arXiv:2605.15388v1 Announce Type: new
Abstract: Stochastic estimators are fundamental to large-scale optimization, where population quantities must be inferred from noisy oracle observations. Although influential methods such as momentum, SPIDER, STORM, and PAGE have been highly successful, their analyses are largely estimator-specific and expectation-based, obscuring the structural tradeoffs that determine reliability. In this paper, we develop a unified framework for stochastic variance-reduced estimation based on a recursion with three components: memory retention, reset probability, and a correction term for iterate movement. This framework recovers several classical estimators, motivates new second-order variants, and yields a bias-variance decomposition of estimation error. Our main result is a unified high-probability bound proved using a new dimension-free vector-valued Freedman inequality, valid for smooth normed spaces involving random sums of vector martingales. The result applies in both Euclidean and non-Euclidean settings, including the analysis of mirror-descent-based methods in Banach spaces. As applications, we obtain high-probability oracle complexities for unconstrained optimization with mirror descent, establishing the logarithmic dependence on the confidence level. We also derive the first $\tilde{\mathcal{O}}(\varepsilon^{-3})$ oracle-complexity bounds for stochastic optimization with expectation constraints, improving upon the existing $\tilde{\mathcal{O}}(\varepsilon^{-4})$ complexity by leveraging variance-reduced estimation for the first time in this setting.
Science Journals
arXiv:2605.16122v1 Announce Type: new
Abstract: Diffusion-based image synthesis has made AI-generated images (AIGI) increasingly photorealistic, raising urgent concerns about authenticity in applications such as misinformation detection, digital forensics, and content moderation. Despite the substantial advances in AIGI detection, how to correct detected AI-generated images with visible artifacts and restore realistic appearance remains largely underexplored. Moreover, few existing work has established the connection between AIGI detection and artifact correction. To fill this gap, we propose GenShield, a unified autoregressive framework that jointly performs explainable AIGI detection and controllable artifact correction in a closed loop from diagnosis to restoration, revealing a mutually reinforcing relationship between these two tasks. We further introduce a Visual Chain-of-Thought based curriculum learning strategy that enables self-explained, multi-step ``diagnose-then-repair'' correction with an explicit stopping criterion. A high-quality dataset with large-scale ``artifact-restored'' pairs is also constructed alongside a unified evaluation pipeline. Extensive experiments on our correction benchmark and mainstream AIGI detection benchmarks demonstrate state-of-the-art performance and strong generalization of our method. The code is available at https://github.com/zhipeixu/GenShield.
arXiv:2605.15731v1 Announce Type: new
Abstract: This paper presents the real-world implementation and field validation of a user-aware bidirectional electric vehicle (EV) charging system developed within the Mobilities for EU and DymoBat projects in Dresden. Building on earlier simulation frameworks, the system enables transition from conceptual models to operational deployment in urban environments.
To support grid flexibility and sustainable mobility, the solution combines real-time vehicle and user data with a centralized optimization platform to enable dynamic charging and discharging decisions. The architecture integrates a wireless On-Board Diagnostic II (OBD-II) interface and an open middleware node connected via a 5G campus network, allowing early access to vehicle state-of-charge before plug-in. A tablet-based interface captures user preferences such as departure time and energy demand, which are incorporated into the optimization together with grid conditions.
A key contribution is a multi-level communication architecture linking the EV, charging station, user interface, and grid control center using the Open Charge Point Protocol (OCPP). The system integrates software, embedded hardware, and network communication for real-time charging management.
Field deployment at Ostra Sport Park in Dresden demonstrates feasibility, improved load balancing, and robust vehicle-to-grid operation. The results show that early data acquisition and predictive control can enhance system efficiency. This work provides a practical benchmark for positive energy districts and future urban e-mobility systems.
