arXiv:2607.17274v1 Announce Type: new
Abstract: Today's data-centric applications demand cache architectures that can scale with growing workloads while maintaining high performance and energy efficiency. Fundamental issues such as excessive area consumption and leakage power are increasingly challenging traditional SRAM-based caches, thereby motivating the exploration of non-volatile alternatives. Among these, racetrack memory (RTM) stands out due to its remarkable storage density, achieved through nanowires hosting sequential magnetic domains that can be manipulated via domain wall or skyrmion techniques. Despite its advantages, racetrack memory's inherent serialized access introduces considerable shift overhead, leading to elevated energy consumption and latency. In this paper, we analyze the placement strategies in conventional RTM-based last-level caches and identify that current methods trigger redundant shift operations as a shift intended to read one block fails to preposition other blocks subsequently accessed. To resolve this, we introduce an innovative data placement and replacement scheme that intelligently groups correlated blocks, ensuring that a single shift not only retrieves the target block but also aligns subsequent blocks closer to the access port. Our simulation results using the gem5 simulator and the SPEC CPU2017 benchmarks reveal that our scheme reduces shift overhead by 49.0% and cache energy consumption by 35.9% with negligible performance impact. In addition, this scheme exhibits robust scalability to longer nanowire tracks for higher cache density.
Science Journals
arXiv:2607.17956v1 Announce Type: new
Abstract: Learning is increasingly introduced into visual-inertial odometry (VIO), ranging from learned feature front-ends to learning-dominant motion and geometry estimation. However, learning more of the pipeline does not necessarily improve robustness when deployment conditions differ from the training distribution. This work asks whether robust VIO under distribution shift truly requires deeper learned estimation, or whether learning can be confined to visual measurement generation. We propose a minimal-learning stereo VIO framework in which SEA-RAFT is used only to propose dense stereo correspondences and predict their uncertainty, while temporal tracking, geometric verification, and state estimation remain explicit. Dense flow is sampled at sparse feature locations, filtered using predicted uncertainty and stereo epipolar consistency, and incorporated into a sliding-window stereo-inertial estimator through uncertainty-weighted reprojection factors. The same uncertainty is further propagated through stereo triangulation for downstream anisotropic 3D Gaussian mapping. Experiments on EuRoC, VIODE, and 4Seasons demonstrate accurate and stable estimation under motion blur, dynamic scenes, illumination changes, and large indoor-to-outdoor distribution shifts. Ablations show that learned flow alone is insufficient: the gains arise from combining learned correspondence proposals with geometric verification and uncertainty-aware weighting. These results suggest that, for OOD-robust VIO, carefully integrated learned visual measurements can be more effective than learning a larger fraction of the estimation pipeline. Code and configs for the benchmark will be open-source upon acceptance. A supplementary video is available at https://drive.google.com/file/d/1EVRhOkhanmNXHbQS1Vr80FoEIAYOYOV2/view
arXiv:2607.16258v1 Announce Type: new
Abstract: The application of artificial intelligence methods in power electronic converter modeling is becoming increasingly widespread, but existing applications still face many challenges, such as difficulties in multi-time-scale hybrid analysis and the lack of physics-aware evaluation criteria and constraints, resulting in poor performance. This paper proposes a Neural Controlled Differential Equation (Neural CDE) framework for learning continuous-time surrogate models of grid-forming inverters for electromagnetic transient (EMT) simulation, which relaxes the constraint of fixed sampling rates and enables multi-time-scale control analysis. Then, an affine-control formulation with dual slow/fast pathways is proposed to capture the hierarchical and multiscale behavior of converter dynamics, and a physics-inspired regularization method is utilized to enhance stability and coherence. Evaluated on EMT-generated trajectories, the model accurately reproduces transient responses, preserves effective damping and the dominant oscillatory characteristics, and maintains bounded long-horizon rollouts. The results show that Neural CDE-based component modeling offers a physically consistent surrogate modeling approach for EMT-level simulation studies.
