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At least 271 records · Page 15

Sparse distributed memory

Theoretical models of the human brain and proposed neural-network computers are developed analytically. Chapters are devoted to the mathematical foundations, background material from computer science, the theory of idealized neurons, neurons as address decoders, and the search of memory for the best match. Consideration is given to sparse memory, distributed storage, the storage and retrieval of sequences, the construction of distributed memory, and the organization of an autonomous learning system.

Kanerva, Pentti↗

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Ashrafi, S.↗

Mars Atmospheric Dynamics

The Martian atmosphere is dynamically similar to the Earth's. Its spin-axis rotation rate is only minutes longer than Earth's so the Coriolois force is nearly identical to Earth's. The inclination of its spin axis is also similar to Earth's giving it similarity in seasonal change. And the Martian atmosphere is nearly transparent to solar radiation (except during dust periods) such that it is heated primarily by upwelling infrared radiation from the surface. These characteristics make Mars an ideal laboratory for studying the dynamics of rapidly rotating differentially heated atmospheres. This talk reviews what we have learned about Mars atmospheric dynamics and how if compares with Earth. The source of information to make such a comparison comes from observations and models. The former are sparse and that the latter have played a major role in shaping our thinking about the general circulation on Mars. However, the models need validation. Fortunately, the first two orbiters in NASA's Mars Surveyor Program have instrumentation to address many of the issues related to the general circulation and climate of Mars. The first, Mars Global Surveyor, is already at Mars gathering data. The second, the Mars 98 Orbiter to be launched later this year, carries a dedicated atmospheric sounder. Thus, much will be learned about Mars' atmosphere in the next few years.

Haberle, Robert↗

Spatial Mapping of Riverbed Grain-Size Distribution Using Machine Learning

Recent alluvial sediments in riverbeds play a significant role in controlling hydrologic exchange flows (HEFs) in river systems. The alluvial layer is usually associated with strong heterogeneity in physical properties (e.g., permeability and hydraulic conductivity), which affects local HEFs and therefore biogeochemical processes. The spatial distribution of these physical properties needs to be determined to inform the numerical models used to reveal the realistic hydro-biogeochemical behaviors. Such information can be obtained based on the intrinsic link between sediment grain-size distribution and hydraulic properties where sediment texture information is available. However, grain-size measurements are usually spatially sparse and do not have adequate coverage and resolution, particularly for a relatively large domain such as the Hanford Reach of the Columbia River. In this paper, we adopted machine learning (ML) approaches for categorizing and mapping the spatial distributions of riverbed substrate grain size and filling in missing areas of substrate data using the ML models along the reach. Such ML models for substrate size mapping were trained at 13,372 locations using measured substrate sizes along with observed and simulated attributes, including bathymetric attributes (e.g., elevation, slope, and aspect ratio) from LIDAR and bathymetric surveys, and hydrodynamic properties (e.g., water depth, velocity, shear stress, and their statistical moments). An ensemble bagging-based ML technique, Random Forest, was adopted to identify the most influential factors as predictors to develop the predictive models with over-fitting issues addressed. The models were evaluated with respect to each individual substrate size class and the lumped group, and then used to generate the final substrate size maps covering all the grid cells in the numerical modeling domain.

54 ENVIRONMENTAL SCIENCES↗

Biochemical Process Modeling and Simulation (BPMS)

