arXiv:2605.01117v2 Announce Type: replace Abstract: Full-f global gyrokinetic simulations of the plasma boundary have until now required heroic computational efforts and case-by-case expert intervention, precluding systematic parameter scans. Here we demonstrate a paradigm shift: hundreds of independent, concurrent, and unsupervised full-f boundary gyrokinetic simulations in a geometry inspired by the Tokamak \`a Configuration Variable (TCV), covering both the closed flux surface region and the open-field-line scrape-off layer (SOL) while scanning triangularity, elongation, and heating power. All simulations are evolved much longer than the turbulence relaxation time until the steady state is reached. Analysis of the steady-state profiles reveals that the impact of plasma shaping on confinement is strongly power dependent: at low power, triangularity primarily controls the SOL ion temperature, while at high power it mostly affects the edge ion temperature gradient. The low-power hot SOL observed for positive triangularity is explained by a neoclassical trapped-ion mechanism in which triangularity modifies the field-line arc length between banana turning points and the high-field-side limiter, altering the interaction with cold neutral-ionization regions. Fingerprint analysis of turbulent transport categorize the simulations in a regime dominated by ion temperature gradient (ITG) or trapped electron modes (TEMs), confirmed by dedicated local linear gyrokinetic calculations. The generated open data represents a previously unobtainable resource. It can serve both as a benchmark for boundary transport models, and as a training dataset for data-driven methods in fusion foundation and surrogate models.
Science Journals
arXiv:2605.02651v2 Announce Type: replace Abstract: Scientific peer review increasingly struggles to assess reproducibility at the scale and complexity of modern research output. Evaluating reproducibility requires reconstructing experimental dependencies, methodological choices, data flows, and result-generating procedures, which often exceeds what human reviewers can provide. Agentic Reproducibility Assessment (ARA) formalizes reproducibility assessment as a structured reasoning task over scientific documents. Given a paper, ARA extracts a directed workflow graph linking sources, methods, experiments, and outputs, then evaluates its reconstructability using structural and content-based scores for reproducibility assessments. Experiments on 213 ReScience C articles - the largest cross-domain benchmark of human-validated computational reproducibility studies considered to date - demonstrate ARA's generalizability and consistent workflow reconstruction and assessment across LLMs, model temperatures, and scientific domains. ARA achieves ~61% accuracy on three benchmarks, and the highest accuracy reported on ReproBench (60.71% vs. 36.84%) and GoldStandardDB (61.68% vs. 43.56%), highlighting its potential to complement human review at scale and enabling next-generation peer review. Code and Data available: https://github.com/AndresLaverdeMarin/agentic_reproducibility_assessment.
arXiv:2605.15475v1 Announce Type: new Abstract: We introduce an empowered transposed Fully Connected Weighted (t-FCW) graph representation to embed point clouds into a metric space. While original t-FCW has shown promising results for point cloud classification, the reasons behind its effectiveness and its broader applicability remained unclear. In this work, we analyze the properties that make the empowered and original t-FCW effective and design a network that uses the empowered t-FCW exclusively as feature extractors. From an interpretability perspective, we build memory banks for classification, part segmentation, and semantic segmentation using the empowered t-FCW. Our analysis reveals that the empowered t-FCW inherits robustness from surface descriptors, provides interpretability through dimension-wise relations. These properties enable a highly efficient and interpretable network, which processes the ModelNet40 classification problem in approximately 7 seconds on an NVIDIA RTX A5000 GPU. Importantly, empowered t-FCW can function both as a lightweight standalone baseline and as a complementary plug-in to existing deep models.
arXiv:2605.15480v1 Announce Type: new Abstract: Stochastic communication delays in teleoperation introduce signal discontinuities that undermine control stability and degrade control performance. Consequently, the conventional reinforcement learning (RL) methods struggle with the delayed observations due to the delay-induced observations, leading to high-frequency chattering. To address this, we propose a hybrid control framework, delay-resilient RL, integrating a state estimator utilizing Long Short-Term Memory (LSTM) with a residual RL policy, which is resilient to stochastic delays. The LSTM reconstructs smooth, continuous state estimates from delayed observations, enabling the RL agent to learn a residual torque compensation policy that balances tracking accuracy with velocity smoothness. Experimental validation on Franka Panda robots demonstrates that our approach significantly outperforms the state-of-the-art baselines, ensuring robust and stable teleoperation even under high-variance stochastic delays.