arXiv:2607.17568v1 Announce Type: new
Abstract: Structured pruning compresses large language models (LLMs) by removing whole computational units, such as attention heads and feed-forward (FFN) channel groups. Most training-free methods, however, rank these units independently, implicitly treating the loss from pruning a set as the sum of its individual losses. This view fails for Transformers, whose sublayers are coupled through a shared residual stream. Two individually weak units can thus be jointly indispensable, yet independent scoring is blind to such dependence and removes them together. We introduce CoCurve (Cross-Module Co-Pruning Curvature), a calibration-only, fine-tuning-free method that prunes attention and FFN units jointly. A second-order Taylor expansion of the token-level KL between the frozen model and its masked copy yields a single Fisher matrix whose diagonal is classical node saliency and whose off-diagonal entries are co-pruning curvature edges: the extra damage of removing two units together. Under a single-ablation additivity approximation this matrix reduces to a Gram product of single-unit ablation features, so the full M x M interaction is recovered from M forward passes, with no pairwise sweeps or gradients. Pruning then reduces to one budgeted quadratic program, solved in a single shot under a shared attention--FFN budget, with no labels, fine-tuning, or recovery.
arXiv:2607.17031v1 Announce Type: new
Abstract: Security-constrained unit commitment (SCUC) couples binary commitment, economic dispatch, reserves, and network security over a multiperiod horizon, making an exact solution computationally expensive for realistic system sizes. This paper proposes a three-layer hybrid framework in which a Bernoulli hybrid soft actor-critic (HSAC) policy proposes hourly commitments, a quantum-sampled auxiliary channel augments the state, and a native SCUC mixed-integer linear program recovers dispatch and security variables after only a limited subset of commitment binaries is enforced. The method is therefore solver-compatible rather than an end-to-end replacement for exact optimization. We formalize the SCUC-to-reinforcement-learning interface, derive the temporal coverage induced by the fixed cap, and evaluate the 14- 57- and 118-bus benchmark cases. The results show stable, low-cost recovery in the 14-bus case, where the best recovered schedule attains the full-horizon optimum; a very low screen-rejection rate in the 57-bus case; and a clear coverage bottleneck in the 118-bus case once the enforcement cap no longer spans a complete commitment period. The study, therefore, identifies the amount of useful commitment information that reaches the recovery model, under an exploratory Bernoulli actor and a small enforcement cap, as the dominant limitation that governs scalability
arXiv:2607.17706v1 Announce Type: new
Abstract: Half-harmonic generation in microresonators with mixed $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities provides access to a rich landscape of two-colour soliton states and frequency combs. We numerically demonstrate the formation of both bright and topological two-colour solitons at relatively modest pump powers and phase-mismatch parameters. At higher powers and larger phase mismatches, we identify a regime where parametric down-conversion assists the formation of dark solitons in the normally dispersive pump field. While the dark-soliton core is primarily shaped by the Kerr nonlinearity, nonlinear coupling between the pump and its half-harmonic modes enables soliton excitation using a standard laser-frequency scanning technique, a capability not normally associated with dark solitons. The simulations are performed using parameters representative of lithium-niobate microresonators pumped near 775 nm and generating a half-harmonic near 1550 nm. These results reveal how the interplay of $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities can substantially expand the range and types of experimentally accessible soliton states in a single integrated frequency-comb platform.
arXiv:2607.17974v1 Announce Type: new
Abstract: FLASH radiotherapy (FLASH-RT) is the phenomenon of relative sparing of normal tissue when ultra-high dose rates (UHDR) are used compared with conventional dose rates (CDR) as clinically used. Despite extensive investigation, the underlying mechanisms remain unexplained. Among the proposed hypotheses, tissue oxygen has consistently been a central theme because oxygen is the most dominant factor known to modulate radiation-induced damage. The factors implicated in FLASH sparing include the baseline partial pressure of oxygen (pO2), transient radiolytic oxygen consumption (ROC), and oxygen-dependent changes in the chemistry of reactive oxygen species (ROS) that vary with dose rate. This review synthesizes current evidence on in vivo oxygen measurement techniques, highlighting their capabilities and limitations in capturing the spatial and temporal heterogeneity of tissue oxygenation. Key experimental studies in skin are summarized and interpreted by modulating oxygen levels via changes in inspired oxygen gas and vascular clamping interventions, demonstrating that the FLASH effect occurs only at intermediate baseline pO2 (normoxic or slightly hypoxic) values, but not at hypoxia or hyperoxia. Direct measurement of oxygen consumption during UHDR irradiation is possible, providing one of the first in situ measurements of radiation chemistry in patients. In parallel, recent advances in fast in vitro radiation chemistry assays indicate that UHDR irradiation alters radical yields, favoring increased production of solvated electrons and reduced hydroxyl radical mediated damage. Taken together, the available data suggest that the FLASH sparing effect arises from an interplay among the delivered dose and dose rate, local oxygen availability, and radiation chemistry, with tissue-specific variation in scavenging, leading to altered biological responses across the CDR-to-UHDR shift.