The Biochemical Process Modeling and Simulation project aims to reduce the cost and time of research by applying theory, modeling, and simulation to the most relevant bottlenecks in the biochemical process. We use molecular modeling, quantum mechanics, metabolic modeling, fluid dynamics, and reaction-diffusion methods in close collaboration with pretreatment, hydrolysis, upgrading, and TEA. The project's outcomes are increased yields and efficiency of the biochemical process, added value to products, and reduced price of fuels by specifically targeting catalytic efficiency, reactor design, enzyme efficiency, and microbial design. We work closely with experimental projects to identify problems and iterate with experiments to find and refine solutions. By working with experimentalists, we decide on problems that can be solved with simulation that could otherwise not be solved or would take too long with experiment alone to reach BETO's targets. Over the years, we have produced solutions that have resulted in determining the most likely fatty-acid derivative for passive transport out of bacteria that upgrade biomass, and we have also designed enzyme mutations for enhanced lignin upgrading. Metabolic models have been developed to tune the activity of 2,3 butanediol production for the 2030 target. A computational method to deliver understanding of how complex omics data can be interpreted in the metabolic pathways of organisms used in the Agile Biofoundry. We have found methods to overcome specific barriers and continue to develop those methods. Our reactor studies have guided the design of both the microbes and reactors for aerobic and micro-aerobic production at all scales and have been instrumental in improving the accuracy of techno-economic analysis models. This project is essential in the process of selecting the final processes for 2030 SAF production targets. More specifically, recently, we have: 1) Predicted the strength of the basic structural interactions in commodity plastics to provide guidance for plastics upcycling strategies. 2) Developed computational tool to improve the characterization of lignin-derived compounds 3) Developed new methodologies to enable Machine Learning-based Directed Evolution for protein engineering. 4) Developed Machine Learning methods to predict protein promiscuity and mutations to further improve microbial and enzymatic driven processes and demonstrated the utility of ML approaches to engineering proteins from sparse experimental datasets. 5) Developed new methods to enable high-fidelity simulation of aerobic fermentation at industrial scale and resolving mismatch of time scales through subcycling/operator splitting 7) Identified the difficulty in preventing local high-oxygen conditions in industrial bubble columns, which leads to less-desirable acetoin production, suggesting future research directions in alternative reactor configurations (e.g loop reactors, shallow-channel reactors).

BIOMASS FUELS↗

Learning earthquake ground motions via conditional generative modeling

Predicting high-fidelity ground motions for future earthquakes is crucial for seismic hazard assessment and infrastructure resilience. Conventional empirical simulations suffer from sparse sensor distribution and geographically localized earthquake locations, while physics-based methods are computationally intensive and require accurate representations of Earth structures and earthquake sources. We propose an artificial intelligence (AI) spectrogram generator, Conditional Generative Modeling for Ground Motion (CGM-GM). CGM-GM leverages earthquake magnitudes and geographic coordinates of earthquakes and sensors as inputs, when postprocessed with phase information, capturing spatially continuous Fourier amplitude spectra (FAS) as well as properties such as P and S arrivals, and waveform durations, without explicit physics constraints. This is achieved through a probabilistic autoencoder that extracts latent distributions in the time-frequency domain and variational sequential models for prior and posterior distributions. We evaluate the performance of CGM-GM using small-magnitude earthquake records from the San Francisco Bay Area, a region with high seismic risks. Here, we report that CGM-GM demonstrates potential for complementing physics-based simulations and non-ergodic empirical ground motion models, as well as shows promise in seismology and beyond.

geophysics↗

Transfer Learning using Denoising Auto-Encoders for Cellular-Level Annotation of Tumor in Pathology Slides

Adversarial examples can produce altered classifications using only seemingly innocuous, imperceptible perturbations to the original image. The imperceptibility of adversarial perturbations suggests that the corresponding classifiers use decision criteria different than those of a human. In a medical setting, inexplicable decision criteria confound a pathologist’s willingness to trust machine-generated annotations. Here, we analyze denoising tumor detection models to see if they are robust to imperceptible adversarial perturbations. Moreover, to be more fully trusted by pathologists, we require tumor detectors that generate interpretable annotations which segment pathology slides into tumorous and normal regions at the cellular level. We therefore compare transfer learning based on two different autoencoder architectures, one derived from a deep denoising bottleneck autoencoder and one from an over-complete sparse autoencoder. Both autoencoders were first trained in an unsupervised manner on a set of pathology slides drawn from the Camelyon16 dataset. The latent representations produced by each autoencoder were then passed to separate neural networks that were trained in a supervised manner on binary tumor-normal masks generated by pathologists at cellular resolution. Both tumor detectors supported better than 90% AUC PR as measured by the area under the precision/recall curve on a held-out pathology slide. To assess the underlying decision criteria used by both tumor detectors, we constructed imperceptible adversarial examples which reduced the AUC PR of both models to less than 70%. Random noise of the same amplitude had almost no effect on the AUC PR of either model. Additionally, each tumor detector was resistant to adversarial “transfer” attacks targeting the other. The adversarial perturbations showed strong characteristic differences: the deep denoising models perturbations were a very diffuse, seemingly unrecognizable pattern while the sparse coding models perturbations showed traces of tissue cells.

