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Second-order optimizers (e.g., Shampoo, SOAP) have emerged as compelling alternatives to Adam/AdamW and promise faster per-step convergence than AdamW in transformer training. However, they still remain costly in practice, and even SOAP still pays substantial optimizer-state memory and eigendecomposition overhead. We ask whether the benefits of SOAP can be retained at nearly the efficiency of AdamW. In this paper, we answer yes with a lightweight SOAP variant, Factored One-sided Adam-Moment (FOAM). The path to practical impact is twofold: first, FOAM employs input-only preconditioning, dropping the output-side Kronecker factor to reduce memory and remove one eigendecomposition. The Kronecker structure of the Hessian shows that this is exact for a diagonal output-side curvature and nearly lossless for a near-diagonal one, as we observe empirically. Second, FOAM replaces SOAP's dense rotated second moment with a factored Adam-moment estimator based on row-by-column statistics. Under the K-FAC Fisher assumption with a diagonal output curvature, this estimator exactly recovers SOAP's dense second moment, and we measure only a 15-20% K-FAC violation, with negligible effect on the update. Our empirical results support the claim that FOAM matches strong SOAP and Muon baselines in validation loss across scales of large language model (LLM) pre-training, uses half of SOAP's optimizer state, runs at Muon-class wall-clock time, and retains robustness across a three-fold learning-rate range. The results hold from 124M to 760M parameters, demonstrating that SOAP's gains need not require SOAP's cost. Code: https://github.com/naver-ai/foam

A large body of work in quantum machine learning has centered on characterizing the expressivity and performance of quantum models. In contrast, little attention has been paid to the reliability of predictions beyond average performance measures such as accuracy. In this work, we introduce an uncertainty-aware quantum classification framework based on Dempster-Shafer theory. This theory allows to express uncertainty through weights assigned not only to individual classification labels but to sets of labels. We introduce a training strategy that enables parameterized quantum circuits to learn such assignments directly from data. This provides an efficient way to prepare the corresponding quantum states and enables the application of different post-processing strategies. In particular, it offers a practical setting for quantum Dempster-Shafer fusion procedures with polynomial resource requirements, even when the corresponding mass functions are defined over exponentially many subsets. Overall, our work represents a step toward enabling quantum models to express uncertainty about their predictions, thereby extending the evaluation of quantum models beyond predictive performance alone.

Quantum software engineering (QSE) lacks validated approaches for translating natural-language non-functional requirements (NFRs) into execution parameters such as shots and transpiler optimization levels. Existing methods emphasize semantic similarity rather than execution outcomes. We evaluate seven large language models (LLMs) against a deterministic heuristic baseline using 540 synthetic and 18 real-world user stories. We assess semantic accuracy and execution outcomes, including time, cost, top-state probability, and two-qubit gate exposure, through Qiskit/Aer simulations. All LLMs significantly outperformed the heuristic in semantic accuracy, achieving 55.6 to 83.3 percent on real-world stories compared to 16.7 percent for the heuristic. However, no LLM demonstrated statistically significant superiority over others on the real-world dataset. Speed- and cost-oriented configurations reduced execution time and cost, but fidelity improvements were not supported. Some failures resulted from provider safety refusals rather than translation errors. Our findings demonstrate the potential of LLMs as middleware for NFR-to-configuration translation in QSE, while emphasizing execution-based validation, human oversight, and careful interpretation of model differences.

