We prove the universal approximation theorem by showing the equivalence of TFN and our model. Complex spherical harmonics are related to Clebsch-Gordan coefficients via [51, 3.7.72] We can therefore adapt Eq. (2) by substituting C To see this, we look at the result's real component null [ H To prove this theorem we first introduce a proposition by Villar et al. [57]. GemNet's variance varies strongly between layers and increases significantly after each block without scaling factors (top). We use 4 stacked interaction blocks and an embedding size of 128 throughout the model.

A.3 Formulation of bound constrained dual problem Proposition 1 . For any non-negative p, q, we generate a feasible p ˆ, ˆ q as follows. In Section 5.3, we describe that it can be helpful to regularize We also mention here a minor difference in derivations for convenience of readers. As expected, this term also appears in these other formulations [ 25, 42 ]. All experiments run on a single P100 GPU. This adjustment was not necessary for CNN experiments.

The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing, respectively.

To enable robots to develop human-like fine manipulation, it is essential to understand how mechanical compliance, multi-modal sensing, and purposeful interaction jointly shape tactile perception. In this study, we use a dedicated modular e-Skin with tunable mechanical compliance and multi-modal sensing (normal, shear forces and vibrations) to systematically investigate how sensing embodiment and interaction strategies influence robotic perception of objects. Leveraging a curated set of soft wave objects with controlled viscoelastic and surface properties, we explore a rich set of palpation primitives-pressing, precession, sliding that vary indentation depth, frequency, and directionality. In addition, we propose the latent filter, an unsupervised, action-conditioned deep state-space model of the sophisticated interaction dynamics and infer causal mechanical properties into a structured latent space. This provides generalizable and in-depth interpretable representation of how embodiment and interaction determine and influence perception. Our investigation demonstrates that multi-modal sensing outperforms uni-modal sensing. It highlights a nuanced interaction between the environment and mechanical properties of e-Skin, which should be examined alongside the interaction by incorporating temporal dynamics.

Teleoperation of beyond-human-scale robotic manipulators (BHSRMs) presents unique challenges that differ fundamentally from conventional human-scale systems. As these platforms gain relevance in industrial domains such as construction, mining, and disaster response, immersive interfaces must be rethought to support scalable, safe, and effective human-robot collaboration. This paper investigates the control, cognitive, and interface-level challenges of immersive teleoperation in BHSRMs, with a focus on ensuring operator safety, minimizing sensorimotor mismatch, and enhancing the sense of embodiment. We analyze design trade-offs in haptic and visual feedback systems, supported by early experimental comparisons of exoskeleton- and joystick-based control setups. Finally, we outline key research directions for developing new evaluation tools, scaling strategies, and human-centered safety models tailored to large-scale robotic telepresence.

Despite the significant advancements in Large Language Models (LLMs), catastrophic forgetting remains a substantial challenge, where models lose previously acquired knowledge upon learning new information. Continual learning (CL) strategies have emerged as a potential solution to this problem, with replay-based techniques demonstrating superior performance in preserving learned knowledge. In this context, we introduce Gauss-Tin, a novel approach that integrates the replay strategy with a Gaussian mixture model to enhance the quality of sample selection during training, supplemented by instructional guidance to facilitate the generation of past learning. This method aims to improve LLMs' retention capabilities by strategically reinforcing important past learnings while accommodating new information. Our experimental results indicate a promising 6\% improvement in retention metrics over traditional methods, suggesting that Gauss-Tin is an effective strategy for mitigating catastrophic forgetting in LLMs. This study underscores the potential of hybrid models in enhancing the robustness and adaptability of LLMs in dynamic learning environments.

One of the key challenges to predict odor from molecular structure is unarguably our limited understanding of the odor space and the complexity of the underlying structure-odor relationships. Here, we show that the predictive performance of machine learning models for structure-based odor predictions can be improved using both, an expert and a data-driven odor taxonomy. The expert taxonomy is based on semantic and perceptual similarities, while the data-driven taxonomy is based on clustering co-occurrence patterns of odor descriptors directly from the prepared dataset. Both taxonomies improve the predictions of different machine learning models and outperform random groupings of descriptors that do not reflect existing relations between odor descriptors. We assess the quality of both taxonomies through their predictive performance across different odor classes and perform an in-depth error analysis highlighting the complexity of odor-structure relationships and identifying potential inconsistencies within the taxonomies by showcasing pear odorants used in perfumery. The data-driven taxonomy allows us to critically evaluate our expert taxonomy and better understand the molecular odor space. Both taxonomies as well as a full dataset are made available to the community, providing a stepping stone for a future community-driven exploration of the molecular basis of smell. In addition, we provide a detailed multi-layer expert taxonomy including a total of 777 different descriptors from the Pyrfume repository.

The GLUE benchmark consists of 8 (originally 9) tasks [Wang et al., 2018]. Hypothesis: "It has a buffet." CoLA (Corpus of Linguistic Acceptability) [8,551 train, 1,063 test] [Warstadt et al., 2019] is a "The higher the stakes, the lower his expectations are." The task is to classify the sentiment as either positive or negative [Socher et al., 2013]. Note that we excluded finetuning on the 9th GLUE task WNLI (Winograd NLI) [Levesque et al., We used the hyperparameters in Table S1 for finetuning all BERT and RapidBERT models.