Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d.

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at the finest relevant scales, leading to a high-dimensional state space. In this work, we propose an approach to learn stochastic multiscale models in the form of stochastic differential equations directly from observational data. Drawing inspiration from physics-based multiscale modeling approaches, we resolve the macroscale state on a coarse mesh while introducing a microscale latent state to explicitly model unresolved dynamics. We learn the parameters of the multiscale model using a simulator-free amortized variational inference method with a Product of Experts likelihood that enforces scale separation. We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to under-resolved direct numerical simulation and closure-type models at equivalent resolution, as well as reduced-order modeling approaches.

Algorithmic fairness has emerged as a central issue in ML, and it has become standard practice to adjust ML algorithms so that they will satisfy fairness requirements such as Equal Opportunity. In this paper we consider the effects of adopting such fair classifiers on the overall level of ecosystem fairness. Specifically, we introduce the study of fairness with competing firms, and demonstrate the failure of fair classifiers in yielding fair ecosystems. Our results quantify the loss of fairness in systems, under a variety of conditions, based on classifiers' correlation and the level of their data overlap. We show that even if competing classifiers are individually fair, the ecosystem's outcome may be unfair; and that adjusting biased algorithms to improve their individual fairness may lead to an overall decline in ecosystem fairness. In addition to these theoretical results, we also provide supporting experimental evidence. Together, our model and results provide a novel and essential call for action.

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence--a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems.

AI-driven discovery can greatly reduce design time and enhance new therapeutics' effectiveness. Models using simulators explore broad design spaces but risk violating implicit constraints due to a lack of experimental priors. For example, in a new analysis across diverse models on the GuacaMol benchmark using supervised classifiers, over 60% of molecules proposed had a high probability of being mutagenic. In this work, we introduce Medex, a dataset of priors for design problems extracted from literature describing compounds used in lab settings. It is constructed with LLM pipelines for discovering therapeutic entities in relevant paragraphs and summarizing information in concise fair-use facts. Medex consists of 32.3 million pairs of natural language facts, and appropriate entity representations (i.e.

Deepfake detection models face two critical challenges: generalization to unseen manipulations and demographic fairness among population groups. However, existing approaches often demonstrate that these two objectives are inherently conflicting, revealing a trade-off between them. In this paper, we, for the first time, uncover and formally define a causal relationship between fairness and generalization. Building on the back-door adjustment, we show that controlling for confounders (data distribution and model capacity) enables improved generalization via fairness interventions. Motivated by this insight, we propose Demographic Attribute-insensitive Intervention Detection (DAID), a plug-and-play framework composed of: i) Demographic-aware data rebalancing, which employs inversepropensity weighting and subgroup-wise feature normalization to neutralize distributional biases; and ii) Demographic-agnostic feature aggregation, which uses a novel alignment loss to suppress sensitive-attribute signals. Across three crossdomain benchmarks, DAID consistently achieves superior performance in both fairness and generalization compared to several state-of-the-art detectors, validating both its theoretical foundation and practical effectiveness.

One main challenge in time series anomaly detection for industrial IoT lies in the complex spatio-temporal couplings within multivariate data. However, traditional anomaly detection methods focus on modeling spatial or temporal dependencies independently, resulting in suboptimal representation learning and limited sensitivity to anomalous dispersion in high-dimensional spaces. In this work, we conduct an empirical analysis showing that both normal and anomalous samples tend to scatter in high-dimensional space, especially anomalous samples are markedly more dispersed. We formalize this dispersion phenomenon as scattering, quantified by the mean pairwise distance among sample representations, and leverage it as an inductive signal to enhance spatio-temporal anomaly detection. Technically, we propose ScatterAD to model representation scattering across temporal and topological dimensions. ScatterAD incorporates a topological encoder for capturing graph-structured scattering and a temporal encoder for constraining overscattering through mean squared error minimization between neighboring time steps. We introduce a contrastive fusion mechanism to ensure the complementarity of the learned temporal and topological representations. Additionally, we theoretically show that maximizing the conditional mutual information between temporal and topological views improves cross-view consistency and enhances more discriminative representations. Extensive experiments on multiple public benchmarks show that ScatterAD achieves state-of-the-art performance on multivariate time series anomaly detection.

Connectomics--the mapping of neural connections in an organism's brain--currently requires extraordinary human effort to proofread the data collected from imaging and machine-learning assisted segmentation. With the growing excitement around using AI agents to automate important scientific tasks, we explore whether current AI systems can perform multiple tasks necessary for data proofreading. We introduce ConnectomeBench, a multimodal benchmark evaluating large language model (LLM) capabilities in three critical proofreading tasks: segment type identification, split error correction, and merge error detection. Using expert annotated data from two large open-source datasets--a cubic millimeter of mouse visual cortex and the complete Drosophila brain--we evaluate proprietary multimodal LLMs including Claude 3.7/4 Sonnet, o4-mini, GPT-4.1,

PU (Positive Unlabeled) learning is a variant of supervised classification learning in which the only labels revealed to the learner are of positively labeled instances. PU learning arises in many real-world applications. Most existing work relies on the simplifying assumptions that the positively labeled training data is drawn from the restriction of the data generating distribution to positively labeled instances and/or that the proportion of positively labeled points (a.k.a. the class prior) is known apriori to the learner. This paper provides a theoretical analysis of the statistical complexity of PU learning under a wider range of setups. Unlike most prior work, our study does not assume that the class prior is known to the learner. We prove upper and lower bounds on the required sample sizes (of both the positively labeled and the unlabeled samples).

Autoregressive (AR) models, common in sequence generation, are limited in many biological tasks like de novo peptide sequencing and protein modeling by their unidirectional nature, failing to capture crucial global bidirectional token dependencies. Non-Autoregressive (NAR) models offer holistic, bidirectional representations but face challenges with generative coherence and scalability. To transcend this, we propose a hybrid framework enhancing AR generation by dynamically integrating rich contextual information from non-autoregressive mechanisms. Our approach couples a shared input encoder with two decoders: a non-autoregressive one learning latent bidirectional biological features, and an AR decoder synthesizing the biological sequence by leveraging these bi-directional features. A novel cross-decoder attention module enables the AR decoder to iteratively query and integrate these bidirectional features, enriching its predictions. This synergy is cultivated via a tailored training strategy with importance annealing for balanced objectives and cross-decoder gradient blocking for stable, focused learning.