Partitioning

Watermarking has emerged as a promising technique for tracing the authorship of content generated by large language models (LLMs). Among existing approaches, the KGW scheme is particularly attractive due to its versatility, efficiency, and effectiveness in natural language generation. However, KGW's effectiveness degrades significantly under low-entropy settings such as code generation and mathematical reasoning. A crucial step in the KGW method is random vocabulary partitioning, which enables adjustments to token selection based on specific preferences. Our study revealed that the next-token probability distribution plays an critical role in determining how much, or even whether, we can modify token selection and, consequently, the effectiveness of watermarking. We refer to this characteristic, associated with the probability distribution of each token prediction, as \emph{watermark strength.} In cases of random vocabulary partitioning, the lower bound of watermark strength is dictated by the next-token probability distribution. However, we found that, by redesigning the vocabulary partitioning algorithm, we can potentially raise this lower bound. In this paper, we propose SSG (\textbf{S}ort-then-\textbf{S}plit by \textbf{G}roups), a method that partitions the vocabulary into two logit-balanced subsets. This design lifts the lower bound of watermark strength for each token prediction, thereby improving watermark detectability. Experiments on code generation and mathematical reasoning datasets demonstrate the effectiveness of SSG.

Federated learning (FL) aggregation on serverless platforms faces a hard scalability ceiling: existing architectures (lambda-FL, LIFL) partition clients across aggregators, but every aggregator must hold the complete model gradient in memory. When gradients exceed the per-function memory limit (e.g., 10 GB on AWS Lambda), aggregation becomes infeasible regardless of tree depth or branching factor. We propose GradsSharding, which instead partitions the gradient tensor into M shards, each averaged independently by a serverless function that receives contributions from all clients. Because FedAvg averaging is element-wise, this produces bit-identical results to tree-based approaches, so model accuracy is invariant by construction. Per-function memory is bounded at O(|θ|/M), independent of client count, enabling aggregation of arbitrarily large models. We evaluate GradsSharding against lambda-FL and LIFL through HPC experiments and real AWS Lambda deployments across model sizes from 43 MB to 5 GB. Results show a cost crossover at approximately 500 MB gradient size, 2.7x cost reduction at VGG-16 scale, and that GradsSharding is the only architecture that remains deployable beyond the serverless memory ceiling.

3D-IC netlist partitioning is commonly optimized using proxy objectives, while final PPA is treated as a costly evaluation rather than an optimization signal. This proxy-driven paradigm makes it difficult to reliably translate additional PPA evaluations into better PPA outcomes. To bridge this gap, we present DOPP (D-Optimal PPA-driven partitioning selection), an approach that bridges the gap between proxies and true PPA metrics. Across eight 3D-IC designs, our framework improves PPA over Open3DBench (average relative improvements of 9.99% congestion, 7.87% routed wirelength, 7.75% WNS, 21.85% TNS, and 1.18% power). Compared with exhaustive evaluation over the full candidate set, DOPP achieves comparable best-found PPA while evaluating only a small fraction of candidates, substantially reducing evaluation cost. By parallelizing evaluations, our method delivers these gains while maintaining wall-clock runtime comparable to traditional baselines.

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Many CAD learning pipelines discretize Boundary Representations (B-Reps) into triangle meshes, discarding analytic surface structure and topological adjacency and thereby weakening consistent instance-level analysis. We present STEP-Parts, a deterministic CAD-to-supervision toolchain that extracts geometric instance partitions directly from raw STEP B-Reps and transfers them to tessellated carriers through retained source-face correspondence, yielding instance labels and metadata for downstream learning and evaluation. The construction merges adjacent B-Rep faces only when they share the same analytic primitive type and satisfy a near-tangent continuity criterion. On ABC, same-primitive dihedral angles are strongly bimodal, yielding a threshold-insensitive low-angle regime for part extraction. Because the partition is defined on intrinsic B-Rep topology rather than on a particular triangulation, the resulting boundaries remain stable under changes in tessellation. Applied to the DeepCAD subset of ABC, the pipeline processes approximately 180{,}000 models in under six hours on a consumer CPU. We release code and precomputed labels, and show that STEP-Parts serves both as a tessellation-robust geometric reference and as a useful supervision source in two downstream probes: an implicit reconstruction--segmentation network and a dataset-level point-based backbone.

Clustering is a central primitive in unsupervised learning, yet practice is dominated by heuristics whose outputs can be unstable and highly sensitive to representations, hyperparameters, and initialisation. Existing theoretical results are largely objective-specific and do not explain these behaviours at a unifying level. We formalise the common optimisation core underlying diverse clustering paradigms by defining the Universal Clustering Problem (UCP): the maximisation of a polynomial-time computable partition utility over a finite metric space. We prove the NP-hardness of UCP via two independent polynomial-time reductions from graph colouring and from exact cover by 3-sets (X3C). By mapping ten major paradigms -- including k-means, GMMs, DBSCAN, spectral clustering, and affinity propagation -- to the UCP framework, we demonstrate that each inherits this fundamental intractability. Our results provide a unified explanation for characteristic failure modes, such as local optima in alternating methods and greedy merge-order traps in hierarchical clustering. Finally, we show that clustering limitations reflect interacting computational and epistemic constraints, motivating a shift toward stability-aware objectives and interaction-driven formulations with explicit guarantees.