arXiv:2607.17281v1 Announce Type: new
Abstract: Auto-bidding plays an essential role in online advertising, automatically adjusting bids for advertisers to optimize their commercial goals. The emerging AI-Generated Bidding (AIGB) paradigm widely adopts generative modeling to optimize bidding strategies, yet suffers from the limited mode coverage of offline datasets and inadequate task-state understanding, hindering effective exploration of optimal strategies. Large Language Models (LLMs), with prior world knowledge and reasoning capabilities, offer a promising approach to overcome these limitations. However, directly applying LLMs to auto-bidding tasks faces inherent challenges in limited numerical precision, hallucinations, and inference latency. To address these limitations, we propose AIGB-R1, a hierarchical self-evolving auto-bidding framework aiming to enhance AI-Generated Bidding via LLMs' Reasoning capabilities, comprising a high-level Planner module for macro-level strategy planning and a low-level Executor module for fine-grained decision-making. Building upon this, we design an experience-driven self-evolving loop, enabling autonomous strategy exploration and optimization from accumulated experience. We adopt a two-stage pipeline of offline pre-training and post-training alignment, and build an interactive bidding simulation environment for strategy rollout. Furthermore, we propose Decoupled Group Relative Policy Optimization (D-GRPO) to achieve end-to-end optimization via advantage decoupling. Experimental results on a large-scale public dataset demonstrate the effectiveness of AIGB-R1.
arXiv:2607.16656v1 Announce Type: new
Abstract: Object removal aims to eliminate target objects specified by a mask while preserving visual consistency with the surrounding regions. Existing methods typically rely on contextual information from surrounding regions. However, in dense scenes where the surrounding regions contain instances visually similar to the removal target, such reliance often leads to semantic interference, resulting in incomplete removal. This problem arises from erroneous information propagation in the attention space, where masked queries tend to align with such instances due to global similarity matching in self-attention. To address this challenge, we propose a Diffusion-based Object Removal framework for dense Scenes, dubbed DORS, built upon a Dynamic Attention Routing mechanism comprising two complementary components: Instance-Filtered Attention (IFA), which suppresses misleading semantic information from similar instances through dynamically constructed mask-guided attention constraints, and Context-Guided Routing (CGR), which dynamically routes complementary scene information to maintain visual consistency. We further introduce DOR-Bench, a benchmark tailored for object removal in dense scenes. Extensive experiments demonstrate that DORS outperforms state-of-the-art methods, particularly in reducing incomplete removal and duplicate artifacts. The code will be available at https://github.com/httang1224/DORS.
arXiv:2607.16570v1 Announce Type: cross
Abstract: Organic mixed ionic electronic conductors (OMIECs) are a promising class of polymer materials for applications spanning neuromorphic computation to energy efficient electronics and bioelectronics. Despite being highly tunable, the relationship between structural features and key performance properties such as charge carrier mobility is poorly understood. Scanning nanodiffraction in the transmission electron microscope (TEM) is a powerful probe for elucidating this structure-property relationship, but produces large, noisy datasets that are difficult to interpret because polymer reflections exhibit several distinct morphologies. To address the complexity, we trained a machine learning (ML) model to detect these polymer diffraction peaks and their intensities from synthetic data. Compared to correlative peak detection algorithms, the conventional method for analyzing nanobeam 4D scanning transmission electron microscopy (4DSTEM) data, we show that the ML model is significantly faster and outperforms correlative algorithms in almost all cases, opening up the possibility of near-live visualization of 4DSTEM experiments.
