The quadratic complexity of softmax attention remains a central bottleneck in scaling large language models (LLMs). [Alman and Song, NeurIPS 2023] proposed a sub-quadratic attention approximation algorithm, but it works only under the restrictive bounded-entry assumption. Since this assumption rarely holds in practice, its applicability to modern LLMs is limited. In this paper, we introduce support-basis decomposition, a new framework for efficient attention approximation beyond bounded entries. We empirically demonstrate that the entries of the query and key matrices exhibit sub-Gaussian behavior. Our approach uses this property to split large and small entries, enabling exact computation on sparse components and polynomial approximation on dense components. We establish rigorous theoretical guarantees, proving a sub-quadratic runtime, and extend the method to a multi-threshold setting that eliminates all distributional assumptions. Furthermore, we provide the first theoretical justification for the empirical success of polynomial attention [Kacham, Mirrokni, and Zhong, ICML 2024], showing that softmax attention can be closely approximated by a combination of multiple polynomial attentions with sketching.

We introduce Small PDE U-Net Solver (SPUS), a compact and efficient foundation model (FM) designed as a unified neural operator for solving a wide range of partial differential equations (PDEs). Unlike existing state-of-the-art PDE FMs-primarily based on large complex transformer architectures with high computational and parameter overhead-SPUS leverages a lightweight residual U-Net-based architecture that has been largely underexplored as a foundation model architecture in this domain. To enable effective learning in this minimalist framework, we utilize a simple yet powerful auto-regressive pretraining strategy which closely replicates the behavior of numerical solvers to learn the underlying physics. SPUS is pretrained on a diverse set of fluid dynamics PDEs and evaluated across 6 challenging unseen downstream PDEs spanning various physical systems. Experimental results demonstrate that SPUS using residual U-Net based architecture achieves state-of-the-art generalization on these downstream tasks while requiring significantly fewer parameters and minimal fine-tuning data, highlighting its potential as a highly parameter-efficient FM for solving diverse PDE systems.

Large scale pretrained models have revolutionized Natural Language Processing (NLP) and Computer Vision (CV), showcasing remarkable cross domain generalization abilities. However, in graph learning, models are typically trained on individual graph datasets, limiting their capacity to transfer knowledge across different graphs and tasks. This approach also heavily relies on large volumes of annotated data, which presents a significant challenge in resource-constrained settings. Unlike NLP and CV, graph structured data presents unique challenges due to its inherent heterogeneity, including domain specific feature spaces and structural diversity across various applications. To address these challenges, we propose a novel structure aware self supervised learning method for Text Attributed Graphs (SSTAG). By leveraging text as a unified representation medium for graph learning, SSTAG bridges the gap between the semantic reasoning of Large Language Models (LLMs) and the structural modeling capabilities of Graph Neural Networks (GNNs). Our approach introduces a dual knowledge distillation framework that co-distills both LLMs and GNNs into structure-aware multilayer perceptrons (MLPs), enhancing the scalability of large-scale TAGs. Additionally, we introduce an in-memory mechanism that stores typical graph representations, aligning them with memory anchors in an in-memory repository to integrate invariant knowledge, thereby improving the model's generalization ability. Extensive experiments demonstrate that SSTAG outperforms state-of-the-art models on cross-domain transfer learning tasks, achieves exceptional scalability, and reduces inference costs while maintaining competitive performance.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of natural language processing tasks. However, their exponentially increasing parameters pose significant challenges for deployment on resource-constrained devices. Vector Quantization (VQ) shows great promise for low-bit quantization (e.g., 2 to 4 bits), but existing work faces two key challenges: unconstrained direction error and suboptimal bit allocation. In this paper, we propose RSAVQ, a novel VQ framework to enhance extremely low-bit quantization for LLMs. RSAVQ introduces two geometry-driven innovations that effectively mitigate above limitations: (1) Error Direction Sensitivity Guidance (EDSG), which leverages the Fisher Information Matrix (FIM)-induced Riemannian metric to project quantization errors onto low-sensitivity directions in the parameter space. Specifically, this projection is performed along the negative natural gradient direction, which effectively suppresses error expansion. (2) Weight Channel Sensitivity Guidance (WCSG) , which constructs a channel-wise sensitivity metric via FIM curvature analysis to dynamically guide bit resource allocation. The approach facilitates a globally optimal quantization solution within prescribed bit constraints. Experiments demonstrate that RSAVQ outperforms existing methods for LLMs. For example, in 2-bit quantization of LLaMA-3 8B, RSAVQ leads baselines like VPTQ and QuIP# by 0.4 in perplexity (PPL) and 1.5 in zero-shot accuracy. This work offers a practical solution for constrained environments and a theoretical bridge between information geometry and the quantization of neural networks, advancing efficient deep learning.

