arXiv:2607.04603v1 Announce Type: new Abstract: Infrared small target detection (IRSTD) aims to identify long distance small targets from complex infrared backgrounds, and is a fundamental task in remote sensing. Deep learning methods have improved IRSTD by learning discriminative image-to-mask mappings, but such feed-forward designs often underuse physical decomposition structure between targets and backgrounds. Deep unfolding methods partially address this issue by embedding model-driven iterations into neural networks, yet existing designs still operate mainly in image domain and use updates and memory mechanisms that are not fully coupled with underlying optimization process. To address these limitations, we propose Latent Consistent Proximal unfolding network (LCPNet). First, we verify that low-rank prior remains valid in latent representations and perform unfolding in this space, preserving physical constraint while avoiding repeated compression of intermediate states. Second, we derive a Latent Consistent Proximal (LCP) solver that evolves each latent variable from its previous state rather than reconstructing through an indirect residual, and stabilizes small target updates through task-adaptive normalization and gain control. Third, we introduce Shared Optimization Memory (SOM), a common historical state shared by all decomposition variables to provide coordinated guidance across unfolding stages. Extensive experiments on four public benchmarks demonstrate that LCPNet outperforms state-of-the-art methods while achieving accurate and robust detection with low false alarms and competitive efficiency. Model and code are available at https://github.com/Tianfang-Zhang/LCPNet.
Science Journals
arXiv:2506.20294v5 Announce Type: replace Abstract: Diffusion models generate conditional samples by progressively denoising Gaussian noise, yet the denoising trajectory can stall at visually plausible but low-quality outcomes with conditional misalignment or structural artifacts. We interpret this behavior as local optima in a surrogate quality landscape: Once early denoising commits to a suboptimal global structure, later steps mainly sharpen details and seldom correct the underlying mistake. While existing inference-time approaches explore alternative diffusion states via re-noising with fixed strength or direction, they exhibit limited capacity to escape steep quality plateaus. We propose Controlled Random Zigzag Sampling (Ctrl-Z Sampling),a scalable sampling strategy that detects plateaus in quality landscape via a surrogate score, and allocates exploration only when a plateau is detected. Upon detection, Ctrl-Z Sampling rolls back to noisier states, samples a set of alternative continuations, and updates the trajectory when a candidate improves the score, otherwise escalating the exploration depth to escape the current plateau. The proposed method is model-agnostic and broadly compatible with existing diffusion frameworks. Experiments show that Ctrl-Z Sampling consistently improves generation quality over other inference-time scaling samplers across different NFE budgets, offering a scalable compute-quality trade-off. Code available at: https://github.com/ShunqiM/Ctrl-Z-Sampling.
arXiv:2412.06792v3 Announce Type: replace Abstract: Diamond's unique physical properties make it a versatile material for a wide range of nonlinear and quantum photonic technologies. However, unlocking diamond's full potential as a nonlinear photonic material with non-zero second-order susceptibility $\chi^{(2)}\neq0$ requires symmetry breaking. In this work, we use a nanoscale cavity to demonstrate second-harmonic generation (SHG) in diamond, and demonstrate, for the first time, that the magnitude of the diamond's effective $\chi^{(2)}$ strongly depends on the electronic configuration of defects in the diamond crystal, such as nitrogen-vacancy centres. The modification of $\chi^{(2)}$ arises from photoionisation from the negative to neutral charge-state, and is manifested by quenching of SHG upon green illumination. Toggling the green illumination allows for optical switching of the device's $\chi^{(2)}$. Optical control of $\chi^{(2)}$ by defect engineering opens the door for second-order nonlinear processes in diamond.
