arXiv subjects

Michael W. Mahoney

Publications and source records attributed to Michael W. Mahoney.

At least 73 records · Page 4Linked to original sources

arXiv2025

SciML Agents: Write the Solver, Not the Solution

Recent work in scientific machine learning aims to tackle scientific tasks directly by predicting target values with neural networks (e.g., physics-informed neural networks, neural ODEs, neural operators, etc.), but attaining high accuracy and robustness has been challenging. We explore an alternative view: use LLMs to write code that leverages decades of numerical algorithms. This shifts the burden from learning a solution function to making domain-aware numerical choices. We ask whether LLMs can act as SciML agents that, given a natural-language ODE description, generate runnable code that is scientifically appropriate, selecting suitable solvers (stiff vs. non-stiff), and enforcing stability checks. There is currently no benchmark to measure this kind of capability for scientific computing tasks. As such, we first introduce two new datasets: a diagnostic dataset of adversarial "misleading" problems; and a large-scale benchmark of 1,000 diverse ODE tasks. The diagnostic set contains problems whose superficial appearance suggests stiffness, and that require algebraic simplification to demonstrate non-stiffness; and the large-scale benchmark spans stiff and non-stiff ODE regimes. We evaluate open- and closed-source LLM models along two axes: (i) unguided versus guided prompting with domain-specific knowledge; and (ii) off-the-shelf versus fine-tuned variants. Our evaluation measures both executability and numerical validity against reference solutions. We find that with sufficient context and guided prompts, newer instruction-following models achieve high accuracy on both criteria. In many cases, recent open-source systems perform strongly without fine-tuning, while older or smaller models still benefit from fine-tuning. Overall, our preliminary results indicate that careful prompting and fine-tuning can yield a specialized LLM agent capable of reliably solving simple ODE problems.

cs.LG↗

arXiv2025

XQuant: Breaking the Memory Wall for LLM Inference with KV Cache Rematerialization

Although LLM inference has emerged as a critical workload for many downstream applications, efficiently inferring LLMs is challenging due to the substantial memory footprint and bandwidth requirements. In parallel, compute capabilities have steadily outpaced both memory capacity and bandwidth over the last few decades, a trend that remains evident in modern GPU hardware and exacerbates the challenge of LLM inference. As such, new algorithms are emerging that trade increased computation for reduced memory operations. To that end, we present XQuant, which takes advantage of this trend, enabling an order-of-magnitude reduction in memory consumption through low-bit quantization with substantial accuracy benefits relative to state-of-the-art KV cache quantization methods. We accomplish this by quantizing and caching the layer input activations X, instead of using standard KV caching, and then rematerializing the Keys and Values on-the-fly during inference. This results in an immediate 2$\times$ memory savings compared to KV caching. By applying XQuant, we achieve up to $\sim 7.7\times$ memory savings with $<0.1$ perplexity degradation compared to the FP16 baseline. Furthermore, our approach leverages the fact that X values are similar across layers. Building on this observation, we introduce XQuant-CL, which exploits the cross-layer similarity in the X embeddings for extreme compression. Across different models, XQuant-CL attains up to 10$\times$ memory savings relative to the FP16 baseline with only 0.01 perplexity degradation, and 12.5$\times$ memory savings with only $0.1$ perplexity degradation. XQuant exploits the rapidly increasing compute capabilities of hardware platforms to eliminate the memory bottleneck, while surpassing state-of-the-art KV cache quantization methods and achieving near-FP16 accuracy across a wide range of models.

cs.LG↗

arXiv2025

SPADE-S: A Sparsity-Robust Foundational Forecaster

Despite significant advancements in time series forecasting, accurate modeling of time series with strong heterogeneity in magnitude and/or sparsity patterns remains challenging for state-of-the-art deep learning architectures. We identify several factors that lead existing models to systematically underperform on low-magnitude and sparse time series, including loss functions with implicit biases toward high-magnitude series, training-time sampling methods, and limitations of time series encoding methods. SPADE-S is a robust forecasting architecture that significantly reduces magnitude- and sparsity-based systematic biases and improves overall prediction accuracy. Empirical results demonstrate that SPADE-S outperforms existing state-of-the-art approaches across a diverse set of use cases in demand forecasting. In particular, we show that, depending on the quantile forecast and magnitude of the series, SPADE-S can improve forecast accuracy by up to 15%. This results in P90 overall forecast accuracy gains of 2.21%, 6.58%, and 4.28%, and P50 forecast accuracy gains of 0.92%, 0.77%, and 1.95%, respectively, for each of three distinct datasets, ranging from 3 million to 700 million series, from a large online retailer.