47 OTHER INSTRUMENTATION↗

Report on PTT Imaging of Defects in AM Metallic Materials-Part 2

Metal Additive Manufacturing (AM) is a promising method for cost-efficient fabrication of complex shape structures for applications in harsh environment, such as in a nuclear reactor. However, internal defects (pores) occur in high-strength AM alloys, which are manufactured with Laser Powder Bed Fusion (LPBF) AM method. Pulsed Infrared Thermography (PIT) is an efficient nondestructive evaluation (NDE) method to examine actual structures, because this method offers one-sided non-contact measurements, and fast processing of large sample areas. However, imaging of material defects, particularly defects with sizes at microscopic level, is challenging. In this report, we benchmark the performance of several Unsupervised Learning (UL) algorithms designed to enhance imaging of microscopic defects in metals with PIT. UL aims to learn the latent principal patterns (dictionaries) in PIT data to detect defects with minimal human supervision. Performance of Independent Component Analysis (ICA), Sparse Coding (SC), Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA) was compared using F-score, UL model training time and defects reconstruction time. We obtained the average F-score of 0.75, and a highest F-score of 0.89 for the EFA algorithm. Overall, EFA outperforms other UL algorithms considered in this study.

36 MATERIALS SCIENCE↗

Understanding and Improving Energy Efficiency of Regional Mobility Systems Leveraging System-Level Data

Increased congestion required urban Americans to travel 6.8 billion hours more and purchase 3.1 billion gallons of fuel for a congestion cost of $\$$153 billion, according to the 2019 Urban Mobility Report. How to effectively manage the regional mobility system and improve the energy efficiency presents a big challenge to public agencies. Recent years have witnessed massive multi-jurisdictional multi-modal system-level data from various sources, which provides an unprecedented opportunity to improve the mobility system and its energy efficiency. However, implications of system-level data for mobility and energy efficiency are unclear. Those system-level data sets are siloed, spatially and temporally sparse, biased, not unified, and lacking of insights for system management. Consequently, there is a real need to acquire, fuse, mine and learn from multi-source system-level data to prepare public agencies to deal more effectively with large-scale energy efficiency modeling, management and planning. This project proposes to intensively review inexpensive, replicable and openly-accessible data from multi-modal systems, develop a data-driven system-level modeling framework enabled and validated by data, identify the energy inefficiencies of mobility systems from infrastructure, vehicles, passenger systems, and quantify the benefits of system-level strategies to improve mobility/energy efficiency. In addition, this research develops models to effectively estimate energy consumption and emissions from various types of vehicles on the roadway networks, with high granularity and high fidelity. Traditional models often heavily rely on aggregated infrastructure or vehicle/passenger data, for example, the census survey, land-use, and traffic counts of one or several classes, which may lead to research gaps considering the emerging vehicle technologies. Those models do not contain individual vehicular information. We propose an integrated data-driven method that combines multiple network modeling components, featuring the utilization of state-wide vehicle registration data. The additional vehicle registration data improve the model performance, and produce high-resolution vehicle-specific estimates of emissions and network performance metrics. Two case studies on the Pittsburgh and Philadelphia regional network show that the proposed method can efficiently and effectively estimate the emissions of a large-scale network, and provide valuable information for evaluating common management strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Transfer learning driven design optimization for inertial confinement fusion

