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At least 91 records · Page 5

Genetic learning in rule-based and neural systems

The design of neural networks and fuzzy systems can involve complex, nonlinear, and ill-conditioned optimization problems. Often, traditional optimization schemes are inadequate or inapplicable for such tasks. Genetic Algorithms (GA's) are a class of optimization procedures whose mechanics are based on those of natural genetics. Mathematical arguments show how GAs bring substantial computational leverage to search problems, without requiring the mathematical characteristics often necessary for traditional optimization schemes (e.g., modality, continuity, availability of derivative information, etc.). GA's have proven effective in a variety of search tasks that arise in neural networks and fuzzy systems. This presentation begins by introducing the mechanism and theoretical underpinnings of GA's. GA's are then related to a class of rule-based machine learning systems called learning classifier systems (LCS's). An LCS implements a low-level production-system that uses a GA as its primary rule discovery mechanism. This presentation illustrates how, despite its rule-based framework, an LCS can be thought of as a competitive neural network. Neural network simulator code for an LCS is presented. In this context, the GA is doing more than optimizing and objective function. It is searching for an ecology of hidden nodes with limited connectivity. The GA attempts to evolve this ecology such that effective neural network performance results. The GA is particularly well adapted to this task, given its naturally-inspired basis. The LCS/neural network analogy extends itself to other, more traditional neural networks. Conclusions to the presentation discuss the implications of using GA's in ecological search problems that arise in neural and fuzzy systems.

Smith, Robert E.↗

Competitive and cooperative electronic states in Ba(Fe1−xTx)2As2 with T = Co, Ni, Cr

Abstract The electronic inhomogeneities in Co, Ni, and Cr doped BaFe 2 As 2 single crystals are compared within three bulk property regions: a pure superconducting (SC) dome region, a coexisting SC and antiferromagnetic (AFM) region, and a non-SC region. Machine learning is utilized to categorize the inhomogeneous electronic states: in-gap, L-shape, and S-shape states. Although the relative percentages of the states vary in the three samples, the total volume fraction of the three electronic states is quite similar. This is coincident with the number of electrons (Ni 0.04 and Co 0.08 ) and holes (Cr 0.04 ) doped into the compounds. The in-gap state is confirmed as a magnetic impurity state from the Co or Ni dopants, the L-shape state is identified as a spin density wave which competes with the SC phase, and the S-shape state is found to be another form of magnetic order which constructively cooperates with the SC phase, rather than competing with it.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Online peak-aware energy scheduling with untrusted advice

This paper studies the online energy scheduling problem in a hybrid model where the cost of energy is proportional to both the volume and peak usage, and where energy can be either locally generated or drawn from the grid. Inspired by recent advances in online algorithms with Machine Learned (ML) advice, we develop parameterized deterministic and randomized algorithms for this problem such that the level of reliance on the advice can be adjusted by a trust parameter. We then analyze the performance of the proposed algorithms using two performance metrics: robustness that measures the competitive ratio as a function of the trust parameter when the advice is inaccurate, and consistency for competitive ratio when the advice is accurate. Since the competitive ratio is analyzed in two different regimes, we further investigate the Pareto optimality of the proposed algorithms. Our results show that the proposed deterministic algorithm is Pareto-optimal, in the sense that no other online deterministic algorithms can dominate the robustness and consistency of our algorithm. Furthermore, we show that the proposed randomized algorithm dominates the Pareto-optimal deterministic algorithm. Our large-scale empirical evaluations using real traces of energy demand, energy prices, and renewable energy generations highlight that the proposed algorithms outperform worst-case optimized algorithms and fully data-driven algorithms.

Lee, Russell↗

5G integrated edge computing platform for efficient component monitoring in coal-fired power plants

This project developed a cutting-edge 5G-integrated edge computing framework to enhance operational efficiency and reliability in coal-fired power plants through real-time component monitoring and anomaly detection. The initiative focused on leveraging distributed machine learning, federated learning, and 5G-based dynamic network slicing to support scalable, fault-tolerant monitoring environments to meet the operational requirements in industrial control systems. With a Distributed Edge Computing Service (DECS) orchestration, this project enabled federated learning at edge for condition monitoring and introduced adaptive client selection strategies to minimize communication overhead. Scalable distributed training was achieved using the Horovod framework, thus enhancing performance across edge nodes. In the realm of 5G networking, the project designed and deployed reconfigurable, QoS-aware network slicing tailored for operational technology (OT) environments, integrating software-defined networks to bolster cyber-resilience and enabling dynamic slicing for federated learning workloads. A significant milestone was the development of a virtualized ICS environment with 5G core integration—which allowed elastic and fault tolerant distributed training on real-world datasets such as NASA Bearings, Hydraulic Systems, and TEP. To broaden the impact of the project, a TRL-3 virtualized ICS testbed for research and education was designed. This project engaged several graduate and undergraduate students to conduct research on the cutting-edge technology, and it resulted in one PhD dissertation, one MS thesis, and over 14 peer-reviewed publications. With the support of this project students also participated in national cybersecurity competitions to improve their professional development skills.