arXiv:2607.16580v1 Announce Type: cross
Abstract: Structural reliability analysis supports the design and safety assessment of buildings and civil infrastructure but requires specialized expertise throughout the workflow. This study presents a multi-agent large language model framework that automates component-level reliability analysis from a natural-language problem statement to interpreted estimates of the reliability index and failure probability. Specialized agents handle problem formulation, method planning, code generation, execution, and result interpretation, with human confirmation at key decision points. The Method Planner is fine-tuned using QLoRA for a priori reliability-method category selection. Analysis results are not generated directly by an LLM; instead, validated deterministic solvers compute the reliability estimates, improving reproducibility and reducing hallucination risk. The framework uses open-weight models and supports local execution without closed APIs. Results show that it lowers the expertise barrier to structural reliability assessment while preserving computational trustworthiness.
arXiv:2607.16606v1 Announce Type: cross
Abstract: Chirality in a discrete $Z_q$ spin interaction distinguishes clockwise from counterclockwise phase differences, but its manifestation in continuous nonlinear dynamics is unclear. We show that any pairwise $Z_q$ Hamiltonian admits a unique equilibrium-preserving embedding into a continuous phase-energy landscape that matches the discrete energy on the $q$-state phase grid, where every grid point is stationary. This embedding reveals that a $Z_q$ kernel is nonchiral if and only if the sine components of the relaxation vanish. Chirality of the discrete $Z_q$ model is therefore exactly the odd part of the continuous phase interaction. In the induced nonlinear phase dynamics, this odd part becomes an orientation-dependent phase shift in the multi-harmonic coupling, and chiral reversal flips this shift while preserving the coupling magnitudes. In self-sustaining oscillator networks, the shift is further realized as a direction-dependent delay. Transistor-level ring-oscillator simulations validate the predicted phase locking and reversal of directed phase bias. These results show that algebraic handedness in a discrete spin Hamiltonian can be represented as tunable time-domain asymmetry in continuous nonlinear dynamics.
arXiv:2607.17080v1 Announce Type: new
Abstract: Base-2 digital nets are practical high-dimensional integration rules: the sample budget $N=2^m$ can be chosen independently of the ambient dimension, and the generating matrices provide algebraic control of projections and Walsh-dual weights. They are therefore well suited to problems whose error is governed by weighted or low-dimensional projection structure. However, when one restricts attention to a smooth low-dimensional projected component, a low-dimensional cubature rule with a comparable number of nodes can be substantially more accurate than the projected digital-net points. This raises the question of whether low-dimensional cubature accuracy can be inserted into a high-dimensional digital-net rule without forming the full tensor product.
We answer this question by a simple coordinate embedding: read the leading $p$ binary digits of each coordinate as an index into $2^p$ equal-weight cubature nodes, and replace the coordinate by the indexed node. When a projection forms the full $p$-bit grid, the transformed rule coincides on that projection with the corresponding product cubature rule; small projected $t$-values provide sufficient conditions for such full-grid recovery. For general integrands, the error separates into the corresponding product cubature error and a residual digital-net term. Experiments with scrambled Sobol' nets in dimension $50$ illustrate this mechanism and show finite-budget improvements for the smooth low-order and coordinate-decaying test functions considered here.
arXiv:2607.16790v1 Announce Type: new
Abstract: Fine-grained offensive language detection organizes labels into a hierarchical structure, for which two modeling paradigms exist: cascaded decomposition and joint multi-task modeling. Prior work rarely provides a direct, controlled comparison of the two paradigms in terms of accuracy, parameter count, and inference latency, and rarely verifies whether a chosen class-imbalance handling strategy is actually optimal. This paper proposes a three-level cascaded detection system whose training strategy is customized per subtask, together with two verification mechanisms. First, a controlled ablation study determines the best class-imbalance handling strategy for each subtask. Second, a joint multi-task model with a shared encoder is trained as an architectural control, yielding real measurements along the dimensions of accuracy, parameter count, and inference latency. Experiments show that the cascaded system attains macro-F1 scores of 0.795, 0.716, and 0.557 on the three subtasks of the official test set. The ablation study reveals that configuring the loss function purely by imbalance-severity intuition is suboptimal; reconfiguring based on the ablation results improves both performance and stability. End-to-end cascade evaluation shows that roughly one-fifth of the errors in the cascade pipeline originate from the first-stage filter and cannot be corrected by subsequent stages. Relative to the joint multi-task model, the cascaded architecture achieves higher accuracy on all three subtasks, with a 7.1-point macro-F1 gain on the most severely imbalanced subtask, at the cost of three times the parameters and 1.67 times the inference latency. Together, these results establish an explicit, quantifiable trade-off between the accuracy advantage of cascaded architectures and their deployment cost.