arXiv:2601.06304v2 Announce Type: replace
Abstract: We develop a framework for localized source detection in dynamical systems governed by nonlinear partial differential equations based on first and second-order sensitivity analysis. Building on the standard adjoint formulation, which relates multiple measurements to external sources through a linear duality relation, we first introduce a linear positional embedding that identifies the source location by aligning the measurement vector with the embedding. To capture weakly nonlinear effects that arise when the source intensity is finite, we then incorporate a quadratic correction represented as a symmetric bilinear operator and approximated via a truncated eigen-expansion obtained with Krylov subspace iterations. This yields quadratic positional embeddings that augment the linear adjoint field, enabling measurement data to be projected onto a higher-dimensional hyperplane, spanned by the linear and quadratic embeddings. A source search algorithm is formulated based on principal angle minimization between this hyperplane and the observation vector, providing a natural probabilistic interpretation of source location. The method operates in a one-shot fashion without iterative updates of candidate source positions, and it can be readily extended to scenarios involving multiple sources. Demonstrations on benchmark inverse problems include perturbation-source identification in the viscous Burgers equation and heat-source detection in a two-dimensional laminar stratified channel. The results with quadratic embeddings show significant improvements in localization accuracy compared with linear adjoint-based sensitivity methods, especially in the region where linear adjoint sensitivity vanishes.
arXiv:2601.00361v3 Announce Type: replace
Abstract: We introduce the first iterative algorithm for constructing a $\varepsilon$-coreset that guarantees deterministic $\ell_p$ subspace embedding for any $p \in [1,\infty)$ and any $\varepsilon > 0$. For a given full rank matrix $\mathbf{X} \in \mathbb{R}^{n \times d}$ where $n \gg d$, $\mathbf{X}' \in \mathbb{R}^{m \times d}$ is an $(\varepsilon,\ell_p)$-subspace embedding of $\mathbf{X}$, if for every $\mathbf{q} \in \mathbb{R}^d$, $(1-\varepsilon)\|\mathbf{Xq}\|_{p}^{p} \leq \|\mathbf{X'q}\|_{p}^{p} \leq (1+\varepsilon)\|\mathbf{Xq}\|_{p}^{p}$. Specifically, in this paper, $\mathbf{X}'$ is a weighted subset of rows of $\mathbf{X}$ which is commonly known in the literature as a coreset. In every iteration, the algorithm ensures that the loss on the maintained set is upper and lower bounded by the loss on the original dataset with appropriate scalings. So, unlike typical coreset guarantees, due to bounded loss, our coreset gives a deterministic guarantee for the $\ell_p$ subspace embedding. For an error parameter $\varepsilon$, our algorithm takes $O(\mathrm{poly}(n,d,\varepsilon^{-1}))$ time and returns a deterministic $\varepsilon$-coreset, for $\ell_p$ subspace embedding whose size is $O\left(\frac{d^{\max\{1,p/2\}}}{\varepsilon^{2}}\right)$. Here, we remove the $\log$ factors in the coreset size, which had been a long-standing open problem. Our coresets are optimal as they are tight with the lower bound. As an application, our coreset can also be used for approximately solving the $\ell_p$ regression problem in a deterministic manner.
arXiv:2605.15254v1 Announce Type: new
Abstract: Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN training still suffers from high-dimensional non-convex loss landscapes, imbalanced multiobjective constraints, and ineffective information propagation. Existing curriculum learning and causality-guided strategies improve training stability, but mainly focus on temporal or parametric progression, lacking explicit treatment of spatial information propagation and inter-region consistency. Moreover, they are not directly applicable to boundary value problems (BVPs) with strong spatial coupling. To address this issue, we propose a spatially correlated curriculum learning framework for PINNs. To the best of our knowledge, this is the first work to address PINN training difficulties from the perspective of spatial coupling among subregions. First, spatial causal weights guide information from near-boundary regions inward, reducing optimization failures and spurious convergence. Second, a low-frequency information bridge enforces pseudo-label-based consistency across spatially separated regions, suppressing global low-frequency drift. Third, a region-adaptive reweighting strategy adjusts subregion losses to reduce local residuals and recover high-frequency details. Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy. The code is available at https://github.com/pigofmomo/CurriculumLearningPINN.
