arXiv subjects

Torsten Hoefler

Publications and source records attributed to Torsten Hoefler.

At least 37 records · Page 2Linked to original sources

arXiv2026

The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm

Quantizing the weights of large language models (LLMs) from 16-bit to lower bitwidth is the de facto approach to deploy massive transformers onto more affordable accelerators. While GPTQ emerged as one of the standard methods for one-shot post-training quantization at LLM scale, its inner workings are described as a sequence of algebraic updates that obscure geometric meaning or worst-case guarantees. In this work, we show that, when executed back-to-front (from the last to first dimension) for a linear layer, GPTQ is mathematically identical to Babai's nearest plane algorithm for the classical closest vector problem (CVP) on a lattice defined by the Hessian matrix of the layer's inputs. This equivalence is based on a sophisticated mathematical argument, and has two analytical consequences: first, the GPTQ error propagation step gains an intuitive geometric interpretation; second, GPTQ inherits the error upper bound of Babai's algorithm under the assumption that no weights are clipped. Leveraging this bound, we design post-training quantization methods that avoid clipping, and outperform the original GPTQ. In addition, we provide efficient GPU inference kernels for the resulting representation. Taken together, these results place GPTQ on a firm theoretical footing and open the door to importing decades of progress in lattice algorithms towards the design of future quantization algorithms for billion-parameter models. Source code is available at https://github.com/IST-DASLab/GPTQ-Babai.

cs.LG↗

arXiv2026

Grid Games: The Power of Multiple Grids for Quantizing Large Language Models

A major recent advance in quantization is given by microscaled 4-bit formats such as NVFP4 and MXFP4, quantizing values into small groups sharing a scale, assuming a fixed floating-point grid. In this paper, we study the following natural extension: assume that, for each group of values, we are free to select the "better" among two or more 4-bit grids marked by one or more bits in the scale value. We formalize the power-of-two-grids (PO2) problem, and provide theoretical results showing that practical small-group formats such as MXFP or NVFP can benefit significantly from PO2 grids, while the advantage vanishes for very large groups. On the practical side, we instantiate several grid families, including 1) PO2(NF4), which pairs the standard NF4 normal grid with a learned grid, 2) MPO2, a grid pair that is fully learned over real weights and activations, 3) PO2(Split87), an explicit-zero asymmetric grid and 4) SFP4, a TensorCore-implementable triple which pairs NVFP4 with two shifted variants. Results for post-training quantization of standard open models and pre-training of Llama-like models show that adaptive grids consistently improve accuracy vs single-grid FP4 under both weight-only and weight+activation. Source code is available at https://github.com/IST-DASLab/GridGames.

cs.LG↗

arXiv2026

ADELIA: Automatic Differentiation for Efficient Laplace Inference Approximations

Spatio-temporal Bayesian inference drives environmental and health sciences using latent Gaussian models. Integrated Nested Laplace Approximations (INLA) enable inference for these models at HPC scale but rely on derivative-based optimization over $d$ hyperparameters. State-of-the-art INLA implementations approximate derivatives via central finite differences (FD), requiring $2d{+}1$ evaluations. These evaluations are embarrassingly parallel, but total work and energy grow with $d$, limiting time-to-solution under fixed budgets. Reverse-mode automatic differentiation (AD) computes exact gradients independently of $d$, but its efficient application to INLA's structured-sparse kernels is an open challenge. We present ADELIA, the first AD-enabled INLA implementation with a structure-exploiting multi-GPU backward pass leveraging model sparsity. We evaluate ADELIA on ten benchmark models, including real-world air-pollution monitoring. We achieve $4.2$--$7.9\times$ per-gradient speedups and reliable convergence on production-scale models with up to 1.9M latent variables, where FD struggles. Even when scaled to 16--32 GPUs to match ADELIA's wall-clock time, FD consumes $5$--$8\times$ more energy.

cs.DC↗

arXiv2026

Resilient AI Supercomputer Networking using MRC and SRv6

Tail latency dominates the performance of synchronous pretraining jobs when running at very large scales. We describe a three-pronged approach: (1) a new RDMA-based transport protocol, MRC, sprays across many paths and actively load-balances between them, eliminating the issue of flow collisions (2) the use of multi-plane Clos topologies to get the benefits of high switch radix and redundancy, allowing training clusters well over 100K GPUs to be built as two-tier topologies while increasing physical redundancy, and (3) the use of static source-routing using SRv6 to allow MRC the freedom to bypass failures by itself. We describe our experiences running MRC and static SRv6 routing in production in OpenAI and Microsoft's largest training clusters, where it has been used to train the latest frontier models. We demonstrate how MRC allows AI training jobs to ride out many network failures that previously would have interrupted training.

