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Michael W. Mahoney

Publications and source records attributed to Michael W. Mahoney.

At least 37 records · Page 2Linked to original sources
arXiv2026

Residual Context Diffusion Language Models

Diffusion Large Language Models (dLLMs) have emerged as a promising alternative to purely autoregressive language models because they can decode multiple tokens in parallel. However, state-of-the-art block-wise dLLMs rely on a "remasking" mechanism that decodes only the most confident tokens and discards the rest, effectively wasting computation. We demonstrate that recycling computation from the discarded tokens is beneficial, as these tokens retain contextual information useful for subsequent decoding iterations. In light of this, we propose Residual Context Diffusion (RCD), a module that converts these discarded token representations into contextual residuals and injects them back for the next denoising step. RCD uses a decoupled two-stage training pipeline to bypass the memory bottlenecks associated with backpropagation. We validate our method on both long CoT reasoning (SDAR) and short CoT instruction following (LLaDA) models. We demonstrate that a standard dLLM can be efficiently converted to the RCD paradigm with merely ~300 million tokens. RCD consistently improves frontier dLLMs by 4-11 percentage points in accuracy with minimal extra computation overhead across a wide range of benchmarks. Notably, on the most challenging AIME tasks, RCD nearly doubles baseline accuracy and attains up to 4-5x fewer denoising steps at baseline's peak accuracy.

cs.CL↗
arXiv2026

AlphaQ: Calibration-Free Bit Allocation for Mixture-of-Experts Quantization

Mixture-of-Experts (MoE) architectures scale model capacity through sparse expert activation, but their deployment remains memory-bound because all expert weights must reside in memory. Mixed-precision quantization can substantially reduce this footprint by assigning different bit-widths to different experts. Existing approaches, however, typically rely on calibration data to estimate expert importance and determine bit allocation. For frontier MoE LLMs, the original training data, and hence the true training distribution, is proprietary and inaccessible. As a result, calibration sets are inevitably imperfect surrogates, and this can misestimate expert utilization and lead to suboptimal bit allocation. Motivated by the substantial cross-expert quality variability observed in modern MoE models, and by the success of Heavy-Tailed Self-Regularization (HT-SR) theory at predicting neural network model quality without access to training or testing data, we propose AlphaQ, a calibration-free bit-allocation method for MoE quantization. AlphaQ draws on HT-SR theory and follows a simple principle: experts with more heavy-tailed weight spectra are typically better trained and hence should receive higher bit-widths, while experts with weaker heavy-tailed structure can be quantized more aggressively. AlphaQ operationalizes this principle by measuring expert-wise spectral heavy-tailedness and solving a budget-constrained optimization problem that minimizes total quantization error under a global bit-budget constraint. Across several MoE models, AlphaQ consistently outperforms calibration-based baselines under matched bit budgets. Notably, on Qwen1.5-MoE, AlphaQ achieves near full-precision accuracy with an average expert precision of only 3.5 bits, while delivering more than 4$\times$ memory compression. Our code is available at https://github.com/Superone77/AlphaQ.

cs.LG↗
arXiv2026

Unveiling Multi-regime Patterns in SciML: Distinct Failure Modes and Regime-specific Optimization

Neural networks trained under different hyperparameter settings can fall into distinct training "regimes," with consistent behavior within regimes and qualitative differences across regimes. In this paper, we study such multi-regime behavior in scientific machine learning (SciML) models through a regime-aware diagnostic framework that jointly analyzes performance, training dynamics, and loss-landscape geometry. We identify three key findings: (i) a consistent three-regime structure emerges across many standard SciML models, different constraint enforcements, and various optimizer designs; (ii) optimization effectiveness is regime-specific, with no single method performing well across all regimes; and (iii) SciML models can exhibit fine-grained failure modes that can challenge conventional interpretations of standard loss-landscape metrics. Our results provide an approach to establish a unified, task-oblivious perspective on failure modes in SciML and to inform regime-aware guidance for improving robustness. We validate these findings across widely-used SciML models, including physics-informed neural networks, neural operators, and neural ordinary differential equations, on benchmarks spanning representative ordinary and partial differential equations.