20 FOSSIL-FUELED POWER PLANTS↗

Direct Ab Initio Simulation of the Synthesis of BaZrO 3 and the Microstructure Impacts on Proton Transport

Controlling and predicting the processing-structure-performance relationship in functional materials is a grand challenge in materials science, with important implications for a wide range of emerging applications; a high fidelity understanding of the performance impact of microstructures formed under synthesis conditions is required to develop advanced materials, such as solid-state fuel cells and electrolyzers. Using the ceramic BaZrO 3 as a case study, we directly simulate the synthesis and investigate how proton transport is dictated by microstructures. We develop a framework that couples density functional theory (DFT), machine-learning interatomic potential (MLIP) driven molecular dynamics, and grand canonical Monte Carlo to perform large-scale, microstructure-resolved, atomistic simulations of proton transport in experimentally representative polycrystalline structures. Our fully ab initio approach, using a MLIP as a proxy for DFT, allows us to quantify the competition between two distinct diffusion mechanisms: one associated with grain-boundary regions and another within grains. When the impacts of grain boundaries are taken into account, proton transport exhibits substantial deviation from the bulk oxide limit. This addresses long-standing discrepancies between theory and experiments. Our integrated approach provides atomistic insight into microstructure-dependent proton pathways in BaZrO 3 and establishes a general protocol for predicting processing-structure-performance relationships.

organic↗

Recent Advances in Small Angle X-ray Scattering for Superlattice Study

Small-angle x-ray scattering is used for the structure determination of superlattice for its superior resolution, nondestructive nature, and high penetration power of x rays. With the advent of high brilliance x-ray sources and innovative computing algorithms, there have been notable advances in small angle x-ray scattering analysis of superlattices. High brilliance x-ray beams have made data analyses less model-dependent. Additionally, novel data acquisition systems are faster and more competitive than ever before, enabling a more accurate mapping of the superlattices' reciprocal space. Fast and high-throughput computing systems and algorithms also make possible advanced analysis methods, including iterative phasing algorithms, non-parameterized fitting of scattering data with molecular dynamics simulations, and the use of machine learning algorithms. As a result, solving nanoscale structures with high resolutions has become an attainable task. In this review, we highlight new developments in the field and introduce their applications for the analysis of nanoscale ordered structures, including nanoparticle supercrystals, nanoscale lithography patterns, and supramolecular self-assemblies. Particularly, we highlight the reciprocal space mapping techniques and the use of iterative phase retrieval algorithms. We also cover coherent-beam-based small angle x-ray scattering techniques such as ptychography and ptycho-tomography in view of the traditional small angle x-ray scattering perspective.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Sparse expansions of multicomponent oxide configuration energy using coherency and redundancy

We report that compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Neural MUSE Analysis

Researchers at Oak Ridge National Laboratory (ORNL) created data as part of the MUSE (Multi-Agency Urban Search Experiment Detector and Algorithm Test Bed) project simulating illicit nuclear materials located in various buildings along a road. In the simulation, a truck containing a radiation detector drives down the road gathering listmode data (counting the and energy of incident gamma radiation). Building materials, source shielding, driving speed, truck direction, truck location on the road, source type, and source placement are all varied between runs of the data set. This data was created using deterministic neutron transport and Monte Carlo methods through a combination of SCALE, MAVRIC, MCNP, and GADRAS. As part of a follow-on NA-22 project, two Kaggle competitions were created to determine the best algorithms for finding and identifying gamma sources in this simulated urban environment. The winning algorithm was neural network-based and had a test accuracy of 76.4% accuracy for source identification. This work seeks to build upon this work and improve the results through the application of novel machine learning techniques. As a first step, the data was classified by a simple Convolutional Neural Network (CNN) To accomplish this, the data was first preprocessed into “waterfall plots.” These plots are composed of energy vs count plots that are stacked vertically to show progression in time. The horizontal axis indicating the particle energy incorporated user defined bin spacing with options for in linear-, logarithmic-, square root-, and user-spaced bins. The z or color dimension showed the number of counts corresponding the energy-time combination. This data was then used to generate more data, by generating a local estimate of the mean of the distribution for a bin and then randomly re-sampling that bin from a Poisson distribution. Once all of this data was generated, it was fed into a well-known CNN architecture, ResNet50. The output layer of this model was removed and replaced with layers corresponding to the shape desired isotope outputs. The provided training data was used to train the classifier and the remaining testing data was used to evaluate the model. Results are soon to be forthcoming.

