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Path Independent Equilibrium Models Can Better Exploit Test-Time Computation
Cem Anil · Ashwini Pokle · Kaiqu Liang · Johannes Treutlein · Yuhuai Wu · Shaojie Bai · J. Zico Kolter · Roger Grosse

Tue Nov 29 09:00 AM -- 11:00 AM (PST) @ Hall J #323

Designing networks capable of attaining better performance with an increased inference budget is important to facilitate generalization to harder problem instances. Recent efforts have shown promising results in this direction by making use of depth-wise recurrent networks. In this work, we reproduce the performance of the prior art using a broader class of architectures called equilibrium models, and find that stronger generalization performance on harder examples (which require more iterations of inference to get correct) strongly correlates with the path independence of the system—its ability to converge to the same attractor (or limit cycle) regardless of initialization, given enough computation. Experimental interventions made to promote path independence result in improved generalization on harder (and thus more compute-hungry) problem instances, while those that penalize it degrade this ability. Path independence analyses are also useful on a per-example basis: for equilibrium models that have good in-distribution performance, path independence on out-of-distribution samples strongly correlates with accuracy. Thus, considering equilibrium models and path independence jointly leads to a valuable new viewpoint under which we can study the generalization performance of these networks on hard problem instances.

Author Information

Cem Anil (University of Toronto)

I'm a first year PhD student at the University of Toronto and Vector Institute, supervised by Roger Grosse and Geoffrey Hinton.

Ashwini Pokle (Carnegie Mellon University)
Kaiqu Liang (Princeton University)
Johannes Treutlein (University of Toronto)
Yuhuai Wu (Google)
Shaojie Bai (Carnegie Mellon University)
J. Zico Kolter (Carnegie Mellon University / Bosch Center for AI)

Zico Kolter is an Assistant Professor in the School of Computer Science at Carnegie Mellon University, and also serves as Chief Scientist of AI Research for the Bosch Center for Artificial Intelligence. His work focuses on the intersection of machine learning and optimization, with a large focus on developing more robust, explainable, and rigorous methods in deep learning. In addition, he has worked on a number of application areas, highlighted by work on sustainability and smart energy systems. He is the recipient of the DARPA Young Faculty Award, and best paper awards at KDD, IJCAI, and PESGM.

Roger Grosse (University of Toronto)

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