cs.LG↗
arXiv2026

Neural equilibria for long-term prediction of nonlinear conservation laws

Nonlinear conservation laws govern a broad class of important physical systems in science and industry and are central to scientific machine learning (SciML). Large general-purpose models offer speed, but replacing the numerical and physical structure of solvers often compromises stability, accuracy, and physical faithfulness. Here, we aim to balance the general inductive bias of conservation with the flexibility and speed of neural networks through a conservation-aware SciML backbone, which we call Neural Discrete Equilibrium (NeurDE). NeurDE places machine learning inside a kinetic solver by learning the local equilibrium closure of a Boltzmann formulation. The kinetic solver still performs transport, relaxation, moment recovery, and conservation; the neural network provides only the nonlinear equilibrium target. We test NeurDE on $6$ conserved systems, including three very challenging subsonic, transonic, and supersonic shock systems. NeurDE outperforms state-of-the-art SciML methods, including neural operators and pretrained SciML foundation models that are $10^4$ and $10^6$ times larger, respectively. Most notably, NeurDE improves upon the numerical method from which it is derived. NeurDE therefore provides a compact target for scientific machine learning in conservative simulation: learn the equilibrium law toward which the system relaxes, not the evolution law itself.

cs.LG↗
arXiv2026

Speculative Interaction Agents: Building Real-Time Agents with Asynchronous I/O and Speculative Tool Calling

There is a growing demand for agentic AI technologies for a range of downstream applications like customer service and personal assistants. For applications where the agent needs to interact with a person, real-time low-latency responsiveness is required; for example, with voice-controlled applications, under 1 second of latency is typically required for the interaction to feel seamless. However, if we want the LLM to reason and execute an agentic workflow with tool calling, this can add several seconds or more of latency, which is prohibitive for real-time latency-sensitive applications. In our work, we propose Speculative Interaction Agents to enable real-time interaction even for agents with complex multi-turn tool calling. We propose Asynchronous I/O, which decouples the core agent reason-and-act thread from waiting for additional information from either the user or environment, thereby allowing for overlapping agentic processing while waiting on external delays. We also propose Speculative Tool Calling as a method to manage task execution when the agent is still unsure if it has received the full information or if additional user information may later be provided. For strong cloud models, our method can be applied out-of-the-box to existing real-time cloud APIs, providing 1.3-1.7$\times$ speedups with minor accuracy loss. To enable real-time interaction with small edge-scale models, we also present a clock-based training methodology that adapts the model to handle streaming inputs and asynchronous responses, and demonstrate a synthetic data generation strategy for SFT. Altogether, this approach provides 1.6-2.2$\times$ speedups with the Qwen2.5-3B-Instruct and Llama-3.2-3B-Instruct models across multiple tool calling benchmarks.

cs.LG↗
arXiv2026

Zatom-1: Towards a Multimodal Foundation Model for 3D Molecules and Materials

General-purpose 3D modeling in chemistry encompasses molecules and materials, requiring both generative and predictive capabilities. However, most existing AI approaches are optimized for a single domain (molecules or materials) and a single task (generation or prediction), which limits representation sharing and transfer. We introduce Zatom-1, a cross-domain, general-purpose model architecture that unifies generative and predictive learning of 3D molecules and materials. Zatom-1 is a deliberately simplified Transformer trained with a multimodal flow matching objective that jointly models discrete atom types and continuous 3D geometries. This approach supports scalable pretraining with predictable gains as model capacity increases, while enabling fast and stable sampling. We use cross-domain generative pretraining as a universal initialization for downstream multi-task prediction of properties, energies, and forces. Empirically, Zatom-1 outperforms or competes with specialized baselines on both multi-task generative and predictive benchmarks in data-controlled settings, while improving generative inference speed by more than an order of magnitude. Our experiments demonstrate positive predictive transfer between data domains from joint generative pretraining: modeling materials during generative pretraining improves molecular property prediction accuracy. Open-source code and model weights are freely available at https://github.com/Zatom-AI/zatom.

cs.LG↗
arXiv2026

Free Decompression with Algebraic Spectral Curves

Tools from random matrix theory have become central to deep learning theory, using spectral information to provide mechanisms for modeling generalization, robustness, scaling, and failure modes. While often capable of modeling empirical behavior, practical computations are limited by matrix size, often imposing a restriction to models that are too small to be realistic. This motivates the inference of properties of larger models from the behavior of smaller ones. Free decompression (FD) is a recently proposed method for extrapolating spectral information across matrix sizes, but its utility is currently limited by strong assumptions that preclude its implementation on more realistic machine learning (ML) models. We use algebraic spectral curve theory to provide a general FD methodology for spectral densities whose Stieltjes transform satisfies an algebraic relation, a modeling assumption that is more likely to hold in practice. This recasts FD as an evolution along spectral curves which can be readily integrated. Our framework enables the expansion of spectral densities that have multiple or multi-modal bulks, that exist at multiple scales, and that contain atoms, all characteristic of real-world data and popular ML models. We demonstrate the efficacy of our framework on models of interest in modern ML, including Hessian and activation matrices associated with neural networks and large-scale diffusion models.

