Papers

We give a deterministic distributed algorithm for $(\Delta+1)$-coloring an $n$-node graph of maximum degree $\Delta$ in $O(\sqrt\Delta+\log^* n)$ rounds in both the LOCAL and CONGEST models. More generally, $(\deg+1)$-list coloring with lists from a color space of size $C\geq\Delta+1$ can be solved in $O(\sqrt\Delta\log(1+C/\Delta)+\log^* n)$ rounds; in CONGEST, we assume $C\leq n^{O(1)}$. The algorithm combines Barenboim's polynomial coloring procedure with arbdefective decompositions, degree reduction, and a short family of hash functions. Using the polynomial procedure in the degree-reduction framework already gives an $O(\sqrt\Delta\log\Delta+\log^* n)$-round algorithm when $C=O(\Delta)$. Hashing adapts the color space to the current degree and removes the logarithmic factor. We prove the existence of the hash family by the probabilistic method and compute it by deterministic exhaustive search, using unrestricted local computation. We also give an explicit variant based on lossless expanders that avoids this search and achieves $O(\sqrt\Delta+\log^* n)$ rounds for $C=O(\Delta)$.

Accurately assessing the convergence of Monte Carlo Markov Chains is crucial for ensuring their validity in Bayesian inference problems. However, convergence assessment in high dimensions is known to be difficult, due to most convergence diagnostics becoming insensitive beyond a few dozen parameters. Conventional convergence statistics analyze marginal distributions which in high dimensions neglects increasing levels of information from the joint and conditional probability distributions. Thus we propose $\texttt{NFDiag}$, which taps into the information of the full multivariate joint posterior with a normalizing flow (NF). Our convergence diagnostic thereby also analyzes information from conditional distributions. In other words, by working in the full multivariate space, it is sensitive with respect to the geometry of the chain in high dimensions. Our diagnostic utilizes that NFs assume independent and identically distributed (iid) training samples, which is a testable assumption that will be violated by a non-converged or strongly correlated chain. Our diagnostic trains NFs on separate parts of a chain, and then assesses whether these correspond to the same multivariate target distribution. We test our diagnostic in up to 250 dimensions, and demonstrate it is universal and unbiased, and detects problematic chain quality also when Gelman-Rubin $\hat{R}$ and the multivarite effective sample size do not.

Bronchoscopy inserts a camera through the airways to diagnose endoluminal disease. Locating the camera along the airway usually requires additional equipment, such as an electromagnetic tracker and a preoperative CT scan. In this paper, we investigate the use of the monocular camera stream to localise the bronchoscope without requiring additional sensing. We introduce a monocular SLAM system that localises the tip of a bronchoscope and reconstructs the airway surface around it from RGB video alone. A Depth Anything 3 backbone, fine-tuned on over a million photorealistic airway renderings, returns metric per-pixel depth and is the system's only source of scale. DINOv3 features routed through a custom cross-attention matcher supply sub-pixel correspondences on mucosa where classical descriptors fail. Both enter a factor graph alongside a dense constraint from projective iterative closest point (ICP) registration against the system's own running reconstruction, so surface evidence stabilises the directions the visual factors leave weakly observable. On six airways rendered from patient CT scans, the system reaches 26.1 mm mean absolute trajectory error and 77.5% mean surface F-score. Its mean surface accuracy exceeds that of five recent monocular SLAM and feed-forward baselines. MASt3R-SLAM, which fits a free scale to the ground truth, has a lower mean trajectory error (22.0 mm). ORB-SLAM3 completes only two of the six airways, whereas our system completes all six and also reconstructs two ex vivo specimens.

Relevance prediction between user queries and items is a fundamental component of e-commerce search systems. Traditionally, high-quality relevance labels are obtained through human judgment, which is reliable but expensive, slow, and difficult to scale. Recent advances in large language models (LLMs) enable automated relevance judgment at scale, achieving performance comparable to human annotators. However, such systems often rely on large commercial LLMs with complex prompts, resulting in high inference costs and limited throughput. In this work, we propose a framework that bridges this gap by distilling a high-performing LLM-based relevance judgment system into efficient multimodal student models. We first curate a small, high-quality human-annotated dataset to serve as ground truth. Using this dataset, we develop a reliable LLM-as-a-judge pipeline through careful prompt engineering and iterative refinement. This pipeline is then used to generate large-scale relevance labels, which serve as training data for compact multimodal models. Our distilled models achieve performance close to the teacher system while significantly improving latency, cost, and scalability. This approach enables practical deployment of high-quality relevance prediction systems in production environments.

