They map random samples (seeds) from a high-dimensional space, conditioned on a user-provided text prompt, to a corresponding image.

For a small training set, CNNs behave similarly.

It can be shown that Stable Diffusion has a permutation-invariance property with respect to the rows of Contrastive Language-Image Pretraining (CLIP) embedding matrices. This inspired the novel observation that these embeddings can naturally be interpreted as point clouds in a Wasserstein space rather than as matrices in a Euclidean space. This perspective opens up new possibilities for understanding the geometry of embedding space. For example, when interpolating between embeddings of two distinct prompts, we propose reframing the interpolation problem as an optimal transport problem. By solving this optimal transport problem, we compute a shortest path (or geodesic) between embeddings that captures a more natural and geometrically smooth transition through the embedding space. This results in smoother and more coherent intermediate (interpolated) images when rendered by the Stable Diffusion generative model. We conduct experiments to investigate this effect, comparing the quality of interpolated images produced using optimal transport to those generated by other standard interpolation methods. The novel optimal transport--based approach presented indeed gives smoother image interpolations, suggesting that viewing the embeddings as point clouds (rather than as matrices) better reflects and leverages the geometry of the embedding space.

Abstract-- Accurate robot kinematics is essential for precise tool placement in articulated robots, but non-geometric factors can introduce configuration-dependent model discrepancies. This paper presents a configuration-dependent kinematic calibration framework for improving accuracy across the entire workspace. Local Product-of-Exponential (POE) models, selected for their parameterization continuity, are identified at multiple configurations and interpolated into a global model. Inspired by joint gravity load expressions, we employ Fourier basis function interpolation parameterized by the shoulder and elbow joint angles, achieving accuracy comparable to neural network and autoencoder methods but with substantially higher training efficiency. V alidation on two 6-DoF industrial robots shows that the proposed approach reduces the maximum positioning error by over 50%, meeting the sub-millimeter accuracy required for cold spray manufacturing. Robots with larger configuration-dependent discrepancies benefit even more. A dual-robot collaborative task demonstrates the framework's practical applicability and repeatability.

They map random samples (seeds) from a high-dimensional space, conditioned on a user-provided text prompt, to a corresponding image.

Spatial interpolation is a crucial task in geography. As perhaps the most widely used interpolation methods, geostatistical models -- such as Ordinary Kriging (OK) -- assume spatial stationarity, which makes it difficult to capture the nonstationary characteristics of geographic variables. A common solution is trend surface modeling (e.g., Regression Kriging, RK), which relies on external explanatory variables to model the trend and then applies geostatistical interpolation to the residuals. However, this approach requires high-quality and readily available explanatory variables, which are often lacking in many spatial interpolation scenarios -- such as estimating heavy metal concentrations underground. This study proposes a Feature-Free Regression Kriging (FFRK) method, which automatically extracts geospatial features -- including local dependence, local heterogeneity, and geosimilarity -- to construct a regression-based trend surface without requiring external explanatory variables. We conducted experiments on the spatial distribution prediction of three heavy metals in a mining area in Australia. In comparison with 17 classical interpolation methods, the results indicate that FFRK, which does not incorporate any explanatory variables and relies solely on extracted geospatial features, consistently outperforms both conventional Kriging techniques and machine learning models that depend on explanatory variables. This approach effectively addresses spatial nonstationarity while reducing the cost of acquiring explanatory variables, improving both prediction accuracy and generalization ability. This finding suggests that an accurate characterization of geospatial features based on domain knowledge can significantly enhance spatial prediction performance -- potentially yielding greater improvements than merely adopting more advanced statistical models.

Identifying minimum-energy paths (MEPs) is crucial for understanding chemical reaction mechanisms but remains computationally demanding. We introduce MEPIN, a scalable machine-learning method for efficiently predicting MEPs from reactant and product configurations, without relying on transition-state geometries or pre-optimized reaction paths during training. The task is defined as predicting deviations from geometric interpolations along reaction coordinates. We address this task with a continuous reaction path model based on a symmetry-broken equivariant neural network that generates a flexible number of intermediate structures. The model is trained using an energy-based objective, with efficiency enhanced by incorporating geometric priors from geodesic interpolation as initial interpolations or pre-training objectives. Our approach generalizes across diverse chemical reactions and achieves accurate alignment with reference intrinsic reaction coordinates, as demonstrated on various small molecule reactions and [3+2] cycloadditions. Our method enables the exploration of large chemical reaction spaces with efficient, data-driven predictions of reaction pathways.

In the realm of online advertising, optimizing conversions is crucial for delivering relevant products to users and enhancing business outcomes. Predicting conversion events is challenging due to variable delays between user interactions, such as impressions or clicks, and the actual conversions. These delays differ significantly across various advertisers and products, necessitating distinct optimization time windows for targeted conversions. To address this, we introduce a novel approach named the \textit{Personalized Interpolation} method, which innovatively builds upon existing fixed conversion window models to estimate flexible conversion windows. This method allows for the accurate estimation of conversions across a variety of delay ranges, thus meeting the diverse needs of advertisers without increasing system complexity. To validate the efficacy of our proposed method, we conducted comprehensive experiments using ads conversion model. Our experiments demonstrate that this method not only achieves high prediction accuracy but also does so more efficiently than other existing solutions. This validation underscores the potential of our Personalized Interpolation method to significantly enhance conversion optimization in real-world online advertising systems, promising improved targeting and effectiveness in advertising strategies.

Data augmentation is a crucial step in the development of robust supervised learning models, especially when dealing with limited datasets. This study explores interpolation techniques for the augmentation of geo-referenced data, with the aim of predicting the presence of Commelina benghalensis L. in sugarcane plots in La R{\'e}union. Given the spatial nature of the data and the high cost of data collection, we evaluated two interpolation approaches: Gaussian processes (GPs) with different kernels and kriging with various variograms. The objectives of this work are threefold: (i) to identify which interpolation methods offer the best predictive performance for various regression algorithms, (ii) to analyze the evolution of performance as a function of the number of observations added, and (iii) to assess the spatial consistency of augmented datasets. The results show that GP-based methods, in particular with combined kernels (GP-COMB), significantly improve the performance of regression algorithms while requiring less additional data. Although kriging shows slightly lower performance, it is distinguished by a more homogeneous spatial coverage, a potential advantage in certain contexts.