a bottleneck by itself, but their naive combination is. CVM-Store exploits this by interleaving them, eliminating redundant copies and OS/hypervisor mediation. CIF guarantees are provided as composable primitives that adapt protection to workload access patterns, from which we derive three concrete authenticated abstractions: a KVS, a log, and a filesystem. An asynchronous trusted counter service provides freshness guarantees with epoch-based batching, which enables rollback protection without dedicated hardware support. CVM-Store delivers full CIF guarantees within $\approx$1% (write) and 1-19% (read) of raw NVMe bandwidth for large objects.

Adapting general-purpose vision-language models (VLMs) to medical visual question answering (VQA) is valuable for helping clinicians read images and make diagnoses, but annotated data are scarce and provide only short answers, without reasoning annotations. Supervised fine-tuning (SFT) fits these labels but overfits to them and amplifies their biases, eroding out-of-domain (OOD) generalization. Reinforcement learning (RL) better preserves generalization but never uses the gold answer as a training target: GRPO-style algorithms learn from the contrast between correct and incorrect answers within a group of sampled responses, so all-correct or all-wrong groups give no correctness signal. Existing SFT-RL hybrids either apply SFT and RL in separate stages or switch between them per question, or need reasoning traces from experts or stronger models, which medical VQA data lack. We propose GRASP, which combines RL and SFT in every update using only short answers: RL lets the model explore its own reasoning, SFT teaches the gold answer after that reasoning to supply the direct supervision RL lacks, and their balance adapts to how well the model answers each question. Tuning only about 1% of the parameters with LoRA, GRASP outperforms all compared training objectives both in domain and on OOD open-ended questions across Qwen3-VL-8B, InternVL3-8B and Gemma 3-4B. On an OOD benchmark spanning eight imaging modalities, GRASP-trained InternVL3-8B and Qwen3-VL-8B beat all 10 compared general and medical VLMs in open-ended accuracy, including models trained on up to 2,600 times more data or with over 250 times more trainable parameters. We release MedTerse, a dataset of 12.9K short-answer questions, and our code at https://github.com/sea-comet/GRASP-MedVQA.