Vision-Language-Action models (VLAs) have achieved high success rates on familiar manipulation tasks, yet it remains unclear whether such scores reflect genuine zero-shot generalization and perturbation robustness. Existing evaluation frameworks provide limited capability-level diagnosis and combinatorial perturbation coverage, often without connecting diagnosis to targeted model refinement. We introduce VLA-GAUGE, a diagnostic framework that unifies both evaluations under a shared executable task representation. It combines (1) paired in-distribution and out-of-distribution tasks across six capability suites, (2) single-factor sensitivity analysis with combinatorial perturbation screening and evaluation, and (3) diagnosis-driven refinement through targeted data augmentation and model fine-tuning. We evaluate 12 VLAs spanning different model sizes and action-modeling paradigms under a unified protocol. We find that (1) The mean Zero-Shot Score on VLA-GAUGE is only 22.3%, with SimpleVLA-RL scoring 8.0% and ranking second to last among the evaluated models. (2) Under three representative combinatorial perturbation configurations, the mean R-Score is 9.3. (3) Diagnosis-driven fine-tuning improves $\pi_{0.5}$'s zero-shot generalization and robustness under a selected perturbation combination on held-out scenarios by 72.4 and 31.8 scoring points, respectively; the latter exceeds the 10.9-point gain from LIBERO-Plus single-factor fine-tuning despite fewer successful training trajectories. These results show that high reported success rates on familiar manipulation tasks do not guarantee strong zero-shot generalization to unseen tasks or robustness to combinatorial perturbations, while diagnostic evaluation provides actionable signals for targeted model improvement.

Human gaze is the primary high-bandwidth interface through which we parse the semantics of our environment. While often modeled as a sequence, the degree to which gaze exhibits transferable local structure across domains remains underexplored. Using motion tokenization as a diagnostic lens across four diverse datasets, we investigate the transferability of local sequence structure. We demonstrate that while gaze can share a reusable motion-token vocabulary, identical motion tokens are organized into different local transition patterns depending on the dataset and task context. Our results show the limitations of naive data-pooling under low-semantic motion-token representations and provide a framework for evaluating behavioral sequences through information-theoretic diagnostics.

The central object in this work is the Boolean network, a function $f:\{0,1\}^V \to \{0,1\}^V$. Often identified with $f$ is its dynamics $D_f$, the digraph with exactly $\{x \to y : f(x)=y\}$ as its arcs. The interaction graph of $f$ is the digraph $G$ on $V$ which can be thought of as representing the dependencies of the components of $f$ on one another. On the other hand, model-checking is a major field of study in graph algorithms and complexity. We consider problems at the intersection of these paradigms: for a given property $\phi$, we say that a digraph $G$ is $\phi$-dynamic if $G$ is the interaction graph of some Boolean network $f$ such that $D_f \models \phi$. The corresponding decision problem $\phi$-DYNAMIC asks whether $G$ is $\phi$-dynamic. Problems of this form are well-studied in the Boolean networks community. For example, it is a well-known result that, letting $\phi$ be 'No fixed points' (i.e. $\nexists x:x\to x$), $\phi$-DYNAMIC is equivalent to the structural digraph problem NON-ACYCLIC, which is solvable in linear time. We establish, for the first time, properties $\phi$ for which $\phi$-DYNAMIC is computationally hard. These include the 'Unique fixed point' property $\exists!x:x\to x$, and a range of properties concerning the periodic points of $f$ (i.e. vertices of $D_f$ which lie on a cycle). More widely, we exhibit an infinite family of natural properties $\phi$ such that $\phi$-DYNAMIC is $\mathrm{NEXPTIME}$-complete, which we call PERIOD PIECE. As a special case, these include all properties of the form 'Unique cycle of length $k$' and 'Exactly $k$ fixed points' for any $k \ge 1$. On the other hand, we show that if the input digraph has bounded in-degree, then for those same problems $\phi$-DYNAMIC collapses down to $\mathrm{NP}^{\mathrm{NP}}$, the second level of the polynomial hierarchy, though it remains $\mathrm{NP}^{\mathrm{NP}}$-complete.