Pairwise graph ``alignments'', usually defined as maximum common subgraphs, have been considered in many application domains, including the comparison of molecular structures. Most commonly, the problem is formulated as maximum common induced subgraph (MCIS) or maximum common edge subgraph (MCES) problems. Sometimes these formulations are restricted to connected common subgraphs. Common subgraph problems readily generalize to more than two input graphs. However, this concept is fundamentally distinct from the notion of multiple sequence alignments. Abstractly, alignments are defined as super-structures from which the individual input objects are recovered via structure-preserving projections. While the mathematical construction readily applies to common induced subgraphs, it does not fully encompass the common edge subgraph problem, which is the variant more commonly employed in cheminformatics applications. In order to consistently define multiple edge-based alignments of graphs we represent a graph $G$ as E-graph $(E,\mathscr{V})$, where $E$ is the edge set of $G$ and $\mathscr{V}$ is the set of sets of incident edges. This representation implicitly encodes the vertices in terms of edge data. Alignments of E-graphs are themselves E-graphs that contain the input (E-)graphs as subgraphs. Maximum edge subgraphs correspond to maximum induced sub-E-graphs, and they can thus be computed using a slightly modified version of the VF2 algorithm without the need to switch from graphs to line graphs. Furthermore, multiple alignments of (E-)graphs yield a natural definition of a consensus graph that is ``on average'' present in the input without having to be a subgraph of every (and in fact of any) input graph.

We introduce TokenStream, an optimization-based framework that composes independently learned subject identities in text-to-video generation without a reference-video training dataset or joint optimization of each new subject combination. Learning from a single reference image makes subject appearance difficult to separate from static-image bias, while merging independently trained adapters can mix identities. Token-wise LoRA (ToRA) restricts low-rank updates to the cross-attention value projections of subject-associated text tokens, providing a separate adaptation path for each subject. A T2V-guided stream copies queries and keys from the frozen base model during early denoising to reuse its layout and motion priors while retaining personalized values. We also introduce Multi-DB, a 30-subject, 122-prompt benchmark with appearance-free prompts and varied interactions. On Multi-DB at 1.3B, TokenStream improves identity preservation from 0.422 for DreamBooth to 0.467 and textual alignment from 0.652 to 0.688.

Post-training of large language models typically combines supervised fine-tuning (SFT) with preference-based fine-tuning such as Direct Preference Optimization (DPO). Human-annotated and synthetically generated preference data differ substantially in per-sample cost, but prior work typically holds sample count fixed when comparing the two. In this work, we explicitly study the interplay between cost and performance by comparing the effect of post-training with human and synthetic preference data under a fixed, dollar-matched annotation budget. We train and evaluate multiple base model families across helpfulness and summarization tasks. We find that synthetic data is far more cost-efficient at low-to-moderate budgets, achieving high win rates with as little as \$200--\$400. On helpfulness, human data closes the gap only at budgets roughly two orders of magnitude larger; on summarization, it does not close the gap at any tested budget. We also find that human-annotated data varies in reliability: one widely used human preference source substantially underperforms another, and the gap persists even after standard remedies such as domain restriction and deduplication.

Workload characterization in performance engineering often replaces expensive target executions with lower-cost proxies, including reduced datasets, miniapps, and training inputs. Such substitutions require empirical verification that the proxy faithfully exercises the target's dynamic execution behavior. This paper presents an address-keyed control-flow profiling methodology and tool suite designed to evaluate workload representativeness directly from compiled, unmodified binaries. We pair time-ordered basic-block vector (BBV) recurrence analysis with exp-branchprof, an experimental Valgrind tool that captures five orthogonal structural profile families spanning branch direction bias, four-bit global history contexts, dynamic indirect targets, function call transitions, and intraprocedural CFG edges. Our method compares weighted event distributions from two executions of the same binary. It reports support coverage, reference event-mass coverage, distribution distance, entropy-derived quantities, and phase structure, rather than claiming that a single similarity score certifies a proxy. We validate the tool with exact-oracle microbenchmarks across AArch64 and x86-64, covering conditional and inverted exits, calls, returns, direct and indirect jumps, and forked processes. We then apply the workflow to SPEC CPU2017 and CPU2026 train/reference pairs and seven refrate/refspeed pairs. The corpus contains both close matches and cases where a shorter execution reaches much of the same code but misses substantial target, callgraph, CFG, or BBV event mass. The accompanying artifact supports the same analysis for proprietary workload/proxy pairs without requiring raw PC-level profiles to leave the collection environment.