arXiv:2512.08964v4 Announce Type: replace Abstract: Graph learning aims to convert data into graph representations, which are fundamental to many problems in machine learning for CAD, where circuits, layouts, designs, and optimization states are often modeled as graph-structured objects. Existing graph learning methods usually rely on carefully designed graph construction rules, extensive parameter tuning, and sophisticated mathematical theory; moreover, achieving good performance often requires task-specific graph construction tailored to the downstream objective. In this work, we study whether a large language model (LLM) can reason about graph structure and infer a useful topology without observing the feature matrix, without knowing the downstream task, and without relying on any carefully designed graph construction algorithm or parameter tuning process. To this end, we propose T2T-LA, a Topology-to-Topology LLM Agent that receives no input other than a set of previously failed topologies and the scores assigned to them by a private scorer. The agent is not told what task or algorithm produces the scores, how these topologies are generated, or what the scores mean. Since none of the observed topologies is satisfactory, T2T-LA cannot simply imitate a good example. Instead, it is forced to infer hidden relationships between graph connectivity patterns and the observed scores, a capability that is particularly relevant to CAD scenarios where useful design structures may be difficult to specify manually. Experimental results show that T2T-LA can generate, in one shot, a graph topology that enables the downstream algorithm to produce a sufficiently good solution, suggesting a new LLM-driven direction for topology reasoning and graph representation learning in ML-for-CAD workflows.
Beyond the Training Data: Confidence-Guided Mixing of Parameterizations in a Hybrid AI-Climate Model
arXiv:2510.08107v5 Announce Type: replace Abstract: Persistent systematic errors in Earth system models (ESMs) arise from difficulties in representing the full diversity of subgrid, multiscale atmospheric convection and turbulence. Machine learning (ML) parameterizations trained on short high-resolution simulations show strong potential to reduce these errors. However, stable long-term atmospheric simulations with hybrid (physics + ML) ESMs remain difficult, as neural networks (NNs) trained offline often destabilize online runs. Training convection parameterizations directly on coarse-grained data is challenging, notably because scales cannot be cleanly separated. This issue is mitigated using data from superparameterized simulations, which provide clearer scale separation. Yet, transferring a parameterization from one ESM to another remains difficult due to distribution shifts that induce large inference errors. Here, we present a proof-of-concept where a ClimSim-trained, physics-informed NN convection parameterization is successfully transferred to ICON-A. The scheme is (a) trained on adjusted ClimSim data with subtracted radiative tendencies, and (b) integrated into ICON-A. The NN parameterization predicts its own error, enabling mixing with a conventional convection scheme when confidence is low, thus making the hybrid AI-physics model tunable with respect to observations and reanalysis through mixing parameters. This improves process understanding by constraining convective tendencies across column water vapor, lower-tropospheric stability, and geographical conditions, yielding interpretable regime behavior. In AMIP-style setups, several hybrid configurations outperform the default convection scheme (e.g., improved precipitation statistics). With additive input noise during training, both hybrid and pure-ML schemes lead to stable simulations and remain physically consistent for at least 20 years.