arXiv:2605.15253v1 Announce Type: new
Abstract: Machine learning research increasingly bifurcates into two disconnected modes: benchmark-driven engineering that prioritizes metrics over understanding, and idealized theory that often fails to transfer to modern systems. In this position paper, we argue that the field focuses too heavily on these endpoints, neglecting the central scientific object: the idea. We propose an Ideas First framework in which ideas are valued for the behavioral signatures they predict in modern models, and these signatures are tested through tailored experiments designed to detect the relevant patterns rather than to win leaderboards. This shift not only bridges the gap between theory and practice but also promotes equity by removing the "complexity premium," enabling rigorous scientific contributions from researchers with modest computational, financial, and human resources. Ultimately, we advocate for a research culture centered on ideas, treating benchmarks and theorems as instruments for testing mechanistic hypotheses rather than as ends in themselves.
arXiv:2512.24366v2 Announce Type: replace
Abstract: Text-based explainable recommendation aims to generate natural-language explanations that justify item recommendations, to improve user trust and system transparency. Although recent advances leverage LLMs to produce fluent outputs, a critical question remains underexplored: are these explanations factually consistent with the available evidence? We introduce a comprehensive framework for evaluating the factual consistency of text-based explainable recommenders. We design a prompting-based pipeline that uses LLMs to extract atomic explanatory statements from reviews, thereby constructing a ground truth that isolates and focuses on their factual content. Applying this pipeline to five categories from the Amazon Reviews dataset, we create augmented benchmarks for fine-grained evaluation of explanation quality. We further propose statement-level alignment metrics that combine LLM- and NLI-based approaches to assess both factual consistency and relevance of generated explanations. Across extensive experiments on six state-of-the-art explainable recommendation models, we uncover a critical gap: while models achieve high semantic similarity scores (BERTScore F1: 0.81-0.90), all our factuality metrics reveal alarmingly low performance (LLM-based statement-level precision: 4.38%-32.88%). These findings underscore the need for factuality-aware evaluation in explainable recommendation and provide a foundation for developing more trustworthy explanation systems.
arXiv:2605.15093v2 Announce Type: replace
Abstract: The life history of an individual coral is archived within the accreting skeleton of the colony. While reef-forming coral colonies (e.g. massive $\textit{Porites}$ sp.) may live for hundreds of years and deposit calcareous structures many metres in height and width, their living tissue is a thin outer surface layer comprised of asexually-dividing polyps that only survive a few years. To understand the rate and timing of polyp division and the consequences for colony skeletal growth, scientists need to track the skeletal corallite deposited around each polyp. Here we propose CoralLite, an annotated $\mu$CT scan dataset of entire calcareous skeletons and an associated, first corallite deep learning reconstruction baseline. CoralLite combines fully quantified volumetric segmentations with cross-slice linking for visualisations of 3D models for each corallite up to colony scale. For segmentation, we propose and evaluate in detail a hybrid V-Trans-UNet architecture applicable to segmenting tiled $\mu$CT virtual slabs of $\textit{Porites}$ sp. colonies. The model is pre-trained on weakly annotated data and topology-aware fine-tuned using fully annotated slice sections with 8k+ manual corallite region annotations. On unseen slices of the same colony, the resulting model reaches 0.94 topological accuracy at mean Dice scores of 0.77 on the same colony and projection axis, and 0.63 mean Dice scores on a different, biologically unrelated specimen. Whilst our experiments are limited in scale and context, our results show for the first time that visual machine learning can effectively support full 3D individual corallite modelling from $\mu$CT scans of coral skeletons alone. For reproducibility and as a baseline for future research we publish our full dataset of 697 $\mu$CT slices, 37 partial or full slice annotations, and all network weights and source code with this paper.