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations research. To overcome the challenges of continuous and high-dimensional domains, we introduce a model-based algorithm that adaptively partitions the joint state-action space. The algorithm maintains estimators of drift, volatility, and rewards within each partition, refining the discretization whenever estimation bias exceeds statistical confidence. This adaptive scheme balances exploration and approximation, enabling efficient learning in unbounded domains. Our analysis establishes regret bounds that depend on the problem horizon, state dimension, reward growth order, and a newly defined notion of zooming dimension tailored to unbounded diffusion processes. The bounds recover existing results for bounded settings as a special case, while extending theoretical guarantees to a broader class of diffusion-type problems. Finally, we validate the effectiveness of our approach through numerical experiments, including applications to high-dimensional problems such as multi-asset mean-variance portfolio selection.

Novel Markov Chain Monte Carlo (MCMC) methods have enabled the generation of large ensembles of redistricting plans modeled as a graph partitioning problem. However, existing algorithms such as Reversible Recombination (RevReCom) and Metropolized Forest Recombination (MFR) have strong preferences for distributions related to the spanning tree measure. In this paper we introduce the Marked Edge Walk (MEW), a novel Markov chain proposal for sampling from the space of graph partitions. The walk operates on the space of spanning trees with marked edges, allowing for calculable transition probabilities for use in the Metropolis-Hastings algorithm. Empirical results on real-world dual graphs show convergence under a broad class of target distributions less constrained by spanning tree counts, including policy-based distributions, such as competitiveness on New Hampshire that are independent of spanning trees, and compactness and partisan symmetry distributions on New Hampshire and Texas that, while related to spanning trees, can now be properly targeted with a smaller degree of spanning tree bias, which represents an advancement in flexible ensemble generation.

Pipeline parallelism is widely used to train large language models (LLMs). However, increasing heterogeneity in model architectures exacerbates pipeline bubbles, thereby reducing training efficiency. Prior approaches typically optimize a single phase of the pipeline schedule (i.e., partitioning, placement, or scheduling), leaving substantial pipeline bubbles. While promising, co-optimization poses three key challenges: (1) complex performance modeling, (2) a combinatorial search space, and (3) irregular execution orders. To address these challenges, we propose OctoPipe, a pipeline parallelism system to jointly optimize partitioning, placement, and scheduling. First, we build a graph-based pipeline simulator to model heterogeneous pipeline execution for co-optimization. Second, on top of the simulator, we develop an iterative bubble-aware tuner to efficiently explore the combinatorial search space. Third, we implement a unified pipeline executor that dynamically orchestrates computation and communication to support irregular execution orders without deadlocks while maximizing communication-computation overlap. Experiments show that OctoPipe achieves 1.09--1.49$\times$ throughput improvement over the state-of-the-art pipeline parallelism approaches across various heterogeneous model configurations and GPU cluster scales.

Reliable detection of bearing faults is essential for maintaining the safety and operational efficiency of rotating machinery. While recent advances in machine learning (ML), particularly deep learning, have shown strong performance in controlled settings, many studies fail to generalize to real-world applications due to methodological flaws, most notably data leakage. This paper investigates the issue of data leakage in vibration-based bearing fault diagnosis and its impact on model evaluation. We demonstrate that common dataset partitioning strategies, such as segment-wise and condition-wise splits, introduce spurious correlations that inflate performance metrics. To address this, we propose a rigorous, leakage-free evaluation methodology centered on bearing-wise data partitioning, ensuring no overlap between the physical components used for training and testing. Additionally, we reformulate the classification task as a multi-label problem, enabling the detection of co-occurring fault types and the use of prevalence-independent metrics based on the ROC curve. Beyond preventing leakage, we also examine the effect of dataset diversity on generalization, showing that the number of unique training bearings is a decisive factor for achieving robust performance. We evaluate our methodology on four widely adopted datasets: Case Western Reserve University (CWRU), Paderborn University (PU), University of Ottawa (UORED-VAFCLS) and Hanoi University of Science and Technology (HUST bearing). This study highlights the importance of leakage-aware evaluation protocols and provides practical guidelines for dataset partitioning, model selection, and validation, fostering the development of more trustworthy ML systems for industrial fault diagnosis applications.

The storage, management, and application of massive spatio-temporal data are widely used in practical scenarios, including public safety. However, due to the unique spatio-temporal distribution characteristics of real-world data, existing methods still face limitations in preserving spatio-temporal proximity and achieving load balancing in distributed storage. This paper proposes an efficient partitioning method for large-scale public safety spatio-temporal data based on information loss constraints, named IFL-LSTP. The model combines a spatio-temporal partitioning module (STPM) and a graph partitioning module (GPM). STPM reduces the scale of data under a predefined information-loss threshold, while GPM uses graph representation learning to obtain balanced graph partitions. Experiments on multiple real-world datasets show that IFL-LSTP can reduce data scale, shorten graph model training time, preserve spatio-temporal proximity, and improve load-balancing effectiveness.

Generative Flow Networks (GFlowNets) have shown promising potential to generate high-scoring candidates with probability proportional to their rewards. As existing GFlowNets freely explore in state space, they encounter significant convergence challenges when scaling to large state spaces. Addressing this issue, this paper proposes to restrict the exploration of actor. A planner is introduced to partition the entire state space into overlapping partial state spaces. Given their limited size, these partial state spaces allow the actor to efficiently identify subregions with higher rewards. A heuristic strategy is introduced to switch partial regions thus preventing the actor from wasting time exploring fully explored or low-reward partial regions. By iteratively exploring these partial state spaces, the actor learns to converge towards the high-reward subregions within the entire state space. Experiments on several widely used datasets demonstrate that \modelname converges faster than existing works on large state spaces. Furthermore, \modelname not only generates candidates with higher rewards but also significantly improves their diversity.