arXiv:2412.05894v2 Announce Type: replace-cross Abstract: Federated learning (FL) enables collaborative analysis of biomedical data without exchanging sensitive patient-level information, but its performance in multi-center studies may be compromised by batch effects which can obscure biological signals. Here, we systematically assess the impact of uncorrected batch effects on FL outcomes using four multi-center omics datasets, including transcriptomic, proteomic, and metabolomic data, and two representative algorithms: federated k-means clustering and federated random forest classification. Our results demonstrate that uncorrected batch effects undermine unsupervised FL and can substantially degrade supervised FL performance, indicating that privacy-aware batch-effect correction is essential for reliable FL. To enable privacy-preserving BEC in distributed bulk omics data, we introduce fedRBE ( https://featurecloud.ai/app/fedrbe ), a federated implementation of limma's removeBatchEffect() method enhanced by secure multi-party computation, suitable for datasets with missing values and non-identical feature sets across clients, including proteomics and metabolomics data.
arXiv:2607.04906v1 Announce Type: new Abstract: Under the Shipping 4.0 paradigm, autonomous and reduced-crew vessels require intelligent internal systems to maintain operational safety and structural stability. Ballast-water control is essential for ship trim and integrity, but conventional rule-based or manual approaches have limited adaptability to hydraulic anomalies such as valve failures and pipe blockages, and often depend on dense pressure or flow sensors for diagnosis. To address these limitations, this paper proposes RL-Ballast, a graph-based deep reinforcement learning framework for adaptive ballast-water path planning and sensor-frugal blockage candidate scoring. The valve-permutation problem is transformed into 54 feasible fluid-transfer routes generated using graph theory and depth-first search. The partially observable ballast environment is approximated with frame-stacked tank levels and action outcomes, allowing the agent to infer hidden blockage effects without explicitly modeling a high-dimensional POMDP. During deterministic inference, episode-level failed-action memory and dynamic action masking prevent repeated ineffective actions and support immediate rerouting. Failed transfer histories are further accumulated to rank suspicious valves or pipe segments without dense instrumentation. Monte Carlo simulations show that RL-Ballast completes all unexpected single-blockage scenarios and reduces average decision steps from 61.0 to 41.5 compared with a Dijkstra rule-based baseline. For diagnostic support, the failure-history scoring scheme achieves a 100% Top-3 hit rate, a 66.7% strict Top-1 hit rate, and an 83.3% Top-1 tie-hit rate under serially indistinguishable blockage conditions. These results suggest that RL-Ballast enables adaptive rerouting and maintenance-oriented blockage diagnosis under limited sensing conditions.
arXiv:2602.20512v2 Announce Type: replace Abstract: This paper investigates a problem called Multi-Agent Path Finding with Elevators (MAPF-E), which seeks conflict-free paths for multiple agents from their start to goal locations that may locate on different floors, and the agents can use elevators to travel between floors. The existence of elevators complicates the interaction among the agents and introduces new challenges to the planning. On the one hand, elevators can cause many conflicts among the agents due to its relatively long traversal time across floors, especially when many agents need to reach a different floor. On the other hand, the planner has to reason in a larger state space including the states of the elevators, besides the locations of the agents.
arXiv:2603.26720v3 Announce Type: replace Abstract: Predicting surgical needle trajectories from endoscopic video is critical for robot-assisted suturing, enabling anticipatory planning, real-time guidance, and safer motion execution. Existing methods that directly learn motion distributions from visual observations tend to overlook the sequential dependency among adjacent motion steps. Moreover, sparse waypoint annotations often fail to provide sufficient supervision, further increasing the difficulty of supervised or imitation learning methods. To address these challenges, we formulate image-based needle trajectory prediction as a sequential decision-making problem, in which the needle tip is treated as an agent that moves step by step in pixel space. This formulation naturally captures the continuity of needle motion and enables the explicit modeling of physically plausible pixel-wise state transitions over time. From this perspective, we propose SutureFormer, a goal-conditioned offline reinforcement learning framework that leverages sparse annotations to dense reward signals via cubic spline interpolation, encouraging the policy to exploit limited expert guidance while exploring plausible future motion paths. SutureFormer encodes variable-length clips using an observation encoder to capture both local spatial cues and long-range temporal dynamics, and autoregressively predicts future waypoints through actions composed of discrete directions and continuous magnitudes. To enable stable offline policy optimization from expert demonstrations, we adopt Conservative Q-Learning with Behavioral Cloning regularization. Experiments on a new kidney wound suturing dataset containing 1,158 trajectories from 50 patients show that SutureFormer reduces Average Displacement Error by 58.6% compared with the strongest baseline, demonstrating the effectiveness of modeling needle trajectory prediction as pixel-level sequential action learning.
