Partitioning

We develop an exact linear programming (LP) formulation for bounded-depth classification trees with binary features, using a junction-tree representation. The formulation is integral and supports recursive subtree optimization. Exact reductions make the model smaller while preserving the optimal value and recovery of an optimal tree. The reduced model supports two solution methods: column generation and message passing. Column generation solves integral restricted LPs and uses bounds over the full feasible domain to certify optimality. Message passing recursively combines optimal subtree costs. Both methods solve common subtree problems that, once the preceding tree decisions are fixed, can be evaluated independently and in parallel. Computational experiments show that the exact reductions substantially reduce the size of the junction-tree formulation. The resulting linear programming formulation certifies instances for which the tested mixed-integer formulation does not establish optimality within the same computational budget, while the column-generation and message-passing methods certify more instances and achieve an order-of-magnitude reduction in geometric-mean runtime relative to an existing state-of-the-art exact method for optimal classification trees.

Principal Component Analysis (PCA) minimises aggregate reconstruction error, which can inadvertently represent majority subgroups with substantially higher fidelity than minority subgroups. Fairness-aware extensions of PCA correct this disparity but require group labels as input. We address the logically prior question: given only a data matrix, which binary partition of the data suffers the greatest representational disparity under a shared PCA projection? We formalise this as the max-disparity partition problem and propose a greedy local-search algorithm, grounded in the Fiduccia-Mattheyses bipartitioning framework, that discovers the disparity-maximising partition without any predefined group labels. Two benchmark algorithms, a fixed-projection sorting baseline and a simulated-annealing variant, confirm that the greedy solution is empirically near-optimal. Having identified the partition, we attribute the disparity to specific features via PCA loading scores and association rule mining, enabling a practitioner to assess whether the disadvantaged group corresponds to a human-meaningful minority. On the Predict Students' Dropout and Academic Success dataset, representational disparity is driven predominantly by institutional and programmatic proxies for socioeconomic disadvantage, with gender emerging as a secondary but consistent contributor within the disadvantaged group. The discovered partition is then passed directly to Fair PCA, completing a detect-explain-mitigate pipeline.

Pretraining followed by fine-tuning introduces a compute-allocation problem: under a fixed training budget, compute spent improving the upstream objective reduces the compute available for downstream adaptation. Despite its practical importance, this trade-off is not yet well understood theoretically, even in simple models. In this paper, we cast this allocation as a compute-split problem under a two-stage pretrain--fine-tune procedure with fixed total optimisation budget, using regularised least squares trained by gradient descent as a tractable setting. We characterise the optimal split under data-dependent evaluation geometries induced by the fine-tuning problem. Our results show that the allocation depends on how pretraining directions affect fine-tuning predictions and how fine-tuning shifts are seen through downstream data geometry. In particular, the relevant quantities are determined by prediction-relevant spectral components of the pretraining and fine-tuning empirical covariances. Technically, the analysis relies on a basis-invariant, eigenspace-level spectral decomposition, together with perturbative control of the non-commuting pretraining and fine-tuning dynamics.

Scene-level point cloud understanding remains challenging due to diverse geometries and spatial layouts. While pre-trained 3D point cloud foundation models (PFMs) offer strong transferability, full fine-tuning (FFT) incurs substantial computational and storage costs. Parameter-efficient fine-tuning (PEFT) provides a promising alternative, but existing PEFT methods largely focus on object-level point clouds and overlook serialization-induced partition variations in large-scale scenes. To address this issue, we propose PointPiT, a partition-invariant tuning framework for scene-level point clouds. Specifically, a Scene-aware Structural Adapter (SSA) integrates local geometric patterns with global scene context to mitigate partition-induced representation shifts. Moreover, Gradient Subspace Optimization (GSO) selects informative and partition-stable update directions, suppressing partition-dependent variations during optimization. Extensive experiments across multiple scene-level benchmarks demonstrate that PointPiT achieves competitive or even superior performance to full fine-tuning with less than 1% of backbone's parameters, while achieving consistent state-of-the-art performance among representative PEFT methods.

Retrieval-augmented generation (RAG) can improve knowledge-intensive question answering, but the first design choice is easy to overlook: how should the source corpus be partitioned into retrievable units? Fixed-size chunks often return long passages whose relation to the question is only implicit. We introduce EAR, an Entity-Aware Partitioning approach for multiple-choice question answering (MCQA). EAR extracts normalized surface anchors from the question, answer options, and corpus; retrieves local windows around matching corpus anchors; and can attach a larger parent passage through an extractive summary. We evaluate EAR on a cleaned Massive Multitask Language Understanding (MMLU)-style subset of 153 questions selected by an automatic corpus-support heuristic and using decontaminated public textbook text. Across same-protocol top-k = 3 and top-k = 8 sweeps with Mistral, Gemma, and DeepSeek, EAR entity-window reduces retrieved words by 37.5-40.2% relative to chunks. Observed accuracy changes are +5.2, +1.3, and -3.9 points at top-k = 3, and +5.9, -3.3, and -4.6 points at top-k = 8; none of the entity-window differences is statistically significant. The scoped contribution is methodological: EAR provides a compact and inspectable retrieval unit, while its rule-based anchor extractor remains domain-specific and requires separate validation before transfer.

Cross-silo Federated Learning (FL) enables geographically distributed institutions to collaboratively train machine learning models without sharing raw data. In wide-area deployments, however, communication delays often dominate round completion time and exacerbate the straggler effect. Hybrid FL addresses this challenge by combining synchronous and asynchronous client participation, but effective partitioning requires visibility into network conditions such as shared bottlenecks, link utilization, and path contention that individual clients cannot observe. We present HybridFLow, a closed-loop SDN-driven orchestration framework that integrates network-layer intelligence directly into hybrid FL. Leveraging the SDN controller's global topology view, HybridFLow generates calibrated per-client communication-time estimates before each training round and uses them to partition clients into synchronous and asynchronous groups while balancing round latency and update staleness. After each round, measured communication times are fed back to the controller to continuously refine future predictions. Experimental results across multiple network topologies show that HybridFLow reaches 80% target accuracy 33-40% faster than SmartFLow and reduces average round duration by 30-40 seconds, while FedAsync fails to reach the target accuracy under non-IID data distributions.

Agent memory systems have demonstrated significant potential in long-term dialogue, personalized assistants, and video understanding. However, continuously accumulated memory introduces substantial storage and retrieval costs during inference. To address this issue, we propose \textbf{MemForest}, a general memory compression framework adaptable to various agent memory systems. Specifically, MemForest partitions historical memory into event-centric units by leveraging global semantic similarity and local temporal continuity. For each unit, it constructs a maximum spanning tree, termed an EventTree, and progressively merges redundant memory nodes by selecting high-weight edges, reducing storage overhead. Furthermore, we introduce an anchor-guided propagation retrieval mechanism that retrieves relevant memory nodes from the temporal neighborhoods of key nodes, improving retrieval accuracy. Extensive experiments demonstrate the effectiveness of MemForest. Under the unimodal Mem0 framework, MemForest retains \textbf{97.1%} of the original performance while compressing \textbf{50%} of historical memory across three benchmarks (LoCoMo, LongMemEval, and PersonaMem), achieving a \textbf{1.89x} retrieval speedup. Under the multimodal M3-Agent framework, it preserves \textbf{99.7%} of the original performance with a \textbf{50%} compression ratio across two benchmarks (M3-Bench-robot and M3-Bench-web), achieving a \textbf{2.24x} retrieval speedup. \textcolor{RoyalBlue}{\textit{Our code is available at https://github.com/Celina-love-sweet/MemForest.}}

Most automated brain parcellation tools are developed and validated on T1-weighted (T1w) MRI. Yet, some clinical workflows for which parcellation is relevant only use contrast-enhanced T1w (T1ce) MRI, on which T1w-trained models are less accurate. We present a unified network that parcellates both pre- and post-contrast agent T1w MRI reliably, trained on a combination of the two with conditioning that spatially modulates its response differently for each. Feature-wise Linear Modulation (FiLM) is a known approach for input-based modulation in networks. It applies a per-channel scale and shift uniformly across the input. However, the appearance change between pre- and post-contrast varies locally across the brain, making FiLM suboptimal for our use case. In this work, we introduce Spatial FiLM (SpFiLM), a conditioning layer whose modulation varies spatially, assembling a voxel-wise scale and shift from image-derived spatial patterns. Using a cohort of 134 patients with paired T1w and T1ce MRI parcellated into 106 classes, the addition of SpFiLM layers in a UNet increased the mean Dice on the test set of 25 patients from 80.2% to 84.1%, a 4.9% relative improvement. Adding SpFiLM layers led to the best performance on both pre- and post-contrast MRI, even when controlling for network parameter counts.