stat.ML↗
arXiv2026

Foundation Models for Discovery and Exploration in Chemical Space

Accurate prediction of atomistic, thermodynamic, and kinetic properties from molecular structures underpins materials innovation. Existing computational and experimental approaches lack the scalability required to navigate chemical space efficiently. Scientific foundation models trained on large unlabelled datasets offer a path towards navigating chemical space across application domains. Here, we develop MIST, a family of molecular foundation models with up to an order of magnitude more parameters and data than prior works. Trained using a novel tokenizer, Smirk, which comprehensively captures nuclear, electronic, and geometric information, MIST learns a diverse range of molecules. MIST models have been fine-tuned to predict more than 400 structure-property relationships and have been shown to match or exceed state-of-the-art performance across diverse benchmarks, from physiology to electrochemistry. We demonstrate the ability of these models to solve real-world problems across chemical space from multiobjective electrolyte solvent screening to stereochemical reasoning for organometallics and mixture property prediction. The clearest demonstration of a foundation model is its ability to solve problems that were neither explicit targets of training nor central to the intentions of its developers. We identify olfactory perception mapping as such a problem, and show that MIST accurately predicted scent profiles and learned a hierarchical representation of olfactory space consistent with hyperbolic geometry. We formulated hyperparameter aware Bayesian neural scaling laws which eliminate the need for hyperparameter sweeps at every scale, making training large compute-optimal models feasible on a limited compute budget. The methods and findings presented here represent a significant step towards accelerating materials discovery, design, and optimization using foundation models.

physics.chem-ph↗
arXiv2026

Recency Biased Causal Attention for Time-series Forecasting

Recency bias is a useful inductive prior for sequential modeling: it emphasizes nearby observations and can still allow longer-range dependencies. Standard Transformer attention lacks this property, relying on all-to-all interactions that overlook the causal and often local structure of temporal data. We propose a simple mechanism to introduce recency bias by reweighting attention scores with a smooth heavy-tailed decay. This adjustment strengthens local temporal dependencies without sacrificing the flexibility to capture broader and data-specific correlations. We show that recency-biased attention consistently improves sequential modeling, aligning Transformer more closely with the read, ignore, and write operations of RNNs. Finally, we demonstrate that our approach achieves competitive and often superior performance on challenging time-series forecasting benchmarks.

cs.LG↗
arXiv2026

FluidGaussian: Propagating Simulation-Based Uncertainty Toward Functionally-Intelligent 3D Reconstruction

Real objects that inhabit the physical world follow physical laws and thus behave plausibly during interaction with other physical objects. However, current methods that perform 3D reconstructions of real-world scenes from multi-view 2D images optimize primarily for visual fidelity, i.e., they train with photometric losses and reason about uncertainty in the image or representation space. This appearance-centric view overlooks body contacts and couplings, conflates function-critical regions (e.g., aerodynamic or hydrodynamic surfaces) with ornamentation, and reconstructs structures suboptimally, even when physical regularizers are added. All these can lead to unphysical and implausible interactions. To address this, we consider the question: How can 3D reconstruction become aware of real-world interactions and underlying object functionality, beyond visual cues? To answer this question, we propose FluidGaussian, a plug-and-play method that tightly couples geometry reconstruction with ubiquitous fluid-structure interactions to assess surface quality at high granularity. We define a simulation-based uncertainty metric induced by fluid simulations and integrate it with active learning to prioritize views that improve both visual and physical fidelity. In an empirical evaluation on NeRF Synthetic (Blender), Mip-NeRF 360, and DrivAerNet++, our FluidGaussian method yields up to +8.6% visual PSNR (Peak Signal-to-Noise Ratio) and -62.3% velocity divergence during fluid simulations. Our code is available at https://github.com/delta-lab-ai/FluidGaussian.

