arXiv:2511.05567v2 Announce Type: replace Abstract: An adaptive structural learning method of Restricted Boltzmann Machine (RBM) and Deep Belief Network (DBN) has been developed as one of prominent deep learning models. The neuron generation-annihilation algorithm in RBM and layer generation algorithm in DBN make an optimal network structure for given input during the learning. In this paper, our model is applied to an automatic recognition method of road network system, called RoadTracer. RoadTracer can generate a road map on the ground surface from aerial photograph data. A novel method of RoadTracer using the Teacher-Student based ensemble learning model of Adaptive DBN is proposed, since the road maps contain many complicated features so that a model with high representation power to detect should be required. The experimental results showed the detection accuracy of the proposed model was improved from 40.0\% to 89.0\% on average in the seven major cities among the test dataset. In addition, we challenged to apply our method to the detection of available roads when landslide by natural disaster is occurred, in order to rapidly obtain a way of transportation. For fast inference, a small size of the trained model was implemented on a small embedded edge device as lightweight deep learning. We reported the detection results for the satellite image before and after the rainfall disaster in Japan. This version of the article was improved the search algorithm at the border around image.
Science Journals
arXiv:2511.05715v3 Announce Type: replace Abstract: We study autonomous pickup-and-delivery routing problems in which internal adversarial agents spoof their locations to attract request assignments and then intentionally leave those requests unserviced. Such attacks disrupt the centralized scheduler, causing delays, cancellations, and routing instability. A routing policy is stable if its cost remains uniformly bounded over time. Existing policy-cost formulations typically characterize cost through the work required to service outstanding requests. Such a formulation requires analyzing agent-specific route execution and is therefore not well suited to adversarial settings, where non-cooperative agents may arbitrarily deviate from assigned routes or fail to service requests altogether. We introduce a new policy-cost formulation based only on observable system signals, namely the numbers of outstanding and canceled requests. Under bounded arrivals and finite request time windows, we show that stability under this formulation is equivalent to keeping the expected cumulative number of canceled requests uniformly bounded over time, an important operational metric in both cooperative and adversarial settings. We also extend cooperative fleet-sizing guarantees to finite time-window settings and highlight that request time windows are not merely a modeling detail, but are essential for ruling out \emph{degenerate stability}, a regime in which policies are certified as stable despite undesirable large request backlogs.
arXiv:2511.05934v2 Announce Type: replace Abstract: Generative modeling frameworks have emerged as an effective approach to capture high-dimensional image distributions from large datasets without requiring domain-specific knowledge, a capability essential for disease progression modeling. Recent generative approaches have attempted to capture progression by mapping images to a latent space and guiding representations to generate follow-up images from previous time points. However, these methods impose constraints on distribution learning, resulting in latent spaces with limited controllability for generating follow-up images without paired subject-specific longitudinal guidance. In order to enable controlled movements in the latent representational space and generate progression images from a previous time-point image without subject-specific guidance, we introduce a conditionable Diffusion Auto-encoder framework that forms a compact latent space capturing high-level semantics and providing means to control generation. Our approach leverages this latent space to condition and apply controlled shifts to the representations of previous time-point images by isolating progression and subject identity information for generating follow-up images. The shifts are implicitly guided by correlating with progression attributes and constraining to Alzheimer's disease specific regions, without paired longitudinal guidance. We validate the generations through image quality metrics, volumetric progression analysis, and downstream tasks in Alzheimer's disease datasets from different sources. This demonstrates the effectiveness of our approach for Alzheimer's progression modeling and longitudinal image generation.
arXiv:2511.06090v3 Announce Type: replace Abstract: Optimizing the performance of large-scale software repositories demands expertise in code reasoning and software engineering (SWE) to reduce runtime while preserving program correctness. However, most benchmarks emphasize what to fix rather than how to fix code. We introduce SWE-fficiency, a benchmark for evaluating repository-level performance optimization on real workloads. Our suite contains 498 tasks across nine widely used data-science, machine-learning, and HPC repositories (e.g., numpy, pandas, scipy): given a complete codebase and a slow workload, an agent must investigate code semantics, localize bottlenecks and relevant tests, and produce a patch that matches or exceeds expert speedup while passing the same unit tests. To enable this how-to-fix evaluation, our automated pipeline scrapes GitHub pull requests for performance-improving edits, combining keyword filtering, static analysis, coverage tooling, and execution validation to both confirm expert speedup baselines and identify relevant repository unit tests. Empirical evaluation of state-of-the-art agents reveals significant underperformance. On average, agents achieve less than 0.23x the expert speedup: agents struggle in localizing optimization opportunities, reasoning about execution across functions, and maintaining correctness in proposed edits. We release the benchmark and accompanying data pipeline to facilitate research on automated performance engineering and long-horizon software reasoning.