Agricultural parcel polygons play a fundamental role in geospatial applications such as precision agriculture, land administration, and crop monitoring. Beyond regular polygon geometry and low vertex redundancy, practical parcel maps should avoid topological conflicts and preserve common boundaries between adjacent fields. Yet this requirement remains largely unresolved: segmentation-based methods mainly produce parcel masks or raster boundary cues and rely on heuristic raster-to-vector conversion, instance- and contour-based methods reconstruct parcels independently, and recent vector-oriented methods improve polygon regularity but do not explicitly recover adjacent parcels from a shared topological structure. To address this gap, we propose a semantic-guided diffusion framework for topologically consistent agricultural parcel vectorization. It couples joint edge--vertex latent diffusion with supervised multi-cue conditioning to generate geometrically regularised parcel-boundary and vertex primitives while suppressing false-positive responses. A topology-aware parcel polygon reconstruction method then converts these primitives into regular polygons by reconstructing parcel faces from a common planar graph, enabling adjacent predicted parcels to reuse shared boundaries and avoid mutual interior intrusion. Extensive experiments on the AI4SmallFarms and iFLYTEK datasets evaluate parcel vectorization in terms of pixel-level coverage, geometric fidelity, object-level correctness, and topological consistency. The results show strong and competitive performance, with zero measured intrusion ratio and the highest shared-edge recall, demonstrating the potential of the proposed framework for accurate, regular, and topologically consistent agricultural parcel vectorization.

Taxonomy induction aims to organize concept sets into coherent hierarchical structures. Recent LLM-based methods can induce taxonomies directly from flat term lists, avoiding the need for corpora, but degrade sharply as concept sets scale up. We argue that this degradation stems not only from context length limitations, but also from structural failures in hierarchical reasoning. To address this, we adopt a divide-and-merge paradigm that partitions concepts into smaller subsets, induces local taxonomies, and merges them into a global hierarchy. However, we identify two structural failure modes inherent to this paradigm: Structural Fragmentation, where partitioning weakens local hierarchical signals, and Parent Displacement, where locally plausible relations are misplaced in the global hierarchy. To address both, we propose SPARROW, a scalable taxonomy induction framework that combines structure-preserving spectral partitioning to retain hierarchical connectivity within each block, and constraint-guided incremental fusion that treats block-level relations as structural constraints rather than ground truth for global placement. Experiments on large-scale benchmarks show that SPARROW consistently achieves the strongest global structural quality across backbones. The code is available at https://github.com/rebeccazyr/SPARROW.

In gossip learning, a network of nodes trains a shared model collaboratively, without a central coordinator, by repeatedly exchanging parts of their local models. The state-of-the-art protocol, Partitioned Token Gossip Learning (PTGL) of Heged{ü}s et al., splits the weight matrix into S fixed partitions and disseminates them using a token-based fairness mechanism coupled with per-neighbor metadata exchange. We revisit partition scheduling by analogy with peer-to-peer live streaming, where model partitions act as video chunks and partition age acts as chunk scarcity. The analogy yields a design space of two-stage selection strategies (partition first, or neighbor first), from which we instantiate ten concrete protocols collectively called Stream Learning. Our main finding is that the simplest of these protocols, which transmits the locally least-trained partition to a uniformly random neighbor (Ri), matches PTGL on fault-free workloads while requiring neither token counters nor metadata exchange. Under an adversarial 30% permanent crash of the best-performing nodes, Ri matches or outperforms PTGL across all complete-graph configurations tested, with the gap reaching 5.53% on HAR and 5.41% on MNIST in the most heterogeneous regime (Dirichlet $β$ = 0.1). In our experiments, partition fairness, captured by a single local rule on partition age, accounts for the gap; token-based rate control and utility maximization do not improve over this rule and, under heterogeneity, sit below it.

Adaptive data-cleaning methods replace manual filtering thresholds with data-driven partitions. However, changing the partition granularity, the number of groups used to segment samples by estimated corruption risk, can implicitly shift the decision boundary and alter the overall number of removed samples. This creates a bias known as removal-budget confounding, where apparent gains in metrics like precision or false-positive rate reflect a smaller removal budget rather than superior corruption discrimination. To address this evaluation bias, we introduce an operating-point-aware evaluation framework that evaluates methods using matched-budget and matched-recall controls alongside threshold-independent metrics (AUROC and AUPRC). We test this framework on a multi-cue adaptive cleaner redesign featuring a reweighted learning-difficulty cue, an auxiliary Euclidean-distance cue, and increased partition granularity intended to isolate clean-but-difficult samples. While naive evaluations (assessing configurations at their own induced operating points) suggest substantial performance improvements for the redesign, these gains disappear once operating points are equalized. False-positive decomposition reveals that clean-but-difficult samples primarily drive error counts at low corruption rates, become threshold-dependent at moderate corruption, and contribute negligibly under severe corruption. Experiments on CIFAR-10 and ImageNet-100 demonstrate that most performance differences observed in naive evaluation shrink or vanish at low-to-moderate corruption when operating points are matched. True ranking advantages only remain in specific low-prevalence settings and in high-recall regions under severe corruption. These findings highlight that adaptive cleaning methods must be benchmarked at matched operating points to ensure performance gains reflect genuine corruption discrimination.

Autonomous robot navigation requires rapid construction of obstacle-points-separated convex regions for trajectory planning. When obstacles are represented as point clouds from LiDAR or depth cameras, these regions must be constructed directly from finite obstacle samples while providing suitable constraints for downstream optimization. However, existing corridor-generation methods often struggle to meet real-time, sensor-rate computational requirements. To address this bottleneck, we introduce RISP, a randomized algorithm that constructs convex polytopes from finite point-cloud data, and PathCover, which chains these polytopes along a reference path to form an overlapping corridor. We prove finite termination, sequential intersection, and complete path coverage with respect to the supplied finite point set. Under a probabilistic elimination condition, the sampling-and-elimination stage of RISP has expected O(n) time and unconditional worst-case O(n^2) time. Extensive benchmarks on synthetic and real-world LiDAR datasets demonstrate an order-of-magnitude speedup over state-of-the-art methods in both corridor generation as well as trajectory optimization, while closed-loop quadrotor simulation and a physical quadruped traversal demonstrate integration with downstream motion planners. These results establish corridor separation from the supplied point-cloud representation and practical implementation feasibility. Source code of the entire pipeline is available at https://github.com/kunalnk123690/PathCover.

Autoregressive models have emerged as an effective paradigm for point cloud generation. However, most existing approaches rely on heuristic tokenization strategies, such as spatial sorting or stochastic downsampling, which often disrupt intrinsic point cloud topology and weaken the structural coherence of the generated shapes. In this paper, we present PointRSP, an autoregressive framework that reformulates point cloud generation as a topology-preserving tessellation process via recursive spectral partitioning. Instead of constructing token sequences heuristically, we introduce a topology-aware partitioning autoencoder that decomposes an unstructured point cloud into a non-balanced binary tree through a hybrid recursive spectral partitioning strategy. This hierarchical representation provides a deterministic geometric blueprint that preserves topological relationships while capturing multiscale structural dependencies within a quantized latent space. To synthesize shapes in this space, we propose a dual-stream cascaded generator that jointly models structural evolution and feature synthesis. In addition, we design a geometry-calibrated positional encoding mechanism that anchors latent embeddings using multi-scale structural centers, which stabilizes cascaded generation during the early stages of structural formation. Extensive experiments show that PointRSP achieves state-of-the-art performance in generation quality and diversity, demonstrating strong generalization across complex 3D topologies.