arXiv:2606.05242v2 Announce Type: replace-cross Abstract: Stochastic gradient Langevin algorithms often use tamed denominators to stabilize superlinear drifts. This paper shows that when the denominator depends on the current stochastic gradient, the transformed update can have a biased conditional mean even if the original stochastic gradient is unbiased. This creates a stationary mean-shift channel that is absent for deterministic denominators.We propose a structure-preserving framework for designing tamed denominators. The construction keeps the denominator deterministic given the current state, and uses localized deterministic envelopes to avoid unnecessary taming in typical regions. These kernels retain the stabilizing effect of taming while avoiding the bias introduced by a gradient-dependent denominator. Our theory bounds the stationary bias through Euler, envelope, and stochastic-gradient residuals. The analysis also shows why purely local taming rules can lose control in the far tail and motivates a hybrid construction with additional tail protection. Experiments confirm the stationary distortions of random denominators, the bias reduction of deterministic-envelope designs, and the stabilizing effect of the hybrid construction.
arXiv:2606.09438v2 Announce Type: replace-cross Abstract: In this paper we clarify the relation between Geometric Thermodynamics and Information Geometry based on the Fisher matrix. On the macroscopic odd-dimensional contact manifold of thermodynamic variables, we introduce for the first time a metric, whose pull-back on the isoentropic symplectic submanifolds transverse to the Reeb field is K\"ahlerian. The pull-back of such metric on equilibrium states, that are lagrangian submanifolds, is the Fisher Hessian. Then we consider the Souriau-like Thermodynamics that uses Calabi-Vesentini (CV) manifolds as Kaehlerian microscopic event manifolds and the Killing moment maps as observable functions. A systematic use of the theory of compact abelian structures and the setup of Special K\"ahler Geometry in which CV manifolds are encoded allows us to perform the explicit integration defining the partition function for any entry in the CV Tits Satake universality class. The additional actions completing the abelian structure are non linear Casimir functions of the Killing moment-maps and suggest a generalization of Souriau thermodynamics that partially breaks the isometry group symmetry by means of the non vanishing mean values of the Casimir functions in a manner similar to the spontaneous magnetization in ferromagnetism. Our new exact Gibbs distributions provide the analogue for Cartan Neural Networks of the Gaussian probability distributions in flat space used in conventional Machine Learning.
arXiv:2606.15360v2 Announce Type: replace-cross Abstract: Moment-constrained maximum entropy (MaxEnt) reconstructs probability densities from a few moments in uncertainty evaluation (GUM) and reliability analysis. The classical method uses monomial constraints x^i. We show that monomials are merely one choice of generating element of the underlying Kunchenko decomposition space, and that this choice -- more than the solver -- governs which densities are representable and how well-conditioned the dual problem is. We study three elements under one dual solver: a fractional-power element (PATP) that reduces fractional-moment exponent selection to a one-dimensional scan on signed supports; a trigonometric (characteristic-function) element whose constraints exist for every distribution and keep the dual Hessian bounded; and a logarithmic-rational element log(1+(x/s)^2) whose single constraint yields the Student/Cauchy family (1+(x/s)^2)^lambda, representing algebraic tails the first two do not produce. A parity-admissibility theorem shows that an element of odd functions cannot represent any non-uniform symmetric density; the unifying lesson is a design map matching the element to the target's tail class. Empirically, on a bimodal Gaussian mixture the scan-selected fractional member cuts reconstruction MSE by 8.5x over the six-moment monomial baseline (all 20 seeds), while the trigonometric element is best-conditioned. On heavy tails the fractional element restores feasibility where monomial MaxEnt is infeasible (19/20 seeds) and reconstructs the body (KS 0.068) but not the tail, whereas the matched logarithmic element recovers the Cauchy tail index from one constraint. A variance-optimal rule (oPMM-alpha) selects the element for the reported functional. An analytical product-moment evaluator makes a measurement-and-verification optimization fitness exactly deterministic and faster than Monte Carlo, removing its noise-induced violations.