arXiv:2510.06062v2 Announce Type: replace Abstract: Reinforcement learning (RL) has shown great promise in large language models (LLMs) post-training, which typically rely on token-level clipping to maintain stability during optimization. Despite the empirical success of GRPO-style methods, we identify a fundamental and previously overlooked challenge in this popular Outcome-Supervised RL (OSRL) paradigm. We reveal that in OSRL, where advantages are shared across tokens within a response, importance sampling (IS) ratios deviate from their traditional purpose of distribution correction as in classic RL, which become token-level weights that allocate the shared advantage signal across tokens. We show that this hidden role shift induces a critical mismatch for positive-advantage tokens, leading to unbalanced token weighting between positive and negative tokens. Specifically, it suppresses the update of underrepresented tokens that are lagging behind, while over-amplifying already high-probability tokens. This mismatch results in rich-get-richer dynamics that over-reinforce confident tokens, weaken catch-up learning that drive entropy collapse, excessive repetition, and premature convergence. To address this, we propose Asymmetric Importance Sampling Policy Optimization (ASPO), a simple yet effective strategy that reverses the ratio-induced weighting of positive-advantage tokens, while stabilizing extreme updates and maintaining gradient flow. This mismatch correction aligns their update direction with the learning dynamics of negative ones. Comprehensive experiments across math reasoning and coding benchmarks demonstrate that ASPO significantly mitigates entropy collapse, improves training stability, and enhances performance over strong GRPO-based baselines. Our analysis provides new insights into the role of token-level weighting in OSRL and highlights the critical importance of correcting ratio-induced weighting in LLM RL.
arXiv:2605.15226v1 Announce Type: new Abstract: We ask whether agentic AI systems built for software engineering transfer to realistic hardware engineering. Existing hardware LLM benchmarks isolate sub-tasks but none jointly requires repository navigation, hierarchy-aware localization, Electronic Design Automation (EDA) executable verification, and maintenance-style patching. We introduce \textbf{Phoenix-bench}, a synchronized corpus of 511 verified Verilator instances from 114 GitHub repositories, each shipped with the developer patch, design-flow labels, fail-to-pass and pass-to-pass testbenches, and a Docker-pinned EDA environment so resolved-rate differences reflect agent behavior rather than toolchain availability. Using Phoenix-bench we run a uniform evaluation of four commercial agents and eight open-source agentic structures across four LLM backbones, plus two diagnostic interventions (file-level oracle localization and one round of testbench-log feedback). Three findings emerge. (i)~Software and hardware are fundamentally different engineering tasks: the same agent loses 37\% to 58\% from SWE-bench Verified to Phoenix-bench because hardware bugs propagate across parallel instantiated modules through signal flow rather than along a software-style call graph, and software-tuned agents stop at the symptom file instead of tracing back through the instantiation chain. (ii)~Failures concentrate on design control-flow / finite state machine (FSM) bugs, verification testbench bugs, and hard cases that demand cross-hierarchy signal-flow tracking and coordinated multi-file edits. (iii)~Localization granularity matters far more than localization itself: a perfect file-level oracle yields only $+1.4$\% because the agent then breaks files that did not need editing, while a single round of test case feedback lifts resolved rate by $42$\% to $45$\% because the test case tells \emph{where} the bug is and \emph{what} the fix has to look like.
arXiv:2605.16089v1 Announce Type: new Abstract: Federated Learning (FL) has emerged as a promising paradigm for collaborative model training across distributed edge devices while preserving data privacy especially with the huge increase amount of data due to the adoption of technologies which contributes to the growing number of IoT devices. Storing this amount of data centrally is challenging due to issues like limited communication, privacy, and regulations. FL can be Centralized (CFL), Decentralized (DFL), and Semi-decentralized (SDFL). Choosing the right FL architecture depends on the application's needs. However, very few research studies have experimentally compared these three types of architectures to not only understand the respective strengths and limitations, but also trade-offs between different performance indicators. This paper overcome this lack of analysis, conducting experimental analyses using the Fedstellar simulator, MNIST dataset, and MLP classifier.