We study the round complexity of learning a hidden partition $\mathcal{P}$ of an $n$-element universe using PAIR queries: PAIR($x,y$) tells us whether $x$ and $y$ belong to the same part of the partition or not. While it is easy to learn using $n|\mathcal{P}|$ queries using a basic algorithm and this query complexity is optimal, this basic algorithm is highly sequential. Black, Mazumdar, and Saha [COLT 2025] recently gave tight deterministic round/query tradeoffs when the number of parts of $\mathcal{P}$ is known. In particular they prove $Θ(\log\log n)$ rounds are sufficient and necessary to limit the number of queries to $n|\mathcal{P}|$. They leave proving a randomized lower bound as an open direction. We show that randomization dramatically changes the picture. When the number of parts $k = |\mathcal{P}|$ is known, we give a simple 3-round randomized algorithm using $O(nk\log n)$ queries with high probability, and prove that 2 rounds require $Ω(n^{4/3}k^{2/3})$ queries -- the same as deterministic algorithms. We also study a more general setting where the number of parts is unknown. In this case, we give a 4-round randomized algorithm using $O(n|\mathcal P|\log^2 n)$ queries with high probability, and prove that 3-rounds cannot achieve near-optimal query complexity. Furthermore, we show an even bigger separation in this regime between randomized and deterministic algorithms: for the latter, $Θ(\log n/\log\log n)$ rounds are necessary and sufficient to obtain near-optimal query complexity.

Graph self-supervised learning aims to learn transferable representations from large-scale unlabeled graph data. Joint-embedding predictive architectures (JEPAs) avoid explicit negative-pair construction and raw-input reconstruction by predicting masked targets directly in latent space. However, existing graph JEPAs typically rely on a single predefined graph partition, biasing the learned representations toward one structural granularity and limiting their ability to capture complementary patterns at different graph scales. To address this limitation, we propose HP-JEPA, a hierarchical partitioning framework for multi-resolution graph joint-embedding prediction. HP-JEPA organizes each graph into an ordered bank of coarse-to-fine partition resolutions and performs context-target latent prediction separately at each resolution using an online encoder, an exponential-moving-average target encoder, and a latent predictor. The resulting resolution-specific graph representations are subsequently integrated through concatenation or task-specific resolution weighting, allowing downstream models to combine complementary local, regional, and global structural information. Experiments on seven graph classification benchmarks and one graph regression benchmark show that HP-JEPA outperforms the fixed-resolution Graph-JEPA baseline on 6 of 8 tasks, improving upon Graph-JEPA on most evaluated benchmarks. Size-stratified analyses further show that HP-JEPA achieves higher accuracy than Graph-JEPA in most evaluated graph-size quartiles on three representative datasets. These results highlight the effectiveness of hierarchical multi-resolution partitioning for transferable graph representation learning.

Rigorous dataset partitioning is a foundational, yet frequently overlooked, prerequisite for reliable deep learning in longitudinal medical imaging. Naively shuffling small clinical cohorts routinely introduces covariate shifts and temporal sampling imbalances across training, validation, and test subsets, exposing downstream models to out-of-distribution evaluation. We address this vulnerability with an auditable Tripartite Dataset Analytics Framework that systematically characterizes spatial grid integrity, multi-parametric intensity fingerprints, and longitudinal temporal trajectories, quantifying the heavy-tailed feature dispersion and irregular, episodic sampling intervals typical of real-world clinical cohorts. Building on this characterization, we formalize an unsupervised spatio-temporal cohort-balancing standard operating procedure (SOP) that combines elbow-optimized K-means clustering over a standardized, six-dimensional joint intensity-temporal feature space with intra-cluster proportionate stratified sampling. On a longitudinal, contrast-enhanced $T1$-weighted brain MRI cohort (N=149), the protocol reduces the maximum cross-subset intensity bias from 34.1% under conventional random shuffling to under 2.1%, while aligning longitudinal follow-up intervals closely around the population mean. Monte Carlo stress testing across ten random seeds and three split configurations confirms that this alignment remains tightly bounded, in clear contrast to the substantial variability of random partitioning. The resulting protocol offers a reproducible, generalizable procedure for cohort engineering in variable-length longitudinal clinical imaging workflows.

Terminology-intensive retrieval, especially in medical settings, depends on preserving multi-word entities, abbreviations, numerical constraints, and compositional concepts. However, existing representations lie at two extremes: single-vector retrievers often over-compress local relevance signals, while token-level late interaction retains every tokenizer subword at substantial indexing, storage, and scoring cost. This mismatch raises a natural question: can context-dependent phrases provide a useful retrieval unit between global vectors and tokens? We introduce H+ Embedding, a unified multi-granularity retriever that predicts variable-length phrase partitions, preserves uncovered tokens as singletons, and applies importance-guided unit selection with weighted MaxSim interaction. Across 16 scientific, medical, and bilingual tasks, its phrase retrieval branch exceeds the global retrieval branch by 6.91 macro nDCG@10. It also nearly matches Token while using 13.7% fewer document vectors and outperforms content-independent grouping rules under moderate vector budgets. Context-dependent phrase interaction therefore provides an intermediate quality-cost point between global compression and token-level interaction for practical retrieval systems.

Covariate shift across training-data partitions biases model selection and parameter estimation in cross-validation, lifelong learning, and federated learning. We propose \textit{Partition-Induced Covariate-shift Correction} (\texttt{PIcsC}), a Fisher information-based regularization framework that mitigates distribution mismatch between data partitions and a reference distribution. \texttt{PIcsC} approximates partition divergence using the Fisher Information Matrix (FIM) and incorporates the resulting statistic as a regularizer during optimization. The same formulation applies to both centrally partitioned datasets (batches or cross-validation folds) and inherently distributed data (federated clients or decentralized nodes), requiring only partition-local gradient statistics rather than raw data. We further introduce a conditional adaptation mechanism that combines FIM shift with KL divergence to detect significant distribution shifts and activates regularization only when necessary. Experiments on more than 40 datasets demonstrate consistent improvements under both natural and synthetic covariate shift. On fragmented batch and fold settings, \texttt{PIcsC} reduces fragmentation-induced performance degradation by more than 20% and 25%, respectively. On seven federated learning benchmarks, it consistently outperforms FedAvg, FedProx, and SCAFFOLD by 3 -5 percentage points without requiring client-specific personalization. These results demonstrate that Fisher information provides an effective and unified mechanism for mitigating partition-induced covariate shift across both centralized and distributed learning.

In large-scale machine learning, distributed training commonly involves multiple workers evaluating the gradients of the model on different dataset partitions. A common challenge is the presence of straggling workers, which may significantly slow down training. Traditional gradient coding (GC) addresses this by duplicating dataset partitions across workers, allowing for the replacement of missing gradients from stragglers. However, GC requires workers to evaluate gradients on multiple dataset partitions in each step, potentially increasing overall training time. In this paper, we propose to pipeline GC, such that gradient evaluation is segmented across multiple steps and each worker evaluates gradients on just a single dataset partition per step. We develop the pipelined version for fractional repetition (FR) and cyclic repetition (CR), two representative dataset placement schemes in GC, and prove convergence guarantees for both. Through extensive simulations and experiments on cloud infrastructure, our schemes not only significantly reduce training time but also accelerate convergence compared to GC and other baselines.

Machine learning models achieve high predictive accuracy in regression tasks, but their deployment in safety-critical and regulated domains requires interpretability. While fuzzy rule-based systems offer transparent, linguistically explicit interpretable models, Mamdani-style fuzzy regression remains underrepresented in modern machine learning software libraries. This paper presents an interpretable regression extension for the Ex-Fuzzy library, enabling Mamdani fuzzy inference with scalar consequents learned directly from data. For this, a target-aware partition initialisation strategy based on Fuzzy C-Means clustering is introduced, in which linguistic variables are derived from an augmented input-output space to emphasise output-relevant regions of the feature space. The proposed extension is evaluated on ten regression datasets from the KEEL repository, comparing Gaussian and trapezoidal partition strategies against standard baselines including linear regression, multilayer perceptron, and random forests. Experimental results show that Gaussian partitions consistently outperform uniform trapezoidal partitions, achieving a mean coefficient of determination of approximately 0.86 while producing compact rule bases of 10-15 human-readable rules. The proposed implementation provides a transparent and competitive alternative to black-box regression models, supporting practical interpretability with competitive predictive performance.