arXiv:2602.07518v3 Announce Type: replace Abstract: Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical analogue KAN architecture in which edge functions are realized in materia using reconfigurable nonlinear-processing units (RNPUs): multi-terminal nanoscale silicon devices whose input-output characteristics are tuned via control voltages. By combining multiple RNPUs into an edge processor and assembling these blocks into a reconfigurable analogue KAN (aKAN) architecture with integrated mixed-signal interfacing, we establish a realistic system-level hardware implementation that enables compact KAN-style regression and classification with programmable nonlinear transformations. Using experimentally calibrated RNPU models and hardware measurements, we demonstrate accurate function approximation across increasing task complexity while requiring fewer or comparable trainable parameters than multilayer perceptrons (MLPs). System-level estimates indicate an energy per inference of roughly 200 pJ and an end-to-end inference latency of roughly 0.6 $\mu$s for a representative workload, corresponding to over 100$\times$ reduction in energy accompanied by $>$10$\times$ reduction in area compared to a digital fixed-point MLP at similar approximation error. These results establish RNPUs as scalable, hardware-native nonlinear computing primitives and identify analogue KAN architectures as a realistic silicon-based pathway toward energy-, latency-, and footprint-efficient analogue neural-network hardware, particularly for edge inference.
arXiv:2504.04133v3 Announce Type: replace Abstract: Standard analyses of expected runtimes for randomized algorithms typically bypass the explicit construction of an underlying probability space. In this paper, we provide a formal, yet intuitive tree-based definition of the probability space for the execution paths of such algorithms. Using this model, we derive the recurrence equation for the expected runtime.
arXiv:2606.30333v1 Announce Type: cross Abstract: The generalized Ising problem captures a broad spectrum of hard combinatorial problems, including MAX-CUT, Number Partitioning (NPP), and Maximum Independent Set. In this work, we consider the notion of one-flip local minima for this problem. We construct a polynomial relaxation and prove the landscape equivalence theorem: there exists a one-to-one correspondence between the local minima of the relaxation and the one-flip minima of the original Ising problem. This guarantee reduces the Ising problem to finding the local minima of a smooth function, allowing us to leverage gradient-based optimizers such as ADAM. We demonstrate that our method is scalable and it achieves strong performance across challenging benchmarks, including spin-glass models, MAX-CUT, and NPP.
arXiv:2504.04447v2 Announce Type: replace Abstract: We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of a non-convex energy cost functional. Our approach employs a discontinuous space for the conductivity tensor that allows us to guarantee the preservation of its positive semi-definiteness throughout the entire minimization procedure arising from the time integration of the gradient flow dynamics using a backward Euler scheme. Extensive tests in two and three dimensions demonstrate the robustness and performance of the solver, highlight the sensitivity of the emergent network structures to mesh resolution and topology, and validate the resilience of the linear preconditioner to the ill-conditioning of the model. The implementation achieves near-optimal parallel scaling on large-scale, high-performance computing platforms. To the best of our knowledge, the network formation system has never been simulated in three dimensions before. Consequently, our three-dimensional results are the first of their kind.
arXiv:2511.08370v3 Announce Type: replace Abstract: This paper presents an $\mathcal{H}_\infty$ model matching control-based approach to the problem of power hardware-in-the-loop (PHIL) interfacing. The objective is to interconnect a grid simulation and a physical device via an interface in a way that is stable and accurate. Conventional approaches include the ideal transformer method (ITM) and its impedance-based variants, which trade accuracy for stability, as well as some $\mathcal{H}_\infty$ control-based approaches, which do not make use of all the available information in their optimization for accuracy. Designing for transparency, as opposed to accuracy as existing approaches do, would achieve both accuracy and stability, while making use of all the dynamical information present in the idealized interconnection of the grid and device. The approach proposed in this paper employs model matching to formulate the PHIL problem as an $\mathcal{H}_\infty$ control problem using transparency as the explicit frequency-domain control objective. The approach is experimentally validated in a real-time resistive-load PHIL setup, and is found to achieve accuracy levels that are comparable or superior to those of an ITM-based interface.