TransitNet: A Compact Attention-Augmented Deep Learning Framework for Low-SNR Transit Blind Searches
arXiv:2606.18932v2 Announce Type: replace-cross Abstract: Motivated by the observational incompleteness of intermediate-to-long-period Earth-size planets, we present TransitNet, a compact attention-augmented deep-learning framework for low-SNR transit blind searches. To enable realistic method development and objective threshold calibration under blind-search conditions, we develop a unified dataset construction, benchmarking, and threshold-selection framework. On recovery benchmarks constructed from unseen Kepler targets, TransitNet attains 95.2 percent accuracy in the challenging SNR range of 6 to 8 and outperforms both TLS and BLS, achieving ROC-AUC and PR-AP values of 0.974 and 0.982, respectively. In an injected Earth-size and sub-Earth-size transit recovery experiment, TransitNet achieves a recovery rate of 93.0 percent, substantially exceeding those of TLS (63.1 percent) and BLS (60.0 percent). In addition to detection, TransitNet provides attention-based estimates of transit windows and midpoints. On an independent evaluation set, 97.4 percent of injected transits are fully covered by the estimated transit window. Applied to real Kepler observations, the model successfully recovers all 34 selected confirmed Kepler planets, with a mean absolute transit midpoint error of 1.24 hours. The model combines a compact footprint of about 1.5 MB with high inference efficiency, yielding speed-ups of about 12 to 25 times relative to CPU-TLS and about 4 to 5 times relative to CPU-BLS. These results demonstrate that TransitNet provides an accurate, scalable, and computationally efficient framework for low-SNR transit blind searches in the tested regime and motivate its extension to longer-period Earth-size planet searches.
arXiv:2602.24115v2 Announce Type: replace Abstract: Open RAN (O-RAN) exposes rich control and telemetry interfaces across the Non-RT RIC, Near-RT RIC, and distributed units, but also makes it harder to operate multi-tenant, multi-objective RANs in a safe and auditable manner. In parallel, agentic AI systems with explicit planning, tool use, memory, and self-management offer a natural way to structure long-lived control loops. This article surveys how such agentic controllers can be brought into O-RAN: we review the O-RAN architecture, contrast agentic controllers with conventional ML/RL xApps, and organise the task landscape around three clusters: network slice life-cycle, radio resource management (RRM) closed loops, and cross-cutting security, privacy, and compliance. We then introduce a small set of agentic primitives (Plan-Act-Observe-Reflect, skills as tool use, memory and evidence, and self-management gates) and show, in a multi-cell O-RAN simulation, how they improve slice life-cycle and RRM performance compared to conventional baselines and ablations that remove individual primitives. Security, privacy, and compliance are discussed as architectural constraints and open challenges for standards-aligned deployments. This framework achieves an average 8.83\% reduction in resource usage across three classic network slices.
arXiv:2501.17685v4 Announce Type: replace-cross Abstract: We compare two procedures for the iterated removal of strictly dominated strategies. In the nested procedure, a strategy of a player is removed only if it is dominated by an unremoved strategy. The universal procedure is more comprehensive for it allows the removal of strategies that are dominated by previously removed ones. Outside the class of finite games, the two procedures may lead to different outcomes in that the universal one is always order independent while the other is not. We provide necessary and sufficient conditions for the equivalence of the two procedures. The conditions we give are based on completely bounded subsets of strategy profiles, which are variations of the bounded mechanisms from the literature on full implementation. The two elimination procedures are also shown to be equivalent in quasisupermodular games as well as in games with compact strategy spaces and upper semicontinuous payoff functions. Finally, we give an example of a game in which the nested procedure is order independent but not equivalent to the universal one, thus showing that order independence is not sufficient to guarantee the equivalence of the two elimination procedures.