cs.CV↗
arXiv2026

On Neural Scaling Laws for Weather Emulation through Continual Training

Neural scaling laws, which in some domains can predict the performance of large neural networks as a function of model, data, and compute scale, are the cornerstone of building foundation models in Natural Language Processing and Computer Vision. We study neural scaling in Scientific Machine Learning, focusing on models for weather forecasting. To analyze scaling behavior in as simple a setting as possible, we adopt a minimal, scalable, general-purpose Swin Transformer architecture, and we use continual training with constant learning rates and periodic cooldowns as an efficient training strategy. We show that models trained in this minimalist way follow predictable scaling trends and even outperform standard cosine learning rate schedules. Cooldown phases can be re-purposed to improve downstream performance, e.g., enabling accurate multi-step rollouts over longer forecast horizons as well as sharper predictions through spectral loss adjustments. We also systematically explore a wide range of model and dataset sizes under various compute budgets to construct IsoFLOP curves, and we identify compute-optimal training regimes. Extrapolating these trends to larger scales highlights potential performance limits, demonstrating that neural scaling can serve as an important diagnostic for efficient resource allocation. We open-source our code for reproducibility.

cs.LG↗
arXiv2026

RELift: Learned Coarse-to-Fine Propagators for Time-Dependent PDEs with Applications to Electron Dynamics

We present RELift (Restrict, Evolve, Lift), a two-phase learning framework that couples coarse-grid numerical solvers with neural operators to super-resolve and forecast fine-grid dynamics for time-dependent partial differential equations (PDEs). In Phase 1, RELift learns a super-resolution operator that maps the solution on a coarse grid to a fine grid. In Phase 2, this learned operator is composed with a coarse-grid numerical integrator to construct an effective fine-grid propagator for the governing equation. We benchmark RELift on three canonical two-dimensional PDEs of increasing dynamical complexity -- the heat equation, the wave equation, and the incompressible Navier--Stokes equations -- and we further demonstrate its performance on a kinetic electron dynamics case study via the 1D1V Vlasov--Poisson system. Across all examples, RELift delivers high-fidelity super-resolution (Phase 1) and accurate long-horizon rollouts (Phase 2), outperforming standard super-resolution and neural operator baselines in both field-level error metrics and physics-relevant diagnostics. Finally, we provide error analysis of the effective fine-grid propagator, characterizing how approximation errors accumulate over time and explaining the observed numerical stability of the RELift framework.

math.NA↗
arXiv2026

Fundamental Bias in Inverting Random Sampling Matrices with Application to Sub-sampled Newton

A substantial body of work in machine learning (ML) and randomized numerical linear algebra (RandNLA) has exploited various sorts of random sketching methodologies, including random sampling and random projection, with much of the analysis using Johnson--Lindenstrauss and subspace embedding techniques. Recent studies have identified the issue of inversion bias -- the phenomenon that inverses of random sketches are not unbiased, despite the unbiasedness of the sketches themselves. This bias presents challenges for the use of random sketches in various ML pipelines, such as fast stochastic optimization, scalable statistical estimators, and distributed optimization. In the context of random projection, the inversion bias can be easily corrected for dense Gaussian projections (which are, however, too expensive for many applications). Recent work has shown how the inversion bias can be corrected for sparse sub-gaussian projections. In this paper, we show how the inversion bias can be corrected for random sampling methods, both uniform and non-uniform leverage-based, as well as for structured random projections, including those based on the Hadamard transform. Using these results, we establish problem-independent local convergence rates for sub-sampled Newton methods.

math.NA↗
arXiv2026

The False Promise of Zero-Shot Super-Resolution in Machine-Learned Operators

A core challenge in scientific machine learning, and scientific computing more generally, is modeling continuous phenomena which (in practice) are represented discretely. Machine-learned operators (MLOs) have been introduced as a means to achieve this modeling goal, as this class of architecture can perform inference at arbitrary resolution. In this work, we evaluate whether this architectural innovation is sufficient to perform "zero-shot super-resolution," namely to enable a model to serve inference on higher-resolution data than that on which it was originally trained. We comprehensively evaluate both zero-shot sub-resolution and super-resolution (i.e., multi-resolution) inference in MLOs. We decouple multi-resolution inference into two key behaviors: 1) extrapolation to varying frequency information; and 2) interpolating across varying resolutions. We empirically demonstrate that MLOs fail to do both of these tasks in a zero-shot manner. Consequently, we find MLOs are not able to perform accurate inference at resolutions different from those on which they were trained, and instead they are brittle and susceptible to aliasing. To address these failure modes, we propose a simple, computationally-efficient, and data-driven multi-resolution training protocol that overcomes aliasing and that provides robust multi-resolution generalization.