cs.NI↗

arXiv2026

SpaDA: A Spatial Dataflow Architecture Programming Language

Spatial dataflow architectures like the Cerebras Wafer-Scale Engine deliver exceptional performance in AI and scientific computing by distributing scratchpad memory across hundreds of thousands of processing elements (PEs). Yet programming these architectures remains difficult: with no shared memory, data movement requires explicit configuration, and asynchronous task management introduces substantial complexity. We present SpaDA, a programming language that offers precise control over data placement, dataflow patterns, and asynchronous operations while abstracting low-level architectural details. We design and implement a compiler targeting Cerebras CSL through multi-level lowering and unique optimization passes. SpaDA functions as a high-level programming interface and an intermediate representation for domain-specific languages (DSLs), demonstrated here with the GT4Py stencil DSL. SpaDA enables concise expression of operations with complex parallel patterns -- including pipelined collective operations, multi-dimensional stencils, and dense linear algebra -- in 14.09x fewer lines than CSL, achieving over 260 TFlop/s across 730,000 PEs on a single device.

cs.DC↗

arXiv2026

SFT-then-RL Outperforms Mixed-Policy Methods for LLM Reasoning

Recent mixed-policy optimization methods for LLM reasoning that interleave or blend supervised and reinforcement learning signals report improvements over the standard SFT-then-RL pipeline. We show that numerous recently published research papers rely on a faulty baseline caused by two distinct bugs: a CPU-offloaded optimizer bug in DeepSpeed that silently drops intermediate micro-batches during gradient accumulation (affecting multiple downstream frameworks including TRL, OpenRLHF and Llama-Factory), and a loss aggregation bug in OpenRLHF that incorrectly weights per-mini-batch losses. Together they suppress SFT performance, with the optimizer bug accounting for most of the gap and the loss aggregation bug contributing a smaller additional effect. Once corrected, the standard SFT-then-RL pipeline surpasses every published mixed-policy method we evaluate by +3.8 points on math benchmarks with Qwen2.5-Math-7B and by +22.2 points with Llama-3.1-8B. Even a truncated variant with just 50 RL steps outperforms mixed-policy methods on math benchmarks while using fewer FLOPs.

cs.LG↗

arXiv2026

Earth System Foundation Model (ESFM): A unified framework for heterogeneous data integration and forecasting

Foundation models (FMs) for the Earth system learn statistical relationships between physical variables across massive datasets to enable versatile downstream applications through finetuning, separating them from task-specific weather models. Here, we introduce Earth System Foundation Model (ESFM), a fully open model building on the 3D Swin UNet backbone of the pioneering Aurora model. ESFM introduces extensions that increase functionality and foster adoption in climate sciences. First, the encoding scheme and training protocols have been extended to handle diverse datasets, including those containing missing values across all spatio-temporal dimensions such as satellite data, as well as station data, all under one backbone. Axial attention is introduced to capture inter-variable dependencies. As a result ESFM skillfully predicts variables in regions or on pressure levels where no data is present at the initial time, while preserving inter-variable relationships, for example between temperature, pressure, and humidity. Individual variable tokenization enables different sets of variables to be shuffled during training and simplifies the process of building extensions for new downstream tasks. Adaptive layer norm-based ensembles allow for a simple yet effective way to transform deterministic ESFM to a probabilistic FM. We present findings using dense gridded data (ERA5, CMIP6), regionally masked dense data, sparse gridded MODIS satellite data, and station data. Results demonstrate competitive or superior performance relative to state-of-the-art benchmarks. Case studies of Super Typhoon Doksuri (2023) and 2024 sudden stratospheric warming events show accurate positional and magnitude estimations of extreme weather. ESFM retains the strengths of previous foundation models, such as long-term stability, but facilitates application to a variety of downstream tasks.

physics.ao-ph↗

arXiv2026

An Engineering Journey Training Large Language Models at Scale on Alps: The Apertus Experience