61 RADIATION PROTECTION AND DOSIMETRY↗

Artificial Intelligence/Machine Learning Technologies for Advanced Reactors (Workshop Summary Report)

A workshop on artificial intelligence and machine learning (AI/ML) for advanced reactors (AR) was held October 5-6, 2021. The workshop was to be attended in-person at ANL but COVID restrictions forced the workshop to go virtual. The objectives of the workshop were to identify the most promising AI/ML opportunities for improving advanced reactor design, optimizing plant performance, and enhancing economic competitiveness and to develop an understanding of the scientific, engineering and licensing challenges facing their application. The workshop planning committee included GAIN, EPRI and NEI and members of three national laboratories (ANL, INL, and ORNL). The workshop was attended by more than 200 individuals representing academic and scientific institutions and the nuclear power industry. The definition put forth for an AI/ML system was one that perceives its environment and takes actions that maximize its chance of achieving its goals. In this report AI/ML refers to next generation algorithms that include deep learning, statistical analysis and data analytics and associated scientific computing and their potential application to the design, licensing, operation and maintenance of ARs. These methods typically incorporate models built from process data and may also include data generated by simulations that represent the behavior of a system. The workshop was organized in response to the growing interest in application of AI/ML for improving the economic competitiveness of nuclear energy. Increasingly more resources are being allocated to investigating the benefits of AI/ML methods. The DOE created the Artificial Intelligence & Technology Office to promote their development. And within the Office of Nuclear Energy, resources have been allocated to explore and understand the potential benefits of AI/ML. Additionally, the national laboratories are strategically positioned with DOE computing facilities such as Summit, Perlmutter, Aurora and Frontier that support large-scale simulations, hybrid HPC models with AI surrogates, and the exploration of new types of generative models emerging from multi-model data streams and sources. The workshop was organized with members of the AR community to understand the effort and to identify the level of interest and progress in this emerging technology. The workshop discussions focused on identifying opportunities for AI/ML across diverse areas of the nuclear industry and identifying current scientific and engineering challenges for advanced reactors that might be addressed through transformational uses of AI/ML. Discussion panels focused on four high-interest technical domains for advanced reactors: design, maintenance and operations, energy storage, and materials. The results of those discussions are summarized in this report. This includes opportunities that were identified for exploiting AI techniques and methods to improve the efficacy and efficiency of reactor analysis and to improve the operation and optimization of advanced reactors. Advanced reactor developers expressed an interest in learning more about AI/ML methods and their application. This included understanding whether ML methods can provide an advantage over existing nonlinear data regression methods for collapsing high-fidelity simulation results into faster running models. A consensus emerged that AR advances planned for the next decade will benefit from the use of AI/ML tools. The need exists to understand and model complex systems across length scales and modalities. AI/ML is a tool for discovery that can yield a set of engineering principles for use by nuclear engineers, licensing bodies, and operators to solve problems in plant design, safety analyses, autonomous operation, and predictive maintenance. While AI/ML represents a new set of tools, an awareness by the nuclear community of the full potential is still in the early stages so there is a need to increase awareness. It appears that the wide-spread adoption of AI/ML tools for ARs would be facilitated by future educational workshops that describe foundational methods and capabilities and describe successful applications.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Superstructure Optimization of Waste Plastic Pyrolysis, Integrating Thermal, Catalytic, and Plasma Technologies with Machine Learning