In this work, we study various graph partitioning problems under a general demand model. In each such task, we are given a graph $G=(V,E,c,w)$ with a capacity function $c\colon E\to \mathbb{N}$ and a demand function $w\colon V\times V\to \mathbb{N}$. Our main focus is the problem of finding a cut $(S, \bar{S})$ minimizing the quantity $$ψ_w( S ) = \frac{c( S, \bar{S} )}{w( S, V )\cdot w( \bar{S}, V )}.$$ Here, $c( S, \bar{S} )$ is the cost of edges between $S$ and the complement of $S$, $\bar{S}$, and $w( S, V )=w( S )+w( S, \bar{S} )$ is the sum of the internal demand within $S$, $w( S )$, and the demand between vertices of $S$ and $\bar{S}$, $w( S, \bar{S} )$. We call $ψ_w( S )$ the \emph{generalized conductance} of the cut $(S, \bar{S})$, and the task of minimizing $ψ_w( S )$ the Generalized Conductance Problem. Our main contribution is an algorithm with an $\mathcal{O}(\log n)$-approximation guarantee for this objective. Our result is achieved via a two-way reduction: first to the well-known Generalized $k$-Multicut Problem, and then to a constrained variant of the classic Sparsest-Cut Problem, with an additional upper-bound constraint on the amount of demand that may be cut. Moreover, we show that the above procedure can be used to obtain an $\mathcal{O}(\log n)$-bicriteria approximation for Graph Partitioning with Demands, where the goal is to find a minimum-cost subset of edges $C$ such that for every component $H$ of $G\setminus C$, $w( H )\leq ρ\cdot w( V )$. This, in turn, yields an $\mathcal{O}(\log n)$-approximation for Hierarchical Clustering with Demands, the problem of finding a hierarchy of cuts that partitions the graph into increasingly refined clusters. For multiplicative demand functions, we improve these guarantees to $\mathcal{O}(\sqrt{\log n})$ and for trees we get an $\mathcal{O}(1)$-approximation for all of our objectives.

Video games are a dynamic medium experienced over time. While there are many Procedural Content Generation (PCG) approaches for generating video game levels, they often use representations that abstract away this dynamic nature. In this paper, we introduce a novel, domain-independent ``cake'' representation for game levels over time which implicitly encodes dynamic information. We present a novel level generation approach Playtrace Reconstructive Partitioning (PRP) specifically developed for this cake representation. We compare against six state-of-the-art PCG approaches in the game domain of \textit{Sokoban}, and find that our approach can generate valid levels without sacrificing solution diversity. We believe our cake representation more neatly encodes the implicit dynamic nature of games compared to existing representations, which allows for our domain-agnostic level generation algorithm PRP.

Self-supervised data splitting has emerged as a promising paradigm for sparse-view CT reconstruction, enabling training from incomplete measurements without fully sampled ground truth. However, the influence of key design choices, including partitioning strategy, preprocessing, and inference, remains insufficiently understood. In this work, we introduce a unified framework that decomposes splitting-based reconstruction into these three components, enabling controlled comparison of existing methods and two incremental extensions: multi-partition splitting and an alternative inference strategy. Experiments on simulated LoDoPaB-CT data under independent and correlated noise, together with validation on the real-world 2DeteCT dataset, show that the optimal partitioning strategy strongly depends on the measurement noise structure. Lattice-based splitting performs favorably under independent noise, whereas angular masking is more robust under correlated noise and real measured data. Multi-partition splitting consistently improves over pure projection-wise splitting in several settings. Complementary perceptual and structural metrics, including LPIPS and HaarPSI, reveal differences between masking strategies that are less apparent from PSNR and SSIM alone. These results provide practical guidelines for designing self-supervised sparse-view CT reconstruction methods and highlight the limitations of common independence assumptions in realistic imaging environments.

We study nearest neighbor search from the perspective of data-driven algorithm design: given a dataset $P \subset \mathbb{R}^d$ of size $n$ and sample access to a query distribution over $\mathbb{R}^d$, the goal is to learn a data structure optimized for queries drawn from that specific distribution. We focus on the class of balanced halfspace trees, which naturally abstracts space-partitioning frameworks like locality-sensitive hashing. Assuming Gaussian-like marginal conditions on the dataset and query distribution, we give an efficient algorithm that learns a tree achieving $o(nd)$ query time, provided that a perfect tree exists. At the core of our algorithmic approach is the balanced halfspace cut problem, where we are given a distribution over $\mathbb{R}^d \times \mathbb{R}^d$ and must find a balanced halfspace that minimizes the fraction of cut pairs. We prove that without distributional assumptions, finding the optimal balanced halfspace is NP-hard. To circumvent this computational barrier, we design an efficient improper learning algorithm: if the optimal halfspace cuts an $α$ fraction of pairs, our algorithm outputs a balanced polynomial threshold function of degree $\tilde{O}(1/\varepsilon^2)$ that cuts at most an $O(\sqrt{α+\varepsilon})$ fraction.

Scaling 3D Gaussian Splatting (3DGS) to large outdoor scenes is costly in both data acquisition and computation. Adopting panoramic images with equirectangular projection (ERP) can reduce capture effort via their full $360^{\circ}$ field of view, yet the resulting omnipresent visibility invalidates existing partitioning strategies that rely on local camera frustums, causing block-wise optimization to degenerate into global training. Thus, we propose PanoLOG, a two-stage coarse-to-fine framework equipped with a Geometry and Gradient-based Partitioning Strategy tailored for large-scale panoramic 3DGS reconstruction. In the global coarse stage, PanoLOG leverages sky-sphere modeling and panoramic monocular depth supervision for reliable geometry, while in the refinement stage, G$^2$PS builds adaptive bounding volumes via parallax-driven uncertainty and assigns cameras via gradient-based importance scoring. Furthermore, we construct Pano360, the first benchmark on large-scale panoramic dataset for outdoor scene reconstruction. Extensive experiments demonstrate that G$^2$PS achieves state-of-the-art rendering quality while maintaining scalable, block-parallel training. Our models, training code, and dataset are publicly available.

This paper studies distributed sketching for ordinary least squares (OLS) regression, an approach that distributes small sketches of a large data set over multiple machines to separately construct OLS estimators and average them. Unlike prior studies that consider sketching on the whole data set, we consider sketching on partitioned subsets to further reduce computational cost. Under the fixed design setting, we characterize the exact excess loss of the averaged OLS estimator. Results show that this loss is comparable to the established loss for sketching on the whole data set when the divergence among subset covariances is small.

Computing-in-Memory (CIM) accelerators execute Matrix-Vector Multiplications (MVMs) in memory, making them a compelling solution for Machine Learning (ML) workloads. However, existing ML workload partitioning approaches for CIM accelerators do not fully account for Resistive Random Access Memory (RRAM) constraints such as limited memory, high write latency, and limited endurance. They also neglect parallelism, low-level architectural effects, or the Central Processing Unit (CPU) as a complementary compute resource. To address these limitations, we propose an Integer Linear Programming (ILP)-based workload partitioning framework for heterogeneous CPU-CIM systems. It minimizes end-to-end inference latency under RRAM constraints, captures parallelism, and combines empirical profiling with analytical models. Using our framework, heterogeneous CPU-CIM execution achieves speedups of up to 30.9x over CPU-only execution on an edge CPU and 7.3x over a high-performance CPU. A Design Space Exploration (DSE) yields further design insights for future CIM accelerators.

