This work studies operators mapping vector and scalar fields defined over a manifold $\mathcal{M}$, and which commute with its group of diffeomorphisms $\text{Diff}(\mathcal{M})$. We prove that in the case of scalar fields $L^p_\omega(\mathcal{M,\mathbb{R}})$, those operators correspond to point-wise non-linearities, recovering and extending known results on $\mathbb{R}^d$. In the context of Neural Networks defined over $\mathcal{M}$, it indicates that point-wise non-linear operators are the only universal family that commutes with any group of symmetries, and justifies their systematic use in combination with dedicated linear operators commuting with specific symmetries. In the case of vector fields $L^p_\omega(\mathcal{M},T\mathcal{M})$, we show that those operators are solely the scalar multiplication. It indicates that $\text{Diff}(\mathcal{M})$ is too rich and that there is no universal class of non-linear operators to motivate the design of Neural Networks over the symmetries of $\mathcal{M}$.

We study the problem of robust forecast aggregation: combining expert forecasts with provable accuracy guarantees compared to the best possible aggregation of the underlying information. Prior work shows strong impossibility results, e.g. that even under natural assumptions, no aggregation of the experts' individual forecasts can outperform simply following a random expert (Neyman and Roughgarden, 2022). In this paper, we introduce a more general framework that allows the principal to elicit richer information from experts through structured queries. Our framework ensures that experts will truthfully report their underlying beliefs, and also enables us to define notions of complexity over the difficulty of asking these queries. Under a general model of independent but overlapping expert signals, we show that optimal aggregation is achievable in the worst case with each complexity measure bounded above by the number of agents $n$. We further establish tight tradeoffs between accuracy and query complexity: aggregation error decreases linearly with the number of queries, and vanishes when the "order of reasoning" and number of agents relevant to a query is $ω(\sqrt{n})$. These results demonstrate that modest extensions to the space of expert queries dramatically strengthen the power of robust forecast aggregation. We therefore expect that our new query framework will open up a fruitful line of research in this area.

The deployment of AI-assisted development tools in compliance-relevant, large-scale industrial environments represents significant gaps in academic literature, despite growing industry adoption. We report on the industrial deployment of WhatsCode, a domain-specific AI development system that supports WhatsApp (serving over 2 billion users) and processes millions of lines of code across multiple platforms. Over 25 months (2023-2025), WhatsCode evolved from targeted privacy automation to autonomous agentic workflows integrated with end-to-end feature development and DevOps processes. WhatsCode achieved substantial quantifiable impact, improving automated privacy verification coverage 3.5x from 15% to 53%, identifying privacy requirements, and generating over 3,000 accepted code changes with acceptance rates ranging from 9% to 100% across different automation domains. The system committed 692 automated refactor/fix changes, 711 framework adoptions, 141 feature development assists and maintained 86% precision in bug triage. Our study identifies two stable human-AI collaboration patterns that emerged from production deployment: one-click rollout for high-confidence changes (60% of cases) and commandeer-revise for complex decisions (40%). We demonstrate that organizational factors, such as ownership models, adoption dynamics, and risk management, are as decisive as technical capabilities for enterprise-scale AI success. The findings provide evidence-based guidance for large-scale AI tool deployment in compliance-relevant environments, showing that effective human-AI collaboration, not full automation, drives sustainable business impact.

We present a novel framework that integrates Large Language Models (LLMs) into the Git bisect process for semantic fault localization. Traditional bisect assumes deterministic predicates and binary failure states assumptions often violated in modern software development due to flaky tests, nonmonotonic regressions, and semantic divergence from upstream repositories. Our system augments bisect traversal with structured chain of thought reasoning, enabling commit by commit analysis under noisy conditions. We evaluate multiple open source and proprietary LLMs for their suitability and fine tune DeepSeekCoderV2 using QLoRA on a curated dataset of semantically labeled diffs. We adopt a weak supervision workflow to reduce annotation overhead, incorporating human in the loop corrections and self consistency filtering. Experiments across multiple open source projects show a 6.4 point absolute gain in success rate from 74.2 to 80.6 percent, leading to significantly fewer failed traversals and by experiment up to 2x reduction in average bisect time. We conclude with discussions on temporal reasoning, prompt design, and finetuning strategies tailored for commit level behavior analysis.

Practical applications of machine learning often involve successive training iterations with changes to features and training examples.

Practical applications of machine learning often involve successive training iterations with changes to features and training examples.

As deep learning (DL) techniques become integral to various applications, ensuring model fairness while maintaining high performance has become increasingly critical, particularly in sensitive fields such as medical diagnosis. Although a variety of bias-mitigation methods have been proposed, many rely on computationally expensive debiasing strategies or suffer substantial drops in model accuracy, which limits their practicality in real-world, resource-constrained settings. To address this issue, we propose a fairness-oriented low rank factorization (LRF) framework that leverages singular value decomposition (SVD) to improve DL model fairness. Unlike traditional SVD, which is mainly used for model compression by decomposing and reducing weight matrices, our work shows that SVD can also serve as an effective tool for fairness enhancement. Specifically, we observed that elements in the unitary matrices obtained from SVD contribute unequally to model bias across groups defined by sensitive attributes. Motivated by this observation, we propose a method, named FairLRF, that selectively removes bias-inducing elements from unitary matrices to reduce group disparities, thus enhancing model fairness. Extensive experiments show that our method outperforms conventional LRF methods as well as state-of-the-art fairness-enhancing techniques. Additionally, an ablation study examines how major hyper-parameters may influence the performance of processed models. To the best of our knowledge, this is the first work utilizing SVD not primarily for compression but for fairness enhancement.

We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of Multi-Distribution Learning (MDL), we show that the optimal sample complexity of an $r$-round algorithm scales approximately as $dk^{Θ(1/r)} / ε$. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of $\widetilde O((d + k) / ε^2)$ within $\widetilde O(\sqrt{k})$ rounds. Of independent interest, we introduce a new framework, Optimization via On-Demand Sampling (OODS), which abstracts the sample-adaptivity tradeoff and captures most existing MDL algorithms. We establish nearly tight bounds on the round complexity in the OODS setting. The upper bounds directly yield the $\widetilde O(\sqrt{k})$-round algorithm for agnostic MDL, while the lower bounds imply that achieving sub-polynomial round complexity would require fundamentally new techniques that bypass the inherent hardness of OODS.

Pairwise evaluation of Large Language Models (LLMs) is a common paradigm, but it is prone to preference bias, where judges systematically favor certain outputs, such as their own. This bias leads to inconsistent and skewed rankings across different judges. To address this, we first empirically demonstrate significant and heterogeneous biases in cross-model evaluations. We then propose UDA (Unsupervised Debiasing Alignment), a framework that reduces inter-judge disagreement by dynamically adjusting the Elo rating system. For each pairwise comparison, a compact neural network learns to adaptively set the K-factor and refine win probabilities. Crucially, UDA operates in a fully unsupervised manner, guided solely by the objective of minimizing the dispersion among the Elo trajectories of all judges. This forces an alignment towards a collective consensus, which serves as an unsupervised proxy for a more stable and reproducible evaluation. In addition, we provide theoretical motivation demonstrating how alignment towards a consensus can reduce aggregate system bias. Experiments show that UDA significantly reduces the inter-judge rating standard deviation by up to 63.4% and improves the average correlation with human judgments by 24.7%. Notably, UDA elevates the performance of poorly performing judges to achieve parity with high-quality ones, fostering a more robust and reliable evaluation ecosystem. Code and data are available at https://anonymous.4open.science/r/62AB93CD-23B4.