Multivariate time series forecasting (MTSF) plays a vital role in a wide range of real-world applications, such as weather prediction and traffic flow forecasting. Although recent advances have significantly improved the modeling of temporal dynamics and inter-variable dependencies, most existing methods overlook index-related descriptive information, such as timestamps and variable indices, which carry rich contextual semantics. To unlock the potential of such information and take advantage of the lightweight and powerful periodic capture ability of MLP-based architectures, we propose IndexNet, an MLP-based framework augmented with an Index Embedding (IE) module. The IE module consists of two key components: Timestamp Embedding (TE) and Channel Embedding (CE). Specifically, TE transforms timestamps into embedding vectors and injects them into the input sequence, thereby improving the model's ability to capture long-term complex periodic patterns. In parallel, CE assigns each variable a unique and trainable identity embedding based on its index, allowing the model to explicitly distinguish between heterogeneous variables and avoid homogenized predictions when input sequences seem close. Extensive experiments on 12 diverse real-world datasets demonstrate that IndexNet achieves comparable performance across mainstream baselines, validating the effectiveness of our temporally and variably aware design. Moreover, plug-and-play experiments and visualization analyses further reveal that IndexNet exhibits strong generality and interpretability, two aspects that remain underexplored in current MTSF research.

As a developing country, Fiji is facing rapid urbanisation, which is visible in the massive development projects that include housing, roads, and civil works. In this study, we present machine learning and remote sensing frameworks to compare land use and land cover change from 2013 to 2024 in Nadi, Fiji. The ultimate goal of this study is to provide technical support in land cover/land use modelling and change detection. We used Landsat-8 satellite image for the study region and created our training dataset with labels for supervised machine learning. We used Google Earth Engine and unsupervised machine learning via k-means clustering to generate the land cover map. We used convolutional neural networks to classify the selected regions' land cover types. We present a visualisation of change detection, highlighting urban area changes over time to monitor changes in the map.

Schedulers are critical for optimal resource utilization in high-performance computing. Traditional methods to evaluate schedulers are limited to post-deployment analysis, or simulators, which do not model associated infrastructure. In this work, we present the first-of-its-kind integration of scheduling and digital twins in HPC. This enables what-if studies to understand the impact of parameter configurations and scheduling decisions on the physical assets, even before deployment, or regarching changes not easily realizable in production. We (1) provide the first digital twin framework extended with scheduling capabilities, (2) integrate various top-tier HPC systems given their publicly available datasets, (3) implement extensions to integrate external scheduling simulators. Finally, we show how to (4) implement and evaluate incentive structures, as-well-as (5) evaluate machine learning based scheduling, in such novel digital-twin based meta-framework to prototype scheduling. Our work enables what-if scenarios of HPC systems to evaluate sustainability, and the impact on the simulated system.

Intuitively, given a behavior generated under one task, Generalized Hindsight returns a different task that the behavior is better suited for. Then, the behavior is relabeled with this new task before being used by an off-policy RL optimizer.

There are two broad strategies for this type of likelihood-free inference problem.

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