arXiv:2605.14859v2 Announce Type: replace Abstract: As coding agents gain access to shells, repositories, and user files, least-privilege authorization becomes a prerequisite for safe deployment: an agent should receive enough authority to complete the task, without unnecessary authority that exposes sensitive surfaces. To study whether current models can infer this boundary themselves, we first introduce permission-boundary inference, where a model maps a task instruction and terminal environment to a file-level read/write/execute policy, and AuthBench, a benchmark of 120 realistic terminal tasks with human-reviewed permission labels and executable validators for utility and attack outcomes. AuthBench shows that authorization is not a simple conservative-versus-permissive calibration problem: frontier models often omit permissions required by the execution chain while also granting unused or sensitive accesses. Increasing inference-time reasoning does not resolve this mismatch. Instead, each model moves toward a model-specific authorization attractor: more reasoning makes it more consistent in its own failure mode, whether broad-but-exposed or tight-but-brittle. This suggests that direct policy generation is the bottleneck, because a single generation must both discover all necessary accesses and reject all unnecessary ones. We therefore propose Sufficiency-Tightness Decomposition, which first generates a coverage-oriented policy by forward-simulating the task and then audits each granted entry for grounding and sensitivity. Across tested models, this decomposition improves sensitive-task success by up to 15.8% on tightness-biased models while reducing attack success across all evaluated models.
arXiv:2605.16208v1 Announce Type: cross Abstract: Flexible continuous-time survival modeling is critical for capturing complex time-varying hazard dynamics in high-dimensional data; however, training such models remains challenging due to the intractable integral required for likelihood estimation. We introduce QSurv, a scalable deep learning framework that enables nonparametric continuous-time modeling without relying on time discretization or restrictive distributional assumptions. We propose a training objective based on Gauss-Legendre numerical quadrature, which approximates the cumulative hazard with high-order accuracy while facilitating efficient end-to-end training via standard backpropagation. Furthermore, to effectively capture non-stationary hazard dynamics in complex architectures, we introduce time-conditioned low-rank adaptation, a mechanism that conditions general neural backbones on time by dynamically modulating weights via low-rank updates. We provide theoretical analysis establishing approximation error bounds for cumulative-hazard evaluation. Comprehensive experiments across synthetic benchmarks, large-scale real-world tabular datasets, and high-dimensional medical imaging tasks demonstrate that QSurv achieves competitive predictive performance with advantages in instantaneous hazard function estimation, enabling more interpretable characterization of time-varying risk patterns.
arXiv:2605.15224v1 Announce Type: new Abstract: Large language model-based agents make mistakes, yet critique can often guide the same model toward correct behavior. However, when critique is removed, the model may fail again on the same query, indicating that it has not internalized the critique's guidance into its underlying capability. Meanwhile, a frozen critic cannot improve its feedback quality over time, limiting the potential for iterative self-improvement. To address this, we propose learning to internalize self-critique with reinforcement learning(ICRL), a novel framework that jointly trains a solver and a critic from a shared backbone to convert critique-induced success into unassisted solver ability. The critic is rewarded based on the solver's subsequent performance gain, incentivizing actionable feedback. To address the distribution shift between critique-conditioned and critique-free behavior, ICRL introduces a distribution-calibration re-weighting ratio that selectively transfers critique-guided improvements compatible with the solver's own prompt distribution. Additionally, a role-wise group advantage estimation stabilizes joint optimization across the two roles. Together, these mechanisms ensure that the solver learns to improve itself without external critique, rather than becoming dependent on critique-conditioned behavior. We evaluate ICRL on diverse benchmarks spanning agentic and mathematical reasoning tasks, using Qwen3-4B and Qwen3-8B as backbones. Results show consistent improvements, with average gains of 6.4 points over GRPO on agentic tasks, and 7.0 points on mathematical reasoning. Notably, the learned 8B critic is comparable to 32B critics while using substantially fewer tokens. The code is available at https://github.com/brick-pid/ICRL.
arXiv:2605.06390v3 Announce Type: replace Abstract: A leading proposal for aligning artificial superintelligence (ASI) is to use AI agents to automate an increasing fraction of alignment research as capabilities improve. We argue that, even when research agents are not scheming to deliberately sabotage alignment work, this plan could produce compelling but catastrophically misleading safety assessments resulting in the unintentional deployment of misaligned AI. This could happen because alignment research involves many hard-to-supervise fuzzy tasks (tasks without clear evaluation criteria, for which human judgement is systematically flawed). Consequently, research outputs will contain systematic, undetected errors, and even correct outputs could be incorrectly aggregated into overconfident safety assessments. This problem is likely to be worse for automated alignment research than for human-generated alignment research for several reasons: 1) optimisation pressure means agent-generated mistakes are concentrated among those that human reviewers are least likely to catch; 2) agents are likely to produce errors that do not resemble human mistakes; 3) AI-generated alignment solutions may involve arguments humans cannot evaluate; and 4) shared weights, data and training processes may make AI outputs more correlated than human equivalents. Therefore, agents must be trained to reliably perform hard-to-supervise fuzzy tasks. Generalisation and scalable oversight are the leading candidates for achieving this but both face novel challenges in the context of automated alignment.