arXiv:2512.19179v3 Announce Type: replace
Abstract: Efficiently harnessing GPU compute is critical to improving user experience and reducing operational costs in large language model (LLM) services. However, current inference engine schedulers overlook the attention backend's sensitivity to request-length heterogeneity within a batch. As state-of-the-art models now support context windows exceeding 128K tokens, this once-tolerable inefficiency has escalated into a primary system bottleneck, causing severe performance degradation through GPU underutilization and increased latency. We present CascadeInfer, a runtime system that dynamically reschedules requests across multiple instances serving the same LLM to mitigate per-instance length heterogeneity. CascadeInfer partitions these instances into length-specialized groups, each handling requests within a designated length range, naturally forming a pipeline as requests flow through them. CascadeInfer devises a dynamic programming algorithm to efficiently find the stage partition with the best QoE, employs runtime range refinement together with decentralized load (re)balance both across and within groups, achieving a balanced and efficient multi-instance service. Our evaluation shows that, under the same configuration, CascadeInfer reduces end-to-end latency by up to 67% and tail latency by up to 69%, while improving overall system throughput by up to 2.89 times compared to the state-of-the-art multi-instance scheduling systems.
arXiv:2605.15998v1 Announce Type: new
Abstract: Coherent perfect absorbers (CPAs) have recently attracted considerable attention due to their ability to enhance light--matter interaction. By exploiting interference, CPAs enable even weakly absorbing materials to achieve complete absorption under appropriate excitation conditions. Generalizing this concept to the simultaneous absorption of arbitrary multimode input states remains challenging, however, since conventional implementations typically operate only for a single or a very small number of input channels. Here, we propose a compact realization of a multimode coherent perfect absorber based on a gradient-index (GRIN) fiber. Using the self-imaging property of the fiber, the bulky free-space architecture of previous approaches is replaced by a monolithic waveguiding platform that supports near-degenerate rephasing of many spatial modes. We show that standard GRIN profiles optimized for minimal intermodal dispersion enable highly efficient absorption of complex multimode fields, with field-of-view reflectivities well below \(1\%\) for realistic parameters. This approach provides a practical and scalable route toward efficient multimode absorption in fiber-based and integrated photonic systems, with potential applications in light harvesting, optical control, and imaging.
arXiv:2605.15999v1 Announce Type: new
Abstract: This paper introduces a motion planning framework to plan morphology and trajectory for morphing quadrotors under extremely constrained environments. We develop a novel obstacle avoidance cost function for nonlinear model predictive control (MPC) that enables navigation through extremely narrow gaps under limited perception from a 2D LiDAR. Classical artificial potential field-based costs typically have a high cost in narrow passages, artificially blocking the navigable path. In contrast, we propose a smooth exponential obstacle cost that preserves low traversal cost within narrow gaps while maintaining strong collision avoidance behavior. The formulation avoids hard activation thresholds and introduces a cost reduction factor to reduce the cost within narrow passages. Direct use of 2D LiDAR measurements in MPC allows navigation around arbitrarily shaped obstacles. The method is embedded within an acados-based nonlinear MPC framework. Simulation and experimental results demonstrate successful traversal of narrow corridors where typical repulsive cost functions would fail. The approach provides a computationally efficient and practical solution for navigating through tight spaces while maintaining safety from the obstacles. While we are implementing the framework on the morphing quadrotors, the cost function formulation is general-purpose for any mobile robot application, and is not limited to the morphing quadrotors. The implementation code is available at \href{https://github.com/harshjmodi1996/morphocopter_mpc}{Github Repo} and a short video is available at \href{https://zh.engr.tamu.edu/wp-content/uploads/sites/310/2026/03/MPC_MorphoCopter_video.mp4}{Video Link}.
arXiv:2605.16001v1 Announce Type: new
Abstract: A broadcast on a connected graph is a function f that assigns each vertex v an integer f(v) with 0 <= f(v) <= ecc(v) where ecc(v) denotes the eccentricity of v. A vertex u hears a broadcasting vertex v (with f(v)>0) if u is at distance at most f(v) from v. Beyond the classical broadcast domination problem, where every vertex is required to hear at least one vertex, two variants raise intriguing combinatorial and algorithmic questions. In an independent broadcast, no broadcasting vertex hears another broadcasting vertex, while a broadcast packing requires that every vertex hears at most one broadcasting vertex. The corresponding problems Broadcast Independence and Broadcast Packing ask for broadcasts of values at least k under these constraints, where the value is the sum of the broadcast values. We initiate a systematic study of the parameterized complexity of such problems. We prove that Broadcast Independence and Broadcast Packing are FPT parameterized by the treewidth plus the diameter of G, with a family of dynamic-programming algorithms over nice tree decompositions. We obtain as a corollary that both problems are FPT parameterized by k and the treewidth of G and XP for treewidth only. The latter result shows that the known algorithm for trees (Bessy and Rautenbach, DAM 2022) can indeed be extended to bounded treewidth graphs. On the negative side, we show that Broadcast Independence is W[1]-hard parameterized by the pathwidth of G. Note that this result completes the picture for parameter k and treewidth for Broadcast Independence since it is known to be W[1]-hard for k only. We complement these results by showing that a weighted version of both problems, where the input comes with a weight function on the edges, is W[1]-hard parameterized by the vertex cover of G. Finally, we provide a constant-factor approximation algorithm parameterized by treewidth for Broadcast Independence.