PAC-Bayesian generalization bounds are among the strongest distribution-dependent guarantees in statistical learning and are typically expressed in terms of the Kullback-Leibler (KL) divergence between a prior and posterior distribution. While analytically convenient, the KL divergence requires the posterior to be absolutely continuous w.r.t. the prior, imposing support constraints that can substantially restrict the choice of posterior. Moreover, the KL divergence does not account for the underlying geometry of the probability space. In this work, we derive new PAC-Bayesian bounds replacing the KL divergence with general optimal transport (OT) distances, including the total variation and Wasserstein-$p$ distances.

We present a scalable method for identifying nonlinear dynamics from partial measurements, supporting physics-based, neural-network, and gray-box models. We use the Prediction Error Method (PEM) coupled with state estimation performed by a Moving Horizon Estimation (MHE) scheme, which can account directly for general nonlinear dynamics. This results in a bi-level optimization problem that scales poorly with increasing model parameters. To improve computational efficiency, we derive a reformulation that avoids explicit parameter-wide sensitivity matrices and exploits the temporal structure of the underlying optimization problem. Numerical comparisons show up to a $215\times$ speedup in hypergradient evaluation. Racing-vehicle simulations demonstrate accurate prediction and physical-parameter recovery in tire-force identification. Real-world data show that the gray-box model improves prediction accuracy with a neural residual while retaining physical interpretability.

World models capture environment dynamics and support counterfactual reasoning for planning. In image-goal navigation, where the target often lies beyond the current field of view, the agent must not only model environmental dynamics but also maintain a persistent spatial memory of the scene. Existing approaches either introduce spatial context by fine-tuning pretrained models on the target task, which underexploits their spatial priors, or rely on external 3D reconstruction, which is computationally expensive for real-world deployment. In this paper, we propose the Geometry Grounded World Action Model (G$^2$WAM) for image-goal navigation. G$^2$WAM encodes spatial cues through a learned scene-coordinate localization module that anchors the current, goal, and history frames in a common reference frame, yielding a stable and consistent spatial context that enables efficient navigation without explicit 3D reconstruction. Following the world-action-model paradigm, G$^2$WAM jointly predicts future states and actions, eliminating the need for costly cross-entropy method (CEM) style planning. In addition, G$^2$WAM operates entirely in latent space, avoiding the computational burden of pixel-level reconstruction and substantially reducing inference cost. Across four trajectory prediction benchmarks, G$^2$WAM reduces average ATE and RPE by 40.1% and 35.2%, respectively. In closed-loop navigation experiments, it improves the success rate from 54.0% to 63.0% and the success weighted by path length (SPL) from 36.4% to 59.2%, while maintaining high efficiency.

State estimation is widely used in networked dynamical systems, but released estimates may inadvertently reveal sensitive information about private state variables. Existing privacy-preserving estimation frameworks often do not explicitly account for adversarial prior knowledge. Motivated by this gap, we study privacy-preserving state estimation for discrete-time linear stochastic systems under prior information exposure using pointwise maximal leakage (PML). We first reveal a privacy anti-optimality property of the Kalman filter: in the absence of additive release noise, the steady-state Kalman filter maximizes PML privacy leakage among the considered class of stable linear estimators. We further establish a nontrivial lower bound on the steady-state estimation error enforced by $(\varepsilon,\delta)$-PML privacy. We then derive sufficient release-noise conditions that guarantee $(\varepsilon,\delta)$-PML privacy, first for the Kalman filter and then for stable linear estimators. Finally, a convex semidefinite program is formulated for a joint design of the estimator gain and release noise covariance, providing a tractable privacy-preserving estimator with an explicit upper bound on the steady-state estimation error. Simulations on a source–load power system demonstrate the proposed privacy–utility tradeoff.