Formal verification of complex algorithms requires expertise in program specification, invariant construction, mathematical proof, and the management of automated theorem provers. Although large language models (LLMs) can generate program code and proof fragments, reliably developing complete machine-checked verifications remains challenging: it requires an iterative process of constructing and validating specifications and invariants, building proofs, diagnosing solver failures, and optimizing verification performance. This paper presents a systematic ten-step workflow for LLM-assisted verification of scientific algorithms using the Dafny verification system. The workflow integrates algorithm formalization, contract development, empirical invariant validation, proof construction, bottleneck profiling, and resource-driven proof optimization. We applied the workflow using Antrhopic's Claude Opus 5 and Opus 5.5 models, combining LLM-driven development with automated testing and verification feedback, while retaining human oversight for correctness-critical decisions and strategic interventions. We evaluate the approach on 37 complex algorithms from graph theory and labelled transition systems. Notably, we verified the Hopfcroft-Tarjan triconnectivity test, demonstrating that even highly challenging algorithmic verification tasks can be carried out through a structured LLM-assisted workflow. Many of our machine-checked verifications were obtained within hours to a few days of interactive development. Our results suggest that LLM-assisted workflows can shift the role of the human verifier from detailed proof construction toward supervision, specification review, and strategic guidance.

Multi-task benchmarks have become a central pillar of machine learning research, yet their growing influence has incentivised benchmark gaming -- strategic actions taken to improve the leaderboard rank of a specific model. Treating datasets as voters and models as candidates, we consider benchmark-specific training -- the inclusion of benchmark data in training -- as a form of election manipulation. For any ordinal benchmark, the problem of choosing datasets to train on so that a target model becomes top-ranked corresponds to shift bribery, a class of manipulation problems from computational social choice. Leveraging this identification, we show that the benchmark-specific training problem is NP-hard under Borda count and mean win rate. Complementing this worst-case perspective, we introduce the instance-level robustness, the minimum number of datasets a model developer must include in training to top a given leaderboard, and derive expressions for it under arithmetic mean, median, mean win rate and pairwise majority. We evaluate these expressions on MMLU under HELM and on BIG-Bench Hard (BBH) under the Open LLM Leaderboard. Across both suites, mean win rate is hardest to manipulate: this gap is clear on BBH (24 tasks, 4507 models), where its median robustness is 22 tasks (92%), compared with 13 (54%) under arithmetic mean and 12 (50%) under median and pairwise majority.

This paper studies all-to-all broadcast scheduling for underwater swarms with collision-resilient physical layers that can decode asynchronously overlapping packets. Propagation-aware collision-free schedulers coordinate packet arrivals but do not account for this reception capability. We first design a data-driven neural reception model that captures per-interferer power and timing effects. The model improves prediction accuracy over SINR baselines while admitting an exact mixed-integer linear programming (MILP) formulation. The resulting neural-network-embedded MILP (NN-MILP) optimizes transmission times while explicitly encoding schedule-dependent overlaps and the predictor's inference, enabling globally optimal scheduling for small-scale instances. For larger networks, a two-stage ant colony optimization (ACO) heuristic combines low-cost transmission-order search with neural-aware timing refinement. Simulation results show that ACO shortens broadcast rounds compared with existing schedulers. It approaches the NN-MILP optimum on small-scale instances while supporting larger networks at substantially lower computational cost.

The $n$-omino fence problem asks how many cells can be surrounded by placing every $n$-omino exactly once in the grid. We present a new dynamic programming approach for this problem, allowing us to prove optimality for the pentomino and hexomino fence and to classify all possible pentomino orders by optimal area. For the first time we also provide strong heuristic solutions and upper bounds for all fences up to $n = 15$, after which we even approximate the $500$-omino fence with computational experiments. Finally, we generalize the problem to 3D, where we prove optimality for pentacubes and derive heuristic solutions for hexacubes and heptacubes.

