Three of the most popular methods for training language models to reason look like three different tricks. They are not. All three adjust a single number: standard deviation, reflecting how much a prompt's sampled answers disagree. When such a model is trained, it answers each problem many times, and an automatic checker marks every answer right or wrong. The standard deviation of those marks measures the disagreement: largest when the answers split evenly between right and wrong, and zero when they all agree. Group Relative Policy Optimization (GRPO) divides by this number, GRPO Done Right (Dr. GRPO) drops the division, and Decoupled Clip and Dynamic Sampling Policy Optimization (DAPO) discards the groups where it is zero. Each is presented as its own fix, yet this paper proves they are three settings of one dial. That dial is not cosmetic: for right-or-wrong rewards, the disagreement is exactly the size of the training update, the group-standard-deviation identity. A split group teaches the most, while a unanimous group teaches nothing and falls silent. The same result says which problems deserve the most weight and how many tries each one needs. This paper confirms the intuition on a large real difficulty dataset (Big-Math) and in a controlled training run. What looks like a harmless normalization step is the dial that decides where learning happens and how strongly.

The modeling of samples of distributions is a major challenge since distributions do not form a vector space. While various approaches exist for univariate distributions, including transformations to a Hilbert space, far less is known about the multivariate case. We utilize a transformation approach to map multivariate distributions to a Hilbert space via a Wasserstein slicing method that is invertible. This approach combines functional data analysis tools, such as functional principal component analysis and modes of variation, with the facility to map back to interpretable distributions. We also provide convergence guarantees for the Hilbert space representations under a broad class of such transforms. The method is illustrated using joint systolic and diastolic blood pressure data.

Two narratives about machine learning ecosystems grew out of the recent algorithmic fairness discourse. In one, dubbed monoculture, algorithmic ecosystems tend toward homogeneity akin to a single model making all decisions. Individuals then face the risk of systematic exclusion with no recourse. In the other, model multiplicity, many models solve the same task with similar accuracy, causing excessive variation in individual outcomes. Both narratives are compelling, yet, seemingly at odds: model multiplicity can't materialize in a strict monoculture.

Deep neural networks are increasingly applied in automated histopathology. Yet, whole-slide images (WSIs) are often acquired at gigapixel sizes, rendering them computationally infeasible to analyze entirely at high resolution. Diagnostic labels are largely available only at the slide-level, because expert annotation of images at a finer (patch) level is both laborious and expensive. Moreover, regions with diagnostic information typically occupy only a small fraction of the WSI, making it inefficient to examine the entire slide at full resolution. Here, we propose SASHA - Sequential Attention-based Sampling for Histopathological Analysis - a deep reinforcement learning approach for efficient analysis of histopathological images.

This position paper challenges the "scaling fundamentalism" dominating AI research, where unbounded growth in model size and computation has led to unsustainable environmental impacts and widening resource inequality. We argue that LLM development should be fundamentally reoriented toward capability-perresource rather than capability alone. We present a theoretical framework demonstrating that resource-allocation decisions guided by gradient influence patterns can dramatically improve efficiency throughout the AI lifecycle. Our analysis shows that in transformer-based models, where a small fraction of parameters exert outsized influence (following heavy-tailed distributions), three critical insights emerge: (1) updating only high-influence parameters strictly outperforms full-parameter tuning on a performance-per-resource basis; (2) simple gradient norms provide computationally efficient proxies for identifying these high-influence components; and (3) coordinated parameter and data selection yields multiplicative efficiency gains, potentially reducing resource requirements by orders of magnitude. Building on these theoretical foundations, we propose a two-stage paradigm--marginalreturn pretraining for foundation developers and influence-guided adaptation for downstream users--bridged by gradient blueprints, metadata describing which parameters matter most for various tasks. This capability-per-resource perspective transforms what were once considered pragmatic hardware workarounds into theoretically optimal strategies, democratizing access to cutting-edge AI capabilities while significantly reducing environmental impact. By embedding resource consciousness into how we develop, adapt, and evaluate models, we can reshape AI progress toward a more sustainable and equitable future.