We introduce $qt$Bench, a benchmark of 29 open problems in algebraic combinatorics. These problems ask for a simple combinatorial algorithm that explains given polynomial coefficients or identities. To help AI agents search for such algorithms, we provide a scaffold for playing with combinatorial objects, countering cheating attempts, and testing candidate solutions. To explore how far frontier AI systems can go on these problems, we collaborated with OpenAI, whose researchers obtained proposed solutions to several of them. This highlights bigger meta-problems: is AI discovery at scale ethical? How should these results be released? How should proof digestion be organized? We discuss these questions and give our views.

An ordered visual code lets a short prefix stand in for an image, and the training loss decides what that prefix contains. Under pixel reconstruction the first bits go to the directions of highest variance, and we prove that a caption can then be independent of the entire first half of a code that is rate-optimal for pixels at every length. In the rate-distortion sense a caption is therefore not the low-rate code of its image, unless the code is built to make it one. We study that construction and what it costs. We cast captioning and text-to-image generation as successive refinement under a distortion measure that changes along the code, from caption log-loss in the early stages to pixel distortion in the last, so that each stage is compared with its own optimum. Putting words first then costs nothing among the caption stages exactly when the captions form a summarization chain, and it costs the pixels at most the caption uncertainty left in a pixel-optimal reconstruction, which is large for short prefixes and small at full length. We build RUNG, an ordered code whose prefixes are supervised by a summarization ladder of captions and whose full length reconstructs the image; generation extends the code past the prompt and captioning truncates it. With data and capacity held fixed, ordering by language instead of reconstruction raises prefix-caption information 2.9 times and GenEval from 0.76 to 0.83, at a measured cost of 2.8 dB PSNR at a quarter of the code and 0.1 dB at full length. RUNG-XL (3.4B) reaches 0.88 GenEval and 87.6 DPG-Bench in 32 network evaluations and 0.91 GenEval when errors are redrawn at the rung where they appear; its coarse and fine captions agree 94.1% of the time, and it edits images without inversion.

General-purpose frontier models are large, expensive to run, and increasingly reluctant to engage with authorised defensive- and offensive-security work. We ask the opposite question: how small can a cybersecurity-specialist transformer be while remaining genuinely useful to a security practitioner? We introduce CT0, a Cybersecurity Transformer architecture, and CT0-Micro, its first incarnation: a compact (~4B-parameter) model built on the open base model, whose backbone is specialised by two-phase on-policy distillation on our Cybersecurity AI (CAI) dataset. CT0 serves two modes from one set of weights: System 1 answers typed security decisions (is this file suspicious, is this request an attack, did the model just refuse) in a single forward pass without generating a token, System 2 is the usual tool-using agent, and a confidence gate spends generation only where the fast path is unsure. Specialisation lifts the agentic path: CT0-Micro solves 21.1% of cybench-subtask against 7.6% for its base, above every open model of comparable footprint and the densest cybersecurity capability per parameter we measured. The fast path is what the architecture buys: CT0-Micro screens eighty files per second for indicators of compromise, catches its own refusals at 96.5% accuracy in 47 ms where the model judging itself reaches 76.5% in 254 ms and misses half of them, flags jailbreak requests at AUROC 0.966 in 8 ms, and, generating only for the facts it is unsure about, extracts vulnerability facts more accurately than either mode alone at a fifth of the generative cost. All of it is built in about 314 RTX PRO 6000 GPU-hours and served from one workstation GPU, with no policy layer between operator and target. Across eighteen benchmarks and use cases run with one checkpoint and head, we report where the design helps, where it does not, and what it still lacks.

Coded computing mitigates stragglers in distributed computation. While Lagrange coded computing (LCC) enables exact polynomial computation over finite fields, Berrut approximated coded computing (BACC) enables approximate computation of arbitrary, including non-polynomial, functions in the analog domain. In applications such as multi-task learning and inference, multiple functions must be evaluated over different subsets of a common dataset, making single-round computation desirable to reduce communication overhead. An existing LCC approach addresses this requirement but is restricted to polynomial functions over finite fields, leaving single-round multi-function computation in the analog domain an open problem. In this work, we develop a single-round construction for computing multiple arbitrary functions using BACC. We first extend the existing multi-function computation approach in LCC to the BACC setting and derive an approximation-error bound. Building on this, we propose a construction based on Berrut basis functions for computing multiple arbitrary functions and derive its approximation-error bound. We analyze the scaling of both bounds with the number of functions and the number of data points per function, and numerically compare the two constructions over a wide range of arbitrary functions. The results demonstrate that the proposed construction achieves lower relative errors than the existing approach in the tested settings.