Current portfolio construction methods are either agnostic to the effects of idiosyncratic shocks (standard factor models) or to the latent data structure driving systematic returns (recent graph-based approaches). This presents an opportunity to combine the complementary market aspects captured by the factor and graph domains, allowing asset allocations to operate directly on the underlying market structure, rather than on its observed co-movement or its finite-sample artefacts. In this work, we introduce the Mutually-INformed Graph-Locality and Exposures framework (MINGLE), which mutually regularises the factor and graph domains by redefining graph locality through systematic factor exposure profiles, rather than via observed co-movements. This is formalised through a unified Alternating Direction Method of Multipliers (ADMM) framework that jointly learns a latent factor representation and its induced graph topology directly from market returns. The resulting exposure-similarity graph aligns more closely with established economic sectors than conventional correlation-based graphs. Portfolios constructed from this representation are shown to consistently outperform their correlation-based counterparts across a range of volatility regimes and transaction cost levels. For rigour, paired statistical testing confirms that these gains stem from the reconciliation of the graph and factor domains.

How does data shape language model (LM) behavior throughout pretraining? We investigate this question through a case study on entity comparison, e.g., Between France and Brazil, which country is larger?, across nine comparison tasks spanning five entity types. We begin with controlled experiments in which we train small LMs (163M parameters) on mixtures of natural text from pretraining corpora and synthetic task data. Our analysis identifies three distinct phases of learning: (1) an early phase where the LM selects entities by frequency, (2) a middle phase where the LM selects entities by position in the prompt (first vs. last mentioned entity), and (3) a late phase where the LM selects the entity that is the correct answer. We show that the emergence of these three phases is causally determined by statistical properties of the training data. With small amounts of task-specific synthetic data, we observe only the first two phases and the model fails to learn the task; with large amounts, the model jumps directly from the frequency-based heuristic to solving the task correctly. Moreover, changing the entity frequency distribution from a naturally occurring Zipfian distribution (a small number of entities are very common and the vast majority are rare) to a uniform one weakens the frequency phase and speeds up learning of the task. Lastly, we show that the three phases of training dynamics from our controlled experiments appear in the open source model OLMo-2 32B. Together, our findings demonstrate that properties of pretraining data are causal drivers of heuristic learning and show that small-scale synthetic experiments can predict training dynamics at larger scales.

Protein language models (pLMs) produce highly accurate contact maps from single-sequence inputs. People often take this accuracy as proof that these models implicitly learn invariant coevolutionary statistics, extracting the same signals as classical alignment-based methods like Potts. In this work, we introduce a diagnostic framework around a global bijective relabeling of the amino-acid alphabet. This transformation permutes residue letters while leaving all alignment-level information, column entropies, and pairwise edit distances unchanged. Pseudolikelihood Potts models and inverse-covariance estimators remain invariant under this transformation, but pLMs fail the test. Across multiple architectures (ESM-2, MSA Transformer, AMPLIFY) and model scales (8M to 3B parameters), pLM contact maps collapse under arbitrary relabeling. Using Hamming distance controls and biochemical grouping interventions, we attempt to isolate what likely causes this degradation and find that these models rely on explicit, canonical residue identities (``alphabet anchoring'') rather than pure coevolutionary statistics. Increasing scale makes models more responsive to biochemical classes, but their performance still degrades under relabeling. Our findings show a gap between how pLMs and classical coevolutionary models compute contacts. More broadly, our work shows how diagnostic perturbations that leave classical models provably unchanged can expose hidden representation biases and prevent over-reliance on neural black boxes in biological modeling.