arXiv:2607.17987v1 Announce Type: new
Abstract: Smart-contract vulnerabilities often arise from inconsistencies between business paths that should correspond to one another, such as single and batch entry points, direct and adapter-based flows, quote and execution paths, or inverse operations such as buy and sell. Existing analyzers are effective for many local syntactic and data-flow patterns, but they provide limited support for bugs whose oracle is relational: whether two semantically paired paths preserve compatible guards, state transitions, value flows, and failure behavior.
This paper introduces chiral analysis, a relational model that treats paired business paths as implicit specifications for each other. We formalize chiral relations as static analogues of metamorphic relations, derive obligations over guards, actors, state, value, ordering, failure behavior, and external interactions, and report a vulnerability when a violated obligation has security impact. We implement this idea in ChiralDetector, a Solidity prototype that extracts business paths, ranks candidate pairs with static facts, applies LLM-based semantic filtering and detection, and validates and deduplicates findings.
In a preliminary evaluation on the Phi protocol, ChiralDetector reduced 3,217 statically ranked path pairs to 1,643 semantic candidates, produced 101 deduplicated finding groups, and retained 44 strict-validator positives that manually collapsed to 13 effective unique issues. These include cross-art Merkle proof reuse, fee unit mismatches, public state-tracking helpers, and refund propagation gaps. The results suggest that chiral analysis can expose business-logic bug classes that are difficult to express as single-function rules while providing a structured way to control LLM cost and validator precision.
arXiv:2607.16259v1 Announce Type: new
Abstract: Pretrained models are typically ranked on multi-task leaderboards to assess their effectiveness across diverse tasks. Rank confidence intervals were recently introduced as a method to quantify the uncertainty in these rankings by aggregating pairwise hypothesis tests. In this work, we analyze the sources of uncertainty in the knowledge evaluation benchmark MMLU and show how hypothesis tests can be modified to account for their effects. We demonstrate that ranking variability across MMLU subjects is substantial and should be considered when comparing LLMs or identifying the top-performing models.
arXiv:2607.17708v1 Announce Type: new
Abstract: Multi-task neural solvers aim to handle multiple Vehicle Routing Problem (VRP) variants within a unified model, avoiding separate training for each constraint combination. However, VRP variants differ in optimization difficulty, while existing methods lack stage-wise feedback on their training status, making the model biased to some specific variants. Although meta-learning can support adaptive training, it typically requires bi-level optimization and additional gradient updates, increasing computational cost. To address this limitation, we propose LLM-as-Trainer (LaT), a plug-and-play training paradigm that uses a pretrained large language model as an external trainer. LaT periodically analyzes cross-task validation metrics to generate a stage-wise guidance vector. This vector is combined with the current task's constraint vector and injected into each encoder layer, providing the neural solver with additional training information during subsequent policy optimization. Experiments on 16 VRP variants show that LaT improves the solution quality of several state-of-the-art multi-task neural solvers on both trained and unseen variants, supporting the effectiveness and generality of the proposed training paradigm.
arXiv:2607.16639v1 Announce Type: cross
Abstract: Biological systems across scales, along with many engineering problems, must control noisy systems with limited information. Here we study information-limited feedback control of stochastic systems to achieve target steady states, and derive a lower bound on the information rate from controlled system to controller. This framework allows us to obtain performance-information Pareto frontiers for wide-ranging control problems with limited information. For systems with state-independent passive dynamics, the bound is saturated by an explicit optimal control protocol which probabilistically time-reverses the passive dynamics. We showcase these results through applications to nonlinear particle localization, microbial navigation, and experimentally realized information engines.