Low dose Computed Tomography (CT) is the standard imaging modality for lung cancer screening. On CT scans, lung cancer typically manifests as pulmonary nodules, whose manual identification is time-consuming and prone to observer variability, image quality limitations, and suboptimal reading conditions. Moreover, subtle temporal changes are often difficult to quantify reliably in CT scans from the same patient across follow-up examinations. Deep learning-based approaches for the automatic detection and segmentation of lung nodules have demonstrated improved accuracy and efficiency. However, most existing approaches provide only coarse region-of-interest localisation, rely on prior lesion annotations or human supervision, or treat detection and segmentation as separate tasks. In this work, we present NoduleFlow, a framework for lung nodule detection, classification, and segmentation directly from series of CT volumes. Our proposal consists of four interconnected modules and operates in an automated manner at inference time, without requiring prior lesion annotations, manual initialisation, or region-of-interest pre-selection. We further investigate whether nodule localization benefits from the propagation of candidate regions across follow-up scans through inter-scan registration fields, as opposed to conventional independent per-scan analysis. The generalisability of the framework is systematically evaluated across four independent datasets. The results underscore the potential of automated pipelines for lung nodule analysis in screening and diagnostic settings.

Sentence representation learning is still an open challenge in Natural Language Processing. In this work, we propose a new self-supervised framework for learning sentence representations, using a special type of neural network called a recursive hypernetwork. Our proposed model composes the representation of a sentence from representations of words by applying a recursive composition through the parse tree. We maintain a separate syntactic and semantic representation, and the semantic composition is guided by the information from the syntactic representation. To train this model, we introduce a novel set of six self-supervised tasks. By analysing the performance on 7 probing tasks, we validate that the generated sentence representation encodes richer linguistic information than both averaging baselines and state-of-the-art alternatives. Furthermore, we assess the impact of the six proposed self-supervised training tasks through ablation studies. We also demonstrate that the representations generated by our model are stable for sentences of varying length and that the semantic composition operators adapt to different syntactic categories\footnote{Code available: https://github.com/vasudev2020/codi/tree/main}.

Basic probabilistic models form the basis of modern deep learning largely by defining the final activation layer of a network and allowing the networks outputs to be interpreted through a probabilistic lens. By increasing the complexity of these final activation layers to include features such as spatial regularisation, allow for these models to improve in performance without requiring significantly more data. The challenge however is to ensure that these more complex probabilistic graphical models adapt well to being used in tandem with deep learning, that is, ensuring they converge and have meaningful derivatives. The goal of this paper is to show two algorithms with provable convergence properties to allow this type of regularisation for image and signal classification models. Through both rigorous mathematical analysis and in silico experiments, we can show the differing performance between these solution types.

Feature caching has become a mainstream training-free strategy for accelerating video diffusion models by reusing intermediate outputs across denoising steps. However, existing adaptive methods rely on heuristic difference measures misaligned with actual generation quality, employ a single global threshold that ignores heterogeneous phase dynamics, and never validate their budget estimates against true approximation error, allowing systematic bias to propagate uncorrected. We propose AlignCache, a closed-loop caching framework that directly aligns scheduling decisions with their true influence on the final generated video through three tightly coupled components: (1) phase-adaptive budget routing that partitions the denoising trajectory into structurally distinct phases, each governed by an independent threshold and a staleness-aware guard; (2) closed-loop threshold calibration that exploits counterfactual error measurement at the classifier-free guided output level to adjust decision boundaries online via an EMA feedback loop; and (3) momentum-augmented draft synthesis combining direction-magnitude gated residual extrapolation with anchor-guided unconditional correction. By transforming scheduling from a static risk accumulator into a feedback-driven, self-correcting controller, AlignCache consistently achieves superior acceleration-quality trade-offs across state-of-the-art video generation models. Our code is available at https://github.com/jiangjyjy/AlignCache.

