Solving and learning partial differential equations (PDEs) lies at the core of physicsinformed machine learning. Traditional numerical methods, such as finite difference and finite element approaches, are rooted in domain-specific techniques and often lack scalability. Recent advances have introduced neural networks and Gaussian processes (GPs) as flexible tools for automating PDE solving and incorporating physical knowledge into learning frameworks. While GPs offer tractable predictive distributions and a principled probabilistic foundation, they may be suboptimal in capturing complex behaviors such as sharp transitions or non-smooth dynamics. To address this limitation, we propose the use of the q-exponential process (Q-EP), a recently developed generalization of GPs designed to better handle data with abrupt changes and to more accurately model derivative information. We advocate for Q-EP as a superior alternative to GPs in solving PDEs and associated inverse problems. Leveraging sparse variational inference, our method enables principled uncertainty quantification - a capability not naturally afforded by neural network-based approaches. Through a series of experiments, including the Eikonal equation, Burgers' equation, and an inverse Darcy flow problem, we demonstrate that the variational Q-EP method consistently yields more accurate solutions while providing meaningful uncertainty estimates.

Sparse plus Low-Rank (S + LR) decomposition of Large Language Models (LLMs) has emerged as a promising direction in model compression, aiming to decompose pre-trained model weights into a sum of sparse and low-rank matrices W S + LR. Despite recent progress, existing methods often suffer from substantial performance degradation compared to dense models. In this work, we introduce 3BASiL-TM, an efficient one-shot post-training method for (S + LR) decomposition of LLMs that addresses this gap. Our approach first introduces a novel 3-Block Alternating Direction Method of Multipliers (ADMM) method, termed 3BASiL, to minimize the layer-wise reconstruction error with convergence guarantees.

Many datasets have inherent "multi-way" structure, where downstream tasks depend on relationships between groups of entities that ordinary graphs, whose edges are pairwise relationships, cannot represent (Bick et al., 2023; Benson et al., 2021; Schaub et al., 2021). Hypergraphs overcome this by allowing hyperedges that connect any number of vertices.

Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an unsupervised method for jointly learning hierarchical representations of samples and features via TreeWasserstein Distance (TWD). Our method alternates between the two data modes. It first constructs a tree for one mode, then computes a TWD for the other mode based on that tree, and finally uses the resulting TWD to build the second mode's tree.

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Active testing enables label-efficient evaluation of predictive models through careful data acquisition, but it can pose a significant computational cost. We identify cost-saving measures that enable active testing to be scaled up to large language models (LLMs). In particular we show that the surrogate model used to guide data acquisition can be constructed cheaply using in-context learning, does not require updating within an active-testing loop, and can be smaller than the target model. We even find we can make good data-acquisition decisions without making predictions with the target model. As a result we are able to achieve much more accurate evaluations of LLM performance relative to using randomly acquired data. We additionally introduce a bootstrap estimator of evaluation error, which we show to be a useful indicator of how well active testing is working within a single run.

AI systems are increasingly able to autonomously conduct realistic software engineering tasks, and may soon be deployed to automate machine learning (ML) R&D itself. Frontier AI systems may be deployed in safety-critical settings, including to help ensure the safety of future systems. Unfortunately, frontier and future systems may not be sufficiently trustworthy, and there is evidence that these systems may even be misaligned with their developers or users. Therefore, we investigate the capabilities of AI agents to act against the interests of their users when conducting ML engineering, by sabotaging ML models, sandbagging their performance, and subverting oversight mechanisms. First, we extend MLE-Bench, a benchmark for realistic ML tasks, with code-sabotage tasks such as implanting backdoors and purposefully causing generalisation failures.

Modern data marketplaces and data sharing consortia increasingly rely on incentive mechanisms to encourage agents to contribute data. However, schemes that reward agents based on the quantity of submitted data are vulnerable to manipulation, as agents may submit fabricated or low-quality data to inflate their rewards. Prior work has proposed comparing each agent's data against others' to promote honesty: when others contribute genuine data, the best way to minimize discrepancy is to do the same. Yet prior implementations of this idea rely on very strong assumptions about the data distribution (e.g.

As distributed optimization scales to meet the demands of Large Language Model (LLM) training, hardware failures become increasingly non-negligible. Existing fault-tolerant training methods often introduce significant computational or memory overhead, demanding additional resources. To address this challenge, we propose Memory-and Computation-efficient Fault-tolerant Optimization (MeCeFO), a novel algorithm that ensures robust training with minimal overhead. When a computing node fails, MeCeFO seamlessly transfers its training task to a neighboring node while employing memory-and computation-efficient algorithmic optimizations to minimize the extra workload imposed on the neighboring node handling both tasks. MeCeFO leverages three key algorithmic designs: (i) Skip-connection, which drops the multi-head attention (MHA) module during backpropagation for memory-and computation-efficient approximation; (ii) Recomputation, which reduces activation memory in feedforward networks (FFNs); and (iii) Low-rank gradient approximation, enabling efficient estimation of FFN weight matrix gradients. Theoretically, MeCeFO matches the convergence rate of conventional distributed training, with a rate of O(1/ nT), where n is the data parallelism size and T is the number of iterations. Empirically, MeCeFO maintains robust performance under high failure rates, incurring only a 4.18% drop in throughput, demonstrating 5.0 to 6.7 greater resilience than previous SOTA approaches.

Autoregressive models have driven remarkable progress in language modeling. Their foundational reliance on discrete tokens, unidirectional context, and singlepass decoding, while central to their success, also inspires the exploration of a design space that could offer new axes of modeling flexibility. In this work, we explore an alternative paradigm, shifting language modeling from a discrete token space to a continuous latent space. We propose a novel framework TarFlowLM, that employs transformer-based autoregressive normalizing flows [73] to model these continuous representations. This approach unlocks substantial flexibility, enabling the construction of models that can capture global bi-directional context through stacked, alternating-direction autoregressive transformations, support block-wise generation with flexible token patch sizes, and facilitate a hierarchical multi-pass generation process. We further propose new mixture-based coupling transformations designed to capture complex dependencies within the latent space shaped by discrete data, and demonstrate theoretical connections to conventional discrete autoregressive models. Extensive experiments on language modeling benchmarks demonstrate strong likelihood performance and highlight the flexible modeling capabilities inherent in our framework.