arXiv:2607.17033v1 Announce Type: new
Abstract: Forecasting the outcomes of transition-metal-catalyzed reactions is notoriously complex due to the interplay of diverse physical and chemical variables. A persistent computational bottleneck has been effectively merging broad electronic descriptors with the localized, three-dimensional geometry of the reactive site. To bridge this representation gap, we present ChemFusion, a hybrid neural network that fuses conventional electronic features with explicit 3D atomic coordinates. Using a cross-attention mechanism, the model enables global electronic states to dynamically attend to specific spatial constraints within un-pooled molecular point clouds. When benchmarked against a diverse library of cross-couplings, this approach delivers exceptional predictive performance, decisively surpassing traditional single-modality frameworks. Importantly, extracting the attention matrices reveals that the architecture autonomously learns to identify and penalize restrictive steric hindrances. This provides a physically grounded interpretability, demonstrating that spatially aware networks can navigate complex reaction sterics that standard statistical models typically miss.
arXiv:2607.16660v1 Announce Type: new
Abstract: The increasing adoption of Large Language Models (LLMs) as AI components in modern software systems introduces distinct security risks to the software supply chain. While many considerations and safety mechanisms are in place for components of the traditional software supply chain, the recent rapid adoption of AI components and platforms has overlooked these hard learned lessons. Selecting and integrating AI models without clear guidance on how these choices affect system security may leave applications vulnerable to threats, such as malicious components, data leakage, and unintended behavior. The goal of this study is to understand practitioners' decision making process and security considerations in selecting and integrating AI components through an exploratory semi-structured interview study. Toward this goal, we conducted semistructured interviews with 22 software developers, architects, and AI practitioners across diverse organizations about how they integrate AI components into their software.
Our analysis finds that practitioners' model selection is predominantly driven by functional criteria, including performance, accuracy, cost, and specific features, e.g., tool calling or multimodal support, while security is rarely considered as an evaluation criterion. We observe a consistent lack of security concern throughout the AI component integration process, with established software supply chain lessons overlooked or ignored. The industry is repeating the historically costly mistakes of early software dependency management, prioritizing rapid reuse and availability over security and provenance. We distill our findings into actionable recommendations for AI adopters, model providers, and researchers, advocating for a proactive, security-by-design approach that integrates security evaluation into component selection and sustains it throughout the software development lifecycle.
arXiv:2607.17569v1 Announce Type: new
Abstract: Open modification search (OMS) in mass spectrometry (MS) is a data-intensive workload whose performance is dominantly limited by reference data movement rather than computation. Prior OMS accelerators have largely been evaluated in isolation, making it difficult to understand system-level trade-offs across platforms. This paper presents the first workload-driven, cross-platform survey of accelerators for MS search by studying not only commodity platforms, but also emerging memory- and storage-centric architectures, including GPUs, near-storage FPGAs, DRAM near-memory processing, ReRAM/PCM in-memory processing, and 3D NAND/FeNAND in-storage processing, under consistent algorithmic and accuracy assumptions. Leveraging a binary hyperdimensional computing (HDC)-based OMS formulation that reduces similarity evaluation to lightweight bitwise primitives and tolerates device-level non-idealities, we enable a robust execution on memory-centric architectures despite device-level non-idealities and limited computing capability. Overall, this study identifies memory- and storage-centric architectures as a key architectural breakthrough for large-scale, high-speed search acceleration, delivering up to >100x speedup and >40,000x improvement in energy efficiency.