Large Language Models (LLMs) have surged as a transformative technology for science and society, prompting governments worldwide to pursue sovereign AI capabilities that ensure data compliance and cultural representation. However, the associated capital costs and engineering complexity required to train these models have largely restricted such capabilities to the private sector, leaving a significant gap for public institutions. This paper details the engineering journey behind training Apertus, a fully open multilingual foundation model, on the Alps supercomputer. Representing a first-of-its-kind achievement for academia at the 70B parameter scale, we successfully deployed a massive pre-training campaign on one of Europe's largest systems for open science, powered by NVIDIA GH200 Grace Hopper Superchips. We detail the challenges encountered in readying HPC infrastructure for training AI models, from overcoming storage bottlenecks to stabilizing large-scale interconnects, and the lessons learned in transforming a supercomputer into a resilient software-defined Machine Learning Platform. Finally, we discuss the post-training requirements and evolution of our Machine Learning platform, outlining how this initial release lays the groundwork for a sustained, iterative operational capability, in particular for fine tuning foundation models, that extends well beyond a single model training run.

cs.DC↗

arXiv2026

PICO: Performance Insights for Collective Operations

Collective operations are cornerstones of both HPC applications and large-scale AI training and inference, yet benchmarking them in a systematic and reproducible way remains difficult on modern systems due to the complexity of their hardware and software stacks. Existing suites primarily report end-to-end timings and offer limited support for controlled algorithm and configuration selection, fine-grained profiling, and capturing the runtime environment. We present PICO (Performance Insights for Collective Operations), an open-source framework that decouples portable experiment setup from platform execution, provides a backend-adaptive parameter selection interface across MPI and NCCL, supplies plain-MPI reference collective implementations, optionally instrumentable, and records the system configuration for reproducible comparisons. Evaluated on three major supercomputers, PICO shows that default collective algorithms and transport settings can be up to $5\times$ slower than the best available choice. It provides diagnostic evidence by isolating topology sensitive algorithmic choices and, through instrumentation, reveals detailed algorithmic breakdowns. To assess end-to-end effects of benchmark-informed tuning and evaluate application-level impacts, we replay open-source LLM training traces in ATLAHS simulator with optimized collective profiles identified by PICO, achieving reductions in training times of up to $44\%$.

cs.DC↗

arXiv2026

Benchmarking Filtered Approximate Nearest Neighbor Search Algorithms on Transformer-based Embedding Vectors

Advances in embedding models for text, image, audio, and video drive progress across multiple domains, including retrieval-augmented generation, recommendation systems, and others. Many of these applications require an efficient method to retrieve items that are close to a given query in the embedding space while satisfying a filter condition based on the item's attributes, a problem known as filtered approximate nearest neighbor search (FANNS). By performing an in-depth literature analysis on FANNS, we identify a key gap in the research landscape: publicly available datasets with embedding vectors from state-of-the-art transformer-based text embedding models that contain abundant real-world attributes covering a broad spectrum of attribute types and value distributions. To fill this gap, we introduce the arxiv-for-fanns dataset of transformer-based embedding vectors for the abstracts of over 2.7 million arXiv papers, enriched with 11 real-world attributes such as authors and categories. We benchmark eleven different FANNS methods on our new dataset to evaluate their performance across different filter types, numbers of retrieved neighbors, dataset scales, and query selectivities. We distill our findings into eight key observations that guide users in selecting the most suitable FANNS method for their specific use cases.

cs.DB↗

arXiv2026

Demystifying Chains, Trees, and Graphs of Thoughts

The field of natural language processing (NLP) has witnessed significant progress in recent years, with a notable focus on improving large language models' (LLM) performance through innovative prompting techniques. Among these, prompt engineering coupled with structures has emerged as a promising paradigm, with designs such as Chain-of-Thought, Tree of Thoughts, or Graph of Thoughts, in which the overall LLM reasoning is guided by a structure such as a graph. As illustrated with numerous examples, this paradigm significantly enhances the LLM's capability to solve numerous tasks, ranging from logical or mathematical reasoning to planning or creative writing. To facilitate the understanding of this growing field and pave the way for future developments, we devise a general blueprint for effective and efficient LLM reasoning schemes. For this, we conduct an in-depth analysis of the prompt execution pipeline, clarifying and clearly defining different concepts. We then build the first taxonomy of structure-enhanced LLM reasoning schemes. We focus on identifying fundamental classes of harnessed structures, and we analyze the representations of these structures, algorithms executed with these structures, and many others. We refer to these structures as reasoning topologies, because their representation becomes to a degree spatial, as they are contained within the LLM context. Our study compares existing prompting schemes using the proposed taxonomy, discussing how certain design choices lead to different patterns in performance and cost. We also outline theoretical underpinnings, relationships between prompting and other parts of the LLM ecosystem such as knowledge bases, and the associated research challenges. Our work will help to advance future prompt engineering techniques.