Neuroimaging research requires manipulating heterogeneous data structures, including raw MRI volumes, volumetric parcellations, cortical surface meshes, tractograms, and connectivity matrices, across tools with incompatible interfaces and file formats, forcing researchers to repeatedly re-implement routine but technically demanding operations. We present CLABTOOLKIT, an open-source Python package that consolidates these operations into a single, coherent framework by representing volumetric, surface, and streamline data as interoperable Python objects. Five core data structures (Parcellation, Surface, AnnotParcellation, Tractogram, and Connectome) encapsulate common neuroanatomical entities and provide consistent methods for loading, processing, and exporting data across standard neuroimaging formats (e.g., NIfTI, GIFTI, FreeSurfer annotations, TCK/TRK), including connectome generation from a parcellation and scalar-map projection onto tractogram streamlines. Complementary modules support BIDS dataset management, FreeSurfer integration, diffusion MRI processing, morphometric analysis, graph-theoretical network analysis, and GPU-accelerated multi-panel visualization via PyVista. The toolkit comprises 19 modules organised into six layers, exposing 13 object-oriented classes with 234 methods and 207 standalone functions, and a JSON-based configuration system enables workflow customization without code changes. Unlike existing neuroimaging libraries, which typically address these tasks separately, CLABTOOLKIT combines color and lookup-table management, parcellation manipulation, multi-surface visualization, and tractography utilities within a single framework. CLABTOOLKIT is compatible with Python 3.9-3.12 and released under the Apache 2.0 license. Source code, documentation, and example workflows are available at https://github.com/connectomicslab/clabtoolkit.

Performance evaluation in AI systems commonly assumes that random dataset splits produce independent and identically distributed (i.i.d.) subsets. We show that this assumption often breaks down in spatiotemporally correlated domains such as aerial surveillance, precision agriculture, and medical imaging, leading to two systematic failures: data leakage, where correlated samples span training and validation splits and inflate performance estimates, and hidden stratification, where errors on minority subpopulations are obscured by aggregate metrics. To address these issues, we propose a unified evaluation and training framework for spatially correlated data. We introduce Structure-Aware Stratified Partitioning (SASP), which constructs validation splits that reduce spatiotemporal leakage while preserving meaningful class balance, and Curriculum Distributionally Robust Optimization (CDRO), a curriculum-based relaxation of distributionally robust training that stabilizes optimization under these stricter splits. Across multiple benchmarks, this combination yields consistently improved generalization, more reliable confidence calibration, and exposes failure modes that remain hidden under conventional random-split evaluation.

Geometry transformers such as VGGT achieve strong performance by jointly reasoning over multiple views with global attention. However, scaling them to large view collections remains challenging due to the quadratic cost of attention. Moreover, our empirical analysis reveals that the reconstruction quality in VGGT is sensitive to the distribution of viewpoints. Simply increasing the number of views without sufficient viewpoint diversity can even degrade performance, as redundant views introduce highly similar tokens that dilute informative geometric signals in the attention mechanism. Motivated by this observation, we propose a training-free and plug-and-play VGGT inference framework that organizes views into diversity-aware balanced chunks. The chunks are constructed through combinatorial graph partitioning over visual dissimilarity and spatial dispersion. This view organization allows the transformer to focus attention on geometrically informative views while reducing redundant attention interactions. To estimate spatial dispersion without full pose estimation, we approximate spatial relationships via a soft pose propagation strategy based on visual similarity from a small set of seed frames. Extensive experiments demonstrate improved performance in camera pose estimation, multi-view depth prediction, and 3D reconstruction while reducing memory usage and inference latency. Our framework also complements existing VGGT variants, enabling scalable multi-view reconstruction without sacrificing geometric fidelity.

Knowledge Distillation (KD) enables training smaller student models under the guidance of larger teacher models, and the widely adopted TRL library implements it. Yet, TRL treats both models symmetrically, missing opportunities to exploit their pronounced asymmetry in memory footprint, and communication requirements. This paper presents an HPC-aware methodology for KD that decouples teacher and student partitioning efficiently. Our approach achieves up to 67% higher samples-per-second than TRL by avoiding unnecessary teacher-model data structures and selecting the best split strategy. We combine vertical and horizontal partitioning of models, deriving an analytical expression that identifies the existence of inflection points between splitting regimes. These results showed that exploiting teacher--student asymmetry through topology-aware parallelism notably accelerated GKD training on production HPC clusters at our company

Traffic prediction is a core task in intelligent transportation systems and urban-scale decision making. Despite the effectiveness of mainstream neural-network based methods, their deployment in real-world settings with thousands of traffic sensors is jeopardized severely by their poor computational scalability. To address this, the community has attempted to incorporate spatial database partitioning techniques (e.g., Grid, Quadtree, and K-D Tree) to improve model scalability. However, these approaches rely on handcrafted geometric heuristics and often produce irregular or imbalanced data partitions, leading to boundary fragmentation, excessive padding overheads, and degraded model accuracy. In this paper, we propose SqLinear, an efficient and effective architecture for large-scale traffic prediction. First, we design Square Partition, a geometry-adaptive algorithm that partitions massive traffic sensors into balanced, non-overlapping, and near-square spatial regions. Unlike existing heuristic-based designs, Square Partition is theoretically grounded and provides provable guarantees on aspect ratio, balance, and partition utilization, establishing a high-quality foundation for downstream spatiotemporal modeling. Next, we propose a Hierarchical Linear Interaction (HLI) module that abandons the costly attention mechanisms commonly used in Transformer-based spatio-temporal models. HLI efficiently captures both local intra-region dynamics and global inter-region dependencies through a lightweight linear interaction scheme, enabling effective spatiotemporal modeling with linear computational complexity. Extensive experiments on four large-scale traffic datasets and 10 baselines show that SqLinear reduces MAE by 2.30% on average under standard setting and by 5.81% under extreme scalability settings, while reducing training runtime by 13.27%--30.84% in spatial- and horizon-scaling scenarios.

A recent line of work has reframed individual decision trees as linear models on engineered features associated with their splits, opening routes for oracle inequalities and feature-importance reinterpretation, but leaving open the question of what unified geometric object a forest induces when one indexes its feature map by nodes rather than by splits. The present paper studies that object. KPP indexes the feature map by the nodes of the forest, weighted by a path metric that turns each coordinate into a component of a squared-Euclidean path-isometric embedding. KPP unifies four pillars under a single node-indexed representation whose Gram is non-diagonal and carries a metric: prediction, exact additive attribution, deterministic Lipschitz robust radius in the KPP metric, and uniform Rademacher risk bounds for regression and classification under fixed, honest, or cross-fit conditioning. All probabilistic guarantees are conditional on the representation and are stated under three explicit conditioning regimes; the robust-radius guarantee is deterministic in the KPP metric rather than in a norm on the raw input. Conjectured fast-rate refinements for both regression and classification are stated as open problems and are not claimed as theorems.

We present IOAH3 (Importance-Oriented Adaptive H3 partitioning), a computational method for constructing data-driven spatial partitions of geo-referenced observation domains. Standard approaches to spatial aggregation adopt fixed areal units, such as administrative boundaries or uniform hexagonal grids at a single resolution, without regard to the informational content of the underlying observations in each region. This leads to the well-known modifiable areal unit problem: statistical and inferential results depend on the arbitrary choice of partition, and spatially concentrated phenomena are averaged out in coarse cells that obscure fine-scale structure. IOAH3 addresses this by constructing an adaptive partition in three stages: multi-source feature extraction and importance scoring via principal component analysis over road density, POI density, building density, and terrain roughness signals, with population and flood-hazard data entering as auxiliary inputs to cell filtering and spatial smoothness; spatial cell selection via Markov Random Field graph-cut optimisation, which jointly maximises per-cell importance while enforcing spatial contiguity; and data-driven hierarchical refinement of high-importance regions to finer H3 resolution levels, with neighbour-propagated support to avoid isolated fine-resolution islands. The resulting partitions serve as input to spatial inference pipelines and provide a principled resolution of the partition-sensitivity problem prior to any modelling step.

Reconstructing surface meshes from multi-view images has remained a core challenge in recent years. Most existing methods, whether implicit or explicit, depend on intermediate representations and post-processing steps like Marching Cubes or TSDF fusion, often resulting in artifacts and fragmented geometry. Directly optimizing explicit meshes is a promising approach. However, it presents two critical challenges. The first is how to adaptively refine mesh topology to capture detail without introducing degenerate faces. The second is how to maintain consistent UV coordinates for high-fidelity texturing as the mesh structure evolves. To overcome these, we propose ExMesh, a novel framework that directly optimizes explicit meshes by integrating differentiable optimization with discrete topology updates. Specifically, we introduce an adaptive vertex splitting and merging strategy, along with real-time UV maintenance, to enable coarse-to-fine optimization while preserving geometric integrity. To our knowledge, ExMesh is the first framework to seamlessly integrate discrete topology operations into a continuous differentiable optimization pipeline. Extensive experiments demonstrate that ExMesh achieves a balance among accuracy, computational efficiency, and mesh conciseness.