Transfer learning is a promising approach to create predictive models that incorporate simulation and experimental data into a common framework. In this technique, a neural network is first trained on a large database of simulations and then partially retrained on sparse sets of experimental data to adjust predictions to be more consistent with reality. Previously, this technique has been used to create predictive models of Omega [Humbird et al., IEEE Trans. Plasma Sci. 48, 61–70 (2019)] and NIF [Humbird et al., Phys. Plasmas 28, 042709 (2021); Kustowski et al., Mach. Learn. 3, 015035 (2022)] inertial confinement fusion (ICF) experiments that are more accurate than simulations alone. Here, in this work, we conduct a transfer learning driven hypothetical ICF campaign in which the goal is to maximize experimental neutron yield via Bayesian optimization. The transfer learning model achieves yields within 5% of the maximum achievable yield in a modest-sized design space in fewer than 20 experiments. Furthermore, we demonstrate that this method is more efficient at optimizing designs than traditional model calibration techniques commonly employed in ICF design. Such an approach to ICF design could enable robust optimization of experimental performance under uncertainty.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Conditional Karhunen-Loève expansion for uncertainty quantification and active learning in partial differential equation models

We use a conditional Karhunen-Lo` eve (KL) model to quantify and reduce uncertainty in a stochastic partial differential equation (SPDE) problem with partially-known space-dependent coefficient, Y (x). We assume that a small number of Y (x) measurements are available and model Y (x) with a KL expansion. We achieve reduction in uncertainty by conditioning the KL expansion coefficients on measurements. We consider two approaches for conditioning the KL expansion: In Approach 1, we condition the KL model first and then truncate it. In Approach 2, we first truncate the KL expansion and then condition it. We employ the conditional KL expansion together with Monte Carlo and sparse grid collocation methods to compute the moments of the solution of the SPDE problem. Uncertainty of the problem is further reduced by adaptively selecting additional observation locations using two active learning methods. Method 1 minimizes the variance of the PDE coefficient, while Method 2 minimizes the variance of the solution of the PDE. We demonstrate that conditioning leads to dimension reduction of the KL representation of Y (x). For a linear diffusion SPDE with uncertain log-normal coefficient, we show that Approach 1 provides a more accurate approximation of the conditional log-normal coefficient and solution of the SPDE than Approach 2 for the same number of random dimensions in a conditional KL expansion. Furthermore, Approach 2 provides a good estimate for the number of terms of the truncated KL expansion of the conditional field of Approach 1. Finally, we demonstrate that active learning based on Method 2 is more efficient for uncertainty reduction in the SPDE’s states (i.e., it leads to a larger reduction of the variance) than active learning using Method 2.

Conditioned Karhunen-Lo` eve expanion, machine lea↗

Operator inference with roll outs for learning reduced models from scarce and low-quality data

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.

97 MATHEMATICS AND COMPUTING↗

Machine learning and shallow groundwater chemistry to identify geothermal prospects in the Great Basin, USA

This study discovers various geothermal prospects in the Great Basin, USA based on shallow groundwater chemical (geochemical) data. The geochemical data are expected to include hidden (latent) information that is a proxy for geothermal prospectivity. We processed the sparse geochemical data in the Great Basin at 14,341 locations including 18 attributes. Next, a non-negative matrix factorization with customized k-means clustering is applied to the geochemical data matrix that automatically finds three hidden geothermal signatures representing modestly, moderately, and highly confident geothermal prospects. The algorithm also evaluated the probability of occurrence of these types of resources through the studied region. There is a consistency between regional geothermal prospectivity as estimated by our ML methodology and the traditional play fairway analysis conducted over a portion of the study area. We also identify the dominant data attributes associated with each signature. Finally, our ML analyses allow us to reconstruct attributes from sparse into continuous over the study domain. The predicted continuous attributes can be used for future detailed geothermal explorations in the Great Basin.