Global plastic waste generation exceeds 430 million tonnes per year, yet fewer than 9% are recycled in the United States. Pyrolysis offers a chemical recycling route at scale, but existing techno-economic and life cycle assessments fix product yields to single pure polymers, producing economic and environmental outputs that break down when the feed composition changes. Here, we present a superstructure optimization framework that addresses this by embedding a composition-aware random forest yield predictor, trained on 566 pyrolysis experiments, within a full-scale process simulation. Product distributions update automatically as feed allocation shifts across four reactor chemistries: conventional thermal, catalytic (HZSM-5), thermal oxo-degradation, and nonequilibrium CO2 plasma. The optimal superstructure achieves minimum selling prices of −0.56 to −0.76/kg feed and global warming potentials of −0.276 to −0.322 kg CO2-eq/kg feed across four commodity price scenarios, confirming profitable, carbon-negative operation without tipping fees. Carbon abatement costs of $\$$0.46 to $\$$1.25/kg CO2-eq are competitive with direct air capture. Sensitivity analysis shows that the catalytic-plasma split fraction is the single largest driver of both economic and climate performance, while hydrocracking allocation in the wax upgrading stage is emission-neutral across the full variable range. Mixed plastic waste streams, evaluated as composition-variable feedstocks rather than pure resins, are profitable and carbon-negative across realistic market conditions. These results give a quantitative basis for reactor selection, circular economy investment, and policy design targeting chemical recycling on a large scale.

Life cycle assessment↗

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗

Using Neural Architecture Search for Improving Software Flaw Detection in Multimodal Deep Learning Models

Software flaw detection using multimodal deep learning models has been demonstrated as a very competitive approach on benchmark problems. In this work, we demonstrate that even better performance can be achieved using neural architecture search (NAS) combined with multimodal learning models. We adapt a NAS framework aimed at investigating image classification to the problem of software flaw detection and demonstrate improved results on the Juliet Test Suite, a popular benchmarking data set for measuring performance of machine learning models in this problem domain.

97 MATHEMATICS AND COMPUTING↗

Using Neural Architecture Search for Improving Software Flaw Detection in Multimodal Deep Learning Models

Software flaw detection using multimodal deep learning models has been demonstrated as a very competitive approach on benchmark problems. In this work, we demonstrate that even better performance can be achieved using neural architecture search (NAS) combined with multimodal learning models. We adapt a NAS framework aimed at investigating image classification to the problem of software flaw detection and demonstrate improved results on the Juliet Test Suite, a popular benchmarking data set for measuring performance of machine learning models in this problem domain.

97 MATHEMATICS AND COMPUTING↗

Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.

36 MATERIALS SCIENCE↗

Machine learning-based interatomic potential development and phase transition analysis of ferroelectric hafnium dioxide

The ferroelectric phase (𝑃⁢𝑐⁢𝑎⁢2 1 , which is in orthorhombic symmetry) of hafnium dioxide (HfO 2 ) has gained much attention due to its potential applications in nanoelectronics and advanced memory devices. However, its complex phase behavior under external stimuli, such as pressure and temperature, remains a subject of intense investigation. This study focuses on developing a machine learning-based interatomic potential (MLIP) that is trained with data from density-functional theory (DFT) calculations to simulate phase transitions and mechanical properties of HfO 2 . The developed MLIP predicts lattice parameters, equations of state, bulk and shear moduli, and elastic constants that closely align with DFT predictions for several phases and at various pressures. Once validated, the MLIP is used to investigate the phase transitions of ferroelectric HfO 2 (𝑃⁢𝑐⁢𝑎⁢2 1 ) under both isobaric and constant stress conditions at elevated temperatures ranging from 200 to 2500 K. We used several complementary methods, including local symmetry identification, radial distribution function, and x-ray diffraction characterization, to identify interesting phase transitions among several competitive hafnia phases predicted from our simulations. The suggested methods uniformly reveal that under pure deviatoric condition, the system favors a transition from the orthorhombic 𝑃⁢𝑐⁢𝑎⁢2 1 phase to a tetragonal (𝑃⁢4 2 /𝑛⁢𝑚⁢𝑐) phase, whereas a zero stress condition drives the system from the 𝑃⁢𝑐⁢𝑎⁢2 1 phase to another orthorhombic (𝑃⁢𝑏⁢𝑐⁢𝑛) phase. These findings provide crucial insights into stress and temperature-induced phase behavior of hafnia, guiding future experimental and theoretical studies for optimizing hafnia-based ferroelectric devices.