cs.LG↗

arXiv2025

Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting

Flow matching has recently emerged as a powerful paradigm for generative modeling and has been extended to probabilistic time series forecasting in latent spaces. However, the impact of the specific choice of probability path model on forecasting performance remains under-explored. In this work, we demonstrate that forecasting spatio-temporal data with flow matching is highly sensitive to the selection of the probability path model. Motivated by this insight, we propose a novel probability path model designed to improve forecasting performance. Our empirical results across various dynamical system benchmarks show that our model achieves faster convergence during training and improved predictive performance compared to existing probability path models. Importantly, our approach is efficient during inference, requiring only a few sampling steps. This makes our proposed model practical for real-world applications and opens new avenues for probabilistic forecasting.

stat.ML↗

arXiv2025

TAT: Temporal-Aligned Transformer for Multi-Horizon Peak Demand Forecasting

Multi-horizon time series forecasting has many practical applications such as demand forecasting. Accurate demand prediction is critical to help make buying and inventory decisions for supply chain management of e-commerce and physical retailers, and such predictions are typically required for future horizons extending tens of weeks. This is especially challenging during high-stake sales events when demand peaks are particularly difficult to predict accurately. However, these events are important not only for managing supply chain operations but also for ensuring a seamless shopping experience for customers. To address this challenge, we propose Temporal-Aligned Transformer (TAT), a multi-horizon forecaster leveraging apriori-known context variables such as holiday and promotion events information for improving predictive performance. Our model consists of an encoder and decoder, both embedded with a novel Temporal Alignment Attention (TAA), designed to learn context-dependent alignment for peak demand forecasting. We conduct extensive empirical analysis on two large-scale proprietary datasets from a large e-commerce retailer. We demonstrate that TAT brings up to 30% accuracy improvement on peak demand forecasting while maintaining competitive overall performance compared to other state-of-the-art methods.

cs.LG↗

arXiv2025

Determinant Estimation under Memory Constraints and Neural Scaling Laws

Calculating or accurately estimating log-determinants of large positive definite matrices is of fundamental importance in many machine learning tasks. While its cubic computational complexity can already be prohibitive, in modern applications, even storing the matrices themselves can pose a memory bottleneck. To address this, we derive a novel hierarchical algorithm based on block-wise computation of the LDL decomposition for large-scale log-determinant calculation in memory-constrained settings. In extreme cases where matrices are highly ill-conditioned, accurately computing the full matrix itself may be infeasible. This is particularly relevant when considering kernel matrices at scale, including the empirical Neural Tangent Kernel (NTK) of neural networks trained on large datasets. Under the assumption of neural scaling laws in the test error, we show that the ratio of pseudo-determinants satisfies a power-law relationship, allowing us to derive corresponding scaling laws. This enables accurate estimation of NTK log-determinants from a tiny fraction of the full dataset; in our experiments, this results in a $\sim$100,000$\times$ speedup with improved accuracy over competing approximations. Using these techniques, we successfully estimate log-determinants for dense matrices of extreme sizes, which were previously deemed intractable and inaccessible due to their enormous scale and computational demands.

stat.ML↗

arXiv2025

Anatomy of High-Performance Column-Pivoted QR Decomposition

We introduce an algorithmic framework for performing QR factorization with column pivoting (QRCP) on general matrices. The framework enables the design of practical QRCP algorithms through user-controlled choices for the core subroutines. We provide a comprehensive overview of how to navigate these choices on modern hardware platforms, offering detailed descriptions of alternative methods for both CPUs and GPUs. The practical QRCP algorithms developed within this framework are implemented as part of the open-source RandLAPACK library. Our empirical evaluation demonstrates that, on a dual AMD EPYC 9734 system, the proposed method achieves performance improvements of up to two orders of magnitude over LAPACK's standard QRCP routine and greatly surpasses the performance of the current state-of-the-art randomized QRCP algorithm. Additionally, on an NVIDIA H100 GPU, our method attains approximately 65 percent of the performance of cuSOLVER's unpivoted QR factorization.