arXiv:2605.07074v2 Announce Type: replace Abstract: Detecting AI-generated images across unseen architectures remains challenging, as existing models often overfit to generator-specific fingerprints and semantic content rather than learning universal forgery traces. We attribute this failure to feature entanglement: detectors learn these factors as a single entangled representation, where universal forgery traces are inextricably confounded with both generator-specific fingerprints and semantic content. Crucially, our spectral analysis reveals that this entanglement is avoidable: distinct generator-specific fingerprints (e.g., GAN stripes vs. Diffusion Model spots) occupy disjoint frequency subspaces and coexist as independent superpositions. Leveraging this physical orthogonality, we propose the Orthogonal Decomposition and Purification Network (ODP-Net) to structurally disentangle these factors. Specifically, ODP-Net employs (1) Instance-aware Orthogonal Decomposition to project features into mutually exclusive subspaces: universal forgery traces, generator-specific fingerprints, and semantic content; (2) Perturbation-based Purification to enforce semantic invariance via cross-sample feature injection; and (3) Manifold Alignment to bridge domain gaps. By explicitly decoupling universal forgery traces from generator-specific fingerprints and semantic content, ODP-Net achieves state-of-the-art performance on unseen architectures (e.g., Stable Diffusion 3), validating that structural disentanglement is key to generalization.
arXiv:2605.07557v4 Announce Type: replace Abstract: Semi-supervised learning faces significant challenges in realistic scenarios where labeled data is scarce and unlabeled data follows unknown, arbitrary distributions. We formalize this critical yet under-explored paradigm as Universal Semi-supervised Learning (UniSSL). Existing methods typically leverage unlabeled data via pseudo-labeling. However, they often rely on the idealized assumption of a uniform unlabeled data distribution or require sufficient labeled data to estimate it. In the UniSSL setting, such dependencies lead to numerous erroneous pseudo-labels, thereby triggering representation confusion. Fortunately, we observe that inter-sample relations captured by representations are more reliable than pseudo-labels. Leveraging this insight, we shift our focus to representation-level structural inference to bypass distribution estimation. Accordingly, we propose Simplex Anchored Graph-state Equipartition (SAGE), which captures high-order inter-sample dependencies to establish structural consensus for guiding representation learning. Meanwhile, to mitigate representation confusion, we employ vectors that satisfy a simplex equiangular tight frame to serve as a coordinate frame for guiding inter-class representation separation. Finally, we introduce a weighting strategy based on distribution-agnostic metrics to prioritize reliable pseudo-labels and an auxiliary branch to isolate potentially erroneous pseudo-labels. Evaluations on five standard benchmarks show that SAGE consistently outperforms state-of-the-art methods, with an average accuracy gain of $\textbf{8.52%}$.
arXiv:2605.15485v1 Announce Type: new Abstract: We report the first observation on the EXL-50U spherical torus that energetic particles injected by neutral beam injection (NBI) can be stably accelerated to significantly higher energies - reaching up to 2.5 times the injection energy, occurring without significant large-scale magnetohydrodynamic (MHD) bursts. Simulations based on EXL-50U parameters indicate that small-scale magnetic reconnection, mediated by multiple magnetic islands, fails to accelerate bulk thermal ions but efficiently energizes seed fast ions. Unlike global MHD events, such small-scale reconnection is ubiquitous in magnetic confinement devices and does not degrade core confinement. This mechanism offers a novel and potentially universal channel for auxiliary ion heating in future fusion reactors.