arXiv:2511.10480v3 Announce Type: replace Abstract: Optimizing the performance of large language models (LLMs) on large-scale AI training and inference systems requires a scalable and expressive mechanism to model distributed workload execution. Such modeling is essential for pre-deployment system-level optimizations (e.g., parallelization strategies) and hardware design-space explorations. While recent efforts have proposed collecting execution traces from real systems, access to large-scale infrastructure remains limited to major cloud providers. Moreover, traces capturing execution on a specific platform cannot be easily adapted to study alternate software and/or hardware configurations, especially at scale. We introduce STAGE, a framework that synthesizes high-fidelity execution graphs to accurately model distributed AI workloads (including LLMs and MoEs). STAGE supports a comprehensive set of parallelization strategies, allowing users to systematically explore a wide spectrum of model architectures and system configurations. STAGE demonstrates its scalability by synthesizing high-fidelity LLM traces spanning over 128K GPUs, while preserving tensorlevel accuracy in compute, memory, and communication. STAGE is publicy available at https://github.com/astra-sim/stage
arXiv:2511.14900v2 Announce Type: replace Abstract: Vision--language models (VLMs) have recently shown promise for assisting clinical reasoning in dermatological diagnosis. However, their trustworthiness and clinical utility remain limited by three key challenges: heterogeneous datasets with inconsistent diagnostic labels and concept annotations, the lack of grounded diagnostic rationales for reliable reasoning supervision, and limited scalability when transferring knowledge from small, densely annotated datasets to large collections with sparse labels. To address these challenges, we propose Skin-R1, a dermatology-oriented VLM that integrates textbook-grounded clinical reasoning supervision with reinforcement learning (RL) to improve the accuracy and robustness of diagnostic prediction. First, we construct a textbook-based reasoning generator that synthesizes hierarchy-aware and differential-diagnosis (DDx) diagnostic trajectories derived from authoritative dermatology knowledge. Second, these trajectories are used for supervised fine-tuning (SFT), establishing a clinically grounded reasoning foundation for the model. Finally, we introduce an RL training framework that incorporates the hierarchical structure of dermatological diseases into the reward design, enabling the model to generalize grounded diagnostic reasoning to large-scale datasets with sparse annotations. Extensive experiments across multiple dermatology benchmarks demonstrate that Skin-R1 consistently improves diagnostic accuracy and robustness compared to state-of-the-art Med-VLM baselines. Ablation studies further highlight the critical role of grounded reasoning supervision introduced during the SFT stage.
arXiv:2511.15503v3 Announce Type: replace Abstract: High-performance Host processors can integrate Processing-In-Memory (PIM) devices, which can accelerate memory-intensive kernels of Machine Learning (ML) models, including Large Language Models (LLMs), by leveraging the large memory bandwidth available at PIM cores. However, Host processor needs consecutive elements distributed across DRAM banks, while PIM cores need consecutive elements within their local banks. This necessitates data rearrangements in ML kernel execution that pose significant performance and programmability challenges, further exacerbated by the need to support diverse PIM devices. Current compilation approaches lack systematic optimization for diverse ML kernels and multiple PIM devices, and may largely ignore data rearrangement costs during the compute code optimization step. We show that data rearrangements and compute code optimization are interdependent, and need to be jointly optimized during the tuning process. Therefore, we design DCC, the first data-centric ML compiler for PIM systems that jointly co-optimizes data rearrangements and compute code in a unified tuning process. DCC integrates a multi-layer PIM abstraction to support multiple PIM backends. DCC enables effective co-optimization of data partitioning strategies with compute loop partitioning schemes. DCC applies PIM-specific code optimizations, and leverages a fast and accurate performance prediction model to select the bestperforming code schedule for a given kernel on a target PIM architecture. Our evaluations in various individual ML kernels show that DCC achieves up to 7.68x speedup (2.21x average) on HBM-PIM, and up to 13.17x speedup (3.92x average) on AttAcc PIM, over GPU-only execution. In end-to-end LLM inference, DCC on AttAcc accelerates GPT-3 and LLaMA-2 by 4.52x average (up to 7.71x in LLaMA-2) over GPU. DCC is open-sourced at https://github.com/SPIN-Research-Group/DCC.