Document understanding systems are typically evaluated as separate components via layout analysis, optical text recognition, reading-order prediction, and image captioning. This separation leaves scientific figures, captions, and visual semantics weakly connected, and fails to measure whether a model can produce a single page-level parse that is both structurally faithful and semantically accessible. We introduce Read-Parse-Describe, a unified dataset for document parsing with visual element description generation. Given a page image, models are required to output an ordered list of layout elements containing bounding boxes, semantic labels, reading-order indices, recognized textual content, and alternative text descriptions for visual elements. The benchmark is built from 2,402 documents, comprising 18,163 continuous pages, 125,218 layout elements, and 11,338 visual instances. Besides, we further propose a plug-and-play space-awareness enhancer that reuses multi-layer visual features and injects grid-aware spatial guidance into vision-language tokens for layout-aware generation. Experiments across end-to-end VLMs and pipeline parsers show that existing systems still struggle to jointly recover reading order and visual semantics, while our enhanced model achieves strong joint performance. These results highlight the need to move beyond isolated document parsing modules toward unified models that jointly read, parse, and describe complex documents. The new dataset and code will be made publicly available at https://github.com/yuheng98chen/RPD-Unidoc

We study online selection problems subject to arbitrary downward-closed feasibility constraints, under different arrival orders, with different distributional assumptions. We establish the following bounds: (1) $Θ(\log^2 n / \log \log n)$ for the standard (adversarial-order) prophet problem, (2) $Ω(\log n)$ for the (Bayesian, random-order) prophet secretary problem, and by extension, for the standard (prior-free, random-order) secretary problem, and (3) $O(\log n / \log \log n)$ for the free-order prophet problem. Together with complementary bounds established in prior work, these results pin down the asymptotically tight competitive ratios for all these variants of prophet and secretary problems subject to downward-closed constraints. Our results refine and reinforce the big-decisions-first principle by Rubinstein and Singla [2026], establishing a superconstant separation between the random-order and free-order models.

AI-RAN distributes network control across multiple autonomous agents, namely xApps and rApps operating over shared radio resources. When an alert or degradation appears, operators currently lack a structured way to trace which decision caused it, what context triggered that decision, and how other agents interacted. Existing explainability tools focus on single-model feature attribution or linear event logging, neither of which captures cross-agent decision chains. We propose the Context Graph, a heterogeneous directed graph that organizes policies, measurements, decisions, and alerts into a queryable explanation layer. Its foundational primitive is the Decision-Event node acting as a causal junction, where incoming edges capture triggering context and outgoing edges track downstream consequences that are progressively upgraded through counterfactual verification. Instantiated over existing E2, A1, and O1 data flows, our proof-of-concept demonstrates that compliance and diagnosis queries are resolved at sub-millisecond latency over graphs of tens of thousands of nodes, while reliably distinguishing true causal impacts from spurious correlations.

Low Earth orbit (LEO) satellites are expected to play a key role in sixth-generation (6G) non-terrestrial networks. The high mobility of LEO satellites necessitates frequent handovers (HOs), posing challenges to service continuity and availability for user equipment. Conventional methods based on handover margin (HOM) and time-to-trigger (TTT) have limited adaptability to time-varying channel conditions and do not explicitly account for the impact of feeder-link and ground station (GS) connectivity on HO interruption time. To address these limitations, this paper develops a topology-aware HO framework based on proximal policy optimization (PPO). The framework uses reference signal received power (RSRP), satellite--GS associations, remaining visibility time, and elevation angles to determine when to initiate an HO and which satellite to select. Simulation results demonstrate that the proposed policy achieves a service availability of 99.32% at a minimum elevation angle of 40 degrees, exceeding that of optimized HOM--TTT (O-HT) and least-delay (LD) satellite selection by 1.67 and 1.41 percentage points, respectively. The policy maintains service availability above 97.52% as the minimum elevation angle increases to 55 degrees, demonstrating its ability to sustain high service availability under stricter elevation constraints.