arXiv:2605.15799v1 Announce Type: new
Abstract: Multi-agent pathfinding (MAPF) under one-shot planning is a core component of warehouse automation, yet classical formulations typically assume four-connected 2D grids with unit-time moves in four directions. To fill reality gaps while still being trackable with discrete combinatorial search, this work proposes a more practical counterpart tailored to differential-drive AGVs. We term this multi-agent warehouse pathfinding (MAWPF), featured with four constraints: (i) agent actions are restricted to straight motion and in-place rotation; (ii) rotations require multi-step costs; (iii) acceleration and deceleration are considered, and; (iv) follower collisions are prohibited to prevent rear-end crashes. To solve MAWPF efficiently, we adapt representative suboptimal MAPF algorithms-PP, LNS2, PIBT, and LaCAM-and conduct comprehensive benchmarking. Our experiments reveal that PP and LNS2 struggle to solve instances with many agents, while PIBT-based approaches achieve preferable scalability with increased solution cost. We believe that these constitute an important step toward adapting classical gridworld MAPF to operational warehouse setups.
arXiv:2605.15803v1 Announce Type: new
Abstract: Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: the rapid decay of intra-group variance. As the distinctiveness among samples within a group diminishes, the variance approaches zero. This eliminates the very learning signal required for optimization, rendering the process unstable and forcing the policy into premature stagnation or reward hacking. Existing strategies, such as varying the initial noise or increasing group sizes, often fail to address this fundamental issue, resulting in training instability or diminishing returns. To overcome these challenges, we propose $\textbf{Embedding-perturbed Exploration Preference Optimization (}E^2\textbf{PO)}$, a novel framework that sustains optimization through embedding-level perturbation. Our method introduces structured, embedding-level perturbations within sample groups, guaranteeing a robust variance that preserves the discriminative signal throughout the training process. Extensive experiments demonstrate that our approach significantly outperforms state-of-the-art baselines, achieving a more faithful alignment with human preference.
arXiv:2605.15663v1 Announce Type: new
Abstract: We study the minimax sample complexity of $\varepsilon$-best arm identification in linear bandits. Given a compact action set $\mathcal{X}$ that spans $\mathbb{R}^d$ and an unknown reward vector $\theta\in\mathbb{R}^d$, the goal is to output an arm $\widehat{x}\in\mathcal{X}$ such that $\langle \widehat{x},\theta\rangle \ge \max_{x\in\mathcal{X}} \langle x,\theta\rangle - \varepsilon$ with probability at least $1-\delta$, using as few samples as possible.
First, we present a non-adaptive fixed-design method with sample complexity $\mathcal{O}\!\left(\frac{d\log(1/\delta)}{\varepsilon^2}+\frac{w(\mathcal{X})^2}{\varepsilon^2}\right)$, where $w(\mathcal{X})$ is a Gaussian width term dependent on $\mathcal{X}$, and we prove a matching lower bound $\Omega\!\left(\frac{d\log(1/\delta)}{\varepsilon^2}+\frac{w(\mathcal{X})^2}{\varepsilon^2}\right)$ for all non-adaptive fixed-design methods.
We then turn to adaptive sampling. We raise an important structural question: beyond the canonical basis, are there structured action sets for which adaptivity yields only logarithmic-factor improvements over the optimal non-adaptive rate? We answer in the affirmative for several natural action sets, namely the hypercube, the $\ell_2$ ball, $m$-sets, and multi-task multi-armed bandits.