cs.CL↗

arXiv2026

Network Design for Wafer-Scale Systems with Wafer-on-Wafer Hybrid Bonding

Transformer-based large language models are increasingly constrained by data movement as communication bandwidth drops sharply beyond the chip boundary. Wafer-scale integration using wafer-on-wafer hybrid bonding alleviates this limitation by providing ultra-high bandwidth between reticles on bonded wafers. In this paper, we investigate how the physical placement of reticles on wafers influences the achievable network topology and the resulting communication performance. Starting from a 2D mesh-like baseline, we propose four reticle placements (Aligned, Interleaved, Rotated, and Contoured) that improve throughput by up to 250%, reduce latency by up to 36%, and decrease energy per transmitted byte by up to 38%.

cs.AR↗

arXiv2026

GraphSeek: Next-Generation Graph Analytics with LLMs

Graphs are foundational across domains but remain hard to use without deep expertise. LLMs promise accessible natural language (NL) graph analytics, yet they fail to process industry-scale property graphs effectively and efficiently: such datasets are large, highly heterogeneous, structurally complex, and evolve dynamically. To address this, we devise a novel abstraction for complex multi-query analytics over such graphs. Its key idea is to replace brittle generation of graph queries directly from NL with planning over a Semantic Catalog that describes both the graph schema and the graph operations. Concretely, this induces a clean separation between a Semantic Plane for LLM planning and broader reasoning, and an Execution Plane for deterministic, database-grade query execution over the full dataset and tool implementations. This design yields substantial gains in both token efficiency and task effectiveness even with small-context LLMs. We use this abstraction as the basis of the first LLM-enhanced graph analytics framework called GraphSeek. GraphSeek achieves substantially higher success rates (e.g., 86% over enhanced LangChain) and points toward the next generation of affordable and accessible graph analytics that unify LLM reasoning with database-grade execution over large and complex property graphs.

cs.DB↗

arXiv2026

Bridging the Gap Between Promise and Performance for Microscaling FP4 Quantization

The recent hardware-accelerated microscaling 4-bit floating-point formats such as MXFP4 and NVFP4, supported on NVIDIA and AMD GPUs, promise to revolutionize large language model (LLM) inference. Yet, their practical benefits remain unproven. We present the first comprehensive study of MXFP4 and NVFP4 for post-training quantization, revealing gaps between their promise and real-world performance. Our analysis shows that state-of-the-art methods struggle with FP4, due to two key issues: (1) NVFP4's small group size provably neutralizes traditional outlier mitigation techniques; (2) MXFP4's power-of-two scale quantization severely degrades accuracy due to high induced error. To bridge this gap, we introduce Micro-Rotated-GPTQ (MR-GPTQ), a variant of the classic GPTQ quantization algorithm that tailors the quantization process to FP4's unique properties, by using block-wise Hadamard transforms and format-specific optimizations. We support our proposal with a set of high-performance GPU kernels that enable the MR-GPTQ format with negligible overhead, by rotation fusion into the weights, and fast online computation of the activations. This leads to speedups vs. FP16 of up to 3.6x layer-wise, and 2.2x end-to-end on NVIDIA B200, and of 6x layer-wise and 4x end-to-end on RTX5090. Our extensive empirical evaluation demonstrates that MR-GPTQ matches or outperforms state-of-the-art accuracy, significantly boosting MXFP4, to the point where it can near the accuracy that of NVFP4. We conclude that, while FP4 is not an automatic upgrade over INT4, format-specialized methods like MR-GPTQ can unlock a new frontier of accuracy-performance trade-offs.

cs.LG↗

arXiv2026

Demystifying NCCL: An In-depth Analysis of GPU Communication Protocols and Algorithms

