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Poster
Discovering Symbolic Models from Deep Learning with Inductive Biases
Miles Cranmer · Alvaro Sanchez Gonzalez · Peter Battaglia · Rui Xu · Kyle Cranmer · David Spergel · Shirley Ho

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1591
in Poster Session 6 »

We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent representations when we train a GNN in a supervised setting, then we apply symbolic regression to components of the learned model to extract explicit physical relations. We find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network. We then apply our method to a non-trivial cosmology example—a detailed dark matter simulation—and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution-data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

Author Information

Miles Cranmer (Princeton University)

Miles Cranmer is an Astro PhD candidate trying to accelerate astrophysics with AI. Miles is from Canada and did his undergraduate in Physics at McGill. He is deeply interested in the automation of science, particularly aspects that are not yet tractable with existing machine learning, such as experiment planning, simulation, and theory. He works on symbolic regression, graph neural networks, normalizing flows, and learned simulation. He is hugely interested in symbolic ML, since, as he argues, symbolic models seem to be a surprisingly efficient basis for describing our universe.

Alvaro Sanchez Gonzalez (DeepMind)
Peter Battaglia (DeepMind)
Rui Xu (Princeton University)
Kyle Cranmer (New York University)

Kyle Cranmer is an Associate Professor of Physics at New York University and affiliated with NYU's Center for Data Science. He is an experimental particle physicists working, primarily, on the Large Hadron Collider, based in Geneva, Switzerland. He was awarded the Presidential Early Career Award for Science and Engineering in 2007 and the National Science Foundation's Career Award in 2009. Professor Cranmer developed a framework that enables collaborative statistical modeling, which was used extensively for the discovery of the Higgs boson in July, 2012. His current interests are at the intersection of physics and machine learning and include inference in the context of intractable likelihoods, development of machine learning models imbued with physics knowledge, adversarial training for robustness to systematic uncertainty, the use of generative models in the physical sciences, and integration of reproducible workflows in the inference pipeline.

David Spergel (Flatiron Institute)
Shirley Ho (Flatiron institute/ New York University/ Carnegie Mellon)

Shirley Ho is a group leader and acting director at Flatiron Institute at Simons foundation, a research professor of physics and an affiliated faculty at Center for Data Science at NYU. Ho also holds associate (adjunct) professorship at Carnegie Mellon University and visiting appointment at Princeton University. She was a senior scientist at Berkeley National Lab from 2016-2018 and a Cooper-Siegel Development chair professor at Carnegie Mellon University before that. Ho was a Seaborg and Chamberlain Fellow from 2008-2011 at Berkeley Lab, after receiving her PhD in Astrophysics from Princeton University in 2008 under supervision of David Spergel. Ho graduated summa cum laude with a B.A. in Physics and a B.A. in Computer Science from UC Berkeley. A cited expert in cosmology, machine learning applications in astrophysics and data science,her interests are using deep learning accelerated simulations to understand the Universe, and other astrophysical phenomena. She tries her best to balance her love for the Universe, the machine and life especially during these crazy times.

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