Multi-agent discussion produces reasoning collaboratively, while deployment still relies on a smaller student that must answer alone. Full-graph distillation transfers such discussions by treating each correct solution as a separate training target, but what teachers provide need not match what the student learns. This mismatch appears in two ways: several correct solutions may amount to the same lesson in the student's representation (over-teaching), while some training questions remain missed after learning (under-learning). We quantify both with rates that are high on discussion graphs. To address them, we introduce FAR (Fold–Attempt–Revisit), a learner-centered distillation procedure that organizes supervision around the student's own state. Before training, FAR folds solutions within each discussion state into representative lessons. After training, the student's own attempts identify missed questions, while poorly represented clusters indicate where folding may have lost useful variation; FAR then writes targeted lessons from retained discussion contexts. Across two students and four reasoning tasks, FAR outperforms full-graph distillation with far fewer training targets and lower under-learning. Further analyses examine the behavior of FAR and the sources of its gains. Overall, the results show that organizing discussion supervision around the student can make distillation both more effective and more efficient.

This work presents a hybrid numerical approach for solving linear systems arising from the discretization of the two-dimensional parametric Helmholtz equation. A convolutional neural network based on the U-Net architecture is trained in an self-supervised manner (i.e., without explicitly generating reference solutions) to approximate the inverse of the discretized Helmholtz operator, using a loss function involving the residual norm of the linear system. The trained network is used as a nonlinear preconditioner within the flexible GMRES (FGMRES) algorithm. Numerical experiments show that while the neural network is not accurate enough to act as a standalone solver, it significantly improves the convergence of FGMRES when employed as a preconditioner. The neural preconditioner demonstrates robust performance and generalization capabilities with respect to variations in the velocity field and the domain size. Comparisons with algebraic preconditioners, based on LU factorizations of approximations of the original system matrices, indicate the superior efficiency of the neural approach under equivalent conditions. We believe that the proposed method is not tied to a specific neural architecture and can be extended to other parametric PDEs.

We present PatTransBench, a 12,000-item Chinese-English/Japanese/Korean patent machine translation (PatMT) benchmark with a four-dimensional evaluation protocol. The benchmark comprises 6,000 short-text (sentence/claim) and 6,000 long-text (paragraph) pairs, evenly split across three language pairs and both translation directions, built via IPC-section-stratified sampling and dualthreshold quality gating from upstream patent-family parallel corpora. The evaluation protocol spans literal n-gram overlap (BLEU, ROUGE-L, chrF), cross-lingual semantic textual similarity (CLSTS), 38-probe-language consistency testing, and serving performance under concurrency. A case study on PatMT2-7B and its fp8/AWQ4/AutoRound-4bit variants reveals direction-dependent quantization effects masked by aggregate scores and non-monotonic language-failure patterns across quantization schemes that are invisible to single-metric evaluation. We plan to release the benchmark, protocol, and case-study results upon publication to support reproducible PatMT evaluation.

In a variety of multi-agent and physical environments, an element's update depends strongly on a few other elements and weakly on many, and both the identity and the number of the elements that matter change with the state of the system. Such graded sparse mechanisms are common, for instance, in flocks, crowds, learned particle simulators and the neighborhood aggregation of graph networks, yet they have received little systematic study as a class of functions with the grading given. In this paper we study the supervised learning of the mechanism when the grading is provided by the environment, as a weight on every element. First, we define the class by axioms, where each element's influence is capped by its weight, the dependence on the weights is regular, and no element is distinguished, and prove a representation theorem: the class is exactly the Lipschitz ball of a transport metric on weighted multisets, and the metric is forced by the axioms. Next, the geometry of the representation gives generalization bounds that depend on the data in two ways. One is via the sparsity profile of the data – the law of how many elements matter and by how much – which bounds the rate over all designs with that profile, with an exponent from the profile and no dependence on the number of elements. In a number of natural cases we also show matching lower bounds, up to constants in the exponent. The other is empirical: due to the representation result, classical empirical discrepancy bounds apply to the class as they stand, and the resulting bound is the transport distance between the two halves of the sample in the class's own metric, computed exactly by a matching, with an additional concentration term. Finally, we study a simulated Vicsek flock under four interaction rules at two noise levels, and show that the certificate is non-vacuous, a small fraction of the trivial value on every rule.