The NVIDIA Collective Communication Library (NCCL) is a critical software layer enabling high-performance collectives on large-scale GPU clusters. Despite being open source with a documented API, its internal design remains largely opaque. The orchestration of communication channels, selection of protocols, and handling of memory movement across devices and nodes are not well understood, making it difficult to analyze performance or identify bottlenecks. This paper presents a comprehensive analysis of NCCL, focusing on its communication protocol variants (Simple, LL, and LL128), mechanisms governing intra-node and inter-node data movement, and ring- and tree-based collective communication algorithms. The insights obtained from this study serve as the foundation for ATLAHS, an application-trace-driven network simulation toolchain capable of accurately reproducing NCCL communication patterns in large-scale AI training workloads. By demystifying NCCL's internal architecture, this work provides guidance for system researchers and performance engineers working to optimize or simulate collective communication at scale.

cs.DC↗

arXiv2026

Multi-Head RAG: Solving Multi-Aspect Problems with LLMs

Retrieval-Augmented Generation (RAG) improves Large Language Models (LLMs) by retrieving supporting documents into the prompt, but existing methods do not explicitly target queries that require fetching multiple documents with substantially different content. Such multi-aspect queries are challenging because relevant documents can be far apart in embedding space, making joint retrieval difficult. We introduce Multi-Head RAG (MRAG), which addresses this gap with a simple yet powerful idea: using Transformer multi-head attention activations rather than the standard decoder-layer embedding, as retrieval keys. It leverages the observation that different heads capture different semantic aspects. This yields multi-aspect embeddings for both documents and queries, improving retrieval accuracy on complex queries. We show MRAG's design advantages over 18 RAG baselines, up to 20% higher retrieval success ratios for real-world use cases, and improved downstream LLM generation. MRAG integrates seamlessly with existing RAG frameworks and benchmarks.

cs.CL↗

arXiv2026

Error bounded compression for weather and climate applications

As the resolution of weather and climate simulations increases, the amount of data produced is growing rapidly from hundreds of terabytes to tens of petabytes. The huge size becomes a limiting factor for broader adoption, and its fast growth rate will soon exhaust all the available storage devices. To address these issues, we present EBCC (Error Bounded Climate-data Compressor). It follows a two-layer approach: a base compression layer using JPEG2000 to capture the bulk of the data with a high compression ratio, and a residual compression layer using wavelet transform and SPIHT encoding to efficiently eliminate long-tail extreme errors introduced by the base compression layer. It incorporates a feedback rate-control mechanism for both layers that adjusts compression ratios to achieve the specified maximum error target. We evaluate EBCC alongside other established compression methods on benchmarks related to weather and climate science including error statistics, a case study on primitive and derived variables near a hurricane, evaluation of the closure of the global energy budget, and a Lagrangian air parcel trajectory simulation. This is the first time that trajectory simulation is used to benchmark compression methods. Our method concentrates most errors near zero, while others tend to distribute errors uniformly within the error bound. EBCC outperforms other methods in the benchmarks at relative error targets ranging from 0.1% to 10% and achieves compression ratios from 15x to more than 300x. In the energy budget closure and Lagrangian trajectory benchmarks, it can achieve more than 100x compression while keeping errors within natural variability derived from ERA5 uncertainty members. This verifies the effectiveness of EBCC in creating heavily compressed weather and climate datasets suitable for downstream applications. The source code of EBCC is available in github.com/spcl/EBCC.

cs.CE↗

arXiv2026

Spritz: Path-Aware Load Balancing in Low-Diameter Networks

Low-diameter topologies such as Dragonfly and Slim Fly are increasingly adopted in HPC and datacenter networks, yet existing load balancing techniques either rely on proprietary in-network mechanisms or fail to utilize the full path diversity of these topologies. We introduce Spritz, a flexible sender-based load balancing framework that shifts adaptive topology-aware routing to the endpoints using only standard Ethernet features. We propose two algorithms, Spritz-Scout and Spritz-Spray that, respectively, explore and adaptively cache efficient paths using ECN, packet trimming, and timeout feedback. Through simulation on Dragonfly and Slim Fly topologies with over 1000 endpoints, Spritz outperforms ECMP, UGAL-L, and prior sender-based approaches by up to 1.8x in flow completion time under AI training and datacenter workloads, while offering robust failover with performance improvements of up to 25.4x under link failures, all without additional hardware support. Spritz enables datacenter-scale, commodity Ethernet networks to efficiently leverage low-diameter topologies, offering unified routing and load balancing for the Ultra Ethernet era.

cs.NI↗