Finally, we provide the first construction of an action set $\mathcal{X}$ for which adaptivity yields a polynomial-factor improvement over every non-adaptive algorithm. A key ingredient behind this separation is an $\ell_2$-norm estimation subroutine: we design an adaptive algorithm that uses $\mathcal{O}\!\left(\frac{d\log(1/\delta)}{\varepsilon^2}\right)$ samples from the unit $\ell_2$ ball in $\mathbb{R}^d$ and outputs an estimate $\widehat r$ satisfying $|\widehat r-\|\theta\|_2|\le \varepsilon$ with probability at least $1-\delta$, where $\theta$ is the unknown reward vector.
arXiv:2605.15750v1 Announce Type: new
Abstract: The rapid expansion of electric vehicles (EVs) necessitates scalable and efficient fast charging station (FCS) infrastructure. These stations often operate in oversubscribed configurations where the total port rating exceeds a station-level cap reflecting infrastructure limits, grid constraints or market setpoints. In such settings, ensuring fairness in real-time power allocation is essential to prevent user bias and secure equitable access to limited resources while maximizing infrastructure utilization. This task is further complicated by state-of-charge dependent EV power limits defined by charge curves, for which accurate data is often unavailable. This paper introduces two fairness-guaranteed online power allocation policies: FAIR-OPAP-C for conventional FCSs with continuously adjustable power delivery, and FAIR-OPAP-M for modular FCSs composed of discrete assignable power modules. Unlike existing methods, these algorithms require no prior knowledge of charge curves, utilizing only instantaneous power requests available via standard protocols. We formalize fairness with a unified framework encompassing envy-freeness, Pareto efficiency, and proportionality, and establish theoretical guarantees for both algorithms. The algorithms rely on lightweight operations, achieving near-linear and logarithmic scalability for the conventional and modular cases, respectively. Comprehensive evaluations show the proposed methods achieve superior performance across various metrics among seven benchmarks from EV charging and fair division literature. Furthermore, they are orders of magnitude faster than optimization-based approaches, with runtimes below 1 ms for up to 300 EVs, validating their suitability for real-time deployment on hardware-constrained edge devices.
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:2512.16933v4 Announce Type: replace
Abstract: The dynamics of a degenerate spherically symmetric wormhole in a vacuum is considered. An extension of the equivalence principle to matter free objects that are the source of a gravitational field is proposed. Using the Klinkhamer metric as an example, it is shown that a degenerate wormhole is precisely such an object. Application of the extended equivalence principle reduces the radial dynamics of the Klinkhamer wormhole to the dynamics of the radial fall of a test particle in a Schwarzschild gravitational field. It is proven that any bound state of the traversable Klinkhamer wormhole eventually collapses into a nontraversable Einstein-Rosen wormhole. An estimate is presented showing that the traversable Klinkhamer wormhole, although nonstationary, is a longlived state.
arXiv:2512.15734v2 Announce Type: replace
Abstract: Differentially flat models are frequently used to design feedforward controllers for electromechanical systems. However, control performance depends on model accuracy, which makes feedback imperative. This paper presents a control scheme for electromechanical systems in which measuring or estimating the output to be controlled -- typically the position -- is not feasible. It employs an identifiable-model-based controller and predictor, coupled with an iterative loop that updates model parameters using the error between a measurable output and its prediction. Simulations on electromechanical switching devices show effective tracking of the desired position trajectory using only coil current measurements.
arXiv:2605.14093v2 Announce Type: replace
Abstract: Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT). Under the Strong Exponential Time Hypothesis (SETH), Parity-SAT admits no $O^*((2-\varepsilon)^n)$-time or $O^*((2-\varepsilon)^m)$-time algorithm for any constant $\varepsilon>0$, where $n$ and $m$ denote the numbers of variables and clauses, respectively. Thus, breaking the $2^n$ or $2^m$ barrier appears impossible in full generality.