arXiv:2606.30402v1 Announce Type: cross Abstract: Molten salts such as FLiBe (2LiF--BeF$_2$) are leading blanket materials for breeding and recovering tritium in fusion reactors. Predicting tritium speciation requires accurate electronic ground-state energies for representative molten-salt clusters, a demanding task for correlated electronic-structure methods. Here we report the first application of heterogeneous quantum--classical computing to tritium binding in FLiBe. Clusters drawn from ab initio molecular dynamics are partitioned by an embedded-wavefunction (EWF) method into atom-centered fragments, and the largest fragments are solved on IBM quantum hardware using extended sample-based quantum diagonalization (ext-SQD). Across nine clusters, the heterogeneous quantum--classical workflow reproduces fragment ground-state energies with agreement to full configuration interaction within 0.7~kcal/mol and a mean absolute deviation of 0.3~kcal/mol. In contrast, fragmented and unfragmented conformational energy differences and tritium binding energies differ by 12~kcal/mol and 110~kcal/mol on average, respectively, identifying fragment construction rather than fragment solution as the dominant source of algorithmic bias. To the best of our knowledge, this is the first such demonstration for a charged ionic system and in particular an inorganic molten salt, where electrostatic and polarization effects make the accurate treatment of electronic correlation particularly challenging. These results also identify areas of future research towards an accurate and scalable quantum--classical workflow to compute free-energy estimates of tritium speciation in fusion blankets.
arXiv:2606.30424v1 Announce Type: cross Abstract: Quantum entanglement is one of the most intriguing features of quantum mechanics. To investigate the entanglement between two excitons in a biexciton, an experimental technique called density matrix spectroscopy (DMS) has recently been developed. DMS combines stimulated emission tomography and pump-probe techniques to obtain a time-resolved density matrix of the polarization state of a photon pair emitted from the biexciton. The reconstructed density matrix is expected to encode information about the biexciton state and its entanglement dynamics, but the precise nature of this connection has remained unclear. In this paper, we derive an analytical relationship between the density matrix obtained by DMS and the biexciton state. In addition, we perform numerical simulations to compare the entanglement dynamics obtained by DMS with the biexciton's entanglement dynamics in a two-dimensional electron-hole system using an extended ionic Hubbard model. We find that DMS can partially capture the entanglement in the biexciton, in particular, the dynamics of the difference $S_{\mathrm{bi}} - S_k$, where $S_{\mathrm{bi}}$ is the entanglement entropy of the biexciton and $S_k$ is the entanglement in terms of the wavevectors of the excitons that constitute the biexciton. These results demonstrate the validity of DMS for obtaining information about the entanglement dynamics of the biexciton.
arXiv:2606.30428v1 Announce Type: cross Abstract: We consider the problem of estimating numerically integrals of the shape $$ \int_P \frac{dt}{t_1 \dotsb t_k} $$ where $P \in {\mathbb R}_{>0}^k$ is a convex polytope, $t=(t_1,\dotsc, t_k)$ and $d t$ is the Lebesgue measure. This type of integral appears frequently in main terms of sieve theory. We propose a simple method, based on the LattE software for integration of polynomials over polytopes, which computes rigorous bounds on this integral in polynomial time with respect to the precision (in bits). We test the method on several examples from the literature of sieve theory. We apply our results to compute numerical approximations to the natural density $$ h(\alpha, \beta) := \operatorname{density}\{n\in{\mathbb N}, \exists d\mid n, d\in [n^\alpha, n^\beta]\}, \qquad (0<\alpha<\beta<1) $$ of integers having a localized divisor, in the region $\beta - \alpha \geq 0.02$. One ingredient involved is a refined formula for $h(\alpha, \beta)$ which involves a manageable number of terms for these $\alpha, \beta$. As a corollary, we give a numerical approximation of the leading constant in a theorem of Haddad and Koukoulopoulos on the average of the logarithm of middle-divisors of integers.