Generating compact polygonal models from point clouds is a key problem in 3D vision and computer graphics. However, due to inherent limitations of LiDAR scanning (e.g. range constraints and occlusions), critical scene information is often missing, leading to degraded reconstruction accuracy. To address this, we propose a plane assembling strategy that effectively recovers missing details while maintaining model compactness. We classify all the planes extracted from the scene into three categories: highly visible, barely visible, and invisible. The invisible planes, which are recovered by scene structure analysis, indicate the missing details. The three types of planes correspond to the three growth priorities. Each plane grows according to the priority level, and the space is partitioned progressively, namely, the hierarchical partition. Subsequently, we generate a watertight polygonal mesh from the partition via a min-cut-based optimization. Finally, comparisons on public datasets show the effectiveness and superiority of our method against mainstream approaches. The project page is available at https://hsr-3dv.github.io/.

Admissible heuristics are essential for optimal planning, yet learning them remains challenging due to the risk of overestimation. Cost partitioning combines multiple abstraction heuristics while preserving admissibility, but computing optimal partitions online is expensive. We propose a framework that learns to infer admissible cost partitions by leveraging the Lagrangian dual equivalence between cost partitioning and multiplier prediction. Planning states and patterns are encoded as labelled graphs, and an action-centric variant of the Weisfeiler-Leman algorithm extracts structural feature vectors. A deep architecture with axial self-attention and a softmax output layer maps these features to cost weights that satisfy the partition constraints by construction, ensuring admissibility. Experiments demonstrate reduced node expansions compared to suboptimal partitioning baselines while maintaining strict admissibility. To our knowledge, this is the first machine-learned heuristic guaranteed to be admissible.

Speech emotion recognition is an important component of modern human-computer interaction systems. However, many state-of-the-art approaches rely on large pretrained models with high computational and memory requirements, limiting their applicability. This paper proposes ResLSTM-SA, a lightweight architecture that integrates residual connections with soft attention within an LSTM-based framework. Evaluated on the RAVDESS dataset under strict speaker-independent partitioning, the proposed model outperforms conventional attention-based LSTM baselines and several previously reported CNN- and hybrid CNN-LSTM architectures in terms of unweighted average recall (UAR). The best-performing variant (ResLSTM-SA-h64) achieves a maximum UAR of 0.6517 with only 46.8k trainable parameters, delivering competitive accuracy with three orders of magnitude fewer parameters than large-scale self-supervised alternatives, thereby enabling efficient deployment on edge devices and real-time voice assistants. The source code is available at https://github.com/Mak-Sim/ResLSTM-SER.

Geometric partitioning has attracted increasing attention by its remarkable motion field description capability in the hybrid video coding framework. However, the existing geometric partitioning (GEO) scheme in Versatile Video Coding (VVC) causes a non-negligible burden for signaling the side information. Consequently, the coding efficiency is limited. In view of this, we propose a spatio-temporal correlation guided geometric partitioning (STGEO) scheme to efficiently describe the object information in the motion field of video coding. The proposed method can economize the bits consumed for side information signaling, including the partitioning mode and motion information. We firstly analyze the characteristics of partitioning mode decision and motion vector selection in a statistically-sound way. Based on the observed spatio-temporal correlation, we design a mode prediction and coding method to reduce the overhead for representing the above mentioned side information. The main idea is to predict the STGEO modes and motion candidates that have higher selection possibilities, which can guide the entropy coding, i.e., representing the predicted high-probability modes and motion candidates with fewer bits. In particular, the high-probability STGEO modes are predicted based on the edge information and history modes of adjacent STGEO-coded blocks. The corresponding motion information is represented by the index in a merge candidate list, which is adaptively inferred based on the off-line trained merge candidate selection probability. Simulation results show that the proposed approach achieves 0.95% and 1.98% bit-rate savings on average compared to VTM-8.0 without GEO for Random Access and Low-Delay B configurations, respectively.

To improve the coding performance, geometric partition (GEO) was proposed for the upcoming VVC standard. GEO provides 140 partition candidates. The index of optimal GEO mode needs to be signaled explicitly. Considering different structural characteristics of different CUs and the correlation between spatial adjacent blocks and temporal collocated blocks, we propose a GEO mode prediction strategy by constructing a Most Probable Mode (MPM) list to reduce the overhead of GEO index and improve coding efficiency. Based on the observation of the high correlation between the partition mode and object boundaries, an edge-directed geometric partition scheme is proposed to construct the MPM list according to spatio-temporal edge information. The proposed method provides an objective BD-rate gain of 0.58% and 1.00% on average for RA and LDB configurations compared to VTM-6.0. Besides, it also promotes the visual quality of object boundaries.

Multi-agent Large Language Model (LLM) systems offer a way to decompose complex tasks, such as coding, through parallelization and context isolation. However, adding agents in practice introduces inter-agent communication overhead, which incurs extra cost and can sometimes offset the efficiency gains. We formalize multi-agent orchestration as a graph partitioning problem that captures the communication-to-computation trade-off: task decomposition can shorten critical-path computation, but cross-agent dependencies require costly context transfer. We instantiate this view in repository-level software engineering and present Cohesion-aware Coder (Co-Coder), which builds dependency graphs from static analysis, isolates structural hub files, partitions the graph via community detection, and executes the partition with a dependency-aware scheduler. Across 28 real-world tasks on DevEval and CodeProjectEval, Co-Coder advances the Pareto-frontier over sequential and file-based parallel baselines as well as Claude Code with Agent Teams, lifting pass rate by up to 14.0%, achieving up to a 2.10x wall-clock speedup, and reducing API cost by up to 35%, with the largest gains on the most dependency-dense projects. Co-coder demonstrates how cohesion-aware orchestration can make parallel coding agents both theoretically grounded and practically efficient, suggesting a broader design principle for multi-agent systems.

State abstraction in reinforcement learning is usually formulated as a partition of states based on reward and transition similarity. This excludes a common structural pattern in navigation, graph, and hierarchical decision problems: interface states such as doors, hubs, and bottlenecks naturally participate in more than one region. We introduce \emph{tangle-core abstraction}, an overlapping state-abstraction framework based on graph tangles of empirical transition graphs. The method constructs abstract states from consistently oriented low-order separations and represents shared interfaces through a membership kernel rather than a hard partition. We give value-preservation guarantees for the induced overlapping abstract MDP under an explicit action-consistency condition, identify an interior-homogeneity/boundary-leakage error decomposition, and prove a quantitative interface-overlap result showing when hard partitions incur an avoidable boundary error. Empirically, tangle-core abstractions achieve favorable compression--return tradeoffs against reward-aware, learned, topological-map, and graph-partitioning baselines across bottlenecked tabular domains, procedurally generated mazes, and MiniGrid representations. We also identify a clear failure regime in which transition topology is uninformative, where tangles predictably offer little benefit. These results position graph tangles as an effective topology-aware abstraction prior for decision problems with shared interface structure.

3D Gaussian Splatting (3DGS) has become the standard for real-time novel view synthesis on commodity GPUs. Its pipeline ties spatial partitioning and rasterization to one tile size, yet the two pull in opposite directions: partitioning, which bins and depth-sorts gaussians, grows cheaper with larger tiles, while rasterization gets cheaper with smaller ones. Prior acceleration work reduces the cost of individual stages but keeps both locked to that single scale, where a few dense tiles dominate frame time. We present Hierarchically Tiled Gaussian Splatting (HiGS), which gives each its own scale: partitioning runs over coarse macro-tiles, while rasterization runs over the fine render tiles within them. Rasterization work is then issued in proportion to the gaussians in each macro-tile rather than per tile, so dense regions spread across many parallel units instead of serializing through one. Across tested scenes, HiGS renders up to 15.8x faster than the original 3DGS and outperforms every other rasterizer we evaluate, while preserving exact front-to-back alpha compositing.