Accurate environmental monitoring relies on Informative Path Planning (IPP) to deploy autonomous systems that maximize information gain. While Gaussian Processes (GPs) provide a robust mathematical foundation for modeling the environment, contemporary IPP approaches remain hindered by heuristic operational constraints and the lack of simultaneous theoretical guarantees for worst-case estimation error and approximation quality. Rather than introducing yet another heuristic, this paper presents a rigorous theoretical analysis of existing error bounds and algorithms to further develop the mathematical foundation for IPP. By evaluating probabilistic and deterministic bounds on reconstruction error, we establish that predictive variance is the theoretically ideal optimization objective for GP-based IPP. Furthermore, we analyze GreedyCover, a recent approach for optimizing predictive variance, and demonstrate that its near-optimal approximation guarantee matches the fundamental hardness-of-approximation limit for the problem. Comprehensive benchmarking confirms that this approach delivers superior estimation accuracy and computational efficiency compared to prominent information-theoretic objectives and optimization methods used in IPP. Finally, this theoretical analysis establishes a rigorous, near-optimal foundation for discrete offline IPP under bounded uncertainty constraints, offering clear and principled guidance for future work in continuous-space and online formulations.

When do mode energies preserve regime information as measurement quality changes? Stochastic Kernel Mode Decomposition (sKMD) fits joint regime laws on signed KMD mode coordinates and transfers the reference mode posterior to regime probabilities and conditional reconstructions. For centered Gaussian regimes with independently varying known noise variances, fixed coordinate energies retain the full regime posterior precisely when all classes share their cross-covariances and class variances can differ only at isolated vertices of the covariance graph. We extend the characterization to nonzero means and show that freely varying correlated noise forces a fixed linear log-odds decoder to retain the full quadratic feature span even for two distinct centered regimes. At fixed quality, a three-regime example has no sufficient two-energy basis. Its smallest Bayes log-loss gap over bases of condition number at most $κ$ has sharp order $κ^{-1}$. Exact Bayes energy posteriors supply numerical gap estimates for specified bases. Additional bounds relate feature compression, independently learned mode spans and sensor-noise error to log loss. Two controlled experiments with 64 independent panels each show that signed information can improve prediction over energy summaries, while integration gives small gains over strong signed controls and depends on how the competing point rule is calibrated and how accurately observation noise is measured.

Resonance-induced structural vibrations can compromise the performance, reliability, and service life of engineering structures. Multi-material topology optimization (MMTO) offers a promising approach to vibration attenuation by tailoring the spatial distributions of material constituents to optimize structural stiffness, mass, and natural frequencies. However, existing eigenfrequency-based MMTO methods face several challenges, including the need for flexible interpolation of multiple material properties, non-smooth optimization objectives associated with mode switching and repeated eigenvalues, and numerical difficulties in imposing differentiable constraints to exclude natural frequencies from prescribed operating frequency ranges. To address these challenges, we propose a novel MMTO framework for structural vibration attenuation based on several innovations: (1) a novel multivariate weight-based multi-material interpolation scheme to simultaneously represent material stiffness and mass density, (2) a bound-based optimization formulation to improve the smoothness and stability of gradient-based optimization by addressing mode switching, and (3) a smooth frequency-band formulation to smoothly approximate the discontinuous Heaviside function while enabling differentiable frequency-band constraints. Additionally, we systematically investigate and compare three different topology optimization formulations for dynamic vibration attenuation, including maximizing the fundamental eigenfrequency, maximizing the gap between adjacent eigenfrequencies, and excluding natural frequencies from prescribed frequency bands. Furthermore, we present the detailed derivation of analytical design sensitivities for the three formulations.

Recent advances in frontier models have pushed the boundaries of agentic robot control, enabling agents to perform complex robotic tasks through reasoning and interaction. However, repeated calls to these models during execution can substantially increase task completion time. Code as Policies (CaP) offers a route for coding agents to acquire physical skills through experience and retain them in executable programs, allowing the reasoning invested in development to be reused across runs. Developing reliable code policies while limiting the cost of physical experimentation remains a central challenge. We investigate human guidance as a source of priors for feasible actions and simulation as an auxiliary environment for exploring and testing candidate policies. Our findings favor robot demonstrations available on request and simulation used selectively during real-world policy refinement. These findings inform ACE-CaP-0, an agentic recipe that couples policy revision with experience acquisition through Demonstrations on Request and Simulation on Demand. Across eight real-world manipulation tasks spanning alignment, multi-object handling, and bimanual coordination, the resulting frozen programs achieve 92.1\% success (221/240 trials). Mean execution times across tasks range from 0.97 to 2.27 minutes. The programs execute with runtime perception and control, without a human or coding agent in the loop. These results highlight CaP's potential to turn experience into reliable, reusable physical skills.