arXiv:2504.20383v3 Announce Type: replace Abstract: Disparity compensation represents the primary strategy in stereo video compression (SVC) for exploiting cross-view redundancy. These mechanisms can be broadly categorized into two types: one that employs explicit horizontal shifting, and another that utilizes an implicit cross-attention mechanism to reduce cross-view disparity redundancy. In this work, we propose a hybrid disparity compensation (HDC) strategy that leverages explicit pixel displacement as a robust prior feature to simplify optimization and perform implicit cross-attention mechanisms for subsequent warping operations, thereby capturing a broader range of disparity information. Specifically, HDC first computes a similarity map by fusing the horizontally shifted cross-view features to capture pixel displacement information. This similarity map is then normalized into an "explicit pixel-wise attention score" to perform the cross-attention mechanism, implicitly aligning features from one view to another. Building upon HDC, we introduce a novel end-to-end optimized neural stereo video compression framework, which integrates HDC-based modules into key coding operations, including cross-view feature extraction and reconstruction (HDC-FER) and cross-view entropy modeling (HDC-EM). Extensive experiments on SVC benchmarks, including KITTI 2012, KITTI 2015, and Nagoya, which cover both autonomous driving and general scenes, demonstrate that our framework outperforms both neural and traditional SVC methodologies.
arXiv:2606.30489v1 Announce Type: cross Abstract: Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a physical effect, a calibration constant, or a source of systematic uncertainty. Learning a separate flow for every parameter configuration quickly becomes intractable, since the number of joint settings grows exponentially with the number of parameters. We introduce Factorizable Normalizing Flows (FNFs), which represent the parameter-dependent density as a fixed, high-fidelity flow for a reference configuration composed with a learnable transformation that is polynomial in the parameters and factorized over them. This structure has a practical consequence: each parameter's effect is learned in isolation, from samples in which that parameter alone is varied. The combined response of many parameters is then recovered by summation at inference, without ever sampling their combinatorially large joint space. On a controlled problem with two interpretable deformations applied jointly to the data, the learned transformation reproduces the true deformations and matches the optimal likelihood, while optional interaction terms capture residual correlations when several parameters vary strongly at once. The resulting model is interpretable, scales linearly with the number of parameters, and keeps the likelihood tractable. This provides a general tool for any inference workflow requiring continuous density morphing, and directly enables the next generation of unbinned likelihood fits in high energy physics.
arXiv:2606.30496v1 Announce Type: cross Abstract: A Pisot numeration system $U$ for $\mathbb N$ is a sequence of natural numbers generated by an integral homogeneous linear recurrence whose characteristic polynomial is the minimal polynomial of a Pisot number. The purpose of this paper is to introduce the analogue of the group of $p$-adic integers for such numerations when they \emph{preserve zeros}, which is equivalent to the `Condition F' introduced by Frougny and Solomyak for $\beta$-numerations. We show that these topological groups $\mathbb Z_U$ project homomorphically onto a torus. Equipping $\mathbb Z_U$ with the appropriate topology, we also show that if $U$ is unimodular, then $\mathbb Z_U$ is continuously isomorphic to a torus.
arXiv:2204.07918v2 Announce Type: replace Abstract: The convergence theory of multigrid methods for symmetric positive definite systems is well established. For nonsymmetric systems, however, the corresponding theory remains far from mature. Two-grid analysis is fundamental to the design and analysis of multigrid methods. This paper presents a convergence analysis of two-grid methods for nonsymmetric positive definite systems. When the coarse-grid system is solved exactly, we derive a succinct identity for the two-grid convergence factor measured in a smoother-induced norm. More generally, under mild assumptions, we develop a convergence theory for inexact two-grid methods, where convergence is measured in a generic norm.
arXiv:2606.30532v1 Announce Type: cross Abstract: We show convergence of solutions to a Navier--Stokes/Allen--Cahn system as the interfacial thickness $\varepsilon>0$ tends to zero for well-prepared initial data as long as the limit system possesses a sufficiently smooth solution. The limit system consists of a two-phase Navier--Stokes system separated by a sharp interface in the presence of surface tension coupled to a convective mean curvature flow equation. In comparison to previous results we obtain improved convergence estimates for higher-order norms. These enable us to prove convergence in the case of three space dimensions and non-constant viscosity, which was unknown before. The convergence results relies crucially on uniform higher-order estimates for the associated linearized Navier--Stokes/Allen--Cahn system in suitably weighted $L^2$-Sobolev spaces. Here a novel problem-adapted weight proportional to the sum of $\varepsilon$ and the distance to the sharp interface of the limit, which gives improved and sharp estimates, is an important new ingredient. This approach can be potentially adapted to other sharp interface limits as well.
