The QM9 Benchmark

e3nn is an artificial neural network which operates on atomic coordinates and achieves equivariance to the special euclidean group in three dimensions by using spherical harmonics as features. The main experiment is to benchmark the model against a standard chemical data set called QM9, on which e3nn achieves state of the art performance on three of twelve regression targets. Along with empirical results, this thesis presents theoretical argumentation for why e3nn outperforms its closest relatives, SchNet and Cormorant, on some regression targets. Significant background regarding machine learning, quantum chemistry, and the special euclidean group is also presented

Finding symmetry breaking order parameters with Euclidean neural networks

Curie's principle states that “when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them.” We demonstrate that symmetry equivariant neural networks uphold Curie's principle and can be used to articulate many symmetry-relevant scientific questions as simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites

Peregrine: Sequential simulation-based inference for gravitational wave signals

The current and upcoming generations of gravitational wave experiments represent an exciting step forward in terms of detector sensitivity and performance. For example, key upgrades at the LIGO, Virgo and KAGRA facilities will see the next observing run (O4) probe a spatial volume around four times larger than the previous run (O3), and design implementations for e.g. the Einstein Telescope, Cosmic Explorer and LISA experiments are taking shape to explore a wider frequency range and probe cosmic distances. In this context, however, a number of very real data analysis problems face the gravitational wave community. For example, it will be crucial to develop tools and strategies to analyse (amongst other scenarios) signals that arrive coincidentally in detectors, longer signals that are in the presence of non-stationary noise or other shorter transients, as well as noisy, potentially correlated, coherent stochastic backgrounds. With these challenges in mind, we develop peregrine, a new sequential simulation-based inference approach designed to study broad classes of gravitational wave signal. In this work, we describe the method and implementation, before demonstrating its accuracy and robustness through direct comparison with established likelihood-based methods. Specifically, we show that we are able to fully reconstruct the posterior distributions for every parameter of a spinning, precessing compact binary coalescence using one of the most physically detailed and computationally expensive waveform approximants (SEOBNRv4PHM). Crucially, we are able to do this using only 2\% of the waveform evaluations that are required in e.g. nested sampling approaches. Finally, we provide some outlook as to how this level of simulation efficiency and flexibility in the statistical analysis could allow peregrine to tackle these current and future gravitational wave data analysis problems.Comment: 14 pages, 5 figures. Code: peregrine available at https://github.com/undark-lab/peregrine-publi

Balancing Simulation-based Inference for Conservative Posteriors

Conservative inference is a major concern in simulation-based inference. It has been shown that commonly used algorithms can produce overconfident posterior approximations. Balancing has empirically proven to be an effective way to mitigate this issue. However, its application remains limited to neural ratio estimation. In this work, we extend balancing to any algorithm that provides a posterior density. In particular, we introduce a balanced version of both neural posterior estimation and contrastive neural ratio estimation. We show empirically that the balanced versions tend to produce conservative posterior approximations on a wide variety of benchmarks. In addition, we provide an alternative interpretation of the balancing condition in terms of the $\chi^2$ divergence

Healing relationships and the existential philosophy of Martin Buber

The dominant unspoken philosophical basis of medical care in the United States is a form of Cartesian reductionism that views the body as a machine and medical professionals as technicians whose job is to repair that machine. The purpose of this paper is to advocate for an alternative philosophy of medicine based on the concept of healing relationships between clinicians and patients. This is accomplished first by exploring the ethical and philosophical work of Pellegrino and Thomasma and then by connecting Martin Buber's philosophical work on the nature of relationships to an empirically derived model of the medical healing relationship. The Healing Relationship Model was developed by the authors through qualitative analysis of interviews of physicians and patients. Clinician-patient healing relationships are a special form of what Buber calls I-Thou relationships, characterized by dialog and mutuality, but a mutuality limited by the inherent asymmetry of the clinician-patient relationship. The Healing Relationship Model identifies three processes necessary for such relationships to develop and be sustained: Valuing, Appreciating Power and Abiding. We explore in detail how these processes, as well as other components of the model resonate with Buber's concepts of I-Thou and I-It relationships. The resulting combined conceptual model illuminates the wholeness underlying the dual roles of clinicians as healers and providers of technical biomedicine. On the basis of our analysis, we argue that health care should be focused on healing, with I-Thou relationships at its core

Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods. In this paper we describe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approach in so-called simulation-based inference) naturally evades these issues, improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthiness of the inferred posteriors. Using measurements of the Cosmic Microwave Background (CMB), we show that TMNRE can achieve converged posteriors using orders of magnitude fewer simulator calls than conventional Markov Chain Monte Carlo (MCMC) methods. Remarkably, the required number of samples is effectively independent of the number of nuisance parameters. In addition, a property called \emph{local amortization} allows the performance of rigorous statistical consistency checks that are not accessible to sampling-based methods. TMNRE promises to become a powerful tool for cosmological data analysis, particularly in the context of extended cosmologies, where the timescale required for conventional sampling-based inference methods to converge can greatly exceed that of simple cosmological models such as $\Lambda$CDM. To perform these computations, we use an implementation of TMNRE via the open-source code \texttt{swyft}.Comment: v2: accepted journal version. v1: 37 pages, 13 figures. \texttt{swyft} is available at https://github.com/undark-lab/swyft, and demonstration code for cosmological examples is available at https://github.com/acole1221/swyft-CM

Balancing Simulation-based Inference for Conservative Posteriors

peer reviewedConservative inference is a major concern in simulation-based inference. It has been shown that commonly used algorithms can produce overconfident posterior approximations. Balancing has empirically proven to be an effective way to mitigate this issue. However, its application remains limited to neural ratio estimation. In this work, we extend balancing to any algorithm that provides a posterior density. In particular, we introduce a balanced version of both neural posterior estimation and contrastive neural ratio estimation. We show empirically that the balanced versions tend to produce conservative posterior approximations on a wide variety of benchmarks. In addition, we provide an alternative interpretation of the balancing condition in terms of the $\chi^2$ divergence

Defining and Measuring the Patient-Centered Medical Home

The patient-centered medical home (PCMH) is four things: 1) the fundamental tenets of primary care: first contact access, comprehensiveness, integration/coordination, and relationships involving sustained partnership; 2) new ways of organizing practice; 3) development of practices’ internal capabilities, and 4) related health care system and reimbursement changes. All of these are focused on improving the health of whole people, families, communities and populations, and on increasing the value of healthcare