Benjamin Franklin and other citizen scientists are core parts of the American experiment. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Benjamin Franklin's kite experiment in 1752 was a pivotal scientific event, which demonstrated the connection between lightning and electricity. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

Scientific discovery via symbolic regression is often viewed as statistically and computationally intractable because the hypothesis space of expressions grows combinatorially with depth. This paper revisits the statistical side through the lens of PAC learning, focusing on compositional function trees built from a finite vocabulary of smooth operators (e.g., $\{+,\times,\sin,\exp\}$ and affine maps). We prove that the relevant generalization quantity, Rademacher complexity, hence the excess risk, does not necessarily blow up exponentially with the number of distinct symbolic structures, but is controlled by (i) the depth $d$ and (ii) the Lipschitz constants of the base operators along the composed computation graph. Concretely, under mild Lipschitz conditions on operators and bounded affine leaves, a finite-union bound over a vocabulary of size $K=|\mathcal{H}_{\mathrm{base}}|$ together with Maurer-type vector contraction yields $\mathfrak{R}_n(\mathcal{H}_{\mathrm{comp}}^{d}) \leq (Kb\sqrt{2}L)^{d-1}\mathfrak{R}_n(\mathcal{H}_{\mathrm{comp}}^{1})$ with arity bound $b$; corresponding high-probability risk bounds scale as $\mathcal{O}(L^{d}/\sqrt{n})$ when $K,b=O(1)$ and $\mathfrak{R}_n(\mathcal{H}_{\mathrm{comp}}^{1})=O(n^{-1/2})$. We complement the theory with a modular codebase that trains differentiable operator trees (not MLPs) on synthetic "physics-like" targets of controlled depth and shows that the empirical generalization gap correlates positively with the predicted complexity term $(\widehat{L}^{d})/\sqrt{n}$.

Why are airplanes so cold? From combating fainting to helping aircraft work efficiently, planes are chilly for a reason. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

We examine hypothesis testing within a principal-agent framework, where a strategic agent, holding private beliefs about the effectiveness of a product, submits data to a principal who decides on approval. The principal employs a hypothesis testing rule, aiming to pick a p-value threshold that balances false positives and false negatives while anticipating the agent's incentive to maximize expected profitability. Building on prior work, we develop a game-theoretic model that captures how the agent's participation and reporting behavior respond to the principal's statistical decision rule. Despite the complexity of the interaction, we show that the principal's errors exhibit clear monotonic behavior when segmented by an efficiently computable critical p-value threshold, leading to an interpretable characterization of their optimal p-value threshold.

AI has the potential to transform scientific discovery by analyzing vast datasets with little human effort. However, current workflows often do not provide the accuracy or statistical guarantees that are needed. We introduce active measurement, a human-in-the-loop AI framework for scientific measurement. An AI model is used to predict measurements for individual units, which are then sampled for human labeling using importance sampling. With each new set of human labels, the AI model is improved and an unbiased Monte Carlo estimate of the total measurement is refined. Active measurement can provide precise estimates even with an imperfect AI model, and requires little human effort when the AI model is very accurate. We derive novel estimators, weighting schemes, and confidence intervals, and show that active measurement reduces estimation error compared to alternatives in several measurement tasks.

Scientific discovery across diverse fields increasingly grapples with datasets exhibiting pathological long-tailed distributions: a few common phenomena overshadow a multitude of rare yet scientifically critical instances. Unlike standard benchmarks, these scientific datasets often feature extreme imbalance coupled with a modest number of classes and limited overall sample volume, rendering existing long-tailed recognition (LTR) techniques ineffective. Such methods, biased by majority classes or prone to overfitting on scarce tail data, frequently fail to identify the very instances--novel materials, rare disease biomarkers, faint astronomical signals--that drive scientific breakthroughs. This paper introduces a novel, end-to-end framework explicitly designed to address pathological long-tailed recognition in scientific contexts. Our approach synergizes a Balanced Supervised Contrastive Learning (BSCL) mechanism, which enhances the representation of tail classes by dynamically re-weighting their contributions, with a Smooth Objective Regularization (SOR) strategy that manages the inherent tension between tail-class focus and overall classification performance. We introduce and analyze the real-world ZincFluor chemical dataset (T = 137.54)