arXiv:2606.30535v1 Announce Type: cross Abstract: Physical heterogeneities in the context of sliding friction, such as a human finger exploring an object, have been well studied, yet the behavior of chemical heterogeneities in mesoscale soft sliding remains underexplored, despite the similar prevalence of chemical and physical variations in real systems. Here, we experimentally characterized the friction of a planar soft elastic probe sliding across a single chemical heterogeneity that was formed at the interface of two silanes on silicon wafers. By constructing phase maps across multiple loads and velocities, we quantified the occurrence of several frictional phenomena at and around the chemical edge, including stiction spike formation, edge slope direction, baseline shifts, and baseline drift, and quantified their sliding direction-dependent formation. We found that chemical heterogeneities made by more disparate materials (butyl- and aminopropyl-terminated) exhibited several phenomena that were more often direction-independent compared to chemical heterogeneities formed from more similar materials (butyl- and hexyl-terminated). We attributed this directional asymmetry to elastic body effects. In subsequent human testing (n=36), we observed that humans also exhibited directional-dependent accuracy (66.7% versus 38.9%) on one pair (butyl- and hexyl-terminated) but not the other (77.8% versus 75%), which in the context of our phase maps, suggests that the slope of the friction force when sliding over a chemical edge is important for generating a clear edge of a tactile feature, rather than the differences in simple material properties or other friction phenomena.
arXiv:2606.30588v1 Announce Type: cross Abstract: We prove Seymour's second neighborhood conjecture on oriented graphs whose minimum out-degree is equal to $7$. This gives, to our knowledge, the first improvement of the minimum out-degree threshold in two decades, since the work of Kaneko and Locke in 2001, who resolved the conjecture for oriented graphs whose minimum out-degree is at most $6$. The proof is partially computer-assisted: after a sequence of local reductions, the remaining finite obstruction models are eliminated by reproducible OR-Tools CP-SAT infeasibility checks.
arXiv:2606.30541v1 Announce Type: cross Abstract: Stars like our Sun expand as they exhaust their core hydrogen fuel, becoming red giants that eventually reach sizes up to 100 times their original radius. These giants have long presented a puzzle: they show systematic changes in their surface chemical composition that can only be explained by the transport of material from their nuclear-burning interior to their surface. The challenge is that this transport must somehow cross a stable layer that acts as a barrier between the star's outer convective envelope and its nuclear-burning interior. The convective motions in the envelope create internal waves that propagate through this barrier layer, but on their own these waves produce very little material transport. Here we show through high-resolution three-dimensional hydrodynamical simulations that stellar rotation dramatically amplifies how effectively these waves can mix material across this barrier. We find that the mixing rates can exceed those in non-rotating stars by over 100 times, increasing with faster rotation rates. This enhanced mixing provides a natural explanation for the observed chemical signatures in typical red giants. The amplification of wave-driven mixing by rotation may have implications beyond red giants to other types of stars.
arXiv:2509.21530v2 Announce Type: replace Abstract: Data augmentation is a widely used strategy to improve model robustness and generalization by enriching training datasets with synthetic examples. While large language models (LLMs) have demonstrated strong generative capabilities for this purpose, their applications in high-stakes domains like healthcare present unique challenges due to the risk of generating clinically incorrect or misleading information. In this work, we propose a novel query-based model collaboration framework that integrates expert-level domain knowledge to guide the augmentation process to preserve critical medical information. Compared to existing LLM-based and traditional augmentation methods, our generated data significantly improves preservation of critical medical information and reduces hallucinations at both the token and concept levels. Experiments on downstream clinical prediction tasks demonstrate consistent performance gains over existing augmentation methods. This lightweight collaborative framework addresses the gap between LLM augmentation potential and the safety requirements of specialized domains.
arXiv:2505.08970v2 Announce Type: replace Abstract: The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent viscosity solution and, respectively, duality solution. We supplement our theoretical analysis with various numerical examples to illustrate the features of the schemes.