arXiv:2607.17570v1 Announce Type: new
Abstract: Graph foundation models (GFMs) with global attention are increasingly used to represent mixed-integer linear programs (MILPs), aiming to capture structure beyond the locality of standard graph neural networks. We study their expressive power through graph isomorphism testing, asking which MILP instances they map to identical representations. We prove that a broad class of hierarchical graph transformers combining global linear attention, edge-weighted cross-attention, and bipartite message passing is bounded by the one-dimensional Weisfeiler-Leman (1-WL) test: under any parameter setting, 1-WL-equivalent MILP graphs receive identical graph embeddings. Our compositional proof shows that each architectural component is a symmetric multiset function and thus preserves 1-WL equivalence. We validate this characterization across ten diverse graph encoders, including Graphormer-, GraphGPS-, Set-Transformer-, and Gasse-style models. Across model capacities, graph scales, and pooling operators, every tested encoder maps 1-WL-equivalent non-isomorphic graph pairs to numerically identical embeddings. Consequently, graph invariants that vary within a 1-WL equivalence class cannot be recovered from these representations. We further show that expressiveness beyond 1-WL arises from input encoding rather than attention: random-walk positional encodings separate the constructed pairs, while additional constructions expose the limits of this remedy. These results characterize the expressive power of global-attention GFMs and provide an encoder-agnostic diagnostic for detecting 1-WL-induced representation equivalence.
arXiv:2607.17282v1 Announce Type: new
Abstract: Given a binary-labeled linearly separable dataset, and the objective is to compute the maximum-margin separating hyperplane, also known as the hard-margin Support Vector Machine (SVM) classifier. This paper investigates whether, if given an initial separating hyperplane, can it be exploited to reach this unique optimum more efficiently. We present a geometric approach that gradually improves the alignment of the hyperplane, starting from an initial separating hyperplane, while preserving separation and continuously increasing its margin until convergence to the global optimum. At each iteration, the method considers only local information, namely the current active set, and aims to re-align the hyperplane according to the optimal separating hyperplane of this reduced subset. Consequently, the original convex quadratic optimization problem is addressed through a sequence of smaller subproblems. The paper presents the algorithm in detail, together with a preliminary experimental evaluation and several theoretical findings. The results suggest that, when an initial separating hyperplane is available, the proposed method can be competitive on larger datasets and, in some cases, can outperform state-of-the-art approaches that solve the optimization problem directly.
arXiv:2607.17283v1 Announce Type: new
Abstract: Single-stream autoregressive decoding of large language models is bound by memory bandwidth: each generated token requires one full forward pass through the target model, and successive passes cannot be parallelized. Speculative decoding restructures this computation: a small draft model proposes $K$ tokens autoregressively, the target model scores all of them in one batched pass, and a rejection-sampling rule provably preserves the target model's output distribution. We present a from-scratch, device-agnostic (CUDA/MPS/CPU) implementation and an empirical study across five draft/target backend configurations on a consumer Apple-silicon laptop. Distribution equivalence is verified at three levels, culminating in a two-sample test over roughly 9,200 real-model tokens per method ($\chi^2 = 162.5$, dof $= 200$, $p = 0.976$) and exact greedy-sequence agreement. The best configuration reaches a measured $1.61\times$ wall-clock speedup at $K=6$, on an acceptance profile declining from 69.7% at $K=1$ to 37.8% at the optimum, while three of five configurations decelerate, either because the draft fails to out-speed a small target or because the quantized Metal backend executes "parallel" verification serially, an effect we isolate and quantify. The failures are as instructive as the successes: speculative decoding pays off only when verification is genuinely batch-parallel and the draft/target latency gap is real.
arXiv:2607.17285v1 Announce Type: new
Abstract: Mixed finite element methods based on Raviart--Thomas spaces are widely used for the numerical approximation of second--order elliptic problems in flux form. On quadrilateral meshes, however, the bilinear mapping from the reference element introduces a spatially varying Jacobian, which may violate the inclusion property $\mathrm{div}\,V_h \subset W_h$ for the standard Raviart--Thomas spaces.
In this paper we propose a simple modification of the classical Raviart--Thomas elements on quadrilateral meshes. The modification consists of adding geometrically motivated correction terms to the local basis functions in order to compensate for the geometric distortion introduced by the bilinear mapping. The resulting spaces retain the same dimension and degrees of freedom as the classical Raviart--Thomas elements while restoring the compatibility property.
We present a general framework for constructing such modified spaces and illustrate the approach by developing modified versions of the lowest order and next--to--lowest order Raviart--Thomas elements. Theoretical analysis establishes optimal approximation properties under the standard shape--regularity assumption for quadrilateral meshes. Numerical experiments on distorted meshes confirm the predicted convergence rates and show that the modified elements yield consistently improved accuracy over the classical Raviart--Thomas formulation as the geometric distortion increases.