arXiv:2607.04904v1 Announce Type: new Abstract: In this paper we present an equivalence result between a randomized version of Anderson Acceleration and of randomized GMRES for linear problems. Namely, we extend the classical result of Walker and Ni (2011) to the case in which the least-squares problem in Anderson Acceleration is solved in a sketched space defined by a random projection. This equivalence suggests potential avenues for further research in the design and analysis of randomized acceleration methods.
arXiv:2505.09484v2 Announce Type: replace Abstract: Face Anti-Spoofing (FAS) is essential for the security of facial recognition systems in diverse scenarios such as payment processing and surveillance. Current multimodal FAS methods often struggle with effective generalization, mainly due to modality-specific biases and domain shifts. To address these challenges, we introduce the \textbf{M}ulti\textbf{m}odal \textbf{D}enoising and \textbf{A}lignment (\textbf{MMDA}) framework. By leveraging the zero-shot generalization capability of CLIP, the MMDA framework effectively suppresses noise in multimodal data through denoising and alignment mechanisms, thereby significantly enhancing the generalization performance of cross-modal alignment. The \textbf{M}odality-\textbf{D}omain Joint \textbf{D}ifferential \textbf{A}ttention (\textbf{MD2A}) module in MMDA concurrently mitigates the impacts of domain and modality noise by refining the attention mechanism based on extracted common noise features. Furthermore, the \textbf{R}epresentation \textbf{S}pace \textbf{S}oft (\textbf{RS2}) Alignment strategy utilizes the pre-trained CLIP model to align multi-domain multimodal data into a generalized representation space in a flexible manner, preserving intricate representations and enhancing the model's adaptability to various unseen conditions. We also design a \textbf{U}-shaped \textbf{D}ual \textbf{S}pace \textbf{A}daptation (\textbf{U-DSA}) module to enhance the adaptability of representations while maintaining generalization performance. These improvements not only enhance the framework's generalization capabilities but also boost its ability to represent complex representations. Our experimental results on four benchmark datasets under different evaluation protocols demonstrate that the MMDA framework outperforms existing state-of-the-art methods in terms of cross-domain generalization and multimodal detection accuracy. The code will be released soon.
arXiv:2511.15727v2 Announce Type: replace Abstract: For a general class of dynamic stochastic multi-player problems, Cs\'oka, Liu, Rodivilov, and Teytelboym (2024) proposed prior-dependent efficient collusion-proof mechanisms. The present paper proves prior-free lifting theorems, at the price of lower guaranteed utility levels that depend on the set of possible initial type profiles. As a special case, we implement a $0.872$-approximately utility-maximizing prior-free collusion-proof mechanism for the Markovian repeated single-good allocation problem studied by Fikioris, Banerjee, and Tardos (2025).
arXiv:2505.12024v2 Announce Type: replace Abstract: A residuated semigroup is a structure $\langle A,\le,\cdot,\backslash,/ \rangle$ where $\langle A,\le \rangle$ is a poset and $\langle A,\cdot \rangle$ is a semigroup such that the residuation law $x\cdot y\le z\iff x\le z/y\iff y\le x \backslash z$ holds. An element $p$ is positive if $a\le pa$ and $a \le ap$ for all $a$. A residuated semigroup is called balanced if it satisfies the equation $x \backslash x \approx x / x$ and moreover each element of the form $a \backslash a = a / a$ is positive, and it is called integrally closed if it satisfies the same equation and moreover each element of this form is a global identity. We show how a wide class of balanced residuated semigroups (so-called steady residuated semigroups) can be decomposed into integrally closed pieces, using a generalization of the classical Plonka sum construction. This generalization involves gluing a disjoint family of ordered algebras together using multiple families of maps, rather than a single family as in ordinary Plonka sums.