cs.LG↗
arXiv2026

HPC-Driven Modeling with ML-Based Surrogates for Magnon-Photon Dynamics in Hybrid Quantum Systems

Simulating hybrid magnonic quantum systems remains a challenge due to the large disparity between the timescales of the two systems. We present a massively parallel GPU-based simulation framework that enables fully coupled, large-scale modeling of on-chip magnon-photon circuits. Our approach resolves the dynamic interaction between ferromagnetic and electromagnetic fields with high spatiotemporal fidelity. To accelerate design workflows, we develop a physics-informed machine learning surrogate trained on the simulation data, reducing computational cost while maintaining accuracy. This combined approach reveals real-time energy exchange dynamics and reproduces key phenomena such as anti-crossing behavior and the suppression of ferromagnetic resonance under strong electromagnetic fields. By addressing the multiscale and multiphysics challenges in magnon-photon modeling, our framework enables scalable simulation and rapid prototyping of next-generation quantum and spintronic devices.

quant-ph↗
arXiv2026

Landscaper: Understanding Loss Landscapes Through Multi-Dimensional Topological Analysis

Loss landscapes are a powerful tool for understanding neural network optimization and generalization, yet traditional low-dimensional analyses often miss complex topological features. We present Landscaper, an open-source Python package for arbitrary-dimensional loss landscape analysis. Landscaper combines Hessian-based subspace construction with topological data analysis to reveal geometric structures such as basin hierarchy and connectivity. A key component is the Saddle-Minimum Average Distance (SMAD) for quantifying landscape smoothness. We demonstrate Landscaper's effectiveness across various architectures and tasks, including those involving pre-trained language models, showing that SMAD captures training transitions, such as landscape simplification, that conventional metrics miss. We also illustrate Landscaper's performance in challenging chemical property prediction tasks, where SMAD can serve as a metric for out-of-distribution generalization, offering valuable insights for model diagnostics and architecture design in data-scarce scientific machine learning scenarios.

cs.LG↗
arXiv2026

Reward Under Attack: Analyzing the Robustness and Hackability of Process Reward Models

Process Reward Models (PRMs) are rapidly becoming the backbone of LLM reasoning pipelines, yet we demonstrate that state-of-the-art PRMs are systematically exploitable under adversarial optimization pressure. To address this, we introduce a three-tiered diagnostic framework that applies increasing adversarial pressure to quantify these vulnerabilities. Static perturbation analysis uncovers a fluency-logic dissociation: high invariance to surface-level style changes reward changes $<$0.1, yet inconsistent detection of logically-corrupted reasoning, with different models failing on different attack types. Adversarial optimization demonstrates that gradient-based attacks inflate rewards on invalid trajectories, with reward landscapes exhibiting wide, exploitable peaks. RL-induced reward hacking exposes the critical failure mode: policies trained on AIME problems achieve near-perfect PRM rewards ($>$0.9), while ground-truth accuracy remains low (below 4%), with 43% of reward gains attributable to stylistic shortcuts. These findings reveal that current PRMs function as fluency detectors rather than reasoning verifiers, creating systematic blind spots that undermine their use as training signals. We release PRM-BiasBench and a diagnostic toolkit to enable robustness evaluation before deployment. The code and dataset are available at https://github.com/SqueezeAILab/reward-under-attack.

cs.LG↗
arXiv2026

Comparing and Contrasting DLWP Backbones on Navier-Stokes and Atmospheric Dynamics

A large number of Deep Learning Weather Prediction (DLWP) architectures -- based on various backbones, including U-Net, Transformer, Graph Neural Network, and Fourier Neural Operator (FNO) -- have demonstrated their potential at forecasting atmospheric states. However, due to differences in training protocols, forecast horizons, and data choices, it remains unclear which (if any) of these methods and architectures are most suitable for weather forecasting and for future model development. Here, we step back and provide a detailed empirical analysis, under controlled conditions, comparing and contrasting the most prominent DLWP models, along with their backbones. We accomplish this by predicting synthetic two-dimensional incompressible Navier-Stokes and real-world global weather dynamics. On synthetic data, we observe favorable performance of FNO, while on the real-world WeatherBench dataset, our results demonstrate the suitability of ConvLSTM and SwinTransformer for short-to-mid-ranged forecasts. For long-ranged weather rollouts of up to 50 years, we observe superior stability and physical soundness in architectures that formulate a spherical data representation, i.e., GraphCast and Spherical FNO. The code is available at https://github.com/amazon-science/dlwp-benchmark.

cs.LG↗