Decentralized training of deep learning models keeps training data local and supports on-device learning over networks. In realistic scenarios, heterogeneity across agents' local data poses an optimization challenge and can severely degrade test accuracy, especially on sparse communication graphs. Building on recent advances in centralized primal averaging, we propose Decentralized Primal Averaging (DPA), a decentralized learning algorithm that combines primal averaging with a local quasi-global momentum buffer. DPA maintains three coupled sequences for optimization, gradient evaluation, and output averaging, while using consecutive mixed iterates to construct a network-aware momentum direction without transmitting an auxiliary tracking variable. For smooth nonconvex objectives, we establish a convergence bound for DPA and identify conditions for linear speedup in the number of agents for sufficiently many iterations. We also introduce DPA-1G, a variant that uses one communication round per iteration and matches the per-iteration communication cost of DSGD-style baselines. Experiments following the GUT decentralized image-classification benchmark show that DPA compares favorably with DSGD, gradient tracking, QG-DSGDm, momentum tracking, and QG-GUTm across datasets, architectures, topologies, and heterogeneity levels, with the largest gains under high heterogeneity on sparse rings. At the same total communication cost, both DPA variants achieve higher mean test accuracy than the best baseline on CIFAR-10 and CIFAR-100 with ResNet-20. Our code is publicly available.

Raysemble reconstructs eight lumbar and pelvic bones from a single X-ray by separating shape and placement. Each 3D query samples regional and global features at its image projection. A shared decoder predicts normalized bone shapes. Predicted depth and camera geometry determine 3D centers and scales for resampling these shapes onto a common grid in millimeters. Evaluation uses 23 held-out patients with 43 CT scans, each generating one simulated anteroposterior radiograph. Without rigid alignment to CT,Raysemble leads 15 evaluated methods, averaging 65.24% Dice, 9.09 mm HD95, and 3.32 mm ASSD over three random seeds. With identical inputs, it improves Dice over VolumeNeRF by 5.86 percentage points.

While language-model agents excel at long-horizon coding and terminal tasks, this success relies on two conditions: explicit text specifications and immediate execution feedback. However, neither condition holds in real-world problems where critical information exists only in images, leaving it unclear whether long-horizon capability transfers from text to visual reasoning. In such visual settings, because rules and clues resist text transcription and lack test-case feedback, agents must repeatedly inspect images, simulate spatial transformations, and autonomously cross-check clues. Despite this challenge, existing evaluations fail to capture such capability: visual reasoning benchmarks largely reduce tasks to single-turn, short-chain question answering, whereas agent benchmarks focus on text-based environments or interactive states that permit trial-and-error. To bridge this gap, we introduce Visual Cipher Bench, a collection of 40 original visual puzzles across four categories: spatial manipulation and simulation, logical constraints and planning, rule induction, and knowledge-based decoding. Each puzzle provides only one to three black-and-white line drawings and a minimal submission instruction, requiring agents to discover the underlying solving mechanism entirely from the images. Across 29 reasoning-effort configurations of eight frontier models, even the strongest model, GPT-6 Astra (max), achieves only 26.7% accuracy, while five of the eight models score below 1%. Yet on a ten-task subset, providing a single non-spoiler mechanism hint boosts accuracy from 7.8% to 55.6%. This sharp contrast shows that the primary bottleneck of current agents lies not in executing multi-step plans, but in autonomously discovering rules from visual evidence. Visual Cipher Bench thus provides a rigorous benchmark for measuring long-horizon visual reasoning in agents.