arXiv:2606.30444v2 Announce Type: replace-cross Abstract: Neural networks are known to be susceptible to over-reliance on spurious correlations. However, the precise mechanism by which models exploit shortcut features is not fully understood, and algorithms to mitigate this behavior rely on as yet unjustified assumptions about the learned representations. In this work, we provide the first end-to-end theoretical characterization of spurious feature learning for two-layer ReLU neural networks trained by online minibatch SGD on the logistic loss. We consider data drawn from the high-dimensional Boolean hypercube with a quadratic signal function (namely XOR) and a linear spurious correlation. We show that SGD learns the spurious feature first, and exponentially fast. Moreover, the optimization dynamics couple the spurious and signal features, with a stronger spurious component inhibiting signal feature learning. Our analysis reveals precise phase transitions in the learning dynamics. In the first phase, alignment between the signs of the spurious feature and second-layer weight drives rapid growth of the spurious feature. In the second phase, large majority group margin slows learning and the signal feature remains suppressed. When the spurious correlation is maximally strong, we show theoretically that the spurious feature dominates even at the sample complexity threshold where XOR would be learned in isolation (i.e., if the spurious feature was absent). In contrast, when the correlation strength is constant, we provide preliminary empirical evidence that the model can eventually learn the XOR signal, although the spurious feature is not forgotten.
arXiv:2607.04835v1 Announce Type: new Abstract: Splitting methods are a natural choice for the numerical time integration of partial differential equations, and arbitrary high order splitting schemes exist for Schr{\"o}dinger equations with periodic boundary conditions. However, in the presence of non-periodic boundary conditions, we show that they suffer in general from an order reduction, even for smooth initial conditions. The reason for such order reduction phenomena are so-called compatibility conditions, which are not preserved by classical splitting schemes. In this paper, we introduce a family of modified splitting methods for one-dimensional linear Schr{\"o}dinger equations with homogeneous Dirichlet boundary conditions, which achieve an arbitrary high order, and do not suffer from any order reduction. This is illustrated with a fourth order splitting scheme considering initial conditions with various regularity properties.
arXiv:2607.05020v1 Announce Type: cross Abstract: Macroscopic observables allow the recovery of intrinsic dynamics from stationary quantum states. I show that, by interpreting the squared amplitude as the probability density for each definite value of intrinsic time, a curvature emerges in the time direction. For example, from the perspective of intrinsic quantum time, the Friedmann-Lema\^itre-Robertson-Walker cosmological model emerges from spherically symmetric stationary solutions in four-dimensional Euclidean space, without presupposing gravity. If there is no unique direction of time, curvature emerges in all spacetime dimensions, without presupposing gravity, from the variable amplitude of the stationary wavefunction alone. This opens a new possibility that general relativity or some modification of it emerges from intrinsic time observables.
arXiv:2503.21022v2 Announce Type: replace Abstract: The higher-order autocorrelations of integer-valued or rational-valued functions on finite Abelian groups appear naturally in X-ray crystallography, and have applications in computer vision systems, correlation tomography, correlation spectroscopy, and pattern recognition. In this paper, we consider the problem of reconstructing a rational-valued function on finite Abelian groups from its higher-order autocorrelations. We describe an explicit reconstruction algorithm, and prove that the autocorrelations up to order $3r+3$ are always sufficient to determine the data up to translation, where $r$ is the rank of the group. We also provide examples of rational-valued functions on finite Abelian group which are not determined by their autocorrelations up to order $3r+2$. In particular, we provide a sharp upper bound on the separating degree of the regular representation of a finite Abelian group in terms of its rank.
arXiv:2506.21887v2 Announce Type: replace Abstract: High-stakes decision-making involves navigating multiple competing objectives with expensive evaluations. For instance, in brachytherapy, clinicians must balance maximizing tumor coverage (e.g., an aspirational target or soft bound of >95% coverage) against strict organ dose limits (e.g., a non-negotiable hard bound of <601cGy to the bladder). Selecting Pareto-optimal solutions that match implicit preferences is challenging, as exhaustive Pareto frontier exploration is computationally and cognitively prohibitive, necessitating interactive frameworks to guide users. While decision-makers (DMs) often possess domain knowledge to narrow the search via such soft-hard bounds, current methods often lack systematic approaches to iteratively refine these multi-faceted preference structures. Furthermore, DMs often require confidence that they have not overlooked superior alternatives, a paramount necessity in high-stakes scenarios. We present Active-MoSH, an interactive local-global framework designed for this process. Its local component integrates probabilistic preference learning with an active sampling strategy to adaptively refine Pareto subsets while minimizing cognitive burden. To bolster decision confidence, Active-MoSH's global component, C-MoSH, leverages multi-objective sensitivity analysis to identify potentially overlooked, high-value points beyond immediate feedback. We demonstrate Active-MoSH's performance benefits through diverse synthetic and real-world applications. A high-stakes case study with real cervical cancer brachytherapy treatment plans and an image selection user study further validate our hypotheses regarding the framework's ability to improve convergence, enhance DM confidence, and provide expressive preference articulation.