Novelty detection in large scientific datasets faces two key challenges: the noisy and high-dimensional nature of experimental data, and the necessity of making statistically robust statements about any observed outliers. While there is a wealth of literature on anomaly detection via dimensionality reduction, most methods do not produce outputs compatible with quantifiable claims of scientific discovery. In this work we directly address these challenges, presenting the first step towards a unified pipeline for novelty detection adapted for the rigorous statistical demands of science. We introduce AutoSciDACT (Automated Scientific Discovery with Anomalous Contrastive Testing), a general-purpose pipeline for detecting novelty in scientific data. AutoSciDACT begins by creating expressive low-dimensional data representations using a contrastive pre-training, leveraging the abundance of highquality simulated data in many scientific domains alongside expertise that can guide principled data augmentation strategies. These compact embeddings then enable an extremely sensitive machine learning-based two-sample test using the New Physics Learning Machine (NPLM) framework, which identifies and statistically quantifies deviations in observed data relative to a reference distribution (null hypothesis). We perform experiments across a range of astronomical, physical, biological, image, and synthetic datasets, demonstrating strong sensitivity to small injections of anomalous data across all domains.

We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce FERMAT, a reinforcement learning (RL) environment that models concept discovery and theorem-proving using a set of symbolic actions, opening up a range of RL problems relevant to theory discovery. Second, we explore a specific problem through FERMAT: automatically scoring the interestingness of mathematical objects. We investigate evolutionary algorithms for synthesizing nontrivial interestingness measures. In particular, we introduce an LLM-based evolutionary algorithm that features function abstraction, leading to notable improvements in discovering elementary number theory and finite fields over hard-coded baselines.

Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate both when each hypothesis is evidenced only by a finite count of null draws, leaving its p-value uncertain, and when the hypothesis space carries arbitrary structure, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules that are both robust to structural mis-specification, yet offer a distinct trade-off between exact FDR control and statistical power. The first rule guarantees exact FDR control; the second maximizes power by adapting mirror-statistic control into count space, utilizing an analytical framework to assess FDR control when exact mirror symmetry is relaxed. Furthermore, the tractability gained by the RKHS framework allows us to directly investigate finite-data uncertainties, which we leverage to suggest a policy for the efficient allocation of null distribution samples.

Open-World Object Detection (OWOD) enriches traditional object detectors by enabling continual discovery and integration of unknown objects via human guidance. However, existing OWOD approaches frequently suffer from semantic confusion between known and unknown classes, alongside catastrophic forgetting, leading to diminished unknown recall and degraded known-class accuracy. To overcome these challenges, we propose Combinatorial Open-World Detection (CROWD2), a unified framework reformulating unknown object discovery and adaptation as an interwoven combinatorial (set-based) data-discovery (CROWD-Discover) and representation learning (CROWD-Learn) task. CROWD-Discover strategically mines unknown instances by maximizing Submodular Conditional Gain (SCG) functions, selecting representative examples distinctly dissimilar from known objects. Subsequently, CROWD-Learn employs novel combinatorial objectives that jointly disentangle known and unknown representations while maintaining discriminative coherence among known classes, thus mitigating confusion and forgetting. Extensive evaluations on OWOD benchmarks illustrate that CROWD achieves improvements of 2.83% and 2.05% in known-class accuracy on M-OWODB and S-OWODB, respectively, and nearly 2.4 unknown recall compared to leading baselines. Figure 1: Overall Architecture of CROWD showing our novel combinatorial data-discovery guided representation learning approach to (a) identify unknown objects3 and (b) learn distinguishable representations of both known and unknown objects.