Achieving strong optimization generalization across diverse optimization problems while requiring limited training resources remains a challenging problem for optimization-oriented large language models (LLMs). Existing learning-based methods, however, typically require large-scale supervised data, expensive intermediate step verification, and extensive computational resources, while exhibiting limited optimization generalization across diverse optimization structures. In this paper, we propose \textsc{MiniOpt}, a lightweight optimization-specialized LLM trained through a reasoning-to-model-and-solve paradigm and a two-stage training framework with reinforcement learning with verifiable rewards (RLVR). MiniOpt encourages structure-oriented optimization learning by reinforcing the completeness of optimization formulations and optimization outcomes. Extensive experiments on eight optimization benchmarks demonstrate that MiniOpt consistently outperforms existing learning-based optimization models while requiring substantially fewer parameters and training data. To further understand optimization generalization, we introduce a complementary parameter-decoupled evaluation protocol that disentangles optimization structure understanding from numerical parameter processing. The results reveal that MiniOpt preserves optimization capability under parameter-decoupled settings significantly better than previous optimization-specialized models, suggesting that its performance gains primarily originate from stronger optimization structure understanding. These findings demonstrate an effective pathway toward efficient and generalizable optimization-specialized LLMs. The code is available at https://github.com/Hsiang-1/MiniOpt.

We present linear codes with parameters [88,8,64]_7, [90,8,65]_7, [98,7,75]_8, [97,8,72]_8, [44,7,31]_9, [97,8,71]_7, [85,6,67]_8 and [78,8,56]_7. Each has a minimum distance one larger than the lower bound listed in Grassl's tables of best known linear codes; codes with parameters [89,8,64]_7, [96,8,71]_8, [95,8,70]_8, [94,8,69]_8, [77,8,55]_7 and [86,6,68]_8 follow. Seven of the eight codes are obtained from a quasi-cyclic code and a vector that is constant on each block, by Construction X with a repetition code. The remaining one, the [90,8,65]_7 code, is obtained from the first by appending two coordinates. The parameters and all weight counts were obtained by exhaustive enumeration, and a short program that repeats these computations is included.

Federated Learning (FL) with Parameter-Efficient Fine-Tuning (PEFT) enables efficient adaptation of Large Language Models (LLMs), yet its energy and carbon costs across hardware remain poorly understood. We evaluated federated Low-Rank Adaptation (LoRA) fine-tuning on NVIDIA A40, RTX 6000 Ada, and A100 GPUs using a $2^2$ full factorial design with 135M/360M models and 10/100 local steps. CodeCarbon tracked energy and estimated CO$_2$-equivalent emissions. Descriptive allocation of variation assigned 84.8-91.2% of energy and emissions variation to local steps within these ranges. On A40 and RTX 6000 Ada, configurations with fewer steps achieved comparable accuracy with roughly 6-8-fold lower energy consumption and higher accuracy per kWh. These findings support smaller local budgets for energy-efficient federated fine-tuning within the evaluated setting.

We study the interplay between two types of graph classes: the ones defined by intersections of geometric objects and the ones defined by the absence of a substructure. More precisely, we study intersection graphs that are grounded, that is, the objects lie above a horizontal line that they touch, and ordered graphs with forbidden patterns, that is, ordered graphs that avoid a set of ordered induced subgraphs. These two approaches are fundamentally different, but it is known that several interesting graph classes have both types of characterizations, and we aim to understand whether this is a general phenomenon. Our contributions are the following. First, we identify a family of patterns on four vertices and a natural hierarchy of intersection graphs of strings whose classes are nicely interleaved. This raises hopes to prove connections between the two perspectives. Second, we dampen these hopes by proving that a class of (ordered) intersection graphs that we study cannot be characterized by a finite set of forbidden patterns. Third, we show a dual impossibility result: there exists a pattern-defined class of our hierarchy that admits no intersection representation, if we require this representation to be closed under natural operations such as translation and scaling. However, it turns out that if we allow slightly more exotic intersection representations, then we can find one for this pattern-defined class.