arXiv:2507.15549v2 Announce Type: replace Abstract: We present a quasi polynomial time approximation scheme (Q-PTAS) for the capacitated vehicle routing problem (CVRP) on $n$ points in the Euclidean plane for arbitrary capacity $c$. The running time is $n^{f(\epsilon)\cdot\log\log n}$ for any $c$, and where $f$ is a function of $\epsilon$ only. This is a major improvement over the so far best known running time of $n^{\log^{O(1/\epsilon)}n}$ time and a big step towards a PTAS for Euclidean CVRP. In our algorithm, we first give a polynomial time reduction of the CVRP in $\mathbb{R}^d$ (for any fixed $d$) to an uncapacitated routing problem in $\mathbb{R}^d$ that we call the $m$-paths problem. Here, one needs to find exactly $m$ paths between two points $a$ and $b$, covering all the given points in the Euclidean space. We then give a Q-PTAS for the $m$-paths problem in the pane. Any PTAS for the (arguably easier to handle) Euclidean $m$-paths problem is most likely to imply a PTAS for the Euclidean CVRP.
arXiv:2510.08051v2 Announce Type: replace-cross Abstract: Around the mean dimensions and rate-distortion functions, using some tools from local entropy theory this paper establishes the following main results: $(1)$ We prove that for non-ergodic measures associated with almost sure processes, the mean R\'enyi information dimension coincides with the information dimension rate. This answers a question posed by Gutman and \'Spiewak (in Around the variational principle for metric mean dimension, \emph{Studia Math.} \textbf{261}(2021) 345-360). $(2)$ We introduce four types of rate-distortion entropies and establish their relation with Kolmogorov-Sinai entropy. $(3)$ We show that for systems with the marker property, if the mean dimension is finite, then the supremum in Lindenstrauss-Tsukamoto's double variational principle can be taken over the set of ergodic measures. Additionally, the double variational principle holds for various other measure-theoretic $\epsilon$-entropies.
arXiv:2509.12993v3 Announce Type: replace Abstract: The deployment of large language models (LLMs) presents significant challenges due to their enormous memory footprints, low arithmetic intensity, and stringent latency requirements, particularly during the autoregressive decoding stage. Traditional compute-centric accelerators, such as GPUs, suffer from severe resource underutilization and memory bandwidth bottlenecks in these memory-bound workloads. To overcome these fundamental limitations, we propose HPIM, the first memory-centric heterogeneous Processing-In-Memory (PIM) accelerator that integrates SRAM-PIM and HBM-PIM subsystems designed specifically for LLM inference. HPIM employs a software-hardware co-design approach that combines a specialized compiler framework with a heterogeneous hardware architecture. It intelligently partitions workloads based on their characteristics: latency-critical attention operations are mapped to the SRAM-PIM subsystem to exploit its ultra-low latency and high computational flexibility, while weight-intensive GEMV computations are assigned to the HBM-PIM subsystem to leverage its high internal bandwidth and large storage capacity. Furthermore, HPIM introduces a tightly coupled pipeline strategy across SRAM-PIM and HBM-PIM subsystems to maximize intra-token parallelism, thereby significantly mitigating the serial dependency of the autoregressive decoding stage. Comprehensive evaluations using a cycle-accurate simulator demonstrate that HPIM significantly outperforms state-of-the-art accelerators, achieving a peak speedup of up to 23.1x compared to the NVIDIA A100 GPU. Moreover, HPIM exhibits superior performance over contemporary PIM-based accelerators, highlighting its potential as a highly practical and scalable solution for accelerating large-scale LLM inference.