arXiv:2605.15486v1 Announce Type: new Abstract: This study introduces intelligent frameworks that use Large Language Models (LLMs) to improve task scheduling for construction robots. The LLM is fed with key data about the desired task, such as agent action abilities, and the desired end goal to be achieved. A well-balanced allocation strategy is developed, optimizing both time efficiency and resource utilization. Our system utilizes a Natural Language Processing interface to streamline communication with construction professionals and adapt in real-time to unexpected site conditions. We concurrently use two LLM agents, specifically generator (GPT-4) and supervisor (Gemma 3/Llama 4/Mistral 7b) LLM agents to provide a more precise task schedule. We evaluate the proposed methodology using a straightforward scenario and provide metric scores to prove the efficacy of the frameworks. Our results highlight that the implementation of LLMs is crucial in construction operational tasks including robots.
arXiv:2604.26126v3 Announce Type: replace Abstract: This paper proposes a deep reinforcement learning (DRL)-based event-triggered controller design for networked artificial pancreas (AP) systems. Although existing DRL-based AP controllers typically assume periodic control updates, networked control systems (NCSs) require a reduction in communication frequency to achieve energy-efficient operation, which is directly tied to control updates. However, jointly learning both insulin dosing and update timing significantly increases the complexity of the learning problem. To alleviate this complexity, we develop a practical DRL-based controller design that avoids explicitly learning update timing by introducing a rule-based criterion defined by changes in blood glucose. As a result, decision-making occurs at irregular intervals, and the problem is naturally formulated as a semi-Markov decision process (SMDP), for which we extend a standard DRL algorithm. Numerical experiments demonstrate that the proposed method improves communication efficiency while maintaining control performance.
arXiv:2605.15487v1 Announce Type: new Abstract: Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.
arXiv:2604.17669v2 Announce Type: replace Abstract: This paper presents a comprehensive review of the NTIRE 2026 Low Light Image Enhancement Challenge, highlighting the proposed solutions and final results. The objective of this challenge is to identify effective networks capable of producing clearer and visually compelling images in diverse and challenging conditions by learning representative visual cues with the purpose of restoring information loss due to low-contrast and noisy images. A total of 195 participants registered for the first track and 153 for the second track of the competition, and 22 teams ultimately submitted valid entries. This paper thoroughly evaluates the state-of-the-art advances in (joint denoising and) low-light image enhancement, showcasing the significant progress in the field, while leveraging samples of our novel dataset.
arXiv:2605.15492v1 Announce Type: new Abstract: Generative models such as diffusion and flow matching have become dominant paradigms for visuomotor policy learning, yet their reliance on iterative denoising incurs high inference latency incompatible with real-time robotic control. We present Fast Legendre-polynomial Action policy via Sparse History-anchored flow (FLASH Policy), which replaces discrete action-chunk generation with continuous Legendre polynomial trajectory representation. Specifically, by fitting expert demonstrations under sparse temporal sampling, FLASH enables a single inference to cover a significantly extended action horizon. To further accelerate generation, FLASH initiates the flow matching process from history polynomial coefficients rather than uninformative Gaussian noise, shortening the transport distance and enabling accurate single-step inference. Moreover, analytic polynomial differentiation directly provides desired velocity feed-forward signals to the torque controller without numerical approximation. Extensive experiments on five simulated and two real-world manipulation tasks demonstrate that FLASH achieves state-of-the-art success rates ($\ge 92\%$ across all tasks), a per-episode inference time of $31.40\,ms$ (up to $175\times$ faster than diffusion policies and $18\times$ faster than prior flow matching policies), up to $4\times$ faster training convergence than ACT, and $5\times$ to $7\times$ reduction in controller tracking error compared to discrete-action baselines.
