Membership in Ris already proven by Abrahamsen, Kleist and Miltzow in [3]. Thealgorithm then needs to verify that the neural network described byΘ fits all data points inD with a total error at mostγ. The goal of this appendix is to build a geometric understanding off(,Θ). We point the interested reader to these articles [6, 26, 49, 66, 92] investigating the set of functions exactly represented by different architecturesofReLUnetworks. To see that this observation is true, consider the following construction.

Right: measurement overthefirst60epochs. Update step adaptation (see Section 4.3)isapplied.

The discovery of next-generation photoinitiators for two-photon polymerization (TPP) is hindered by the absence of large, open datasets containing the quantum-chemical and photophysical properties required to model photodissociation and excited-state behavior. Existing molecular datasets typically provide only basic physicochemical descriptors and therefore cannot support data-driven screening or AI-assisted design of photoinitiators. To address this gap, we introduce QuantumChem-200K, a large-scale dataset of over 200,000 organic molecules annotated with eleven quantum-chemical properties, including two-photon absorption (TPA) cross sections, TPA spectral ranges, singlet-triplet intersystem crossing (ISC) energies, toxicity and synthetic accessibility scores, hydrophilicity, solubility, boiling point, molecular weight, and aromaticity. These values are computed using a hybrid workflow that integrates density function theory (DFT), semi-empirical excited-state methods, atomistic quantum solvers, and neural-network predictors. Using QuantumChem-200K, we fine tune the open-source Qwen2.5-32B large language model to create a chemistry AI assistant capable of forward property prediction from SMILES. Benchmarking on 3000 unseen molecules from VQM24 and ZINC20 demonstrates that domain-specific fine-tuning significantly improves accuracy over GPT-4o, Llama-3.1-70B, and the base Qwen2.5-32B model, particularly for TPA and ISC predictions central to photoinitiator design. QuantumChem-200K and the corresponding AI assistant together provide the first scalable platform for high-throughput, LLM-driven photoinitiator screening and accelerated discovery of photosensitive materials.

We present an updated deep neural network model for inclusive electron-carbon scattering. Using the bootstrap model [Phys.Rev.C 110 (2024) 2, 025501] as a prior, we incorporate recent experimental data, as well as older measurements in the deep inelastic scattering region, to derive a re-optimized posterior model. We examine the impact of these new inputs on model predictions and associated uncertainties. Finally, we evaluate the resulting cross-section predictions in the kinematic range relevant to the Hyper-Kamiokande and DUNE experiments.

Hu et al. [1] suggested using uncrewed vehicles in civil infrastructure asset management. Similarly, Bechtsis et al. [2] propose using uncrewed ground vehicles (UGVs) in precision farming. One of the emerging areas where such vehicles can prove helpful is assisting in postdisaster evacuation. Natural disasters, including earthquakes, tsunamis, hurricanes, and volcanic eruptions, can severely damage the urban infrastructure, leading to considerable losses. Following such events, providing timely relief and disseminating crucial information, such as safe evacuation routes, becomes essential for affected individuals' safe and organized movement. Recently, among the advanced technologies integrated into disaster response missions include uncrewed aerial vehicles (UAVs) that have been crucial in assessing the state of critical infrastructure essential services, including telecommunications, transportation, and buildings, to facilitate efficient disaster response and evacuation [3]. UAV systems have proven to be increasingly valuable in disaster relief and emergency response (DRER) efforts by enhancing the capabilities of the first responders, offering advanced predictive insights, and enabling early warning systems [4]. UAVs have assisted in diverse tasks, including remote sensing, search and rescue, forest fire detection, survey and surveillance [5].

We provide an accessible description of a peer-reviewed generalizable causal machine learning pipeline to (i) discover latent causal sources of large-scale electronic health records observations, and (ii) quantify the source causal effects on clinical outcomes. We illustrate how imperfect multimodal clinical data can be processed, decomposed into probabilistic independent latent sources, and used to train taskspecific causal models from which individual causal effects can be estimated. We summarize the findings of the two real-world applications of the approach to date as a demonstration of its versatility and utility for medical discovery at scale.

F or each line ℓ L the change of the gradient of f when crossing ℓ is constant along ℓ. Then there is a fully connected two-layer neural network with m hidden neurons computing f . To see that this observation is true, consider the following construction. Describing all gadgets purely by their data points is tedious and obscures the relatively simple geometry enforced by these data points. A weak data point relaxes a regular data point and prescribes only a lower bound on the value of the label.

Planning collision free trajectories in complex environments remains a core challenge in robotics. Existing corridor based planners which rely on decomposition of the free space into collision free subsets scale poorly with environmental complexity and require explicit allocations of time windows to trajectory segments. We introduce a new trajectory parameterization that represents trajectories in a nonconvex collision free corridor as being in a convex cartesian product of balls. This parameterization allows us to decouple problem size from geometric complexity of the solution and naturally avoids explicit time allocation by allowing trajectories to evolve continuously inside ellipsoidal corridors. Building on this representation, we formulate the Orthogonal Trust Region Problem (Orth-TRP), a specialized convex program with separable block constraints, and develop a solver that exploits this parallel structure and the unique structure of each parallel subproblem for efficient optimization. Experiments on a quadrotor trajectory planning benchmark show that our approach produces smoother trajectories and lower runtimes than state-of-the-art corridor based planners, especially in highly complicated environments.

We investigate a WIMP dark matter (DM) candidate in the form of a singlino-dominated lightest supersymmetric particle (LSP) within the $Z_3$-symmetric Next-to-Minimal Supersymmetric Standard Model. This framework gives rise to regions of parameter space where DM is obtained via co-annihilation with nearby higgsino-like electroweakinos and DM direct detection~signals are suppressed, the so-called ``blind spots". On the other hand, collider signatures remain promising due to enhanced radiative decay modes of higgsinos into the singlino-dominated LSP and a photon, rather than into leptons or hadrons. This motivates searches for radiatively decaying neutralinos, however, these signals face substantial background challenges, as the decay products are typically soft due to the small mass-splits ($Δm$) between the LSP and the higgsino-like coannihilation partners. We apply a data-driven Machine Learning (ML) analysis that improves sensitivity to these subtle signals, offering a powerful complement to traditional search strategies to discover a new physics scenario. Using an LHC integrated luminosity of $100~\mathrm{fb}^{-1}$ at $14~\mathrm{TeV}$, the method achieves a $5σ$ discovery reach for higgsino masses up to $225~\mathrm{GeV}$ with $Δm\!\lesssim\!12~\mathrm{GeV}$, and a $2σ$ exclusion up to $285~\mathrm{GeV}$ with $Δm\!\lesssim\!20~\mathrm{GeV}$. These results highlight the power of collider searches to probe DM candidates that remain hidden from current direct detection experiments, and provide a motivation for a search by the LHC collaborations using ML methods.