We consider a federated learning (FL) system in which Industrial Internet-of-Things (IIoT) devices collaboratively train a global model over wireless channels without sharing local data. In such systems, communication time is a primary bottleneck that constrains overall training efficiency. Unlike conventional networks that prioritize individual quality-of-service requirements, FL systems collectively aim to converge to an optimal global model as efficiently as possible, which calls for a fundamentally different approach to bandwidth allocation. In this paper, we propose a novel bandwidth allocation policy that exploits the heterogeneity of device computing capabilities to minimize total training time. Rather than distributing bandwidth among all selected devices simultaneously, the proposed policy partitions the participating devices into ordered subsets and sequentially grants each subset exclusive access to the full bandwidth. We formally prove that this partitioning-based policy achieves a strictly lower training time than any bandwidth allocation scheme without partitioning, irrespective of the underlying scheduling algorithm. Furthermore, by reducing per-device transmission duration, the proposed policy also minimizes uplink energy consumption, which is particularly beneficial for battery-constrained IIoT devices. Extensive experiments on real-world datasets - including GC10-Det, an industrial surface defect benchmark, and CIFAR-10, a standard image classification benchmark - demonstrate that the proposed policy consistently reduces training time and energy consumption compared to existing bandwidth allocation schemes, approaching the theoretical lower bound on round time.

Cluster analysis is a widely applied machine learning technique to understand the existing patterns in the population of gamma-ray bursts (GRBs), in order to explore their physical sources. In the present scenario, the number of clusters corresponding to differentiable groups is still under conflict, in spite of numerous attempts with the state-of-the-art clustering procedures. This crucial unknown parameter needs to be evaluated, either directly or indirectly in terms of other tuning parameters, to produce the clusters in GRBs through implementation of an appropriate clustering algorithm. While most of the applied algorithms reached two physically explained groups of merger and collapsar predominated by the short and long bursts respectively, other statistical approaches violated this binary partition. However, physical establishment of any additional cluster(s) is not yet confirmed. Therefore, we propose a new algorithm, from a different stream of clustering referred to as `completely parameter-free', which carries out the classification of GRBs in a manner that has not been tried so far. It indicates two main groups, of short and long duration bursts from the BATSE sample, compatible with the merger-collapsar theory.

In recent years, the field of artificial intelligence has undergone a paradigm shift from task-specific small-scale models to general-purpose large language models (LLMs). With the rapid iteration of LLMs, objective, quantitative, and comprehensive evaluation of their capabilities has become a critical link in advancing technological development. Currently, the mainstream static benchmark dataset-based evaluation methods face challenges such as the diversity of task types, inconsistent evaluation criteria, and fragmentation of data and processing workflows, making it difficult to efficiently conduct cross-domain and large-scale model evaluation. To address the aforementioned issues, this paper proposes and open-sources OpenCompass, a one-stop, scalable, and high-concurrency-supported general-purpose LLM evaluation platform. Adhering to the design philosophy of modularization and component decoupling, the platform boasts three core advantages: high compatibility, flexibility, and high concurrency. The core architecture of OpenCompass comprises five key components: the Configuration System, Task Partitioning Module, Execution and Scheduling Module, Task Execution Unit, and Result Visualization Module. Its workflow provides rule-based, LLM-as-a-Judge, and cascaded evaluators to adapt to the requirements of different task scenarios. Supporting mainstream benchmark datasets across multiple domains, including knowledge, reasoning, computation, science, language, code, etc., the platform offers a unified and efficient LLM evaluation tool for both academia and industry, facilitating the accurate identification of strengths and weaknesses of LLMs as well as their subsequent optimization.

Graph Partitioning is a critical problem in numerous scientific and engineering domains including social network analysis, VLSI design, and many more. Spectral methods are known to produce quality partitions while minimizing edge cuts for a wide range of problems. However, the computational cost associated with the calculation of the Fiedler vector, an eigenvector associated with the second smallest eigenvalue of the graph Laplacian, remains a significant bottleneck due to memory issues and computational costs. In this paper, we present an accelerated approach to spectral bisection partitioning by replacing the traditional eigenvalue calculation with a simple artificial neural network model to approximate the Fiedler vector. We demonstrate that our approach achieves partitioning quality comparable to spectral bisection while significantly reducing the computational overhead, making it more scalable and efficient for large-scale problems

Modern reasoning agents are increasingly evaluated on their ability to generate multiple valid solution paths, plans, or tool-use traces for a given input. Standard reward-maximizing RL tends to collapse onto the most easily reinforced high-reward mode, whereas distribution-matching RL aims to allocate probability mass across the entire reward-shaped solution set. Achieving this objective requires computing a prompt-dependent partition function over the trajectory space. Because existing distribution-matching methods learn this partition function online alongside the policy, calibration errors in the partition function directly distort policy updates and remain impossible to diagnose independently. We introduce DISA, short for Decoupled Importance-Sampled Anchoring, which moves this calibration problem outside the RL loop. DISA draws proposal trajectories offline, estimates the partition function via importance sampling, and freezes the resulting partition-function estimate before policy optimization begins. This decoupling preserves the distribution-matching objective while strictly separating partition-function estimation from policy learning in data, gradients, loss, and diagnostics. Empirically, on two open-weight backbones across six math and three code benchmarks, DISA matches or exceeds the online-coupled distribution-matching baseline FlowRL, outperforms rewardmaximization baselines GRPO and GSPO on math averages, and exceeds LoRASFT distillation by up to 13.8 Mean@8 points on the same offline trajectories. An LLM-as-judge evaluation further shows that DISA retains substantially more strategy-level diversity than reward-maximization baselines, and sensitivity studies on the proposal strength and inverse temperature follow the bias-variance pattern predicted by the analysis.

Low-rank adaptation (LoRA) has become the dominant paradigm for parameter-efficient fine-tuning (PEFT) of large language models (LLMs). However, its bilinear structure introduces a critical limitation: the mapping from trainable parameters to weight updates is not distance-preserving, distorting the optimization landscape. Methods that project a low-dimensional vector into LoRA's parameter space, such as Uni-LoRA, improve parameter efficiency, but the subsequent bilinear LoRA map breaks end-to-end isometry, leaving the core distance-preservation problem unresolved. We propose GPart (Global Partition fine-tuning), a highly parameter-efficient fine-tuning method which removes the low-rank bottleneck entirely. Our method uses a single isometric partition matrix to map a $d$-dimensional trainable vector directly into the full weight space of the model. The result is an extremely minimal fine-tuning pipeline: one random projection, end-to-end isometric, with a single clean hyperparameter ($d$) and storage cost of $d+1$ values (the trainable vector plus a random seed). GPart builds on the theoretical premise that effective fine-tuning can emerge from random low-dimensional subspaces of the full weight space, without imposing low-rank matrix structure. We empirically demonstrate the superior or comparable performance of GPart to existing PEFT methods on natural language understanding, computer vision tasks, and mathematical reasoning. Overall, GPart achieves state-of-the-art efficiency and performance by removing structural constraints, offering a straightforward and elegant path to PEFT.

We introduce Exemplar Partitioning (EP), an unsupervised method for constructing interpretable feature dictionaries from large language model activations with $\sim 10^3\times$ fewer tokens than comparable sparse autoencoders (SAEs). An EP dictionary is a Voronoi partition of activation space, built by leader-clustering streamed activations within a distance threshold. Each region is anchored by an observed exemplar that serves as both its membership criterion and intervention direction; dictionary size is not prespecified, but determined by the activation geometry at that threshold. Because exemplars are observed rather than learned, dictionaries built from the same data stream are directly comparable across layers, models, and training checkpoints. We characterise EP as an interpretability object via targeted demonstrations of properties newly accessible through this construction, plus one head-to-head benchmark. In Gemma-2-2B, EP dictionary regions are interpretable and support causal interventions: refusal in instruction-tuned Gemma concentrates in a region whose exemplar ablation can collapse held-out refusal. Cross-checkpoint matching between base and instruction-tuned dictionaries separates the directions preserved through finetuning from those introduced by it. EP regions and Gemma Scope SAE features decompose activation space differently but agree on a shared core: $\sim$20% of EP regions match an SAE feature at $F_1 > 0.5$, and EP one-hot probes retain $\sim$97% of raw-activation probe accuracy at $\ell_0 = 1$. Nearest-exemplar distance provides a free out-of-distribution signal at inference. On AxBench latent concept detection at Gemma-2-2B-it L20, EP at $p_1$ reaches mean AUROC 0.881, +0.126 over the canonical GemmaScope SAE leaderboard entry and within 0.030 of SAE-A's 0.911, at $\sim 10^3\times$ less build compute.