cs.MS↗

arXiv2025

Spectral Estimation with Free Decompression

Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in scale, the corresponding covariance and kernel matrices become increasingly large, often reaching magnitudes that make their direct formation impractical or impossible. Existing techniques typically rely on matrix-vector products, which can provide efficient approximations, if the matrix spectrum behaves well. However, in settings like distributed learning, or when the matrix is defined only indirectly, access to the full data set can be restricted to only very small sub-matrices of the original matrix. In these cases, the matrix of nominal interest is not even available as an implicit operator, meaning that even matrix-vector products may not be available. In such settings, the matrix is "impalpable," in the sense that we have access to only masked snapshots of it. We draw on principles from free probability theory to introduce a novel method of "free decompression" to estimate the spectrum of such matrices. Our method can be used to extrapolate from the empirical spectral densities of small submatrices to infer the eigenspectrum of extremely large (impalpable) matrices (that we cannot form or even evaluate with full matrix-vector products). We demonstrate the effectiveness of this approach through a series of examples, comparing its performance against known limiting distributions from random matrix theory in synthetic settings, as well as applying it to submatrices of real-world datasets, matching them with their full empirical eigenspectra.

stat.ML↗

arXiv2025

Squeezed Attention: Accelerating Long Context Length LLM Inference

Emerging Large Language Model (LLM) applications require long input context in order to perform complex tasks like document analysis and code generation. For these long context length applications, the length of the input prompt poses a significant challenge in terms of inference efficiency since the inference costs increase linearly with sequence length. However, for many of these applications, much of the context in the prompt is fixed across different user inputs, thereby providing the opportunity to perform offline optimizations in order to process user inputs quickly, as they are received. We propose Squeezed Attention to accelerate LLM applications where a large portion of the input context is fixed. We first leverage K-means clustering offline to group the keys for the fixed context based on semantic similarity and represent each cluster with a single centroid value. During inference, we compare query tokens from the user input with the centroids to predict which keys from the fixed context are semantically relevant, and then compute exact attention using only the important keys, thereby reducing bandwidth and computational costs. We also present a hierarchical version of our algorithm which can reduce the complexity of attention from linear to logarithmic with respect to the fixed context length. We evaluate our method on long-context benchmarks including LongBench, where it achieves a 3.1$\times$ reduction in KV budget with no noticeable accuracy loss and up to an 8$\times$ reduction with only a 0.5 point accuracy gap for the LLaMA-2-7B-32K, LWM-Text-Chat-1M, and Longchat-7B-v1.5-32K models. Futhermore, we implement kernels for centroid comparison and sparse FlashAttention with important keys, achieving more than 4$\times$ speedups during both the prefill and generation phases for long-context inference. Our code is available at https://github.com/SqueezeAILab/SqueezedAttention.

cs.CL↗

arXiv2025

ETS: Efficient Tree Search for Inference-Time Scaling

Test-time compute scaling has emerged as a new axis along which to improve model accuracy, where additional computation is used at inference time to allow the model to think longer for more challenging problems. One promising approach for test-time compute scaling is search against a process reward model, where a model generates multiple potential candidates at each step of the search, and these partial trajectories are then scored by a separate reward model in order to guide the search process. The diversity of trajectories in the tree search process affects the accuracy of the search, since increasing diversity promotes more exploration. However, this diversity comes at a cost, as divergent trajectories have less KV sharing, which means they consume more memory and slow down the search process. Previous search methods either do not perform sufficient exploration, or else explore diverse trajectories but have high latency. We address this challenge by proposing Efficient Tree Search (ETS), which promotes KV sharing by pruning redundant trajectories while maintaining necessary diverse trajectories. ETS incorporates a linear programming cost model to promote KV cache sharing by penalizing the number of nodes retained, while incorporating a semantic coverage term into the cost model to ensure that we retain trajectories which are semantically different. We demonstrate how ETS can achieve 1.8$\times$ reduction in average KV cache size during the search process, leading to 1.4$\times$ increased throughput relative to prior state-of-the-art methods, with minimal accuracy degradation and without requiring any custom kernel implementation. Code is available at: https://github.com/SqueezeAILab/ETS.