arXiv:2605.15496v1 Announce Type: new Abstract: Neural distance fields offer a compact and continuous representation of 3D geometry, making them attractive for incremental LiDAR mapping. However, their online optimization is vulnerable to catastrophic forgetting, where new observations can degrade previously reconstructed geometry. Replay-based training is commonly used to address this issue, but existing methods typically rely on passive replay buffers and uniform sampling, which can waste memory on redundant observations and under-train poorly constrained regions. We propose LAPS, a replay management framework for incremental neural mapping that improves both replay retention and replay allocation during online updates. LAPS combines reliability-based active pooling to retain reliable historical samples under limited memory with uncertainty-guided active sampling to focus optimization on under-constrained regions. Experiments on synthetic and real-world benchmarks show that LAPS consistently improves reconstruction completeness while maintaining competitive geometric accuracy. On Oxford Spires, it improves recall by 4.66 pp and F1-score by 3.79 pp over PIN-SLAM on the Blenheim Palace 05 sequence. We release our open source implementation at: https://github.com/dongjae0107/LAPS.
arXiv:2605.15498v1 Announce Type: new Abstract: From a new perspective, this paper rederives Lagrange's equations. By applying the chain rule of differentiation, the intrinsic relationship between the momentum theorem and the kinetic energy theorem is first established. Subsequently, expressing the differential form of energy conservation in an arbitrary coordinate system and performing suitable differential operations yields Lagrange's equations. Generalized forces and generalized displacements are shown to be component representations of forces and displacements in a chosen coordinate system. Consequently, the essence of Lagrange's equations is identified as the transformation of the kinetic energy theorem into the momentum theorem via the chain rule for composite functions, thereby revealing how energy conservation constructs momentum conservation.
arXiv:2605.09403v2 Announce Type: replace Abstract: Architectural choices inside the Transformer feedforward network (FFN) block do not merely affect the block itself; they reshape the computations learned by the rest of the model. We study this effect in one-layer Transformers trained on digit addition with carry, modular arithmetic, and histogram counting. Comparing dense FFNs, gated linear units (GLUs), mixture-of-experts (MoE), and MoE-GLUs, we find that sparse MoE routing can shift computation from FFN to attention, with the strongest ablation-visible effect on carry-based addition. We decompose this redistribution into reduced per-token FFN capacity and sparse partitioning across experts. Critically, frozen random routing nearly matches learned routing, suggesting that redistribution is driven largely by architectural sparsity rather than router-learned specialization. As a secondary finding, GLU-style multiplicative gating rotates task-relevant Fourier structure out of the per-neuron basis and into distributed subspaces, making neuron-level interpretability less informative while preserving structured computation. We validate these conclusions with random-routing, narrow-FFN, and top-2 MoE controls, plus parameter-matching, activation-function, and width-scaling analyses. Together, these results show that local FFN design choices can have nonlocal consequences for Transformer computation.
arXiv:2605.15506v1 Announce Type: new Abstract: Over the past several decades, CDCL SAT solvers have proven remarkably effective on large industrial formulas, despite SAT being NP-complete and widely believed to be intractable. While considerable empirical research has been done on solver performance over benchmarks like the SAT competition, as well as scaling studies on random and crafted families, surprisingly little effort has gone into systematic scaling studies over industrial instances. To address this gap, we collect a large benchmark of Bounded Model Checking (BMC) instances (76,600+ across 766 families) and perform a systematic scaling study of solver performance. We observe a spectrum: some families scale linearly, others polynomially or exponentially. Building on this foundation, we study the structural parameters that have been proposed to explain this phenomenon. We first show that previously proposed parameters -- clause-variable ratio, treewidth, and community structure -- fail to discriminate between the linear and exponential regimes. By contrast, the recently proposed \emph{proofdoor} parameter explains this phenomenon well. Informally, a proofdoor is a sequence of interpolants between chunks of a formula, where each interpolant represents the solver's memoization of reasoning effort on chunks it has already analyzed. In support of the proofdoor hypothesis, we make three key contributions. First, we empirically show that CDCL solvers do compute small proofdoors for linearly-scaling BMC instances. Second, we show that for exponentially-scaling instances, sampled proofdoors scale exponentially and are typically not incrementally absorbed. Third, we show that scrambling linearly-scaling instances yields larger proofdoor sizes relative to pre-scrambling, relating poor branching order to larger proofdoor sizes and drop in solver performance.