The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii) topology-blind parameter initialization that leads to optimization cold starts. To bridge these gaps, we propose Neural QAOA$^{2}$, an end-to-end differentiable framework that jointly generates graph partitions and initial parameters. By integrating a generative evaluative network (GEN), our method utilizes a differentiable quantum evaluator as a high-fidelity performance surrogate to provide direct gradient guidance, enabling the joint generator to learn the intrinsic mapping from graph topology to high-quality partition and parameter configurations. Extensive experiments on 183 QUBO, Ising, and MaxCut instances (21 to 1000 variables) demonstrate that our gradient-driven approach broadly outperforms heuristic baselines, ranking first on 101 instances. It exhibits zero-shot generalization across out-of-distribution graph topologies and scales.

While Graph Neural Networks (GNNs) have demonstrated significant efficacy in node classification tasks, where predictions rely on local neighborhood information, the performance of GNNs often drops when prediction tasks depend on long-range interactions. These limitations are attributed to phenomena such as oversquashing, where structural bottlenecks restrict signal propagation across the network topology. To address this challenge, we introduce RAwR, a computationally efficient rewiring framework that augments the input graph with a quotient graph derived from equitable partitions. This approach facilitates accelerated communication between nodes that share identical structural roles, as identified by the Weisfeiler-Leman graph coloring, and thereby reduces the total effective resistance of the system. Furthermore, by employing an approximate definition of the equitable partition, RAwR enables a controllable reduction of the quotient graph, which, in its most condensed state, recovers the conventional Master Node rewiring technique. Empirical evaluations across a diverse suite of benchmarks -- including homophilic, heterophilic, and synthetic long-range datasets -- demonstrate that RAwR achieves state-of-the-art results. Our contribution is further supported by an analytical investigation using a teacher-student model of linear GNNs, which elucidates the theoretical foundations of role-based rewiring. This analysis leads to the formulation of Spectral Role Lift (SRL), a metric designed to identify the optimal approximate equitable partition for maximizing predictive performance.

This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain $[0,1]^d$ and $d$-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for Transformers that builds local approximations of the target function and aggregates them into a global approximation via softmax partition of unity. This approach leverages the attention mechanism to achieve spatial localization through affine transformations of the input. The softmax activation plays a crucial role in aggregating local approximations to a global output. From an approximation perspective, we prove that a dense Transformer equipped with only two encoder blocks and standard single-hidden-layer point-wise feed-forward networks can achieve a uniform $\varepsilon$-approximation error for $α$-Hölder continuous functions with $α\in (0,1]$ using $\mathcal{O}(\varepsilon^{-d/α})$ total parameters. Building upon this approximation guarantee, we establish a near minimax-optimal generalization error bound of order $\mathcal{O}\big(n^{-\frac{2α}{2α+d}} \log n\big)$ for the empirical risk minimizer, where $n$ is the training data size. The Transformer architecture studied in this paper is dense, shallow and wide, and employs softmax activation and sinusoidal positional encodings, closely reflecting practical implementations.

Denoising wearable electroencephalogram (EEG) is inherently challenging since neural activity is not only subtle but also inseparable from spectrally overlapping noise artifacts. Classical signal processing methods, relying on fixed or heuristic rules, cannot handle the time-varying pervasive artifacts in wearable EEGs. Deep learning methods, on the other hand, show promise in decomposition-free EEG denoising using highly expressive neural networks, but the training requires artifact-free EEG, which is inherently unobtainable. To address this, we propose Intelligent Partitioning for Self-supervised Denoising (iPSD). Our method eliminates the need for clean references by learning to partition an input EEG segment into independent noisy realizations with the same underlying signal. This enables self-supervision of deep learning denoisers, even in zero-shot settings where only a single EEG segment to be denoised is available. We validate iPSD through extensive experiments, including validations on wearable EEG from in-ear sensors. The results show that iPSD achieves state-of-the-art performance, most notably under extremely low signal-to-noise ratios (down to -10 dB) and challenging artifacts (e.g., EMG), with spectral fidelity orders of magnitude higher than competitive baselines.

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.

Generative Recommender (GR) inference places embedding hot caches (EMB) and KV caches in direct competition for limited GPU HBM: allocating more memory to one improves its efficiency but degrades the other. Existing systems optimize them in isolation, overlooking that the optimal EMB-KV allocation ratio can shift by up to 0.35 across workload regimes, leaving 20-30% latency improvement unrealized. While online reallocation is required to close this gap, naive approaches introduce H2D refill traffic on the critical path, causing P99 SLO violations. To address this, we present HELM, which jointly manages HBM allocation and request routing at runtime through two key components: (1) Adaptive Memory Allocation, a three-layer PPO-based controller (frozen base policy, online residual adapter, and burst-aware recovery controller) that achieves $32\,\mathrm{μs}$ decision latency while staying within 0.024-0.029 of the offline-optimal ratio; and (2) EMB-KV-Aware Scheduling, which routes requests by jointly considering KV residency, embedding locality, and node load to avoid routing inefficiencies under heterogeneous allocations. Evaluations on three production-scale datasets over a 32-node A100 cluster show that HELM reduces P99 latency by 24-38% over the best static policy and achieves 93.5-99.6% SLO satisfaction across Steady, Trend, and Burst workloads, significantly outperforming state-of-the-art baselines without sacrificing throughput.

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.

While autoregressive Large Vision-Language Models (LVLMs) demonstrate remarkable proficiency in multimodal tasks, they face a "Visual Signal Dilution" phenomenon, where the accumulation of textual history expands the attention partition function, causing visual attention to decay inversely with generated sequence length. To counteract this, we propose Persistent Visual Memory (PVM), a lightweight learnable module designed to strengthen sustained, on-demand access to visual evidence. Integrated as a parallel branch alongside the Feed-Forward Network (FFN) in LVLMs, PVM establishes a distance-agnostic retrieval pathway that directly provides visual embeddings for enhanced visual perception, thereby structurally mitigating the signal suppression inherent to deep generation. Extensive experiments on Qwen3-VL models demonstrate that PVM brings notable improvements with negligible parameter overhead, delivering consistent average accuracy gains across both 4B and 8B scales, particularly in complex reasoning tasks that demand persistent visual perception. Furthermore, in-depth analysis reveals that PVM shows improved robustness in longer generations and accelerates internal prediction convergence.

Gaussian basis functions provide an efficient and flexible alternative to spline activations in KANs. In this work, we introduce the partition-of-unity Gaussian KAN (PU-GKAN), a Shepard-type normalized Gaussian KAN in which the Gaussian basis values on each edge are divided by their local sum over fixed centers. This produces a partition-of-unity feature map with trainable coefficients, while preserving the standard edge-based KAN structure. The normalized construction gives exact constant reproduction at the edge level and admits an explicit finite-feature kernel interpretation. We formulate both the standard Gaussian KAN (GKAN) and PU-GKAN from a finite-feature and additive-kernel viewpoint, making the induced layer kernels and empirical feature matrices explicit. Using the first-layer feature matrix as the reference object, we adopt a practical scale-selection interval for $ε$, with the lower endpoint determined by adjacent-center overlap and the upper endpoint determined by a conservative conditioning threshold. Numerical experiments show that PU-GKAN reduces sensitivity to $ε$, improves validation accuracy for most smooth and moderately non-smooth targets, and gives more stable training behavior. The benefit persists across sample-size and center-number sweeps, higher-dimensional architectures, Matérn RBF bases, and physics-informed examples involving Helmholtz and wave equations. These results indicate that Shepard-type partition-of-unity normalization is a simple and effective stabilization mechanism for RBF-based KANs.