cs.LG↗

arXiv2025

Models of Heavy-Tailed Mechanistic Universality

Recent theoretical and empirical successes in deep learning, including the celebrated neural scaling laws, are punctuated by the observation that many objects of interest tend to exhibit some form of heavy-tailed or power law behavior. In particular, the prevalence of heavy-tailed spectral densities in Jacobians, Hessians, and weight matrices has led to the introduction of the concept of heavy-tailed mechanistic universality (HT-MU). Multiple lines of empirical evidence suggest a robust correlation between heavy-tailed metrics and model performance, indicating that HT-MU may be a fundamental aspect of deep learning efficacy. Here, we propose a general family of random matrix models -- the high-temperature Marchenko-Pastur (HTMP) ensemble -- to explore attributes that give rise to heavy-tailed behavior in trained neural networks. Under this model, spectral densities with power laws on (upper and lower) tails arise through a combination of three independent factors (complex correlation structures in the data; reduced temperatures during training; and reduced eigenvector entropy), appearing as an implicit bias in the model structure, and they can be controlled with an "eigenvalue repulsion" parameter. Implications of our model on other appearances of heavy tails, including neural scaling laws, optimizer trajectories, and the five-plus-one phases of neural network training, are discussed.

stat.ML↗

arXiv2025

Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods still require a large amount of PDE data. This reintroduces the need for expensive numerical PDE solutions, partially undermining the original goal of avoiding these expensive simulations. In this work, seeking data efficiency, we design unsupervised pretraining for PDE operator learning. To reduce the need for training data with heavy simulation costs, we mine unlabeled PDE data without simulated solutions, and we pretrain neural operators with physics-inspired reconstruction-based proxy tasks. To improve out-of-distribution performance, we further assist neural operators in flexibly leveraging a similarity-based method that learns in-context examples, without incurring extra training costs or designs. Extensive empirical evaluations on a diverse set of PDEs demonstrate that our method is highly data-efficient, more generalizable, and even outperforms conventional vision-pretrained models. We provide our code at https://github.com/delta-lab-ai/data_efficient_nopt.

cs.LG↗

arXiv2025

A Statistical Framework for Ranking LLM-Based Chatbots

Large language models (LLMs) have transformed natural language processing, with frameworks like Chatbot Arena providing pioneering platforms for evaluating these models. By facilitating millions of pairwise comparisons based on human judgments, Chatbot Arena has become a cornerstone in LLM evaluation, offering rich datasets for ranking models in open-ended conversational tasks. Building upon this foundation, we propose a statistical framework that incorporates key advancements to address specific challenges in pairwise comparison analysis. First, we introduce a factored tie model that enhances the ability to handle ties -- an integral aspect of human-judged comparisons -- significantly improving the model's fit to observed data. Second, we extend the framework to model covariance between competitors, enabling deeper insights into performance relationships and facilitating intuitive groupings into performance tiers. Third, we resolve optimization challenges arising from parameter non-uniqueness by introducing novel constraints, ensuring stable and interpretable parameter estimation. Through rigorous evaluation and extensive experimentation, our framework demonstrates substantial improvements over existing methods in modeling pairwise comparison data. To support reproducibility and practical adoption, we release leaderbot, an open-source Python package implementing our models and analyses.

stat.ML↗

arXiv2025

KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization

LLMs are seeing growing use for applications which require large context windows, and with these large context windows KV cache activations surface as the dominant contributor to memory consumption during inference. Quantization is a promising approach for compressing KV cache activations; however, existing solutions fail to represent activations accurately in sub-4-bit precision. Our work, KVQuant, facilitates low precision KV cache quantization by incorporating several novel methods: (i) Per-Channel Key Quantization, where we adjust the dimension along which we quantize the Key activations to better match the distribution; (ii) Pre-RoPE Key Quantization, where we quantize Key activations before the rotary positional embedding to mitigate its impact on quantization; (iii) Non-Uniform KV Cache Quantization, where we derive per-layer sensitivity-weighted non-uniform datatypes that better represent the distributions; and (iv) Per-Vector Dense-and-Sparse Quantization, where we isolate outliers separately for each vector to minimize skews in quantization ranges. By applying our method to the LLaMA, Llama-2, Llama-3, and Mistral models, we achieve < 0.1 perplexity degradation with 3-bit quantization on both Wikitext-2 and C4, outperforming existing approaches. Our method enables serving LLaMA-7B with a context length of up to 1 million on a single A100-80GB GPU and up to 10 million on an 8-GPU system. We develop custom CUDA kernels for KVQuant, showing that we can achieve up to ~1.7x speedups, compared to baseline fp16 matrix-vector multiplications, for the LLaMA-7B model.

cs.LG↗

arXiv2025

FLEX: A Backbone for Diffusion-Based Modeling of Spatio-temporal Physical Systems