The idea that learning is closely tied to compression has long served as both a powerful principle and, at times, an informal analogy across machine learning and learning theory. Here we focus on settings in which that intuition can be made mathematically precise, surveying formal connections among learning algorithms, data compression, and computational complexity theory, with an emphasis on recent progress and current frontiers. We describe how techniques from complexity theory can guide the design of both supervised and unsupervised learning algorithms with provable guarantees, and conversely, how learning algorithms can yield new insights and results in complexity theory. A central theme is the role of data compression as a bridge between learning and complexity, especially through an area called meta-complexity, which studies the computational difficulty of compression problems and time-bounded variants of Kolmogorov complexity.

Deployed models can fail silently as the world they describe evolves. Attribution drift has served as an early warning in tabular data; we ask whether, in graph streams, a model's own explanations can forewarn the loss of nominal conformal coverage. Doing so requires repairing the naive drift statistic twice. A vanishing edge loses mask mass regardless of whether the model relied on it, so we condition the importance on edge presence. Evolving graphs also break edge identity: a relabelling that changes nothing shifts the identity-based statistic by 0.69 on synthetic graphs and 0.83 on real ego-networks, whereas aggregating over structural roles brings both to 0.0 and stays well-defined when the support changes. We test six pre-registered regimes on thirty seeds each. A two-channel monitor, tracking conditional mask mass and its distribution over roles, precedes coverage collapse by 8 to 14.5 steps across four gradual regimes (node addition, removal, replacement, and edge thinning), all surviving Holm correction. A sudden knockout yields the expected zero lead, and a harmless change triggers no alarm. Leads track the length of the transitional phase (Spearman 0.79 over 150 runs). On real transaction ego-networks, the untuned mass channel forewarns staged drift by 27 steps and is the only channel, attributional or structural, that never alarms on a stationary stream. The main limitation is that the mass channel is blind to covariate drift, which breaks the guarantee in every run; the distributional channel detects it and also rescues the rewiring regime, so we report the two channels separately rather than as a union.

Reinforcement learning with verifiable rewards (RLVR) is reshaping how large language models (LLMs) acquire reasoning capabilities, yet the optimizers used remain largely inherited from teacher-forcing training. This raises a fundamental question: does RLVR induce a distinct optimization geometry that calls for a different optimizer? We investigate this question through the spectral structure of LLM gradients and find that gradient energy progressively concentrates into a shrinking effective subspace, which is characteristic of RLVR, as it is absent under supervised fine-tuning (SFT) and is largely removed when the verifiable reward is replaced by a random one. Moreover, the rank required to capture a fixed fraction of gradient energy steadily decreases over training, revealing that the effective dimensionality of useful updates itself evolves with training. These findings motivate a new optimization principle: rather than prescribing the update rank externally, an optimizer should adapt its rank to the evolving spectral structure of the gradient. We introduce Ares (Adaptive Rank-Effective Spectral Optimization), which estimates the effective update rank from the gradient's spectral energy distribution, tracks its evolution, and confines the gradient signal driving each update to the resulting low-rank subspace. Across LLMs of different scales, Ares improves accuracy over widely used optimizers and generalizes across RLVR algorithms and tasks. Results suggest that effective optimization may require optimizers to be designed around the geometry and dynamics of the training process. We release the code and data at https://github.com/RUCAIBox/Ares.

This work develops a geometric theory of aerodynamic promptness for multirotor platforms whose propeller directions depend on a smooth orientation-mechanism configuration. The actuator state consists of the actual signed propeller speeds and the mechanism configuration, and the nonlinear actuator map retains both the signed-quadratic propeller law and the configuration-dependent thrust directions. Constant direction maps represent fixed propellers, while shared dependence on mechanism coordinates represents mechanically coupled tilts. A Riemannian metric on the product actuator manifold compares propeller accelerations and orientation-mechanism rates through physically interpretable scales. Composing the actuator-map differential, the musical isomorphism induced by this metric, and the dual differential defines a task-rate authority map from wrench covectors to wrench-rate vectors. In fixed task coordinates, the square root of the determinant of its matrix defines aerodynamic promptness. Positive promptness is equivalent to local wrench-rate surjectivity, while the associated spectrum resolves directional authority and conditioning. The same construction yields the metric horizontal inverse, the orthogonal projector onto wrench-fiber directions, and task-preserving internal motions that regulate promptness without changing the instantaneous wrench. The construction is related intrinsically to dynamic feedback linearization and specialized to the independently tilting, radially arranged Holocopter and Voliro architectures, clarifying how their established allocation and rank constructions fit within the same actuator-manifold geometry.