The constant πhas fascinated scholars throughout the centuries, inspiring numerous formulas for its evaluation, such as infinite sums and continued fractions. Despite their individual significance, many of the underlying connections among formulas remain unknown, missing unifying theories that could unveil deeper understanding. The absence of a unifying theory reflects a broader challenge across math and science: knowledge is typically accumulated through isolated discoveries, while deeper connections often remain hidden. In this work, we present an automated framework for the unification of mathematical formulas. Our system combines large language models (LLMs) for systematic formula harvesting, an LLM-code feedback loop for validation, and a novel symbolic algorithm for clustering and eventual unification. We demonstrate this methodology on the hallmark case of π, an ideal testing ground for symbolic unification. Applying this approach to 455,050 arXiv papers, we validate 385 distinct formulas for π and prove relations between 360 (94%) of them, of which 166 (43%) can be derived from a single mathematical object--linking canonical formulas by Euler, Gauss, Brouncker, and newer ones from algorithmic discoveries by the Ramanujan Machine. Our method generalizes to other constants, including e, ζ(3), and Catalan's constant, demonstrating the potential of AI-assisted mathematics to uncover hidden structures and unify knowledge across domains.

The recent success of generative AI highlights the crucial role of high-quality human feedback in building trustworthy AI systems. However, the increasing use of large language models (LLMs) by crowdsourcing workers poses a significant challenge: datasets intended to reflect human input may be compromised by LLM-generated responses. Existing LLM detection approaches often rely on high-dimensional training data such as text, making them unsuitable for structured annotation tasks like multiple-choice labeling. In this work, we investigate the potential of peer prediction--a mechanism that evaluates the information within workers' responses--to mitigate LLM-assisted cheating in crowdsourcing with a focus on annotation tasks.

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of observed entries; they may fail under overparametrization, when their assumed rank is higher than the correct one; and many of them fail to recover even mildly ill-conditioned matrices. In this paper we propose a novel RMC method, denoted RGNMR, which overcomes these limitations. RGNMRis a simple factorization-based iterative algorithm, which combines a Gauss-Newton linearization with removal of entries suspected to be outliers. On the theoretical front, we prove that under suitable assumptions, RGNMR is guaranteed exact recovery of the underlying low rank matrix. Our theoretical results improve upon the best currently known for factorization-based methods. On the empirical front, we show via several simulations the advantages of RGNMR over existing RMC methods, and in particular its ability to handle a small number of observed entries, overparameterization of the rank and ill-conditioned matrices. In addition, we propose a novel scheme for estimating the number of corrupted entries. This scheme may be used by other RMC methods that require as input the number of corrupted entries.

We study a two-institution stable matching model in which candidates from two distinct groups are evaluated using partially correlated signals that are groupbiased. This extends prior work (which assumes institutions evaluate candidates in an identical manner) to a more realistic setting in which institutions rely on overlapping, but independently processed, criteria. These evaluations could consist of a variety of informative tools such as standardized tests, shared recommendation systems, or AI-based assessments with local noise. Two key parameters govern evaluations: the bias parameter β (0,1], which models systematic disadvantage faced by one group, and the correlation parameter γ [0,1], which captures the alignment between institutional rankings. We study the representation ratio R(β,γ), i.e., the ratio of disadvantaged to advantaged candidates selected by the matching process in this setting.

The rapid growth of data-driven technologies and the emergence of various datasharing paradigms have underscored the need for efficient and stable data exchange protocols. In any such exchange, agents must carefully balance the benefit of acquiring valuable data against the cost of sharing their own. Ensuring stability in these exchanges is essential to prevent agents--or groups of agents--from departing and conducting local (and potentially more favorable) exchanges among themselves. To address this, we study a model where n agents participate in a data exchange. Each agent has an associated payoff for the data acquired from other agents and a cost incurred during sharing its own data.