In this work, we revisit this barrier through structural restrictions and a refined exploitation of parity. We study Parity-$d$-occ-SAT, where each variable appears in at most $d$ clauses, and obtain three main results. First, we design a randomized $O^*(2^{m(1-1/O(d))})$-time algorithm, thereby breaking the $2^m$ barrier for every fixed $d$. Second, for the special case $d=2$, we develop a significantly sharper branching algorithm running in $O^*(1.1193^n)$ time or $O^*(1.3248^m)$ time. Third, leveraging the structural insights underlying the $d=2$ case, we obtain an $O^*(1.1052^L)$-time algorithm for general Parity-SAT, where $L$ denotes the formula length. All algorithms use only polynomial space. Notably, our running-time bounds are better than the best known bounds for the corresponding exact counting counterparts, highlighting a genuine algorithmic advantage of parity over counting. Conceptually, our results demonstrate that parity admits finer structural reductions and more efficient branching than exact model counting, and that bounded occurrence can be systematically leveraged to circumvent classical exponential barriers.
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.
arXiv:2605.15235v1 Announce Type: new
Abstract: Multimodal physiological data powers clinical AI systems from intensive care units to wearable devices, but sensors routinely fail in practice. Two failure modes are common: modality missing, where an entire channel is absent, and within-modality missing, where a contiguous time segment is lost. No existing benchmark evaluates multiple fusion architectures under both failure modes at controlled severity levels across diverse clinical datasets. We present MuteBench, a benchmark covering 9 datasets from 7 clinical domains, 6 fusion architectures, and 2 missing-data modes over 125,000 samples. Through this benchmark, we find that architecture family is the strongest predictor of robustness, outweighing parameter count. Channel-independent models tolerate modality missing well but can be sensitive to within-modality missing, especially on short sequences. Curriculum modality dropout protects reliably only up to the maximum dropout rate used in training. We also find that channel count, sequence length, and modality alignment jointly determine which failure mode poses the greater threat. Finally, a PTB-XL case study suggests that diffusion-based imputation can improve downstream classification under within-modality missing, with the largest gains for models whose expert routing is most sensitive to corrupted inputs, though broader validation across datasets remains an open direction. MuteBench provides practitioners with concrete guidance for both selecting existing architectures and informing the design of future robust multimodal fusion methods.
arXiv:2512.08052v3 Announce Type: replace
Abstract: Embodied agents, such as robots and virtual characters, must continuously select actions to execute tasks effectively, solving complex sequential decision-making problems. Given the difficulty of designing such controllers manually, learning-based approaches have emerged as promising alternatives, most notably Deep Reinforcement Learning (DRL) and Deep Imitation Learning (DIL). DRL leverages reward signals to optimize behavior, while DIL uses expert demonstrations to guide learning. This document introduces DRL and DIL in the context of embodied agents, adopting a concise, depth-first approach to the literature. It is self-contained, presenting all necessary mathematical and machine learning concepts as they are needed. It is not intended as a survey of the field; rather, it focuses on a small set of foundational algorithms and techniques, prioritizing in-depth understanding over broad coverage. The material ranges from Markov Decision Processes to REINFORCE and Proximal Policy Optimization (PPO) for DRL, and from Behavioral Cloning to Dataset Aggregation (DAgger) and Generative Adversarial Imitation Learning (GAIL) for DIL.
arXiv:2512.04457v2 Announce Type: replace
Abstract: Removing specific data influence from large language models (LLMs) remains challenging, as retraining is costly and existing approximate unlearning methods are often unstable. The challenge is exacerbated when the forget set is small or imbalanced. We introduce RapidUn, an influence-driven and parameter-efficient unlearning framework. It first estimates per-sample influence through a fast estimation module, then maps these scores into adaptive update weights that guide selective parameter updates -- forgetting harmful behavior while retaining general knowledge. On Mistral-7B and Llama-3-8B across Dolly-15k and Alpaca-57k, RapidUn achieves up to 100 times higher efficiency than full retraining and consistently outperforms Fisher, GA, and LoReUn on both in-distribution and out-of-distribution forgetting. These results establish influence-guided parameter reweighting as a scalable and interpretable paradigm for LLM unlearning.