15 GEOTHERMAL ENERGY↗

mystic : software for autonomous discovery and design under uncertainty

Throughout the diverse range of science and engineering applications, there is a growing desire to develop computational methods that can reliably predict the behavior of complex systems. Specifically, there is a strategic need for tools that can robustly forecast the behavior of complex physical systems, where data may be high-dimensional, noisy, or sparse, and models of the system may be time-dependent or include uncertainty. We use mystic to build tools that leverage statistical learning, physics-informed learning, and active learning in the efficient generation of reliably predictive surrogates for complex physical systems. mystic is a robust, proven, open-source optimization and uncertainty quantification toolkit with over a decade of use in the design and optimization of neutron instrumentation, solar-powered drones, and gasguns, and in iterative tuning of models for Raman spectroscopy and elastoplastic materials strength. Recent developments have focused on automated learning of statistically robust surrogates under uncertainty, with applications in materials in extreme environments, nanostructures, materials simulations and strength models, and the failure of shielding under particle radiation. In 2020, McKerns demonstrated active learning of optimally robust surrogates with respect to new simulated data for molecular dynamics simulations of materials mixing in warm dense matter, and is currently applying active learning to the automated steering of particle accelerator beams and the optimal design and control of quantum optical sensor instrumentation.

42 ENGINEERING↗

Predictive Modeling for Differential Diagnosis and Mortality Risk Assessment

The prevalence of electronic health record (EHR) systems has brought prodigious biomedical informatics opportunity. Automated machine learning methods can effectively utilize such data and have become common tools for healthcare predictive modeling. Researches in medical informatics have explored the potential of deep learning and classical models in emergent care scenarios. In particular, predicting differential diagnoses for admissions have proven useful in decreasing unnecessary lab tests and improving inpatient triage decision-making. Moreover, identification of high-risk patients for in-hospital mortality is vitally important to maximize allocation of medical resources.The Medical Information Mart for Intensive Care (MIMIC-III) database, containing de-identified critical care inpatient was used in our study. This data set captures hospital patient laboratory measurements, pharmacologic prescriptions, diagnostic data and procedure event recordings. When considering adult patients and discounting admissions with ICU length of stay less than 24 hours, there were 37,787 unique admissions and 30,414 total patients. We examined the top 25 most prevalent ICD-9 group-level disease specificities in MIMIC-III using a multi-label classification model. In-hospital mortality was modeled as binary classification with 4,155 (13%) adult patients that expired, of which 3,138 (75.5%) were in the ICU setting. The metrics AUC, F1 score, sensitivity and specificity values calculated for each disease label measured prediction performance.The usage of ICD-9 group codes reduced feature dimension from 14,567 to 942 and greatly improved distribution of patient diagnostic categories. Disease temporal patterns were captured by considering the most frequently sampled 6 vital signs and 13 laboratory values. Missing data were imputed at each time-stamp. Time-series raw hourly average values were converted into 5 summary features (mean, standard deviation, number of observations, min & max values). Patient demographic variables such as age, gender, marital status and ethnicity were also factored into the modeling. Choi et al showed that contextual embedding of medical data, diagnostic and procedural codes alone can predict future diagnoses with sensitivity as high as 0.79. We utilized an embedding technique called word2vec which allowed sparse representations of medical history to be transformed into dense word vectors. The mappings captured contextual information by treating each admission as a sentence and learning the most likely neighboring words in a sliding window fashion. Binary and multi-label classification was achieved via collapse models, which do not consider temporal information, as well as recurrent neural networks with regularization, Softmax output layer activation together with categorical cross-entropy as the loss function.

US Army collaboration↗

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

Distributed Inference with Sparse and Quantized Communication

Here, we consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We prove that our rule guarantees convergence to the true state exponentially fast almost surely despite sparse communication, and that it has the potential to significantly reduce information flow from uninformative agents to informative agents. Next, to deal with finite-precision communication channels, we propose a distributed learning rule that leverages the idea of adaptive quantization. We show that by sequentially refining the range of the quantizers, every agent can learn the truth exponentially fast almost surely, while using just 1 bit to encode its belief on each hypothesis. For both our proposed algorithms, we rigorously characterize the trade-offs between communication-efficiency and the learning rate.

42 ENGINEERING↗