machine learning infrastructure engineers

Abstract: Low-precision GPU kernels are commonly tested against a reference using hand-picked absolute and relative tolerances. Legitimate numerical error varies with the input, format and precision plan, so a fixed tolerance trades false alarms for missed faults. We present numoracle, which derives per-element acceptance regions from precision-annotated reference programs. Its calculus tracks shared rounding errors, provenance-ordered products, block-scaled quantizers and calibrated math-library errors. A rounding-interval check detects faulty stores that symmetric bounds can admit. Soundness is conditional on explicit rounding, hardware, domain and implementation assumptions; a fixed-input mode removes the zero-mean rounding assumption. We evaluate 13 Triton operators from Liger-Kernel, Unsloth and vLLM on two GPU generations. The main campaigns produce no false alarm on 33,960 correct-kernel and behavior-preserving-variant runs per GPU. Under input shift, the GPU campaigns record no false alarm while tuned tolerances flag up to 30% of correct runs; final-version reference checks identify inputs without complete finite-range certificates. On the RTX PRO 6000, numoracle kills 116 of 124 effective mutants, versus 59-83 for four fixed baselines. Among 400 tuned tolerance configurations, requiring at most 1% false alarms in every evaluated Liger input group permits at most 31 of 53 main-mutant kills, versus numoracle's 50. Historical replays expose accuracy faults in eight change pairs without rejecting their matched corrected controls; a ninth change concerns rounding parity.

Abstract: Sparse attention reads only a small subset of the key-value cache, and how to treat the unread tail remains a key challenge. Discarding the tail biases the output, and sampling it as previous approaches do fails at reads of 5% and below, where the tail likely holds heavy hitters the selector missed. Our key observation is that the simplest possible proxy, one token that folds the entire tail into its count-aware mean, already yields lower output error than a sample at every read behind a practical selector. We further show in closed form that at low reads sampling nearly doubles the weight error of discarding while a single proxy stays below it. Building on these findings, we explore approximating the dense attention distribution with a few proxies that target the tail. We propose OpenAttention, a pipeline of clustering, ErrorGate and top-k selection followed by a count-aware mean proxy. To implement clustering and selection both efficiently and effectively, we design training-free Query-Geometry Clustering (QGC) and a Query-Geometry Selector (QGS), which compress the keys while respecting the query directions. Additionally, unlike prior methods that rank clusters by centroid alone, ErrorGate allocates the exact read by the estimated weight error of each cluster. On RULER-32K HARD with Llama-3.1-8B, OpenAttention retains 99% of dense accuracy at a 1% read. It also achieves state-of-the-art accuracy across models, context lengths and datasets. Our customized attention kernel, OpenAttention.flash, runs the decode attention stage 10$\times$ faster than dense attention at a 1% read.

Abstract: Vision-language models (VLMs) face a fixed-budget trade-off between processing more visual information for fine-grained perception and using a larger language backbone for complex reasoning. Existing studies do not tell us which combination of backbone size and input resolution to deploy, especially in high-resolution deployments. To address this gap, we propose the Separable Law that describes how VLM performance changes with language backbone size and visual token count. We fit the law to measurements from 26 InternVL and QwenVL models, with language backbone sizes from 1B to 72B, on four high-resolution benchmarks with image sizes from 224 pixels to 8K. We find that the questions responding to scaling can be predicted from the skill they require, while a substantial fraction never responds at all. We also find that the two model families gain similarly from a larger backbone, while their gains from more visual tokens differ sharply. Combined with a cost law, the Separable Law gives a closed-form rule for allocating compute between backbone size and visual tokens. When deployment is limited to available configurations, the law identifies model and image sizes that perform close to the best feasible choice under the same budget. We hope our work offers a principled way to decide how much a model should be allowed to see at high resolution, given what it must reason about.