Ferroelectric HfO2↗

Learning Coagulation Processes With Combinatorial Neural Networks

Abstract Simulating the evolution of a coagulating aerosol or cloud of droplets in a key problem in atmospheric science. We present a proof of concept for modeling coagulation processes using a novel combinatorial neural network (CombNN) architecture. Using two types of data from a high‐detail particle‐resolved aerosol simulation, we show that CombNN models outperform standard neural networks and are competitive in accuracy with traditional state‐of‐the‐art sectional models. These CombNN models could have application in learning coarse‐grained coagulation models for multi‐species aerosols and for learning coagulation models from observed size‐distribution data.

54 ENVIRONMENTAL SCIENCES↗

Subseasonal Forecasting and MJO Teleconnections in Machine Learning Weather Prediction Models

Abstract In recent years, machine‐learning (ML) models trained on reanalysis data have rivaled physics‐based forecast models in terms of performance skill for global weather forecasting. With increased rollout stability, the question of how these models perform for subseasonal to seasonal (S2S, week 3–8) forecasting has emerged. In this study we run a large set of subseasonal hindcasts over 2004–2023 to evaluate two ML weather forecast models at the S2S time scale, SFNO‐HENS (Nvidia, fully ML) and NeuralGCM (Google Research, hybrid). Corresponding hindcasts from the European Centre for Medium‐Range Weather Forecasts (ECMWF) are used as a baseline for comparison to a physics‐based model. Because our focus is on predicting moisture transport over the Western United States between October and March, we evaluate the models' prediction skill for the Madden‐Julian Oscillation (MJO) and its associated teleconnections in the North Pacific. We find that both ML models are competitive with the ECWMF model, with comparable skill in predicting the North Pacific large‐scale circulation and the MJO at week 3 and beyond. Even though overall the mid‐latitude subseasonal prediction skill remains low, the ML models exhibit interesting behavior such as a realistic propagation of the MJO across the Maritime Continent and realistic teleconnections. A SFNO‐HENS sensitivity experiment with altered initial conditions in the tropics demonstrates the stability of the model, and it illustrates the capability of ML models to represent important physical processes of the atmosphere at the S2S time scale. Plain Language Summary Predicting weather patterns and precipitation a few weeks in advance (subseasonal time scale) is of great interest for stakeholders such as water managers in the Southwest United States (US), where arid conditions prevail. Subseasonal forecasts from traditional weather forecast models exhibit low skill in the region, limiting their applicability. Here we examine whether the recent breakthrough in weather forecasting made with machine learning/artificial intelligence models can translate to improved subseasonal forecasts. Recently‐developed machine learning models exhibit comparable skill to a state‐of‐the‐art physics‐based model for predicting weather patterns in the North Pacific/North America region, and associated moisture transport. The same applies to their skill in predicting the tropical pattern, the Madden‐Julian Oscillation, and its important remote perturbations over the midlatitude East Pacific and Southwest US. Additionally, a perturbation experiment carried out with one of the machine learning models illustrates their ability to not only predict the evolution of atmospheric fields, but also to learn and represent physical processes such as tropics‐extratropics Rossby wave propagation. Key Points Two machine learning weather forecast models exhibit state‐of‐the‐art prediction skill at the subseasonal time scale in the Pacific sector The models equal ECWMF in terms of Madden‐Julian oscillation (MJO) prediction skill, and they accurately predict the MJO propagation and associated teleconnections The two machine‐learning models represent key physical processes for subseasonal prediction, despite being trained for weather forecasting

Peings, Yannick↗

Analysis and Benchmarking of feature reduction for classification under computational constraints

Abstract Machine learning is most often expensive in terms of computational and memory costs due to training with large volumes of data. Current computational limitations of many computing systems motivate us to investigate practical approaches, such as feature selection and reduction, to reduce the time and memory costs while not sacrificing the accuracy of classification algorithms. In this work, we carefully review, analyze, and identify the feature reduction methods that have low costs/overheads in terms of time and memory. Then, we evaluate the identified reduction methods in terms of their impact on the accuracy, precision, time, and memory costs of traditional classification algorithms. Specifically, we focus on the least resource intensive feature reduction methods that are available in Scikit-Learn library. Since our goal is to identify the best performing low-cost reduction methods, we do not consider complex expensive reduction algorithms in this study. In our evaluation, we find that at quadratic-scale feature reduction, the classification algorithms achieve the best trade-off among competitive performance metrics. Results show that the overall training times are reduced 61%, the model sizes are reduced 6×, and accuracy scores increase 25% compared to the baselines on average with quadratic scale reduction.

97 MATHEMATICS AND COMPUTING↗