We introduce FLEX (FLow EXpert), a backbone architecture for generative modeling of spatio-temporal physical systems using diffusion models. FLEX operates in the residual space rather than on raw data, a modeling choice that we motivate theoretically, showing that it reduces the variance of the velocity field in the diffusion model, which helps stabilize training. FLEX integrates a latent Transformer into a U-Net with standard convolutional ResNet layers and incorporates a redesigned skip connection scheme. This hybrid design enables the model to capture both local spatial detail and long-range dependencies in latent space. To improve spatio-temporal conditioning, FLEX uses a task-specific encoder that processes auxiliary inputs such as coarse or past snapshots. Weak conditioning is applied to the shared encoder via skip connections to promote generalization, while strong conditioning is applied to the decoder through both skip and bottleneck features to ensure reconstruction fidelity. FLEX achieves accurate predictions for super-resolution and forecasting tasks using as few as two reverse diffusion steps. It also produces calibrated uncertainty estimates through sampling. Evaluations on high-resolution 2D turbulence data show that FLEX outperforms strong baselines and generalizes to out-of-distribution settings, including unseen Reynolds numbers, physical observables (e.g., fluid flow velocity fields), and boundary conditions.

cs.LG↗

arXiv2025

Gated Recurrent Neural Networks with Weighted Time-Delay Feedback

In this paper, we present a novel approach to modeling long-term dependencies in sequential data by introducing a gated recurrent unit (GRU) with a weighted time-delay feedback mechanism. Our proposed model, named $τ$-GRU, is a discretized version of a continuous-time formulation of a recurrent unit, where the dynamics are governed by delay differential equations (DDEs). We prove the existence and uniqueness of solutions for the continuous-time model and show that the proposed feedback mechanism can significantly improve the modeling of long-term dependencies. Our empirical results indicate that $τ$-GRU outperforms state-of-the-art recurrent units and gated recurrent architectures on a range of tasks, achieving faster convergence and better generalization.

cs.LG↗

arXiv2025

Removing Watermarks with Partial Regeneration using Semantic Information

As AI-generated imagery becomes ubiquitous, invisible watermarks have emerged as a primary line of defense for copyright and provenance. The newest watermarking schemes embed semantic signals - content-aware patterns that are designed to survive common image manipulations - yet their true robustness against adaptive adversaries remains under-explored. We expose a previously unreported vulnerability and introduce SemanticRegen, a three-stage, label-free attack that erases state-of-the-art semantic and invisible watermarks while leaving an image's apparent meaning intact. Our pipeline (i) uses a vision-language model to obtain fine-grained captions, (ii) extracts foreground masks with zero-shot segmentation, and (iii) inpaints only the background via an LLM-guided diffusion model, thereby preserving salient objects and style cues. Evaluated on 1,000 prompts across four watermarking systems - TreeRing, StegaStamp, StableSig, and DWT/DCT - SemanticRegen is the only method to defeat the semantic TreeRing watermark (p = 0.10 > 0.05) and reduces bit-accuracy below 0.75 for the remaining schemes, all while maintaining high perceptual quality (masked SSIM = 0.94 +/- 0.01). We further introduce masked SSIM (mSSIM) to quantify fidelity within foreground regions, showing that our attack achieves up to 12 percent higher mSSIM than prior diffusion-based attackers. These results highlight an urgent gap between current watermark defenses and the capabilities of adaptive, semantics-aware adversaries, underscoring the need for watermarking algorithms that are resilient to content-preserving regenerative attacks.

cs.CV↗

arXiv2025

SuperBench: A Super-Resolution Benchmark Dataset for Scientific Machine Learning

Super-resolution (SR) techniques aim to enhance data resolution, enabling the retrieval of finer details, and improving the overall quality and fidelity of the data representation. There is growing interest in applying SR methods to complex spatiotemporal systems within the Scientific Machine Learning (SciML) community, with the hope of accelerating numerical simulations and/or improving forecasts in weather, climate, and related areas. However, the lack of standardized benchmark datasets for comparing and validating SR methods hinders progress and adoption in SciML. To address this, we introduce SuperBench, the first benchmark dataset featuring high-resolution datasets, including data from fluid flows, cosmology, and weather. Here, we focus on validating spatial SR performance from data-centric and physics-preserved perspectives, as well as assessing robustness to data degradation tasks. While deep learning-based SR methods (developed in the computer vision community) excel on certain tasks, despite relatively limited prior physics information, we identify limitations of these methods in accurately capturing intricate fine-scale features and preserving fundamental physical properties and constraints in scientific data. These shortcomings highlight the importance and subtlety of incorporating domain knowledge into ML models. We anticipate that SuperBench will help to advance SR methods for science.

cs.CV↗