Model-internal signals, such as neuron activations and gradients, have been used for instruction data selection, yet how neuron relevance should be characterized remains underexplored. In particular, should selection prioritize the magnitude of relevance or how broadly it is distributed across neurons? To investigate this question, we construct sample-level relevance profiles using AttnLRP-guided attribution and introduce two complementary criteria: Effective Relevance Support (ERS), which measures the effective support of positive relevance, and Positive Relevance Magnitude (PRM), which captures its average strength. Our analyses reveal that these characterizations produce distinct sample rankings and selection preferences despite sharing the same underlying relevance profiles. On Qwen2 models, PRM exhibits stronger associations with activation-based selection, whereas ERS produces substantially different rankings. These differences extend to task composition, within-task sample preferences, and semantic selection patterns, with varying degrees of agreement across backbones. Experiments across three language models and five downstream benchmarks demonstrate the practical value of relevance-guided selection, with ERS achieving the best overall average performance rank among the evaluated methods. Our findings highlight that how neuron relevance is distributed and characterized, rather than its magnitude alone, matters for instruction data selection.

Plant fibers are increasingly used as sustainable reinforcements in composites, but the intrinsic variability of their microstructure causes substantial scatter in transverse mechanical behavior, complicating composite design. Characterizing this behavior relies on finite element (FE) simulations requiring several minutes of high-performance computing per fiber, making high-throughput characterization across realistic fiber populations impractical. In this study, we propose a deep learning framework replacing this FE bottleneck with a fast pipeline. It includes two coupled recursive U-Nets predicting the step-by-step evolution of fiber deformation and internal stress fields under transverse compression, followed by a regression CNN estimating the transverse Young's modulus from the final stress field. Unlike prior approaches predicting stress fields for fixed configurations or idealized geometries, our framework recursively resolves the full temporal stress evolution for synthetic fibers derived from real hemp cross-sections, with or without a lumen. Trained on 1,000 synthetic fiber geometries with FE ground truth, it reproduces the stress field sequence with a Structural Similarity Index Measure (SSIM) of $0.9574 \pm 0.0074$ and a Root Mean Squared Error (RMSE) of $0.0345 \pm 0.0079$. It estimates transverse Young's modulus with an $R^2$ of $0.938 \pm 0.024$, a Mean Absolute Error (MAE) of $24.31 \pm 1.23$ MPa, and a Mean Absolute Percentage Error (MAPE) of $5.25 \pm 0.91\%$. Inference requires under one second per fiber versus five minutes per FE simulation, drastically reducing computational cost. This offers a fast, reliable tool for mechanical characterization of synthetic plant fibers, with promising applications in designing natural fiber-reinforced composites.

Market making under realistic order-flow dynamics is challenging due to the clustered, self-exciting nature of order arrivals, which are naturally modeled by non-Markovian Hawkes processes. We propose a model-free reinforcement learning (RL) framework for market making with general Hawkes order-flow dynamics. We first establish non-asymptotic performance bounds that quantify the loss incurred by approximating the infinite-dimensional Hawkes state using a finite collection of exponentially weighted features. Guided by this analysis, we introduce the Hawkes-Structured Network (HSN), a novel neural architecture that encodes historical order flow through a learnable mixture-of-exponentials filter. HSN is trained end-to-end using model-free RL, jointly optimizing the feature representation and quoting policy directly from reward feedback. Experiments on single- and multi-asset market-making problems with mixture-of-exponentials, power-law, and regime-switching kernels demonstrate that HSN outperforms general-purpose neural architectures, achieving higher trading rewards while implicitly recovering the underlying order-flow intensities.